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Coastal Zone Information Center 12386 C2 THE STRATEGIC ROLE OF PERIGEAN SPRING TIDES In Nautical History and North American Coastal Flooding, 1635 - 1976 COASTAL ZONE INFORMATION CENTER GC 356 U.S. DEPARTMENT OF COMMERCE .A1 NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION W66 1978 f I Ti, ",e- A, Uk" 44 I It% n Mt.; y 0." W 4 N, f @XTVIY "Y j" f d , @_ 4' @P,@ @ il , -fl I It , " , , , 44 , @V riq 4.1 rhb 14 1 7 01-@,! f. 7@t V NA oill 'Pay T@ F 14 I-J 4 At 4 5" ujg , ME A'11,1 ZON A Ad-," A 7@z 0@" 6'. e4 Wit '*W ik' PIZ y V'f'- rv, ' W'41 gg- t d In 44 41@ C j 31 -Auv-, % M, W MIR,, T 1;- -4 @5' RE 7ER C IN Nov z 0"1 @p v C@ 'I' 7@ N tj; jw 0, 411 _j 4"to" ij , 1-71 , " @_L I It, Zi WWI @;c Ag- v t Breaching of ihefamous Steel Pier (extreme left) andformer Million Dollar Pier (extreme right) at Atlantic City, N.Y., by the great tidal flooding of March 6- 7, 1962. wow Z - V4 -A'i -AMA#. :7 -A% Al en -jr-4W 'On 4* 74. 7, tV 3- J A AA7 W Vsk- 44, 4*' A@ COASTAL ZONE Courtesy of United Press International IN F' 0 RuA'A T 10 N 0 E N T E R Aerial photograph showing the extreme damage to homes along the beach at Point-o-Woods, Fire Island, N.Y., created by tidal flooding associated with the coincidence of perigean (proxigean) spring tides and strong onshore winds. This active coastal flooding persisted throughout five successive high tides, March 5-7, 1962. THE STRATEGIC ROLE OF PERIGEAN SPRING TIDES In, Nautical History and North American Coastal Flooding, 1635-1976 Fergus J. Wood Research Associate National Ocean Survey Office of the Director Ln OF US tp@a@ent of Commerce WOAAC I Services Center LibrarY 2234 South Robson Avenue Charlestor4 SC 29405-2413 U.S. DEPARTMENT OF COMMERCE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION UNITED STATES NATIONAL OCEANIC AND National Ocean DEPARTMENT OF COMMERCE ATMOSPHERIC ADMINISTRATION Survey Juanita M. Kreps, Secretary Richara A. Frank, Administrator Allen L. Powell, Director For sale by the Superintendent of Documents, U.S. Government Printing Office WashingtoD@ D.C. 20102 (Paper Cover) Stock No. 003-017-00420-1 Foreword Within recent years, increasing demands on the shoreline have led to its national redefinition as the "coastal zone." Thus emerged the concept of treating the area as a natural "system" in which multiple uses must somehow be accom- modated. The sociopolitico, economic, and scientific debates that ensued have resulted in what is now known as "coastal zone management." This treatise deals with the natural forces at work in the domain of the coastal zone manager, and perhaps will lead him to ponder on events of Nature that should be con- sidered in his planning. The manager must be aware that the shoreline portion of the coastal zone is a shifting triple boundary, fleeting by nature, and forever seeking a stability with sea, beach, and air that is never achieved. Here, where earth, sea, and sky meet, often to wash hands in mischief, is where the most violent physical action occurs in the coastal zone. The National Ocean Survey, and its predecessor agencies, have lived and worked in the coastal zone for 169 years. Even after so long and active a tenure it still seemed reasonable -that we should ask ourselves the question: "Have we overlooked anything that would be useful to the coastal zone manager, the planner, the developer, and the citizens who live in this increasingly popular locale?" For years we have published maps, charts, and tide tables. We have established tidal bench marks and geodetic control around the coasts and across the country, all necessary for the apportionment of appropriate jurisdictions among Federal, State, and local governments, between these governments and private landholders, and between our Nation and the rest of the world. Accordingly, we began to think of other areas that might fruitfully occupy our attention. We examined many natural occurrences including coastal sub- sidence, shoreline erosion, loss of coastal marshlands, coastal development, shifting bottom topography, coastal currents, and tide observing systems, always keeping in mind the idea that something might have been overlooked that could be useful to those concerned with the coastal zone. Coastal flooding came under our scrutiny, which led Fergus Wood to examine what is known about the tides. He kept digging and studying all aspects of the tides, ranging from our batting average on tidal prediction to the historical effects of tides on man. It was out of such analytic studies that this work was born. The tides affect man most adversely when coastal flooding occurs. Not all high tides cause flooding, nor do all coastal onshore storms. Given, however, a set of circumstances wherein uncommon tides, called perigean spring tides, coincide with strong onshore winds from an offshore storm, such as a nor'easter along the Atlantic coast, the coast will be flooded at all lowland points. The catastrophic event -of March 1962 along the mid-Atlantic seaboard was such a iv Foreword circumstance and provided a grim reminder that two strong forces of Nature acting in concert can create havoc. During the times of perigean spring tides, the controlling astronomical forces are enhanced. Sun, Moon, and Earth are aligned, the Moon is closer to the Earth, and along with the Sun, is exerting the increased and concentrated gravitational forces due to their alignment. The Moon is moving faster in its orbit, the length of the tidal day is increased, and there is created what Wood refers to as "a window for potential flooding." At these times the tides build up faster, tidal currents increase, and when accompanied by a strong onshore wind, the ocean waters pour into the estuaries faster than they can escape on the ebb. The pileup of water behind offshore bars results in a destructive breaching from the landward side, and the ocean begins to reshape the shoreline, moving whatever is in its path. Fergus Wood is an interdisciplinary scientist. He treats the astronomy, meteorology, and oceanography in this volume in a thorough manner for the. attention of the scientist. For the interested nonscientist, he has included a less technical discussion, and for the historian he has exhaustively investigated events of the past that were influenced by perigean spring tides. As a research geo- physicist, he has approached cautiously another aspect of the perigean spring situation-how it affects the solid earth. The same forces responsible for perigean spring tides in the ocean also create enhanced earth tides, the results of which are obscure. In the present state of knowledge, there seems to be no satisfactorily provable connection, for example, between perigean spring tides, earth tides, and seismic events. But curious and openminded geophysicists are beginning to examine the connections, if any, between earth tides and earth movements, especially microseismic swarms. Perhaps this book will encourage them to look carefully at what, if anything, occurred in the solid earth on past occasions of perigean spring tides, notably of the "proxigean" type, which are explained in part 11, chapters 3, 4, 5, and 8. It has been my pleasure to encourage Fergus Wood in this work and to participate with him in many discussions.on the research that went into it. I hope that the reader will find profitable the result which consumed nearly four years of his unflagging attention. AUGUsT 2, 1976. GORDON LILL, Depuo Director, National Ocean Survey. Author's Preface PERIGEAN SPRING TIDES: A Potential Threat Toward Coastal Flooding Disaster This book deals with the origin, nature, and impact of severe tidal flooding of lowland coastal regions resulting from the coincidence of astronomical and meteorological forces. On March 6, 1962, such a catastrophic occurrence struck from the sea in the darkness of predawn, and for the following 65 hours inundated the entire n-lid-Atlantic coastline of the United States from the Carolinas to Cape Cod. This disastrous event resulted in a loss of 40 lives and over $0.5 billion in property damage. As other representative examples, severe tidal floodings of similar origin occurred in regions of the Atlantic coast on December 30, 1959, March 4-5, 193 1, and April 10- 12, 1918-and at points along the Pacific coast on March 6, 1970, February 3-4, 1958, and January 3-5, 1939. Still further floodings were experienced simultaneously on both coastlines on December 11, 1973, March 26, 197 1, and January 6, 193 1. All of these instances of coastal flooding were caused by a special combina- tion and reinforcement of the gravitational forces of the Sun and Moon producing unusually higl! tides-which were concurrently lifted onto the land by strong, persistent, onshore winds. Such exceptionally high tides and their accelerated ocean currents- coupled with intense sea-surface winds-accompanied the total destruction of an offshore Air Force radar tower on February 12, 1963. The foundational erosion and subsequent toppling of the Marconi experimental transatlantic radio tower on Hatteras Island on April 4, 1915, was associated with a comparable situation of perigean spring tides and strong onshore winds. The previously mentioned astronomical alignment of Earth, Moon, and Sun-known as perigee-syzygy- also was present (although exerting a more limited influence due to the small tidal ranges encountered in the Gulf of Mexico) during the great Galveston, Tex., hurricane and tidal flooding of September 8, 1900. A computerized search of the scientific literature reveals that none of the above aspects of perigean spring tides has been analyzed and discussed in a thoroughly comprehensive manner. In a more modem concept emphasizing the ongoing risk, this semiregularly recurring type of tide-when supported by sustained onshore winds-obviously can pose a threat to the development of offshore oil storage platforms and pump- ing stations engaged in the transfer or distribution of crude oil to coastal refineries' A potential for inland as well as shoreline flooding is created by the increased amplitudes and strongly running currents associated with these tides, which may Vi Author's Preface bring saltwater far up estuaries beyond the ordinary tidewater reaches. The alternating extreme low waters, if diluted by heavy rain, may exercise a severe detrimental influence on the oyster and hardshell fishing industries. Such tides likewise may impact adversely upon coastal wildlife sanctuaries, and interfere with the normal breeding cycles of freshwater fish. At a low-tide phase occurring near a perigee-syzygy alignment, the ex- tremely low waters both preceding and following the astronomically produced extremely high waters can cause the stranding of deep-draft vessels such as modern supertankers plying coastal waterways. This situation imposes an addi- tienal threat of oilspills and irremedial damage to the coastline. These and other influences of perigean spring tides which possess a definite practical impact on maritime commerce, the coastal ecology, and the status of the marine en- vironment are thoroughly treated in this work. A definitive review of these numerous special properties of perigean spring tides and their effects constitutes the raison dY re for the present monograph. Because of the many different degrees et and grades of perigean spring tides, the documentation and analysis of a large number of examples has been necessary. In pursuit of this supporting material, a detailed investigation was insti- tuted, based upon interdisciplinary sources of data. With the cooperation of the U.S. Naval Observatory, a computer printout was prepared, indicative of the considerable variation in astronomical alignments responsible for perigean spring tides throughout the 400-year period from 1600 to 1999. With the dates of such augmented tide-raising forces duly tabulated, a systematic search was begun through heretofore uncoordinated accounts of tidal flooding on the North American coastline as presented in newspaper and other more definitive sources extending historically to the year 1635. The pieces of a complex puzzle began to fall in place. @ The documentation of more than a hundred of these major coastal flooding events of the past, and a discussion of the associated hazards to maritime com- merce, seashore habitations, and the coastal environment posed for the future by such recurring flooding events have been set down respectively in tabular and case-study form in this work. Part I summarizes the historical, practical, and environmental aspects of perigean spring tides. In the second, scientific part of the work, the precise astronomical factors causing close perigee-syzygy alignments under certain conditions are explained in detail. The associated increased perturbations of the lunar orbit which result in diminished Earth-Moon distances, enhanced gravitational forces upon the Earth's ocean waters, and augmented tidal ampli- tudes are mathematically analyzed and described. A numerical quantifier (known as the delta-omega syzygy coefficient) designed to serve as a predictor term in establishing the relative potential for tidal flooding generated by such astronomically augmented tides (when sup- ported by the necessary meteorological conditions) also has been developed. On December 26, 1973, based on the foregoing research, the first actual warning -of potential tidal flooding during a period bracketing a very close perigee-syzygy alignment of January 8, 1974, was announced to the public by NOAA through the press, radio, and television media. A counteracting high Author's Preface Vii atmospheric pressure system and calm winds prevented any further rise of the very high astronomical tides produced along the east coast on this date. How- ever, front-page headlines in the Los Angeles Times for January 9 told of the "tidal assault" supported by the strong onshore winds of the day before. The accompanying news article summarized the extent of coastal damage and the advance opportunity provided for preventing damage to homes and shoreline installations by sandbagging, backfilling, and other precautionary measures. A confirming instance of tidal flooding based on the same very close perigee- syzygy alignment (termed proxigee-syzygy throughout this work), in which the resulting proxigean spring tides were accompanied by onshore winds, occurred along the western and southern shores of Great Britain on January 11-12, 1974. The 3-day time delay is a'function of oceanographic factors. A second tidal flooding (related to a similarly announced perigee-syzygy alignment a month later) occurred along the southern coast of England on February 9. Yet another example of active astronomical tidal flooding potential, contributed to by strong onshore winds, materialized on March 17, 1976, when 5 feet of seawater flooded at Halifax, Nova Scotia, following considerable tidal erosion in lowland coastal regions of Massachusetts, New Hampshire, and Maine. Again, on January 8-9 and January 11-12, 1978, perigean spring tides associated with the perigee-syzygy alignment of January 8 were reinforced by strong onshore winds. The resulting high waters caused serious flooding damage both along the lowland shores of southern California and New England, and 'those of Great Britain, respectively. On February 6-7, 1978, significantly one lunar month later, these incidents were followed by even more severe tidal flooding in nearly identical locations on the east and west coasts of the United States. The documented analysis of such major tidal flooding episodes of the past, and the rational precautionary measures to be taken to prevent extensive damage from such flooding events in the future, constitutes a considerable portion of both parts I and 11 of this monograph. An analysis of the astronomical principles underlying the production of these tides, the varying forces which create them, and the perturbations in the lunar orbit which modify the amplitude of these forces and the duration of time in which they are active, all are contained in the second, scientific portion of the work. The last chapter contains a tabulation of all dates vulnerable to especially severe tidal flooding (should the weather and wind conditions also conspire) down to the year 1999. A Definitive Scientific Study of Perigean Spring Tides, Among the results of the research documented in this publication are: 1. Correlations between more than 100 cases of major tidal flooding-sus- tained over 293 years of history-and the coincident existence of perigean spring tides. This volume also includes separate case studies of outstanding examples of tidal flooding along the North American coastline, supplemented by tidal growth curves, daily weather maps, contemporary news accounts of the flooiling damage, and other data. Viii Author's Preface 2. Discussion of certain representative cases of perigean spring tides which have altered the course of naval history. 3. Evaluation of the practical impact of perigean spring tides on such diversified areas as coastal and inshore navigation, marine engineering, hydro- logical runoff, bioecological imbalance, and erosional damage to the coastal environment. 4. Examination of various instances of ship groundings, strandings, and collisions caused by the extreme low-water phase associated with perigean spring tides-or by their accompanying strong currents. 5. Delineation of examples of unusual tidal flooding which reached far inland, as the result of the coincidence of hurricanes and perigean spring tides. A comparison is made between the flooding potential of hurricaiies with and without the association of perigean spring tides, also between the flooding damage caused by hurricanes and by onshore winds generated by winter storms occurring coincidentally with perigean spring tides. 6. Expansion of those portions of classic tidal theory involving the mean positions and mean motions of the Moon and Sun to suggest further refine- ments in computed heights and amplitudes 'based upon the true positions and motions of these bodies and the true motion of perigee. 7. Analysis of the perturbational influences of the Sun on the orbit of the Moon during the critical period resulting from the alignment of perigee and syzygy. The results incorporate entirely new concepts substantiated by U.S. Naval Observatory data which provide a considerable modification of previous theories regarding the direction and speed of motion , of the lunar perigee at these times. 8. Formulation of appropriate new terminology for the classification' of a range of intensities of astronomically produced perigean spring tides. Included among these developments is the origination of the needed additional descriptor terms Proxigee and exogee, and a system for categorizing various degrees of perigear) spring tides based upon the, lunar parallax. 9. Derivation of a numerical coefficient or index expressing tidal flooding potential-which combines astronomical, hydrographic, dynamical oceano- graphic, meteorological, and other factors. Through auxiliary tables published in the book, the astronomical portions of this multiparameter index at the time Of any perigee-syzygy alignment are immediately available to marine weather forecasters, beacliguards, harbormasters, Coast Guard officials, civil defense agencies, and others directly concerned with coastal hazards and with protection against tidal flooding. 10. Review of numerous interdisciplinary fields in which the astronomical phenomenon of perigee-syzygy-and the inc reased gravitational forces it en- tails-might show some causal connection with other geophysical phenomena. The areas cited include the known augmentation of earth tides and ocean load- ing, the possible triggering of earthquakes, influences on geodetic leveling and deflection of the vertical, and geomagnetic effects. The possible excitation of biological tidal rhythms is also considered. Author's Preface ix A Note of Caution Relative to the Interpretation of Data A brief commentary of purely objective nature is desirable in order to satisfy the author's sense of responsibility to the scientific, community concerning the content of this work. The following treatise involves, in part, a comprehensive series of case studies on perigean spring tides covering 341 years of historical record. The analytical deductions made have been rigorously tested against this complex of empirical data. Out of this research effort, certain patterns of con- sistency have emerged which are beyond the realm of random chance and which render scientifically tenable the development of appropriate principles relating to the strong flooding potential of perigean spring tides. Coincidentally, certain definite conclusions are possible concerning the strategic importance of these tides in producing tidal flooding-if reinforced by strong onshore winds. In addition, evidence from this research supports a considerable credibility in the practical significance of these tides resulting from their economic, environmental, and ecological influences. A peremptory note of caution must be sounded, however. It is essential to observe that, because of the complexities involved in tidal prediction, many technical statements in connection with the tides must be accompanied by qualifications, reservations, and limitations-and, upon occasion, by individual exclusions and exceptions. One of the easiest available pitfalls and most in- cautious professional errors it is possible to commit in presenting any aspect of the tides is to allow any overgeneralized statement in connection therewith. The empirical data and analytical procedures used in this volume for determining tidal flooding potential are those applicable specifically to lowland regions on the Atlantic and Pacific coasts of North America. Likewise, although any measure of tidal flooding potential derived therefrom may pertain un- equivocably to a dozen or so related tide stations responsive to the same resonance mode, it may be totally or partially inapplicable to a location possessing different harmonic constants situated, perhaps, only a few score miles from the more consistent stations. In short, making any too general statement regarding tidal responses subject to a purely astronomical influence (in this case, a combined lunisolar influence) is, at best, a dangerous undertaking. Such astronomical forces will inevitably be modified by local oceanographic conditions, by tidal harmonics, and by such other variables as geographic latitude and longitude, sea-floor and coastal hydrography, strong hydrological runoff from the land, climate, season, and weather. In this concept, it would be totally pretentious to make unqualified state- ments for the absolute, permanent validity of either the Hfactor or the Aco-syzygy coefficient forming a part of it (cf., ch. 8) which are both subject to the need for continuing test and evaluation over time (permitting any desirable modification in their constituent parameters). A working hypothesis advanced upon the strength of evidence provided by even a large and diverse number of cases, however widely distributed in terms of time, hemispheric geography, and local conditions, is acceptable only insofar as it can adequately represent all circum- stances throughout the entire, period of past history for which observeddata are available, and be capable of similar accurate reproducibility of tidal flooding Author's Preface potential in the future-on a worldwide basis. This word of caution is not intended in any sense to weaken the analytic procedures or formulae developed in this investigation, but only to point up that ultimate definitiveness of the method requires consideration to a massive, totally representative, and globally adequate body of tide data. The groundwork, however, is at hand. The rate-of-growth tide curves alone in this project involved the computation and plotting of over 18,1100 individual data points. More than 100 years of daily tide tables were available, extending back to the original "High Water Only" predictions of the U.S. Coast Survey (which later became the U.S. Coast and Geodetic Survey and is now the National Ocean. Survey, a component of the National Oceanic and Atmospheric Adminis- tration). Separate tide tables were first published by the Coast Survey in 1866, following upon a series of simple tabular. data showing the relationship of the tides to the "full and change of the moon" which were issued in the annual volumes of the Report of the Superintendent of the Coast Surve starting in 1859. All :Y) 'such basic data have come under scrutiny, as appropriate to this study, for the validation of perigean spring tides. On the meteorological, side of the research effort, 105 years of daily surface synoptic weather maps (published since 1871, successively, by the U.S. Signal Corps, the U.S. Weather Bureau, and the present National Weather Service) were reviewed for the presence or absence of strong, persistent, onshore winds at the established times of perigean spring tide. Evidences of accompanying tidal flooding were then sought from newspaper, journal and special report literature dating back to the early colonial period in American history. From the astronomical point of view, the task of correlating these tidal and meteorological data was made possible through the cooperation of the U.S. Naval Observatory in providing a computer printout of all perigee-syzygy alignments having a separation-interval less than, or equal to =i= 24h, occurring during the 400-year period from 1600 to 1999. The exact method of application of these numerous sets of data, and the principles of random selection utilized to provide a space-saving but statistically valid base of comparison throughout widespread geographic locales on both the east and west coasts of North America, in succeeding decades of history, in different seasons of the year, and distributed at variousi times of the day, is thoroughly explained on pages 10-114 and 327-331 of this work. The alphanu- meric system for coding individual tidal flooding events, making possible a ready intercomparison between the associated astronomical, meteorological, and oceanographic circumstances-as well as a comparison with documented accounts of the accompanying tidal flooding-is described in these same pages. It should be emphasized from the outset that the evaluations made in this treatise concerning the effects of perigean spring tides do not overlook the possibility that other lesser influences (such as-sufficiently strong onshore winds coinciding with ordinary spring tides) may cause tidal flooding of generally smaller degree-nor do they in any way play down the role of hurricanes as a very major source of coastal flooding. However, this study does focus upon the particularly vulnerable role of perigean spring tides, with supporting wind accompaniment, in producing such coastal flooding effects. Author's Preface Xi The inherent danger of misconstrual of scientific information on the part of sources bent on sensationalizing such potentially catastrophic events of Nature through a lack of awareness of the total forces and concepts involved has been fully noted on pages 406-408. Further education and enlightenment of the large segment of the coastal population subject to the effects of such devastating flooding is the most effective method to forestall the unnecessary and costly confusion resulting from this type of misrepresentation. The purely scientific conclusions derived from this study are summarized both in the immediately preceding section of the preface and in the abstract which precedes the main text. Finally, a note of apology is extended to professional colleagues for the, author's shortcoming in not more rigorously avoiding certain minor redundancies in the following pages of text-an inconsistency which belies previous experiences in encapsulating some 180 articles written on astronomical and geophysical subjects in seven different encyclopedias and reference sources. Such are the vicissitudes of Government agency reorganization that, early in this project, the author found himself pursuing alone, not only the necess 'ary research aspects, the writing, associated computations, compilation of tables, and drafting of diagrams, but also the editing of his own manuscript-while at the same time racing a deadline for publication before his intended retirement from Govern- ment. Under these demanding circumstances, the inevitable result was a certain duplication between the contents of small sections of different chapters, prepared variously, as the associated analyses were accomplished, over a period of more than 4 years. ' On the positive side, somewhat salving a conscientious attitude regarding such compositional refinement, these same 'technical areas of the work may, however, benefit from an additional self-containment helping to minimize cross- referrals between chapters by readers who are less conversant with the subject material. A similar occasional repetition of nomenclatural definitions-useful to a prospective student of the subject in recovering his bearings among the otherwise complex technical developinent-requires, perhaps, a lesser apology. The author naturally assumes responsibility for any errors of technical nature which may, through the very comprehensiveness of the work, have escaped attention in reviewing proofs on an accelerated time scale. Acknowledgments The number 'and variety of persons contributing to, and in a very real sense ultimately responsible for, the realization of this complex technical mono- graph over nearly a 5-year period represent a degree of individual effort making regrettable 'an inability more properly to credit the assistance of each, in fitting detail. Such extensive individual cooperation may, parenthetically, be .regarded as indicative of the wide range of personal interests in a subject so meaningful to those utilizing the coastal environment. From-the very outset of the investigation as a scientific concept suggested for further study-through its subsequent development into a full-scale project as pieces of the puzzle began to fall into place-and the intensive research Xii Author's Preface endeavor culminating in the present volume-the continuing interest, support, and personal encouragement of Dr. Gordon G. Lill, deputy director of the National Ocean Survey, and the matching confidence of its director, Rear Admiral Allen L. Powell, have provided a staunch undergirding for the work. Over this same period of monograph preparation, the close cooperation, interdisciplinary rapport, and many stimulating hours of discussion with Dr. Thomas C. Van Flandern, lunar specialist in the Nautical Almanac Office, U.S. Naval Observatory, have contributed immeasurably to the technical significance and completeness of the project. Through his assistance, and that of Dr. P. Kenneth Seidelmann, director of the Nautical Almanac Office, and Dr. P. M. Janiczek, the extensive data presented in table 16 became possible- for which the availability of the computational facilities of this observatory is also duly acknowledged. The diligent application of Mr. Aaron S. Blauer, formerly of the U.S. Government Printing Office, now retired, in copy-editing, styling, marking, and otherwise preparing the material for publication-as well as in coordinating the multitudinous aspects of readying the text proofs, graphics, tables, and photoreproducibles before release to the Government Printing Office-warrants an enormous debt of gratitude. The administrative support of Mr. John R. Morrison, deputy director of the Office of Publications, U.S. Department of Commerce, and the staff services of Mr. Armand G. Caron of this same office, are deserving of similar recognition. Mr. James L. Moore, Mr. Irving C. Brainerd, and Mr. Philip Gambino handled publication liaison through the National Ocean Survey, the National Oceanic and Atmospheric Administration, and the U.S. Department of Commerce, respectively. Mr. M. Kenneth Miller of the Office of Publications, DOC, coordinated with the Naval Observatory the linotron preparation of computer printout data. Special appreciation must be extended to Mr. Francis X. Oxley, formerly chief of NOAA's Photographic Section, for his meticulous reduction and com- pilation processing of weather maps and composite overlays providing many of the illustrations for this work. He was assisted by Mr. Harold M. Goodman and Mr. John A. Roseborough. These photographic reproductions were initially made possible thr iough the exacting negative copy work accom- plished by Mr. Joseph E. Bradshaw, and Mr. Robert C. Robey, Jr., under the direction of Mr. William C. Bugbee, formerly chief of the photographic labora- tory in the National Ocean Survey's (Chart) Reproduction Division. Inestimable support in the area of literature search was provided by the late Mrs. Sharlene G. Rafter, reference librarian in NOAA's Marine and Earth Sciences Library, and by Mrs. Bettie L. Littlejohn of this same facility. Mr. Robert Walter conducted a computerized literature search of seven different data banks for relevant citations. Mr. Douglas L. Stein, assistant librarian for manuscripts at Mystic Seaport, Mystic, Conn., substantially aided the project in its historical research phases, as did Mr. Thomas A. Stevens, historian of the Connecticut River, Mr. Thompson R. Harlow, director of the Connecticut Historical Society, Mr. A.W.H. Pearsall, historian, National Maritime Museum, Greenwich, England, plus Mrs. Caroline Rutger and Mrs. Margery Ramsey of the library of The Mariners Museum, Newport News Va. Further assistance was Author's Preface Xiii provided by the William L. Clements Library of the University of Michigan and the Ships' Histories Branch, Naval History Division, U.S. Navy Department. Mr. Timothy C. O'Callaghan aided with the compilation of the bibliography and index. Contributions of illustrative material were made by the many organ- izations to which individual credits are given as a part of the figure captions throughout the treatise. The Library of Congress provided the source for repro- duction of many early newspaper accounts of tidal flooding. Typing and revision of the extensive manuscript through its numerous stages of preparation was accomplished by Mrs. Mary Lou Lapelosa, to whom appreciation is also due for handling the many secretarial duties attendant upon the project, and for maintaining the considerable quantity of graphic material connected with the publication. A special tribute is owing to Miss Rhonda M. LaSaine, summer employee, for a diligent research application to Library of Congress newspaper sources, and to Ms. Beatrice S. Drennan, NOS, for similar assistance with resource literature. During the early stages of monograph pro- duction, support in preparing certain of the diagrams used was provided by Mrs. Gayle Brodnax. Various members of the Tide Prediction Branch, Oceanography Division, National Ocean Survey-especially Mr. Donald C. Simpson and Mr. Samuel E. McCoy-provided tide data necessary to the project. To all of the above, the author expresses his permanent gratitude. Table of Contents Page Foreword.... iii Author's Preface.....,........ v Table of Contents... xv List of Tables. . . . XXV Abstract... .......... xxvii PART I-BACKGROUND ASPECTS Chapter 1. Representative Great Tidal Floodings of the North American Coastline The Evidences From History. . . .. .. .. .. .. .. .. .. '. .. '. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . I Case No. 200-Perigean Spring Tides (near the time of a total lunar eclipse).. . .. .. 1 Technical Commentary.. 4 Case No. 4-Perigean (Proxigean) Spring Tides (7r=61'26.6", P-S= -61). 7 Case No. 7-Perigean Spring Tides (P-S=-17h). 8 Case No, 8-Perigean Spring Tides (P-S=+ 10h).. 8 Case No. 13-Pseudo-Perigean Spring Tides (P - S 53h) ................. 8 Case No. 36-Near-Ordinary Spring Tides. 9 Coastal Flooding as an Ongoing Risk.. 10 Methods of Identification and Evaluation of Representative Cases of Tidal Flooding.. 12 Remarks Concerning the Fundamental Astronomical, Tidal, and Meteorological Data Sources Used in Connection With Computations for this Volume. . . . . . . . . . 13 Chapter 2. The Impact of Peris-yean Spring Tides Upon Representative Events in American Nautical History Perigean Spring Tides as an Aid to Navigation..., 59 The Fate of the Frigate Trumbull. . .......... 59 Contemporary Knowledge of Perigean Spring Tides. . . 68 Tidal Analysis.. 68 Hydrographic Analysis. . . . 69 The Second Battle of Charleston Harbor. 70 Tidal Analysis.... 72 Hydrographic Analysis. . 74 The Battle of Port Royal Sound, S.C. 78 Tidal Analysis.. 82 Hydrographic analysis. 84 Data Concerning the Draft of the Wabash. 84 The Perigean SpringTide asanAgentof CoastalErosion. ...... 84 The Hatteras Campaign. 85 xv xvi Table of Contents PART I-BACKGROUND ASPECTS-Continued Chapter 3. The Practical, Economic, and Ecological Aspects of Perigean Spring Tides Page The Effectsof Extremely Low Waters... 93 Dangers of Explosive Decompression in Submarine Environments.. 93 Ship Grounding. 95 The Effects of Accelerated Currents. . 95 Impact Upon Marine Engineering Projects 96 Dangers to Navigation and Docking 96 The Influences of Improvements in Navigation Aids. . 96 The Optimum Dispersal of Engineering Demolition Products...... 97 Ecological Influences of Perigean Spring Tides.. 98 Variations in Salinity... 99 Variations in Carbon Dioxide Content, . . . . 100 Variations in Water Temperature 100 The Effect Upon Grunion Runs. . 100 Miscellaneous Environmental influences. 102 Recapitulation of the Practical Influences of Perigean Spring Tides. . . 103 Influences of Perigean Spring Tides for Which Substantiating Evidence is Available.. 103 Chapter 4. Survey of the Scientific Literature on Perigean Spring Tides Historical Origin of the Concepts of Perigee-Syzygy and Perigean Spring (Perigee-Spring) Tides. . . 109 18th Century Tidal Literature.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. _ .. .. .. .. .. .. .. .. .. .. ill Early 19th Century Tidal Literature... 112 The " Saxby Tide" of October 5, 1869. 112 Late 19th Century Tidal Literature. 114 20th Century Tidal Literature.. 115 PART JI-SCIENTIFIC ANALYSIS Chapter 1. General Background Considerations of Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides Astronomical Factors Significant to Tidal Nomenclature.... . . 121 Astronomical Positions... 121 Coordinate Systems. . . 121 1. Equitorial System. 121 2. Ecliptic System. . . 123 3. Horizon System. . .......................................................... 123 General Equations for Transformation of Coordinates From the Equatorial to the Ecliptic System or the Reverse. 124 General Equations for Transformation of Coordinates From the Equatorial to the Horizon System or the Reverse. 124 Table of Contents xvii PART II-SCIENTIFIC ANALYSIS-Continued Chapter I-Continued Astronomical Factors Significant to Tidal Nomenclature--Continued Page Astronomical Motions. 124 The Diurnal Rotation of the Earth. 124 The Earth's Annual Revolution Around the Sun. 125 The Moon's Revolution Around the Earth ........................................... 125 The Motions of the Earth and Moon in Elliptical Orbits ................................ 127 1. The Anornalistic Month ............. I ........................................ 130 2. Effect of the Solar Parallactic Inequality ........................................ 131 Declinational Effects on the Apparent Motions of the Moon and Sun ...................... 132 Auxiliary Influences Affecting the Daily Rate of Lunar Motion in Right Ascension ................. 132 The Effect of Parallax on the Moon's Apparent Motion .................................... 133 Changes in Right Ascension Associated With the Apparent Diurnal Motion of the Moon ........ 133 The Relationship of the Moon's Motion in Right Ascension to Its Declination ................. 135 Chapter 2. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces Principal Effects .......................................................................... 137 The Daily Lunar Retardation .......................................................... 137 1. The Lunar Day ................................................................ 139 2. The Tidal Day ................................................................. 139 Relationship of the Tidal Day to Lunar Transit Times, Hourly Differences in Right Ascension of the Moon, and Other Factors ...................................................... 140 Apparent Diurnal Motion of a Body "Fixed" in Space ..................................... 141 Apparent Diurnal Motion of a Body Possessing Its Own Motion in Right Ascension ............ 141 Variations in the Tide-Raising Force Associated With Lunar Parallax ........................ 141 The Effect of the Parallax Inequality Upon the Comparative Lengths of the Tidal Day ......... 143 Ancillary Effects .......................................................................... 147 Lunar Augmentation ................................................................... 147 Regional and Latitudinal Effects on the Tides Resulting from Changing Lunar and Solar Declinations ........................................................................ 148 1. Solstitial Tides ....................... ......................................... 149 2. Tropic Tides .............. : .................................................... 149 3. Equinoctial Tides .............................................................. 150 4. Latitudinal Effects of the Diurnal Inequality ....................................... 150 Subordinate Factors Influencing the Length of the Tidal Day ............................... 150 1. Solar Declinational Effects ....................................................... 150 2. Effects Due to Changing Parallax and the Obliquity of the Ecliptic .................... 150 3. Lunar Declinational Effects ............................................ ......... 150 4. Effect of the Moon's Orbital Inclination to the Horizon. . . . 150 5. Supplementary Influences. 151 Seasonal Factors Influencing the Production of Heightened Tides. . 151 Effects of the Phase Inequality and Diurnal Inequality. 151 202-509 0 - 78 - 2 Xviii Table of Contents PART II-SCIENTIFIC ANALYSIS-Continued Chapter 3. The Action of Various Perturbing Functions in Establishing, Altering, and Controlling the Amplitudes of Perigean Spring Tides Page The Effects of Perturbations Upon Lunar Distances and Orbital Motions. 153 The Lunar Evection .......................... 153 The Lunar Variation.. 155 1. Alternating Acceleration and Deceleration of the Moon's Orbital Motion ............... 156 2. Changing Lunar Orbital Velocity With Respect to the Earth. . . . . 157 3. Changes in Curvature of the Lunar Orbit.... 158 The Elliptic Variation. 159 The Annual Variation. 159 The Lunar Reduction. 159 Differences Between the Mean and True Astronomical Positions of the Moon and Sun.. 159 The Derivation of True and Mean Astronomical Positions. . 161 The Assumption of Mean Positions.. 161 The Special Perturbative Influences of Lunar Evection and Lunar Variation ...................... 162 Summary of the Effects of the Principal Lunar Perturbations in Differentiating Between the Mean and True Orbital Pos itions of the Moon.. 164 1. Effects of Elliptic Inequality. . . 164 2. Effects of Evection (combined with the elliptic inequality). 164 3. Effects of Lunar Variation... 165 4. Effects of the Annual Equation... 165 Corrections for Lunar Perturbations as Used in the Tidal Equations .......................... 166 Chapter 4. Identification of the Specific Astronomical Forces and Influences Contributing to the Production of Perigean Spring Tides The Principal Concurrent Tidal Forces ...................................................... 169 The Effects of a Near-Alignment of Perigee and Syzygy in Producing Tides of Increased Ampli- tude and Range ............................................................. I ....... 169 Basic Force Equation Defining the Magnitude of Tidal Uplift .... ...... ............... 169 1. Lunar Evection Effects ........................................................... 170 2. Lunar Variation Effects .......................................................... 172 3. Summary Analysis ............................................................. 17@ The Effect of Perigee-Syzygy Alignment in Increasing the Value of the Lunar Parallax ......... 174 1. Effect of the Elliptic Inequality .................................................. 175 2. Effect of the Lunar Evection ............. I....................................... 175 3. Effect of the Lunar Variation .................................. ...... 175 4 Summary Analysis .............................................................. 176 The Concepts of Mean Motion vs. True Motion in Relation to the Earth, Moon, and Lunar Perigee ............................................................................ 177 1. The True Motion of Lunar Perigee ............................................... 177 2. Short-Period and Long-Period (Averaged) Perturbational Motions of Perigee ........... 1177 3. The Special Motion of Perigee Close to the Position of Perigee-Syzygy Alignment ....... 179 4. The Comparison of True and Mean Motions ....................................... 182 5. The Minor Sinusoidal Variation Between True and Mean Longitude ................. 184 Table of Contents xix PART II-SCIENTIFIC ANALYSIS-Continued Chapter 4-Continued Page Subordinate and Counterproductive Effects on Perigean Spring Tides ............................ 185 Effects of Declination on the Tide-Raising Forces .......................................... 186 Maximization of Declination in the 18.6-Year Period of the Lunar Nodical Cycle ............. 189 Aside From a Lack of Onshore Winds, Why Does Coastal Flooding Not Occur With Every Perigean Spring Tide? ....................................................................... 191 Combined Effect of Changing Parallax and Large Dedlination on the Moon's Hourly Motion in Right Ascension ........................................ I ............................ 192 Effects of Extreme Lunar Declination on Motions in Right Ascension ........................ 193 1. Decrease of Motion in Right Ascension, and Shortening of the Tidal Day at Times of High Lunar Inclination to the Celestial Equator ......................................... 195 2. Increase of Motion in Right Ascension, and Lengthening of the Tidal Day at Times When the Moon Is at an Extreme Declination ........................................... 196 Chapter 5. The Essential Conditions for Achieving Amplified Perige'an Spring Tides The General Concepts of Maximization of Perigean Spring Tides.. 197 Factors Increasing the Intensities of the Tidal Forces Acting. . 197 A Quantitative Evaluation of the Various Tide-Maximizing Factors .......................... 199 Summary of Relative Gravitational Force Influences. 199 Astronomical Influences Producting Uneven Heights Among Perigean Spring Tides; Lack of a Current Procedure for Variable-Intensity Classification. . 202 Perigean Spring and Other Tidal Equivalents in International Terminology ................... 203 Compensating and Counterproductive Tidal Force Influences. 204 Variation in Parallax and Orbital Curvature with Lunar Configuration. 204 Comparitive Effects of Various Lunisolar Configurations Upon Lunar Distance From the Earth and the Curvature of the Lunar Orbit. 205 1. Apogee-Syzygy..... 207 2. Apogee-Quadrature. 207 3. Ordinary Syzygy- 208 4. Ordinary Quadrature... 208 5. Perigee-Quadrature..... 209 6. Perigee-Syzygy ............... 209 A Quantitative Comparison of the Lunar Parallax at Times of Perigee and Apogee ............. 210 Causes of Variation in the Shape of the Lunar Orbit and in the Consequent Tide-Raising Forces ..... 214 Effects of the Individual Syzygies. . . . 214 1. Case One: Full Moon at Perigee. 214 2. Case Two: New Moon at Perigee..... 216 The Effect of Solar Perigee... 218 The Effect of Coplanar Lunisolar Declinations. . . . 218 The Effect of Nodal Alignment. 218 Summary Evaluation of Extreme Lunar Parallaxes. 219 xx Table of Contents PART II-SCIENTIFIC ANALYSIS --Continued Chapter 6. Conditions Extending the Duration of Augmented Tide-Raising Forces at the Times of Perigee-Syzygy Page The General Principles of"Stern Chase" Motion.. 269 Factors Increasing the Length of the Tidal Day. 269 1. Lunar Parallactic Inequality. ........... 269 2. Declination Effects. . . 270 3. The Counterproductive Influences of Solar Perigee (Perihelion). 270 4. Summary. . . 271 Reintroduction of the Concepts of the Lunar and Tidal Day. . 271 Fluctuations in the Lunar and Tidal Days. . . 271 1. Derivation of the Length of the Mean Lunar Day... 272 2. Variations in the Lunar Day. . . 272 3. Variations in the Tidal Day. 273 Causes of Systematic Variations in the Length of the Tidal Day. . . 273 The Role of the Increased Tidal Day Viewed in Perspective ................................ 274 The Effect of Increased Lunar Orbital Velocity Upon the Length of the Tidal Day ............ 274 Quantitative Evaluation of Changing Periods in the Moon's Monthly Revolution. 275 Conditions Lengthening the Synodic and Anornalistic Months... 275 Maximized Lengths of Those Months Bracketing Perigee-Syzygy. 285 Cycles of Alternation in Perigee-Syzygy Alignments.... 285 The Meaning and Relationships of High and Low Maxima in the Lengths of the Lunar Months. 286 1. Variation in Length of the Anonialistic Month. . 287 2. Variation in Length of the Synodic Month... 287 The Correlation Between Smaller Perigee-Syzygy Separation-Intervals and Longer Months ...... 287 Analysis of the Relative Gains in the Lengths of the Anomalistic Months Containing a Close Perigee-Syzygy Alignment.... 288 1. Anomalistic Month. 286 2. Synodic Month. . 288 Prolongation of a Small Separation-Interval at Close Perigee-Syzygy Alignments... . .. .. .. .. .. .288 Declinational Influences on the Length of the Tidal Day. . 299 The Effect of the Lunar Apsides Cycle. 290 Modification of the Lunar Period by the Lunar Apsides Cycle. . . . . . . . 292 Other Time-Related Factors Susceptible to Analysis by the Methods of Harmonic Analysis.. 296 Evaluation of the Principal Harmonic Constituents. . 296 The Phase Age and the Parallax Age. . 297 Variation in Tidal Range, and in the Types of Tides ......... 298 Table of Contents xxi PART 11-SCIENTIFIC ANALYSIS-Continued Chapter 7. The Classification, Designation, and Periodicity of Perigean Spring Tides, With Outstanding Examples of Accompanying Tidal Flooding From Recent History Page Comparison of Ordinary Spring Tides and Perigean Spring Tides. . . . 301 Concepts of Tidal Priming and Lagging ..................................................... 302 Lunar Phase Effects-Qualitative Evaluation. . . . . 302 Priming and Lagging as Shown in Tide Curves. . . 302 1. Tidal Priming. . . 303 2. Tidal Lagging. 303 Quantitative Analysis of the Effects of Tidal Priming and Lagging. 306 Relative Tide-Raising Forces at Quadratures and S@zygies. @06 Confirmation of the Extended Duration of Peak Tide-Raising Forces at Perigee- SyZygy. 306 Examples of Tidal Priming and Lagging... 311 1. Application to Ordinary Spring Tides. . . . 311 2. Application to Perigean Spring Tides..... 312 A Proposed New System for the Quantitative Designation of Perigean Spring Tides ................ 312 Basis for the Classification of Perigean Spring Tides.. 313 1. Maximum Perigean Spring Tides (or Ultimate Proxigean Spring Tides); Maximum .Proxigean Spring Tides. . . 313 2. Extreme Proxigean Spring Tides. 316 3. Proxigean Spring Tides. 316 4. Perigean Spring (or Perigee-Spring) Tides. . . 317 5. Pseudo-Perigean Spring Tides.. 317 6. Ordinary Spring Tides.. 318 Periodic Relationships 318 The Mean Period Between Successive Occurrences of Perigee-Syzygy... 318 Short-Period Cycles of Repetition of Perigean Spring Tides. . 319 The 31-Year Cycle of Perigee-Syzygy .................................................... 321 Meteorological Aspects of Coastal Flooding at Times of Perigean Spring Tides. . . . . . . 326 Selection of Multidisciplinary Data Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 The Correlation of Meteorological and Astronomical Data ................................... 328 Grouping of the Weather Maps. 328 Explanatory Comments Concerning the Manner of Designation of Weather Maps and the Concurrent Perigee-Syzygy Data. . . 329 1. The Tidal Flooding of 1931 March 4-5..... 331 2. The Tidal Flooding of 1939 January 3-5. . . 374 3. The Tidal Flooding of 1959 December 29-30.... 383 4. The Tidal Flooding of 1962 March 6-7..... 386 5. The Aborted Tidal Flooding of 1962 October 13 ............................... 403 6. The Tidal Flooding of 1974 January 8 (N-99) ............. 404 A Note on Storm Tide Announcement Effectiveness.. 406 Data on Tidal Flooding and Associated Damage... 408 7. Tidal Flooding in-the British Isles on 1974 January 11-12 and February 9 ......... 420 8..Tidal Flooding of 1976 March 16-17... 424 9. Tidal Flooding of 1978 January 8-9. 429 10. Tidal Flooding of 1978 February 6-7..... 430 xxii Table of Contents PART 11-SCIENTIFIC ANALYSI S-Continued Chapter 8. Tidal Flooding Potential, and the Relationship of Perigee-Syzygy to Other Oceanographic and Geophysical Factors and Influences Page Development of a Numerical Index Designating the Astronomical Potential for Tidal Flooding ....... 434 1. TheNeedfor Combined Lunisolar Representation. . 434 2. Significance dthe Aw-Syzygy Coefficient. 435 3. Evaluation of the Aw-Syzygy Coefficient. 436 Establishment of a Combined Astronomical-Meteorological Index to Potential Tidal Flooding ....... 437 Empirical Support for the Validity of the Delta Omega-Syzygy Coefficient Provided by Predicted and Observed Tidal Height Data, 440 The Lengthened Tidal Day as an Indicator of Increased Tidal Flooding Potential.... . .. . 440 Accelerated Rate of Tide Rise as an Indicator of Increased Tidal Flooding Potential 448 1. Semidiurnal Tide. . 448 2. Mixed Tides (Affected by the Diurnal Inequality). 474 An Independent Check on the Validity of the Aw-Syzygy Coefficient. 475 Summary and Conclusions A. The Tidal Aspects of Perigee-Syzygy Alignment.. 477 B. The Subsidiary Effects of Extreme High and Low Waters and Strong Tidal Currents at Times of Perigee-Syzygy.. 482 Representative Instances of Ship Groundings in Shallow Depths Produced at the Low- Water Phase of Perigean Spring Tides. 483 Representative Instances of the Effects of Strong Current Flow Associated With Periods of Perigean Spring Tides.. 485 Extreme Tide and Current Impact on Offshore Platforms in Shallow Ocean Areas.. 485 Influences of Perigean Spring Tides Upon the Ecology of the Coastal Zone .... ; .. .. 485 C. Unproven Geophysical Relationships With the Phenomenon of Perigee-Syzygy ............. 485 1. Wholly Conjectural Relationships Between Meteorological Factors and Perigee-Syzygy. 486 2. Other Possible Geophysical Influences.. 487 D. Geomagnetic Illustration of the Increase in Velocity of Tidal Currents at Times of Perigee - Syzygy- 489 Supplementary Comments, Specific Literature Citations and Case Examples in Connection with the Influences of Perigee-Syzygy Alignments and Perigean Spring Tides. 490 1. Storm Surge Models and Tidal Flooding. . 490 2. Engineering Protection Against Storm Surges and Tidal Flooding. 490 3. Possible Coincidence of Tsunamis and Perigean Spring Tides.. 490 4. Concepts of Earthquake Triggering. 490 5. Tidal Loading. . 493 6. Earth Tides. . 493 7. Crustal Tilt. 494 8. Deflection of the Vertical.. . 494 9. Geornagnetic Effects. 494 10. Ecological Aspects.., 494 11. Internal Waves. 494 12. Turbidity Currents. . 49.4 113. Fish Migration... . 494 14. Biological Rhythms 495 15. Breakup of River Ice. . . . 495 The Challefige of Geophysical Discovery: An Advocacy of Interdisciplinary Cooperation ............ 495 Table of Contents xxiii APPENDIX The Basic Theory of the Tides Introduction Page The Astronomical Tide-Producing Forces: General Considerations. 497 Origin of the Tide-Raising Forces. 497 Detailed Explanation of the Differential Tide-Producing Forces.... 498 1. The Effect of Centrifugal Force. 498 2. The Effect of Gravitational Force... . 498 3. The Net or Differential Tide-Raising Forces: Direct and Opposite Tides. 499 4. The Tractive Force... 500 5. TheTidal Force Envelope.. 501 Variations in the Range of the Tides: Tidal Inequalities.. 501 1. Lunar Phase Effects: Spring and Neap Tides... 501 2. Parallax Effects (Moon and Sun). 502 3. Lunar Declination Effects: The Diurnal Inequality ..................................... 503 Factors Influencing the Local Heights and Times of Arrival of the Tides.. 503 Prediction of the, Tides..... 506 Reference Sources and Notes. 511 Bibliography on Tides (in42 Categories). 517 Index. 531, List of Tables TABLE Page 1. List of 100 Representative Examples of Major Coastal Flooding Along the North American Coastline, 1683-1976, Related to the Near-Contiguous Occurrence of Perigean Spring Tides Coupled With Strong, Persistent, Onshore Winds .............................. 15 2. A Representative List of North American Hurricanes Occurring Nearly Concurrently With Perigean Spring Tides ........................................................... 26 3. Representative Cases of Coastal Flooding Associated With Ordinary Spring Tides, Coupled With Strong, Persistent, Onshore Winds .......................... .................. 29 4a. Representative Cases of the Highest High Waters of Record Observed at Various Tidal Stations, Within 2 Days of Perigee-Syzygy .......................................... 32 4b. Representative Cases of the Lowest Low Waters of Record Observed at Various Tidal Sta- tions, Within 2 Days of Perigee-Syzygy ............................................. 33 4c. Examples of Perigean Spring Tides Resulting in, or Contributing to, Coastal Flooding Through Impaired Hydrological Runoff .................................................... 35 4d. Illustrative Cases of Coastal Erosion Produced at Times of Perigean Spring Tides Coincident With Strong, Persistent, Onshore Winds ................. ........................... 36 5. A Representative Sample of Newpaper Articles Covering Tidal Flooding Events Associated With Perigean Spring Tides, 1723-1974 ............................................ 39 6. Comparative Tides at Charleston Harbor, S.C., October 13-19, 1974 .................... 72 .7. Apparent Daily Motion of the True Sun in Right Ascension and Longitude for Selected Dates in 1975 .................................................................. 131 8. Comparison of Geocentric Horizontal Parallax and True Geocentric Distance of the Moon for a Case of Widely Separated Perigee-Syzygy ...................................... 142 9. The Changing True Distance of the Earth From the Sun ............................... 144 10. Approximate Orbital Angular Velocity of the Moon, Expressed as a Difference in Celestial Longitude, Showing the Variation at Times of Close Perigee-Syzygy, (Proxigee-Syzygy) Apogee-Syzygy (Exogee-Syzygy), and Perigee-Quadrature ............................ 146 11. Approximate Dates on Which Maximum Lunar Declinations Occurred, According to the 6,798.4-Day Nodical Cycle ............................ )........................... 195 12. Selected Cases of Perigee-Syzygy, Showing the Relationship Between the Equinoctial Posi- tion of the Moon and the Lunar Parallax Over the 400-Year Period 1600-1999 .......... 200 13. Compilation of All Cases of Extreme Proxigee-Syzygy Occurring Over the 400-Year Period 1600-1999 .............. I................ ...................................... 201 14. Selected Cases of Perigee-Syzygy Occurring Simultaneously at a Lunar Node (Total Solar Eclipse) and Near Perihelion .......... 202 15. True Geocentric Distance of the Moon ... ...... 206 16. Computer Printout of All Cases of Perigee-Syzygy Occurring Between 1600 and 1999 Which Have a Separation Interval <_24h (With Accompanying Astronomical Data) ............ 221 17. Increase in the Lengths of the Synodic and Anornalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments ..................................... 276 18. Variation in the Length of the Synodic Month Within the 8.849-Year Lunar Apsides Cycle. 292 19. Types of Tides (With Index and Range) at Various Locations Along the Atlantic, Pacific, and Gulf Coasts of North America ................................................ 299 20. Effects of Tidal Priming and Lagging (at Perigee-Syzygy) .............................. 309 21. Effects of Tidal Priming and Lagging (at Ordinary Syzygy) ............................. 310 22. Proposed Classification System for Perigean (including Proxigean) Spring Tides ........... 313 23. Examples of Scientific and Technical Terminology in the English Language Involving Inter- lingual Combinations of Prefixes and Suffixes ....................................... 315 xxv xxvi List of Tables Table Page 24. Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Align- ments ......................................................................... 321 25. Cases of Extreme Tidal Flooding Coinciding With Long-Term Astronomical Cycles of Close Alignment Between Perigee and Syzygy ............................................ 326 26. Surface Synoptic Weather Maps for'Twenty Representative Cases of Coastal Flooding As- sociated With Perigean Spring Tides and Strong, Sustained, Onshore Winds ............ 332 27. Surface Synoptic Weather Maps for Twenty Representaive Cases of Nonflooding Conditions Associated with Perigean Spring Tides Which Were Accompanied by Light and Variable Winds and High Atmospheric Pressure ............................................. 353 28a. Surface Synoptic Weather Maps for Four Representative Cases of Hurricanes Occurring in Near-Coincidence With Perigean Spring Tides ..................................... 374 28b. Representative Surface Synoptic Weather Map at a Time During Which a Perigean Spring Tide Caused Blocking and Backup of Hydrological Runoff ............................ 374 29. Surface Synoptic Weather Maps for Cases of Tidal Flooding Receiving Special Attention in the Text ....................................................................... 387 30. Examples Involving the Use of the Aco-S Coefficient in Establishing a Combined Astro- k nomical-Meteorological Index ([I) of Potential Tidal Flooding ......................... 439 31a, b, Data Used in Evaluating the Increased Length of the Tidal Day at Perigee-Syzygy (Made c, d. Comparatively More Effective by the Greater Gravitational Force at These Times) as Plotted on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-Decem- ber,1962 ...................................................................... 441 32a, b, Data Used to Determine the Accelerated Rate, of Tide Rise at Times of Perigee-Syzygy, c, d. Superimposed on the National Ocean Survey Tide Tables for Breakwater Harbor, Del., January-December, 1962 ........................................................ 449 33. Sixteen Instances of Major Tidal Flooding Near a Time of Perigee-Syzygy, Represented (in Figs. 153-163) by Plots Showing the Predicted Rate of Rise of the Astronomical Tide at Nearby Tidal Reference Stations (Listed in the Table) ................................ 453. 34. A Checklist of the Central Dates (Mean Epochs) of Perigean Spring Tides (P-S< �24 b) Occurring Between 1 7 and 1999 ................................................ 480 Abstract Tides are caused by the gravitational attractions of the Moon and Sun acting upon the oceans and major water bodies of the Earth. Two times during each month, at new moon (conjunction) and full moon (opposition), the Earth, Moon, and Sun come into direct alignment in celestial longitude and, in the combination of their gravitational forces, enhanced tide-raising forces result. Tides produced at these times are called spring tides. Since the lunar orbit is elliptical in shape, once each revolution the Moon also attains its closest monthly approach to the Earth, a position known as perigee. Ordinarily, the passage of the Moon through perigee and the alignment of Moon, Earth, and Sun at new moon or full moon (either position being called SYZY9Y) do not take place at the same time. Commensurable relationships between the lengths of the synodic and anomalistic months do, however, make this possi- ble. On the relatively infrequent occasions when these two phenomena occur within I I/ days of each other, the resultant astronomical configuration is de- /2 scribed as perigee-@yzygy, and the tides of increased daily range thus generated are termed. perigean spring tides or, simply, perigee springs. Whenever such alignments between perigee and syzygy occur within a few hours or less of each other, augmented dynamic influences act to increase sensibly the eccentricity of the lunar orbit, the lunar parallak, and hence also the orbital velocity of the Moon itself. Such solar-induced perturbations also reduce the Moon's perigee distance in each case by an amount which is greater the closer is the coincidence of alignment between these two astronomical positions, but which also fluctuates with other factors throughout the years. The tide-raising force varies inversely as the cube of the distance between the Earth and Moon (or Sun). On certain.occasions, lunar passage through perigee involves a particu- larly close approach of the Moon to the Earth. To distinguish these cases of unusually close perigee, the new term "proxigee" has been devised, and the associated tides of proportionately increased amplitude and range are designated as 44proxigean spring tides." Evidences presented in this technical monograph indicate that the appreci- ably enhanced influences on the tides produced at the time of proxigee-syzygy are revealed, not so much in increasing the height of the tide (usually a'maximum increase of about 0.5-1 foot above mean high water springs) but in accelerating the rate at which these augmented high waters are reached. This accelerated growth rate in the height of the tides, together with an increased horizontal current rnoyement, creates a sea-air interface situation particularly susceptible to the coupling action of surface winds. Although the perigean spring tides do not, of themselves, constitute a major flooding threat to coastlines, friction be- XXVII Xxviii Abstract tween strong, persistent, onshore winds and the sea surface can raise the astro- nomically produced tide level to cause extensive flooding of the coast in low- land regions. In addition, at the times of perigee- (proxigee-) syzygy, various dynamic influences combine to lengthen the tidal day, increasing the period within which the enhanced tide-raising forces, effective for some few days on either side of the perigee-syzygy alignment, can exert their maximized effects. In this monograph, covering a 341-year period of history relative to the coastal environment of North America, a large number of examples of major tidal flooding produced by the combination of the above causes have been collated to provide a detailed case study. A composite table of 100 such cases, including all pertinent astronomical and meteorological source data, has been compiled. Graphic, textual, and mathematical analysis have been used to demonstrate the individual astronomical, oceanographic, meteorological, hydro- graphic, climatological, and hydrological influences which are involved during the production of the phenomenon commonly-referred to as a "storm surge." Quantitative correlations between these various factors have been established. A proposed new index of tidal flooding potential based upon the combina- tion of astronomical influences augmenting the tides at the times of perigee- syzygy and known as the Aco-syzygy coefficient has been developed. This has been combined with other physical quantities representative of the local and prevailing tidal, meteorological, and hydrographic circumstances to establish a second index known as the nfactor. The latter term is designed to provide a quantitative measure of the probability of tidal flooding occurrences along a lowland coast- line, should strong, persistent, onshore winds coincide with perigean spring tides. In contrast to the traditional method which involves a simple consideration to the highest tides of the year to determine flooding potential when such tides are accompanied by strong onshore winds (a procedure which can be shown to be both ambiguous and erratic in numerous instances), the combination of the Aco-syzygy coefficient with appropriate meteorological indicators is demonstrated to be an effective new tool for the evaluation of tidal flooding potential at coastal stations having a daily tidal range of 5 feet or more. The usefulness of this method can be further enhanced by future empirical refinements. The particular vulnerability to tidal flooding exhibited by those perigean spring tides which possess a sharply accelerated rate of growth is one of the primary points of consideration in this monograph, inasmuch as the graphical- analytical methods applied do not appear elsewhere in scientific literature. .Separate methods for obtaining a meaningful rate of tide growth in the case of both semidiurnal and mixed tides are shown. Such rate-of-growth tide curves are presented for actual cases of tidal flooding occurring over a wide range of latitudes, on both the east and west coasts of North America. These specially analyzed instances of coastal flooding are randornly," chosen throughout all months of the winter storm season for a wide range of stations and are distributed, in each decade, over 80 years of record to permit a scientifically representative basis of correlation between the circumstances of tidal flooding and associated astronomical and meteorological data. Numerous examples of perigean spring tides accompanied by nearly simultaneous tidal flooding on both the Atlantic Abstract XXiX and Pacific coasts-and other floodings displaying a definite relationship to- various astronomical cycles of perigee-syzygy-are included. The observed and predicted hourly height tide records for selected cases of tidal flooding are compared to show the separate effects of astronomical and wind actions. A selection of daily synoptic weather maps matching the incidents of tidal flooding is used to demonstrate the contributing influence of strong onshore winds; an equal number of cases of nonflooding on occasions of perigean spring tides which were not enhanced by strong onshore winds is included to emphasize this necessary meteorological accompaniment. Supported by such winds, the far greater coastal flooding potential of perigean spring tides compared with ordinary spring tides or other tidal situations-often exceeding the inundating effects of hurricanes-is clearly pointed out. The always devastating effects of the combination of a hurricane with perigean spring tides is also discussed. Selected cloud-cover photographs made from weather satellites near the time of flooding perigean spring tides are incorporated in the treatise to reveal the exact atmospheric frontal conditions and disposition of each low pressure center responsible for strong onshore winds. In the preliminary chapters, which trace the effects of perigean spring tides upon nautical history, navigation, marine engineering, and marine science, the various practical, economic, environmental, and ecological influences of these tides are outlined. This evaluation includes the combined effects of the elevated high waters, their corresponding low-water extremes, and the accompanying accelerated flood and ebb currents. In the final chapter, various other possible geophysical effects related to the phenomenon of perigee-syzygy and the increased gravitational forces produc ing perigean spring tides are discussed. t I Part I-Background Aspects I I Chapter L. Representative Great Tidal Floodings of the North American Coastline ITTLE did our colonial forefathers know that, Indies. It began in the morning a little before day, and within 5 years after they settled in Massachu- grue not be [sic] degrees, but came with a violence in the etts Colony early in 1630, their New World beginning, to the great amasmente of many.-It con- home would be beset by disaster involving two tinued 'not (in the extremities) above 5 or 6 hours, but natural forces of a type with which they had no previous the violence began to abate. The signes and marks of it experience, but whose enon-nously destructive influences will remaine this 100 years in these parts wher it was upon life, limb, and property they and subsequent genera- sorest." tions would have occasion to witness repeatedly through- An additional account of this great coastal storm and out ensuing years. This first recorded coastal flooding of accompanying tidal flooding in colonial New England catastrophic proportions on the American continent hap- appears in a contemporary work by Nathaniel Morton pened in the fall of 1635. Like other early incidents of this titled New England Memorial in which the event likewise type, it has never been thoroughly analyzed from the stand- is described as a disaster-causing one that: point of its complex natural origins. Although purely ". . . blew down houses and uncovered divers others; meteorological factors are commonly given as the cause of divers vessels were lost at sea in it, and many more in such coastal flooding phenomena, certain specific astro- extreme danger. It caused the sea to swell in some places nomical tide-raising forces of periodic nature are also def- to the southward of Plymoth, as that it arose to 20 feet initely involved, whose specific contribution will form right up and down, and made many of the Indians to the subject of the present study. climb into trees for their safety . . . It began in the southeast, and veered sundry ways, but the greatest force The Evidences From History of it at Plymoth, was from the former quarter, it con- tinued not in extremities above 5 or 6 hours before the William Bradford, author of History. of Plimoth Plan- violence of it began to abate; the mark of it will remain tation, wrote dramatically of the impact of this early this many years, in those parts where it was sorest; the coastal flooding event which occurred on August 14-15, moon suffered a great eclipse 2 nights after it." 2 [At 9:49 1635, Old Style Calendar.' A portion of his narrative p.m., 75* W.-meridian time,' on August 27.] follows: "This year the 14[24] or 15[25] of August (being Sat- CASE No. 200-Perigean Spring Tides (ne-ar the urday) was such a mighty storm of wind and.raine as time of a total lunar eclipse). none living in these parts, either English or Indians, ever The last statement is that which has been generally saw. Being like (for the time it continued) to those Hurri- overlooked in previous accounts, attributing the flooding canes and Tuffoons that writers make mention in the entirely to winds. As noted in footnote (c), on page 7, ' For the purpose of exact comparison of astronomical, tidal, and By the 16th century, because of an astronomical phenomenon meteorological events in the historical portion of this work, all dates known as "precession of the equinoxes," the difference between the given in the Old Style or Julian Calendar must be corrected by the Julian Calendar year, invented by the Alexandrian astronomer addition of 10-11 days to give the corresponding date in the New Sosigenes, and the period of the Sun's apparent annual movement Style or Gregorian Calendar, our present usage. The New Style date with respect to the vernal equinox amounted to 10 days. Contin- is indicated in square brackets following all such early dates quoted. uing divergence threatened to throw out the existing alignment Some of the cases of coastal flooding under discussion occurred prior between the calendar months and the seasons. It therefore became to 1752. In this year, a change was made in England and through- necessary to drop 10 days from the Julian Calendar, and by a new out the British Colonies (including America) from the Julian system of accounting for Leap Years, to convert from the Julian Calendar (Old Style) to the Gregorian Calendar (New Style). This Calendar to the Gregorian Calendar. (cont. on next page) s chanze came about from practical necessity. Superior figures refer to sources listed at end of book. 202-509 0 - 78 - 3 2 Strategic Role of Perigean Spring Tides, 1635-1976 the same alignments of Sun, Earth, and Moon responsible Scotia, together with exceptionally high astronomical for either solar or lunar eclipses ' provide a geometric re- tides, their combined effects were felt over this entire inforcement of the gravitational forces of the Moon and region in severe coastal flooding and extensive damage. Sun and thereby also augment the tide-raising forces pres- At Buzzards Bay, and Providence, R.I., the tides reached ent. The tidal forces are also sometimes further amplified heights of 20 ft. by a special proximity of the Moon to the Earth resulting With consideration to all related factors, and in main- from such alignments. taining a proper perspective between the combined astro- What the inhabitants of the Massachusetts Colony did nomical. and meteorological forces responsible for coastal not know was that this great coastal storm very nearly flooding, it is necessary that the meteorological conditions coincided in time with another phenomenon of nature- at this time be carefully documented. the astronomical condition known. as perigee-syzygy (see Governor John Winthrop of the Massachusetts Colony page 5 under "Technical Commentary"). In this phe- also kept a journal in which, under the date August 16 nomenon, the average between the exact time of full [26], he cites the meteorological conditions prevailing at moon and that of the Moon's closest monthly approach to the time and notes that, at midnight of this date, a mod- the Earth occurred between August 28 and 29 (Gregorian erate southwest wind of the previous week changed sud- Calendar), within 2 days of the maximum intensity of denly to a violent northeast gale. He states that the force the storm. With a significance which will appear in later of the storm was sufficient to destroy houses in Boston, discussions (see chapter 7), the separation in time be- and to separate the cables of ships in the harbor. The tween perigee and syzygy on this occasion also was less strong gale blew steadily off the water f6r 8 hours, fur- than 42 hours. This comparatively small difference in time ther heightening the evening high tide, and then shifted between -perigee and syzygy is an indication of the com- as abruptly to the northwest, now blowing offshore. bined, nearly coincident application of the tide-raising In his diary account, corresponding to the Gregorian forces of the Sun with those of the Moon-the Moon Calendar date August 26, Winthrop relates: being at its monthly position of closest approach to the "About eight of the clock the wind came about to N.W. Earth, and in addition being brought by solar dynamic very strong, and it be then about high water, by nine the influences to an even smaller separation from the Earth. tide was fallen about three feet. Then it began to flow In consequence of these enhanced gravitational forces, again about one hour and rose about two or three feet, tides possessing an exceptionally great rise and fall known which was conceived to be that the sea was grown so high as perigean spring tides were produced. Subject to the abroad with the N.W. wind, that, meeting with the ebb simultaneous action of strong, persistent, onshore winds it forced it back again." ' (serving to reinforce water movement toward and onto The impeding and forced backing up of the outgoing the land), severe tidal coastal flooding was a near- (ebb) tide by the next succeeding incoming and wind- certainty. With onshore winds prevailing from southern driven (flood) tide resulted in two high tides within far Massachusetts through Maine to Cape Sable, Nova less than a 12-hour period-in itself an unusual phenom- (cont. from preceding page) Although this Gregorian or New Style Calendar was adopted table 16. Since the latter dates are given in the New Style Calendar, throughout most of the Roman Catholic countries in 1582, Protes- either 10 or 11 days must be added to the Old Style dates to con- tant countries held out, and only in 1752 (because of the steadily vert them to this Gregorian system. The fact that, prior to the year increasing time difference) England and her colonies dropped 11 1752, the calendar year in England and her colonies also began on days from the calendar previously used. In comparing dates prior to March 25 rather than January 1, as thereafter, also accounts for the 1752 with date's on the modern Gregorian Calendar, the difference usage of a dual year in conjunction with dates prior to 1752, where must be. allowed for, and results from the somewhat different pro- the period January 1-March 25 is involved (e.g., February 24, cedures used in determining those century years which are Leap 1722/23). Years under the two systems. In the Julian Calendar, all century years divisible by four are regarded as Leap Years. According to the b in Theodor Ritter von Oppolzer's Canon der Finsternisse Gregorian Calendar, only those century years divisible by 100 which (1887) all eclipses of the Sun between 1207 B.C. and A.D. 2161 are also divisible by 400 (or whose first two digits are divisible by and lunar eclipses between 1206 B.C. and A.D. 2163 are cata- four) are considered to be Leap Years. Thus, in the Julian Calendar, loged together with pertinent astronomical data. This lunar 1600, 1700, 1800, and 1900 are all Leap Years. eclipse of August 1635, the midpoint of whose total phase occurred Subsequent to the change in 1752, the difference between the two at 0249 G.c.t. on August 28 (New Style Calendar), is listed as systems had increased to 12 days by 1800 and 13 days by 1900. having a magnitude of 18.1 on an arbitrary 22.8-point scale repre- However, in chapter 1, only Julian Calendar dates occurring be- senting maximum central totality. This value indicates* a well- tween March 1, 1500 and February 18, 1700 (retluiring a 10-day - centered eclipse, with the Sun and Moon in closely opposite (gra- correction) and between February 19, 1700 and September 3, 1752 vitationally reinforcing) longitudes and declinations. The tidal (requiring an 11-day correction) overlap the computer printout of forces would be augmented in proportion. Representative Great Tidal Floodings of the North American Coastline 3 enon and, as will be discussed in later instances, one very has been shown in contemporary accounts of the 1635 conducive to tidal flooding (e.g., ch.. 7 "Meteorological coastal flooding event. Under the action of strong, sus- Aspects . . .," case 4. tained, onshore winds, the previously mentioned backup The sequence of wind shifts noted by John Winthrop of water between successive high tides (occurring as a new was from southwest (for a week) to a strong northeast flood tide comes in before the preceding ebbtide has had gale-at midnight of August 16[26]-swinging around an opportunity to recede) provides a natural condition for to a Strong northwest wind-at 8 a.m. on August 17[27]. land flooding. In an actual recorded circumstance more He adds that the morning high tide was depr essed 3 than 325 years later, this fact was clearly substantiated feet in I hour by this strong offshore wind. The storm is by the great east coast flooding of 1962, whose intervening described as being felt as far north as Cape Sable, Nova low tides were built up by sustained onshore winds to be- Scotia, but possessing maximum strength south of Boston. come effective high tides (see chapter 7, Case 4). William Bradford suggests its similarity to hurricanes and The preceding 1635 example typifies a case of coastal "tuffoons" of the Indies. This violent storm is, indeed, in- flooding occurring largely as the result of hurricane-force cluded among a, list of hurricanes occurring historically on winds acting upon astronomically augmented tides, which the east coast of the United States .4 in turn played a very significant role in the extent and So-called "storm-surges" and coastal flooding associated severity of the flooding. with hurricanes have been widely treated in the scientific In the following treatise dealing with coastal flooding literature from a meteorological standpoint (see Bibli- produced by onshore wind effects acting on the higher- ography) and will not, therefore, be extensively discussed than-usual waters of perigean spring tides, primary con- in this work. Hurricanes possess sufficiently strong wind sideration will be given to those cases of coastal flooding velocities to cause coastal flooding, in varying degrees, at associated with winter storms. any phase of the tides-although, as will be seen in sub- In addition, although meteorologically oriented param- sequent comparisons between various types of hurricanes eters are duly considered in all examples given, it will involved in coastal flooding, wind damage is of greater be the principal purpose of this volume dealing with peri- consequence where astronomically induced high tides are gean spring tides to analyze the astronomical causes con- not an immediate accompaniment. The present and a few tributing to severe coastal flooding. It is these astronomi- subsequent examples are included to show the extent to cal circumstances forming the principal thesis of this work which the tidal flooding influence of a hurricane may be with which the discerning reader should gradually become further augmented by coincidence with a perigean spring familiar. To permit appropriate emphasis on the astro- tide to produce coastal inundation (in addition to wind nomical forces present, the various factors creating a setup damage) of extremely disastrous and destructive 'propor- condition of unusually rapidly rising tidal waters, upon tions. The extensive tidal flooding damage experienced in which sustained onshore winds act to. produce coastal Massachusetts, Rhode Islane, and Connecticut in 1635 is flooding will, therefore, be introduced, one by one, a typical example. This strong tidal flooding is the first throughout the remaining historical examples. Signifi- which was made a matter of record in American histor,, candy, these involve, in several cases, a winter storm situa- but was by no means the last, as attested to by subsequent, tion familiaxly known today throughout New England as similarly documented examples. a "nor 'easter." The additional flooding potential resulting from the Because the fundamental astronomical causes for the combination of a hurricane with perigean spring tides- high tides which lend themselves to coastal flooding are and the extremely hazardous effects of the combination twofold in nature, the circumstances and tide-raising of perigean spring tides with severe coastal storms in forces resulting from the simple phase alignment of Moon, winter-are evaluated, in their relative significance, in Earth, and Sun at syzygy will be considered first, followed chapter 7. It is an observed fact that a fast-moving hurri- by a discussion of the combined astronomical perigee- cane does not usually provide as much time for a buildup syzygy relationship which adds appreciably to the bi- of water level by friction at the air-sea interface as does a monthly syzygian tide-raising forces. In this historical see- stagnant, offshore extratropical storm possessing a long tion-as in part 11, throughout the scientific portions of overwater wind path. the text-supplementary technical analyses and explana- By contrast, the special setup condition provided by tory footnotes are included for those interested in greater perigean spring tides which occur as a protracted, height- detail. ened water-level condition coincident with onshore winds 4 Strategic Role of Perigean Spring Tides, 1635-1976 Technical Commentary moon, the Moon and Sun in their respective real and ap- I . parent revolutionary motions with respect to the Earth, Although the scientific discussion of the cause and effect come into direct alignment with the Earth in celestial Ion- of perigean spring tides will be reserved for part 11, a brief gitude (see figs. 1-2). In this relationship, the Moon may introduction to the phenomenon of perigee-syzygy nec "essary either lie along a straight line connecting the Earth and Sun, to an understanding of its flood-producing potential will be between the Earth and Sun (at new moon or conjunction) included in this present chapter, couched in descriptive or on the far side of the Earth@ from the Sun (at full moon terms, and pointing up the relationship with various his- or opposition). If, in either case, the Moon simultaneously torical cases of coastal flooding. Such a technical explanation crosses the plane in which the Earth revolves around the is incorporated in the following 3-page section, supplement- Sun, or comes within a limiting angular distance thereof, a ing the main text and subordinated in smaller type. The solar or lunareclipse also must take place. However, these reading continuity of the main text is thereby preserved. events occur, on the average, far less often. The alignment of the Sun and Moon with the Earth in celestial longitude occurs twice in each period of 29.53 days. The astronomical tides are produced solely by the gravita- The result'ing combination of gravitational forces of the first tional attractions of the Moon and the Sun acting upon two bodies creates higher-than-average tides on the Earth. large bodies of water. Twice each month, at new and full Either of these two positions of alignment between Earth, PERIG'EE-SYZYGY ALIGNMENTS. DURING 1974 PRODUCTIVE OF PERIGEAN SPRING TIDES Earth at perihelion January 4, and at aphelion July 5 Inclination of moon,s orbit to ecliptic 509' FEBRUARY 6 SUN 8= 160 FULL MOON &=+17* SUN 6 220 JANUARY 8 --------------- FULL MOON 8=+21' 00"'S ORBIT C j@@rl-,-ST AL Q1JATr01R HIS ORBIT (EC0- EART EARTH, MOON, AND SUN IN DIRECT ALIGNMENT ON ALL FOUR DAYS (within 10 of longitude in each case) JULY 19 NEW MOON 6= +20' SUN 8=+210 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - A- 0 AUGUST17 ORBIT NEW MOON 8=+13' SUN 8=+140 STIAL UATOR AM am 4fn 4fo% O_ 'S FIGURE I.-A typical series of close perigee-syzygy alignments occurring in the year 1974. Earth and Moon reach syzygy alignment with the Sun (i.e., at new or full moon) very nearly at the same time the Moon reaches its position of perigee (closest monthly approach to the Earth). The mutually reinforcing gravitational attractions of the Moon and Sun, combined with that of the Moon at its close approach, considerably enhance the tide-raising forces on the Earth's oceans. Representative Great Tidal Floodings of the North Arnerican Coastline 5 T 0 T 0 S SUN SUN S_ APOGEE-SYZYGY PERIGEE-SYZYGY D I DIRECT@ON OF NM RECTION OF M --7 ..... . ....... NJM .......... . . ................. . .... DIRECTION SLOWER ANGULAR SUN'S APPARENT OF MOON'S SUN'S APPARENT VELOCITY AND MOTION ON ORBITAL MOTION MOTION ON AP.OG,EE SMALLER ORBITAL CELESTIAL CELESTIAL MOTION OF MOON SPHERE SPHER,E AT APOGEE DIR CTION T !All OF AR H's E REVOLUTION AROUND SUN F L 0 THE MOON'S PERIGEE-SYZYGY ORBITAL VELOCITY RECURS AT NEW MOON IS DETERMINED BY EITHER 6-1/2 OR 7-1/2 ITS DISTANCE FROM B SE -M-I-MI-NO -AAXIS 01 SYNODIC MONTHS AFTER THE EARTH AND 'ell 1 PERIGEE-SYZYGY I AT FULL MOON KEPLER'S LAW OF EOUAL AREAS. DIRECTION OF EARTH'S MAXIMUM D REVOLUTION IAMETER E A RT H@ . ..... . ........ LUNAR E LO ACROSS THE, :z AROUN'D S_U N ORBIT S 1 ?, 763,109 K M 10 474,173 MI A2 % 1@ FASTER ANGULAR DIRECTION VELOCITY AND OF MOON'S PERIGEE GREATER ORBITAL A ORBITAL MOTION MOTION OF MOON M F'M AT PERIGEE F@4 PERIGEE@SYZYGY APOG@E-SYZYGY NOTE:FOR CLARITYOF PRESENTATION BOTH THE OR81TAL ECCENTRICITY AND DAILY MOTION OF THEMOON ARE EXAGGERATED IN SOME DIAGRAMS OF THIS WORK. FIGURE 2A.-Syzygy alignment of Moon and Sun at new. FIGURE2B.-Revolution of the Moon around the Earth in moon, with the Moon between Earth and Sun. A near- an ellipse brings it to perigee each anomalistic month, coincidence of perigee and syzygy can also occur at full averaging 27.555". It then reaches maximum orbital moon (fig. 2B). velocity. Moon, and Sun in celestial longitude is called syzygy (pro- Much less frequently-on the average not more than once nounced 'siz-oj@) and the increased tides thus produced are in about one and one-half years-the Moon, which is the called spring tides (which refers to their behavior as they greatest single influence on the tides, moves into a perigee CwelP or "spring" up,-not to the season of the year). position which, as the result of additional dynamic influences The Moon revolves monthly around the Earth in an orbit diminishing the distance of the Moon from the Earth, lies which is slightly "out-of-round," or eccentric, with the Earth especially close to the Earth. For purposes of distinction in occupying one of the two foci (C in fig. 2A) of the geometric tidal discussions throughout the present work, such a particu- ellipse thus produced, and located slightly to one side of its larly close perigee position of- the Moon with.respect to the center, (0). At least once a month also (the 27.55-day revo- Earth, hitherto unnamed in astronomy, will be termed a lution period can actually allow two occurrences in a calen- proxigee, and the especially amplified type of tide produced dar month), as the Moon revolves in this elliptical orbit, it as this condition coincides with syzygy will be called a proxi- reaches its position of closest approach to the Earth, known gean spring tide. as perigee (P). Such especially close (proxigean) distances between the Generally, the individual phenomena of perigee and syzygy Moon and the Earth always coincide with a very small sep- do not coincide in time but, due to numerous approximately aration in time between perigee and syzygy. This results (see commensurable relationships between 29.53 and 27.55, the part II, chapter 3) in a combination and interaction of the two events can approach each other within various intervals gravitational forces of the Sun and Earth in a manner to of close' agreement. When this happens, the additional rein- change slightly and transitorily the shape of the Moon's forcement of gravitational forces caused by (1) the solar- orbit. Because of a dynamic perturbation in the lunar orbit lunar alignment and (2) the concurrent proximity of the known as "evection," the Moon at perigee-sy7ygy draws even Moon to the Earth producestides whose high- and low-water closer to the Earth than at its ordinary perigee position and phases are even more pronounced than those associated'with recedes to a greater distance from the Earth at apogee, ap- spring tides. The increased tides thus created are termed proximately 2.weeks later. The tide-raising force varies in- perigean spring tides. versely as the cube of the distance between the Earth and E P 1A OR E.1 M. 6 Strategic Role of Perigean Spring Tides, 1635-1976 the Moon. Accordingly, as a further immediate consequence shore wind is blowing (fig. 3), a major coastal flood in low- of this closer approach of the Moon to the Earth at proxigee, lying areas is almost inevitable. A nonfrozen condition of the increased gravitational forces come into play which, in turn, surface waters in large bays or the near-shore region is, of augment the tide-raising influence exerted by the Moon course, assumed in this connection. It has been found that upon the Earth's major water bodies. over 100 cases of major coastal flooding associated with these The progressive buildup of these gravitational forces conditions have occurred on the North American coastline toward an increasingly significant tide-producing role is in the past 341 years. Such a strong, sustained, onshore wind, treated in successive stages in part II, chapters 3-6. which tends to pile up the waters along the coast and en- For various reasons, among which are the discrete reso- hance the effect of the already high, astronomically produced nance responses of each individual ocean and portions of tides, is an essential ingredient for coastal flooding. these oceans to tide-raising forces, the inertia of the moving Conversely, a continuous, strong, offshore wind tends to water mass, friction with the ocean floor, internal viscosity of lower the tidal water level and to negate the effects of a the water, and the imposition of continental land masses, the perigean spring tide. The atmosphere and the ocean act maximum heights attained by perigean spring tides do not together like an inverted barometer. As the atmospheric always coincide exactly with the times of maximum attain- pressure rises, the water level goes down; as the atmos- ment of the forces which produce them. As will be brought pheric.pressure diminishes, the water level rises. The adjust- out in later chapters, two of these very important delays are ment in ocean level in either direction is approximately known as the phase age and parallax age. 13 inches for each change of I inch in barometric pressure. These various combinations of astronomical forces acting Only lowland coastal regions and those with a sufficiently upon the ocean waters, when taken together with supporting large daily range between high and low phases of the tide are meteorological circumstances, may exert a very practical in- subject to the flooding effects noted. (The combined condi- fluence in causing flooding and erosion of, and other dam- tions of perigee-syzygy add about 40 percent to the tidal range.) Thus, the entire coast of the Gulf of Mexico and age to, the coastal environment. The associated impact of much of the southeastern coast of the United States are ex- g such coastal zone changes upon human affairs will become cluded from this particular influence, except during hurri- increasingly evident throughout part 1, chapters 2-4. canes. Hurricanes possess sufficient wind velocity to lift even If the high-water phase of either the perigean spring or relatively shallow waters onto the land. As a result of the proxigean spring tides occurs while a strong, persistent, on- continuous frictional effects made possible by the large-scale movement of wind over the surface of the water (the lateral extent of this overwater wind movement is known as the PE "fetch"), a hurricane passing even well off the coast and RIGEA14 SPRING TIDES producing a strong swell which impacts a low shoreline can MAY'@BE CONDUCIVE TO cause coastal flooding. COASTAL FLOODING In the case of the coastal storm system of August 24-26, 1635, it is difficult because of the ensuing lapse of time- NORMAL TIDES and lacking either manuscript or published weather data- to know whether this system persisted as a true tropical storm originating from energy provided by warm tropical waters, or was partially modified by a contrast of atmospheric air masses in extratropical latitudes. While seemingly maintain- ing-as indicated in the several descriptive accounts avail- -its basic identity as a true hurricane, nevertheless at able FE this high latitude of occurrence it may possibly have taken on PERIGEAN 4 some of the characteristics of an extratropical storm, such as were instrumentally recorded and plotted on the synoptic weather map, 303 years later, during the great New England hurricane of September 21, 1938.' This hurricane began as a tropical storm of comparable NO _TF@F-D"; intensity and possessed a similar northward movement along the Atlantic coast to New England, accompanied by strong, JAL onshore winds. It was separated by 1 day from the mean epoch of an only approximate perigee-syzygy situation. The corresponding separation between perigee and syzygy was 69 hours. The flood waters raised at Providence, R.I., in this instance were 18.3 ft above mean low water, compared with approximately 20 ft at the closer perigee-syzygy align- FIGURE 3.-Strong, persistent, onshore winds may create ment accompanying the storm of August 24-26, 1635. tidal flooding on low coasts, as friction between wind and sea lifts amplified perigean spring tides onto the land. Representative Great Tidal Floodings of the North American Coastline 7 CASE No. 4-Perigean (Proxigean) Spring Tides occurred, on February 24 (Old Style Calendar), 1722/ (-=61'27.0", P-S=-6') 23, one day after the perigee-syzygy date of February 23, At approximately 7 o'clock in the evening, 75'W.- very nearly coincided with the arrival of a very strong meridian time, on Saturday, February 23, 1722/23. O.S. coastal storm on the east coast of New England. This [March 6, 1723] the Moon in its monthly revolution storm-although of extratropical. origin (i.e., formed out@ around the Earth reached a position of direct alignment side of the nonrial tropical region of hurricanes) -rapidly with the Sun in the angular reference. system known in approached the wind velocities associated with such a astronomy as celestial longitude.' The result was the tropical disturbance and sent strong, sustained, onshore familiar phenomenon of new moon 'd which happens once winds lashing for many hours against the coastlines of each month and is of no unusual consequ 'ence. As an Massachusetts and New Hampshire. The ensuing ca- astronomical occurrence which preceded this one by only tastrophe was described, in the somewhat colorful lan- 6 hours on the same date, the Moon also passed through guage of the period, in a report by the contemporary its' position of closest monthly approach to the Earth, American cleric-scientist-philosopher, Cotton Mather, to known as perigee-again a regular monthly happening, the Royal Society of London: and by itself of no special significance. However, the near- It was Feb 24, 1723, when our American phi- coincidence of new moon and perigee is of particular sig- losophers observed an uncommon concurrence of all those nificance. In the combination of these two events, a far causes which a high tide was to be expected from.. The less common astronomical circumstance occurred, which moon was then at the change, and both sun and moon was made the more meaningful by the simultaneous, un- together on the meridian. The moon was in her perigee, usually close proximity of the Moon to the Earth. and the sun was near to his having, past, [i.e., the closest In the orderly astronomical cycle of events which distance between moon and sun, occurring about January govern and alter both the distances and motions of the 4] . . . finally the wind was high and blew hard and Moon, such a condition of close agreement between the long . . . Then veering eastwardly it brought the eastern time of the closest monthly approach of the Moon to the seas almost upon them [these shores] . . . They raised Earth (perigee) and the alignment of Earth, Moon, and the tide unto a height which had never been seen in the Sun responsible for the production of a new moon or full memory of man among us . . . The City of Boston par- moon (either alignment being called syzygy) is termed, ticularly suffered from its incredible mischiefs and appropriately, perigee-syzygy. The resulting forces created losses . . ." r, are manifest by their action in producing, within the It is significant that without actually being given the Earth's tidal waters, the phenomenon of perigean spring name perigee-syzygy, all of the requisite conditions for a tides. close occurrence of this phenomenon were present: ". . . On the east coast of the United States, the normal lag moon was then at the change (new phase); . . . moon time between the occurrence of such a combined astro- was then in her perigee; . . . sun was near to his having nomical event and the resulting perigean spring tides pro- past." duced is approximately 1 to I V2 days. As it happens, The Boston News-Letter of that time reported that therefore, the force-amplified perigean spring tides which the inundation in Boston looked very dread- 'Definitions of many of the astronomical and tidal terms used tance from the Earth, an annular eclipse of the Sun will result. in this publication will be found in the appendix and in part 11, As indicated earlier, a total eclipse of the Moon followed within chapter 1. To avoid any ambiguity in meaning possible through 2 days of the August 24-26, 1635 coastal flooding event. The overgeneralization, extreme caution must be exercised in the exact conditions of this eclipse resulted in a faster apparent motion of specification of terminology even in this nont6chnical introduction. the Moon, a shorter (relative) duration of the eclipse, and a greater Thus, for the phenomena of new moon or full moon to occur, only duration of the lunar and tidal days (see chapter 6) in addition the celestial longitudes of the Moon and Sun need be the same. However, if, at the time of full moon, the Moon's longitude is to more closely aligned tidal forces of the Moon and Sun. between 9'30' and 12*15' of one of the two positions (the so- As previously noted, such an alignment in longitude (or, alter- called "nodes") where, twice each month, the Moon crosses the orbital path of the Earth around the Sun (the "ecliptic") the natively, right ascension) between Sun, Earth, and Moon at either Moon will also be aligned (within the diameter of its disc) with new moon (conjunction) or full moon (opposition) is known in the Earth and Sun in celestial latitude and a total lunar eclipse astronomy as syzygy (from the Greek syn "together" and zygon, will occur. 11 yoke"). At conjunction, lost in the glare of the Sun's rays, the Similarly, at new moon, if the Moon is within 9'55' and 11 *50' of new moon is actually invisible to the eye; too often, people associate one of these same nodes, a central (total) eclipse of, the Sun will the slim crescent appearing immediately before or after the new take place-or, if the Moon is then beyond a certain limiting dis- moon with this descriptive term. Strategic Role of Perigean Spring Tides, 1635-1976 ful . . . the tide rising to a height of 16 ft . . . At and many vessels lost their fastenings, some being driven Hampton, New Hampshire, the storm caused the great on shore and others greatly damaged by being beaten waves of the full sea to break over its natural banks for against the wharves . . . miles together, and the ocean continued to pour its water "At Portsmouth, N.H. wharves were injured and sev- over them for several hours.' 1 7 eral vessels driven ashore . . . With the causes of such coastal flooding now firmly "At Gloucester the water was two or three feet deep established, additional' important historical examples will on the wharves, and much movable property was washed be considered in terms of their effects only, without ex- away, the waves being covered with articles and debris planatory comments. of all kinds . . . "The tide rose at Boston one and one-half inches higher CASE No. 7-Perigean Spring Tides than the great tide of December, 1786, which was ten (P-S= - ir) inches higher than the highest that any person then living A similar severe coastal storm struck Boston and New remembered. The water broke through the dam along the England on December 4-5 (New Style), 1786. Strong Roxbury canal . * * sweeping away fences and out- onshore winds again acted upon perigean spring tides houses, and prostrating buildings. resulting from the combination of a lunar perigee reached "Much property was set afloat at Charlestown and at 2 p.m. in the afternoon of the 4th, local time, and a Cambridgeport. The navy yard was overflowed, and the tide broke through the coffer-dam, about three feet of full moon occurring 18 hours later. water coming into the dry dock." As reported in The Boston Gazette and The Country Journal for December 11, 1786: ". . . The wind at east, and northeast, blew exceeding CASE No. 13-Pseudo-Perigean Spring Tides heavy, and drove in the tides with such violence on Tues- (P-S-- -53 h) day, as overflowed the pier,several inches, which entering Between the 14th and 16th of April 185 1, a severe the stores on the lowest parts thereof, did much damage case of tidal flooding occurred as a result of an event to the sugars, salt, etc. therein--considerable quantities which has come to be known as the "Minot's Light of wood, lumber, etc., were carried off the several Storm"--since this famous lighthouse of Boston's Outer wharfs . . ." ' Harbor was temporarily destroyed as a result. The associ- This great coastal storm, which became known as the ated tidal contribution to coastal flooding provides an December Gale of 1786-with its associated tidal flood- example of a type later to be described in this volume as ing-also was accompanied by subfreezing conditions, a pseudo-perigean spring tide (i.e., having characteristics and left a 5-6 ft snowfall throughout New England. As generally similar to, but-for lack of an equal gravita- the direct cause of numerous cases of drownings and ship- tional force acting-not precisely the same as, those of a wrecks, it was long remembered as one of New England's perigean spring tide). In this case, the two elements con- worst tidal flooding disasters.' cerned, perigee and syzygy, were more than 36 hours, but * . less than 84 hours apart-the arbitrary limits set as a CASE No. 8-Perigean Spring Tides terminology standard throughout this case study. (P- S = + 10.) With perigee occurring at I o'clock in the afternoon Perigean spring tides produced under similar circum- (local time) of April 13 and full moon at 6 p.m. on the stances (a perigee-syzygy configuration centered around 15th, the gravitational forces of Moon and Sun were not 2 p.m. in the afternoon, local time, on March 24) reached united to the fullest possible extent as when these condi- their peak on March 25, 1830. Their flooding potential tions occur within less than a day of each other. How- became manifest the next day when: ever, coupled with a strong, sustained, onshore gale-one "A cold, northeast storm of wind, rain and snow raged of the severest of the century-the tidal flooding potential along the coast of New England . . . producing a great became extremely high. A vivid account of the disaster tide, which in some parts exceeded the highest tide re- has been given in Sidney Perley's book, Historic Storms membered there. The storm began on the morning of of New England: Friday, the twenty-sixth, and continued till one o'clock "It [the storm] commenced at Washington, D.C. on in the afternoon, the tide being at its height at noon of Sunday [the 13thl, reached New York Monday morning, that day. and during the day extended over New England . . . "At Portland, Me., several wharves were carried away, The Moon was at its full, and the water having been Representative Great Tidal Floodings of the North American Coastline 9 blown in upon the shores for several days the tide rose washed over Tuck's Point and over Water Street, while to a greater height in many places than was remembered the tide in Gloucester was said to have been the highest by the people then living. It swept the w1rarves and in fifty years... The passage through Shirley Gut was lower streets like a flood, and at Dorchester, Mass., rose widened to twice its former size. . . The storm raged nearly seven feet higher than the average tide . . . all along the coast from New York to Portland, Me. "On all parts of the coast where the northeast wind The feeling was general that the storrn brought a higher could exert its force the tide rose over the wharves from tide and greater gale than any since December 1786. . . one to four feet. At Provincetown, on Cape Cod, many Damage to shipping was estimated in hundreds of thou- wharves and salt mills were swept away; and in several sands of dollars, while property all along the coast was places people left their houses, which were flooded, water destroyed. being six inches on the lower floors in some of them. "At Boston [where the tide averaged 15-62 feet] the CASE No. 36-Near-Ordin,ary Spring Tides water was three or four feet deep on Central and Long An ordinary spring tide situation in which a moderate wharfs, and the wooden stores on the latter wharf were 3V2-day proximity to the time of perigee set up an addi- completely inundated . . . tional potential for tidal flooding occurred on the mom- "Deer Island in Boston harbor suffered extensively ing of December 26, 1909, in connection with the by the great tide which made a complete breach over so-called "Christmas Gale" of that year. Full moon oc- the island, covering nearly the whole of it. The sea-wall curred at4:30 in the afternoon on December 26, preceded that had been built there a few years before by the govern- by perigee at about 4: 00 a.m. on December 23 local ment was washed away; and three buildings were carried time, a difference of 84V2 hours. This is marginal'to the out to sea, one of them being the school-house . . ." " maximum separation-interval adopted for a pseudo- Excerpted and abridged, in part, from Edward Rowe perigean spring tide (84 hours)-but the associated tidal Snow's work on Great Storms and Famous Shipwrecks flooding took place only some 36 hours from the mean of the New England Coast, and somewhat rearranged time between perigee and syzygy, computed to be approx- in terms of the importance of the tidal disaster involved, is the following description of this catastrophe: imately 10: 00 p.m. on December 24. As will be discussed "The City of Boston actually became an island during in note,t table 1, even such a 3V2-day proximity the Wednesday high tide a Is the water swept across the between the time of perigee and the time of syzygy (or, necl, cutting the city off from the mainland completely. more meaningfully, the occurence of a spring tide within On Harrison Avenue the water was four feet deep, and IV2 days of the mean epoch, or average time between the tide flowed entirely across Washington Street near perigee and syzygy) can reinforce, and provide a definite the comer of Waltham Street. In downtown Boston the amplitude contribution to, an ordinary spring tide. waves swept right up State Street, with the area around In every sense of the word, therefore, the spring tide the Custom House three feet under water . . . Brown must be regarded as the basic higher-than-usual high tide, Street was partially submerged, the waves continuing up to which the effects of a near-coincidence between peri- Central and Milk Streets. It is said that Merchants Row gee and syzygy are added. The concept of perigean tides was reached by the great tide. The record high tide standing alone without any contribution from syzygy can submerged both the Charlestown and Chelsea bridges only be realized once in any given lunation and during . . . on Pleasant Beach in Cohasset . . . a large three- certain nonconsecutive months, when the Moon is story hotel was floated right out from its underpinning, simultaneously a.t.perigee and quadrature. The concept of with almost a score of guests escaping in time . . . syzygian (spring) tides standing alone without sensible The tide at Dorchester, Mass., rose seven feet higher reinforcement from perigee, on the other hand, is valid on twice as many occasions throughout an extended than usual. . . The boys at Deer Island school . . . period of time-viz., at those apogee-syzygy positions oc- were caught in their dormitory with the water steadily curring at either new or full moon. rising around them. . . By midnight the water. had The ordinary spring tide is, therefore, more logically the risen to a height of five feet, and the roof of the building comparative standard for a greatef-than-average high fell in. . . Derby Wharf in Salem was ruined. The tide, upon which the effects of pengee-syzygy are addi- railroad track at Collin's Cove and the bridge between tionally superimposed-rather than the effects of a Forrester Street and Northey's Point were carried away, syzygian tide being thought of as impressed upon those of and the sea rushed into the tunnel. In Beverly the sea a perigean tide. 10 Strategic Role of Perigean Spring Tides, 1635-1976 The present case of tidal flooding is an example of the curring either in near-coincidence with, or comparatively sea surface being raised to comparatively high levels by close proximity to (i.e., within even several days of), new the joint action of winds and tides (either of which is sub- moon or full moon, has reinforced spring tides on many ject to varying intensities and amplitudes)-a funda- occasions and in varying degrees down through history. mental principle that will be enunciated many times in Also, in repeated examples throughout history, perigean the present volume. , spring tides, combined with intense onshore winds, have As reported in the Monthly Weather Review for provided an important source of coastal flooding. January 1910: Subsequent technical discussionswill include an evalua- "The morning tide of December 26, 1909, attending tion of the increased flood-producing potential of hurri- the severe storm of this date on the New England coast, canes which occur at the same time as perigean spring was one'of the highest ever recorded in Boston Harbor. . . tides. A proposed intensity scale also will be developed "At Boston Light the predicted time of high tide was to indicate the comparative degrees of coastal flooding 10: 20 a.m. The wind from the later afternoon of the 25th possible from various intensities of onshore wind com- until nearly noon of the 26th was from the east and north- bined with the separate categories of ( 1 ) proxigean spring east over Boston Harbor and Massachusetts Bay, rapidly tides, (2) perigean spring tides, (3) pseudo-perigean increasing in force during the evening of the 25th to very spring tides, and (4) ordinary spring tides. In the light high velocities soon after midnight, which continued un- of this intensity grouping by classes, the foregoing exam- diminished through the morning and day of the 26th. At ples (in addition to their historical significance) have Cape Cod, Highland Light, the velocity at 8 a.m. of the been chosen as being representative of each of these four 26th was 48 miles, northeast [the wind velocities stated types of astronomically augmented tides. A more mean- are. uncorrected values-not adjusted for instrumental ingful expansion from these few introductory cases is now error; corrected values are about three-fourths of the desirable. values given]; noon, 72 miles; 2:15 p.m., 84 miles; at Table I contains a list, of 100 representative examples 5 p.m., 66 miles-all from the east-northeast-and at of major tidal flooding occurring along the North Ameri- midnight was 60 miles, north. At Boston the hourly move- can coastlines between 1683 and 1976, associated with ments from midnight to noon of the 26th ranged between the near-simultaneous occurrence of perigean spring tides 25 and 39 miles,,the hourly maximum rates between 32 (as a generic term) and strong, sustained, onshore winds. and 45 mph-the latter occurring at 5: 10 a.m., from the This list includes, and distinguishes between, cases . of northeast. . . proxigean spring, perigean spring, and pseudo-pe-rigean "The increasing and high wind, occurring with the ris- spring tides according to the nomenclatural definitions ino, tide, together with a high run of tide, caused the water given in table 22 and the accompanying text. in Boston Harbor to reach approximately the record Other representative cases in which landfalling hurri- height of the tide of April 14, 1851 (The Lighthouse canes have provided a source of intense winds, resulting Storm), which at the U.S. Navy Yard was 15.0 to 15.1 in severe coastal inundation in addition to wind damage ft-the height of the tide of December 26, 1909, being, at (and a. greater degree of flooding than is experienced the same station, 14.98 ft. In general the tide in Boston in hurricanes occurring at other times than perigee- Harbor and Massachusetts Bay was approximately 3.5 syzygy) are contained in table 2. feet above the predicted height. The actual height as Surface synoptic weather maps are included in part given by the U.S. Engineers and other reliable authorities 11, chapter 7, to match more than 25 cases of tidal at the following places was as follows: Newburyport, flooding. These graphically portray the condition of Massachusetts Harbor, Black Rock Wharf, 12.68'; Sand coastal weather and distribution of the wind pattern at Bay, Rockport Harbor, 13.64'; Boston Harbor, Deer Is- the time the flooding occurred. Because of total space land, 14.56'; Plymouth Harbor, 14.8'; Barnstable Bay, limitations, these examples were chosen at random from 13.25'; Provincetown Harbor, 14.35'; the tide at all these the master lists, but include one case in each decade from stations with the exception of Plymouth and Barnstable 1890 to 1970, distributed in latitude from Halifax, Nova was approximately 5 feet above mean high water." Scotia, to Long Beach, Calif., on both the east and west coasts of North America (representing both semidiurnal Coastal Flooding As an Ongoing Risk and mixed tides), in all months from October through The detailed case-study forming a part of the preserit April (and with perigee-syzygy separations from --L I to research effort shows that the phenomenon of perigee oc- - j4 hours. Numerous illustrations of the destructive ef- Representative Great Tidal Floodings of the North American Coastline 11 fects of such coastal flooding incidents are also interspersed them especially vulnerable to tidal flooding which, throughout the latter portions of the text. paradoxically, did not occur. In this wealth of available previous examples, there As a first and most important consideration, these ex- is a pattern of recurring significance. On both the At- amples have been chosen on the basis of an extremely lantic and Pacific shorelines of the United States, wherever small difference between the times of perigee and syzygy lowland coastal regions exist, perigean spring tides coupled (less than I to a maximum of 12 hours). Secondly, each with strong, sustained, onshore winds become an all has been selected as possessing one or more special features too frequent harbinger of tidal flooding. On the east which, in terms of the exceptionally high tides produced coast of Florida, along the coast of the Gulf of Mexico, thereby, should make the situation one extremely suscepti- and at certain other specific coastal locations, as will be ble to tidal flooding. seen in part 11, chapter 8, limited daily tidal ranges Among these conditions occurring either singly or in greatly reduce the attendant hazard of tidal flooding combination and contributing in various degrees to the except in the case of hurricanes. production of exceptionally high tid6s are: (1) an un- The most outstanding 20th century example of coastal usually large value of the lunar parallax, indicating an flooding associated with perigean spring tides, which oc- exceptionally close approach of the Moon to the Earth; curred on March 6-7, 1962, will be discussed at length (2) the location of the Moon directly in the zenith (i.e., in part II, chapter 7. The more recent tidal floodings, at altitude=90') ; (3) the position of the Sun very close of January 8, 1974 along the southwest coast of Cali- to solar perigee (around January 1-4 of the year) ; (4) fornia and-allowing for the appropriate tidal delays- the location of the Moon very near to the vernal or 2 to 3 days later along the southwest coasts of England autumnal equinox, around March 21 or September 23, and Wales and on the Islands of Guernsey and Lewis, respectively, thus being on the Equator and aligned with also will be treated separately in this chapter. Satellite the Sun in both declination and celestial longitude; (5) weather photographs revealing offshore cloudcover by the location of the Moon at, or very near to, one of its day and night (infrared) indicate the frontal and weather nodes (positions of crossing the ecliptic) at the same time patterns that existed during these 1974 incidents of tidal the Sun is near this same longitude, resulting in a solar flooding. eclipse (at new moon) or a lunar eclipse (at full moon); A further group of cases of coastal flooding which (6) the new moon being simultaneously at the same high have occurred at times of ordinary spring tides, supported declination, or the full moon at an opposite high declina- by the necessary wind velocities and varying degrees of tion (in algebraic sign) with the Sun, causing a force proximity to perigee, are listed in table 3. alignment in declination as well as an increase in the tidal Numerous additional instances of the highest tides of day; and (7) the presence of the Sun at the summer or record at various coastal localities are given in table 4. winter solstice (greatest an nual declination), increasing its These particular cases were all observed at times of apparent motion in right ascension, and lengthening the perigee-syzygy, but lacked-the simultaneous existence of tidal day in the same manner as a high declination of the sufficiently high or sustained onshore winds to cause no- Moon. These various effects will be completely described ticeable flooding. in part II, chapters 1-4. A system of scientific controls also has been imple- With such very favorable astronomical conditions add- mented (see table 27 and figs. 70-89), suitable for the ing their individual effects to thai of the perigean spring analysis of certain cases of strongly potential tidal flooding tide already present, the immediate question from the which failed to materialize. All such cases were associated standpoint of the premise subsequently advanced (calling with a close perigee-syzygy alignment and other astro- for a strong tidal flooding potential under these condi- nomical tide-raising factors which, although they lifted the tions) is why no reported tidal flooding actually occurred. water to unusual levels, did not produce flooding. In this And here again a very definite emphasis must be placed control system, an equal number of representative exam- upon the necessity that the two natural forces-astro- ples has been included for a wide variety of dates and nomical and meteorological-work together in close uni- circumstances agreeing in statistical randomness with the son if tidal flooding is to occur. cases of active 'flooding (table 1 ) in order to provide Neither a powerful offshore winter storm nor an excep- statistical comparability therewith. As an acid test of tionally uplifted astronomical high tide-one without the principles to be developed in part II, chapters 3-6, they, other-can produce the devastating flooding effects like the first group of cases, possess properties rendering abundantly illustrated among the many cases resulting 12 Strategic Role of Perigean Spring Tides, 1635-1976 from the combination of these factors documented in Both in the case of very early newspaper accounts and table 5. The considerably augmented astronomical high those published in relatively small coastal communities, it tide resulting from the condition of perigee-syzygy, which is necessary to consider that most of the newspapers in- will be discussed extensively in the ensuing chapters- volved are weeklies. Accordingly, the reporting time of a often supported by additional astronomical factors such coastal storm accompanied by tidal flooding which oc- as tliose listed above-provides the setup condition for sub- curred just prior to a weekly publication date and too late sequent wind action. An active coupling between strong, for inclusion at that time may be delayed as much as a sustained, onshore winds, if present, and the surface of the week. sea provides the second factor necessary to cause active It must also be remembered that, in the documenta- coastal flooding. tion of such tidal floodings, the news value of these na- The absence of flooding in these control cases is clearly tural events as determined by the news editor is at all times shown by the accompanying weather maps to be due to in competition with other news of the day, of political, high atmospheric pressure and a condition of calm-or international, economic, or other topical interest. The offshore (rather than onshore) winds along the coast, act- timing of the flooding in relation to press deadlines and ing to negate the effect of the astronomically induced high follow-on editions, as well as the writing skills, thorough- tides. ness, and even the working habits of the reporter can'all The action of negative (depressed) tides produced by affect the degree of prominence given to one story com- intense offshore winds during the low-water stage of peri- pared with another whose flooding consequences are gean spring tides is also duly considered on pages 93, 103, ostensibly as great. A lack of technical knowledge on the in terms of the threat for ship groundings and strandings. part of the reporter, a desire to achieve a sensational story, As a followup to the cases of tidal flooding listed in the or an excessive shortening of the article by a news editor- all can affect the accuracy of the pertinent data. Any tables of this chapter, and as an indication of the con- tinuing, open-ended relationship of this historical over- quantitative comparison and analysis made from newspa- view, facsimile copies of newspaper articles describing tidal per accounts is, therefore, subject to some degree of qual- floodings which have occurred widely along the North ification in keeping with these considerations. In conclusion, a brief explanation is desirable concern- American coastlines are included, in chronological order, ing the examples of tidal flooding cited in different chap- on the following pages (table 5). These serve to sum- ters of this work. marize, from an at-once historical and yet contemporary, firsthand point of view, the effects of a quite considerable Methods of Identification and Evaluation number of cases of coastal flooding resulting from the co- of Representative Cases of Tidal Flooding incidence of sustained, onshore winds and perigean spring The 100 representative cases of coastal flooding asso- tides over a period in history covering the 18th, 19th, and ciated with perigean spring tides which are listed in table early 20th centuries. Appropriate data for each occurrence I are chronologically arranged and numbered for con- are contained in the accompanying captions. The events venience in reference. In order to provide for a greater reported speak for themselves in the intensity of the tidal variety in the case-study analysis used in different portions flooding damage sustained. of the text-as permissible within space limitations-the From the standpoint of the contribution made to such cases variously chosen from among the 100 for individual events by perigean spring tides, certain of these cases of evaluation are not always the same. However, a common coastal flooding will be further individually evaluated in thread of comparison has been maintained by including part II, chapter 7. The gradual reduction in the frequency data for a single, consistent group of cases throughout the of reported cases of severe tidal flooding in more recent volume. years, as the result of an increased construction of seawalls, To permit a ready means of correlation between such breakwaters, groins, and other devices designed to prevent related sets of data covering various aspects and influences coastal flooding, will also be given appropriate attention of perigean spring tides in different chapters of the text, in this later chapter. an alphanumeric system of identifying these common In connection with these reproduced news articles from cases has been adopted. The several randomly selected a fairly extensive range of. coastal communities, and cover- listings of perigean spring tides (distributed widely in time ing a span of 251 years, several pertinent comments are and geography, and both accompanied and unaccom- in order: panied by tidal flooding) which have been mentioned Representative Great Tidal Floodin .gs of the NAh American Coastline 13 earlier in this section constitute control groups. Each of However, several possible pitfalls exist in the compari- the events in these individual groupings carries the same son of the times of tidal flooding events taking place in identifying number, allocated in chronological order, different years, particularly in the past: (I ) Prior to given to it in the first columns of tables 1-4. In addition, January 1, 1925, Greenwich mean time (G.m.t.) was for those cases which appear repeatedly among the tide used, in which the 24-hour day be-an at Greenwich mean curves, weather maps, newspaper articles, etc., published noon, rather than the preceding midnight. Although throughout the volume, a key letter has been assigned. Greenwich civil time came into use in the 1925 issue of The keying letter and/or number serve to identify a The American Ephemeris and Nautical Almanac, the des- flooding or nonflooding situation as the same tidal cir- ignation universal time did not appear until the 1939 cumstance, no matter where it appears in the text, with- edition. In converting to Greenwich civil time or universal out reference to the accompanying date. In some cases time, 12 hours always have to be added to Greenwich this is a weather map date (usually the same as the date mean time; (2) The term Greenwich mean time (but of tidal flooding), in others, it is the date of the published reckoned from Greenwich midnight) also continued in newspaper article (often a day or so later) relating to the use in the British Nautical Almanac during the same tidal flooding, and in still others represents the mean period that Greenwich civil time was being used in The epoch of perigee-syzygy. Wherever a numerical or alpha- American Ephemeris, and Nautical Almanac and before numerical designation is given in the caption accompany- they both converted to universal time and then ephemeris ing graphical or tabular material, these data form a cor- time; and (3) The designation, Greenwich mean- time is relatable set with any similarly labeled perigee-syzygy data still used today in the navigational and tide publications appearing elsewhere in the volume. of some English-speaking countries. Although this other- Due care should be exercised in making all intercom- wise abandoned nomenclatural usage implies a time 12 parisons to check the standard time zone for w hich the hours earlier, it pertains to a value which is intended to be data apply. Most of the synoptic weather map, coastal the same as universal time or Greenwich civil time, start- ing at Greenwich midnight. flooding, or related tide table data are given either for To avoid confusion with the similarly named Green- the time meridian of 75' W. (eastern standard time) or wich mean time which had been used in the United 120' W. (Pacific standard time) -depending, in the last two instances, on the coastline involved. States before January 1, 1925, the more complete desig- All astronomical and ephemeris data relating to the nation of Greenwich mean astronomical time should be Sun, Earth, or Moon (including the computer printouts assigned to any reckoning system which is based upon are referred to ephemeris time (e.t. e Greenwich mean noon. In early editions of The American . First adopted in- Ephemeris and Nautical Almanac, the meridian of Wash- temationally for use starting in 1960, and based upon the ington D.C., was also used for various astronomical posi- comparison of exact lunar, observations with gravitational tion and time determinations, and the exact designation data rather than upon the rotation of the Earth, as here- of this meridian has undergone several changes over the tofore, ephemeris time is the modem form-with some years. small distinctions and corrections-of Greenwich civil The lengths of all days (solar or lunar) specified time. Between January 1, 1939 and January 1, 1960, throughout the text are given in terms of their equivalents astronomical data were given in universal time (u.t.), in mean solar time ( t mean solar day= 1,440 mean solar otherwise known as world time or Weltzeit (W.Z.), temps minutes= 86,400 mean solar seconds), based on the ficti- universel (t.u.), or Greenwich zone time (Z)-all of tious motion of the mean Sun. which are equivalent. to Greenwich civil time (G.c.t.). Reference should also be made to the note in connec- In each case, 24 hours constitute the d ay, starting at tion with Julian (Old Style) and Gregorian (New Style) midnight (0000') and lasting until the next midnight calendars on, page 1. (2400 '). Universal time is still used instead of ephemeris Remarks Concerning the Fundamental Astronom- time in astronomical applications other than those that ical, Tidal, and Meteorological Data Sources relate to the Sun, Moon, and planets, and likewise always Used in Connection With Computations for this refers to an astronomical day starting at Greenwich mid- Volume night, no matter in what year it occurs. The times of perigee and szyygy, the separation-interval I' This abbreviation should not be confused with that for eastern between them, and the mean epoch of this combined phe- standard time (e.s.t.) also used in the text. nomenon are given for each case of tidal flooding listed in 14 Strategic Role of Perigean Spring Tides, 1635-1976 tables 1, 2. In the reductions leading to these tab ulations, tervals are involved-to the nearest half-hour. One 'excep- as elsewhere throughout the volume, the data contained in tion to this procedure exists: In order to separate and the computer printout of table 16 have been used, for con- emphasize the effects of particularly close perigee-syzygy sistency, in all instances where P - S > � I < � 24 hours. An alignmenis, where the difference P-S<�111, its precise arbitrary interval of one mean solar day has been set as the value has been computed, in minutes of time, directly from separation limit between perigee and syzygy for all cases of the data in an astronomical ephemeris. perigee-syzygy "alignment" appearing in this latter table. Within this _L24-hour limitation, table 16 (compiled from magnetic tape data by the U.S. Naval Observatory) Of significance to certain tables contained in later chap- provides the means for extending such perigee-syzy 'y data ters of this study are the earliest years in which ( 1 ) for- 9 backward in time to historical dates even prior to the exist- malized tide data were available, and (2) synoptic weather ence of published nautical almanacs and astronomical maps were issued in the United States. ephemerides. Among the earliest of such published data Between 1853 and 1867, the first rudimentary tide tables sources, the French Connaissance des Temps was first issued resulting from studies made at certain larger seaports on in 1679, the British Nautical Almanac in 1767, the Italian the east coast of the United States were contained among E,ffemeridi astronomiche (original Latin title Effemeridl the text and appendixes of the annual Reports of the Super- 1 0 intendent of the Coast Survey. These consisted, for the most astronom cae) in 1775, the German Berliner astronomisches part, of related tidal data requiring further self- computation Jahrbuch in 1776, and The American Ephemeris and Nauti- and use by the navigator. cal Almanac in 1855. In 1867, the actual prediction of high tides for 15 stations Where the P-S separation-interval is greater than 4-24 on the east coast of the United States was begun. hours, the corresponding data have been obtained from these astronomical ephemerides, within their dates of availability. Because of the special demands made necessary for safe For earlier dates, these data have been calculated retro- navigation over shoals, bars, and reefs, the prediction of actively on the computer, resorting to the same analytical daily low waters for the west coast of Florida as well as for approach involving the application of periodic terins and the Pacific coast of the continent was begun in 1868. In coefficients in the solution of the lunar disturbing function 1887, the prediction of both high and low waters for 16 which is used in the compilation of table 16. stations on the east coast also was inaugurated. Table 16 is prepared from computer-programmed equa- In 1885, the use of the first tide-computing machine in the 0 United States, devised by William Ferrel of the U.S. Coast tions and theoretical methods of analysis which differ, for and Geodetic Survey and utilizing 19 harmonic constants, example, from the standard interpolation method for de- was instituted. In 1896, such tidal predictions were extended termining the times of perigees from maximum values of the to include 70 standard reference stations throu hout the parallax, used in The American Ephemeris and Nautical Al- 9 manac and other ephemerides. Rounding-off procedures in- world, together with tidal differences for an additional 3,000 volving data truncation to the nearest significant figure also stations. have been employed in the computer printouts. In 1912, annual tide tables were computed for the first As a result, variations of up to one-half hour may exist time by USC&GS tide-predicting machine No. 2 (developed between corresponding values obtained by the several meth- by Rollin A. Harris and E. G. Fischer of this organization in ods noted above (or, if the rounding-off errors add in the 1910, and utilizing 37 harmonic constituents) - same direction, differences of up to I hour may occasion- Beginning with the tide tables for 1966, the use of an elec- ally result). These variations are the most critical when tronic computer was introduced, by which all tide predic- P-S is very small, and the solar perturbation of the lunar tions published by the National Oceanic and Atmospheric line of apsides is, correspondingly, at its greatest value. Administration/ National Ocean Survey are now calculated. However, the maximum influence of the strong, onshore surface winds required to produce coastal flooding in con- In connection with the availability of various meteorologi- nection with perigean spring tides usually extends over at cal sources cited in part 11, chapter 7, the first issue of the least several hours. The influences of phase and parallax Monthly Weather Review was published (by the Signal ages, variable with location, also affect the interval between Service, U.S. Army) in June 1872; the earlir-st issue of the the occurrence of perigee-syzygy and the production of the U.S. Weather Bureau publication Climatological Data- maximum perigean spring tides. Such small differences pos- National Summary appeared in Tanuary 1950 (vol. 1, No. 1). sible in the mean time of perigee-svzygy are, therefore, not Information concerning individual coastal storms was first detrimental to the accuracy of the present study. tabulated in a section designated "Severe Storrns" in the In this same connection, a greater uncertainty exists in latter publication from January 1950 until December 1953. determining the exact time of perigee than in the case of This section was retitled "Storm Data and Unusual syzygy, and the former value is now, customarily given only Phenomena" from January 19,54 to December 1958. There- to the nearest hour, whereas the time of syzygy is given to after, and to the present, similar information has appeared the nearest minute. Carried to the accuracy of the less well- in a separate publication titled Storm Data, whose first edi- known component of the pair, the value of the mean epoch tion (vol. 1, No. 1) was issued in January 1959. of perigee-syzygy is rounded off throughout this book to The first daily surface synoptic weather map of the United the nearest hour only, or-where odd-value separation-in- States, including adjoining waters of the Atlantic and Pacific Representative Great Tidal Floodings of the North American Coastline 15 oceans (but of course lacking synoptic weather data from cal data sources and nomenclature, storm surges may or may ships at sea until the advent of marine radio) was published not be accompanied by coastal flooding. as a War Department Weather Map by the Signal Service, The arrangement of items in table I which, as a master U.S. Army, on January 1, 1871. The first representation of listing, will be referred to repeatedly throughout this volume weather fronts on these maps was not begun until Au- is: gust 1, 1941. Other data are given in the explanatory com- (1) the key number of the flooding event, as explained ments preceding the appropriate groups of weather maps in complete detail on page 13 (col. 1), and in the Ex- included in part 11, chapter 7. planatory Comments preceding table 5; Data on storm surges are also available in many sources, (2) the date(s) of tidal flooding at the locations in including those listed in the bibliography at the end of this question. Both Old Style and New Style Calendar dates are volume. However, it is important to note in connection with given where applicable, according to the procedure for the list of tidal flooding events contained in tables 1, 2 that reckoning these dates specified in the aforementioned por- the existence of*a storm surge doe-3 not necessarily imply tidal tion of the main text; flooding unless the amplitude of the surge exceeds the land- (3) the cities, towns, seaports, coastal or beach loca- flooding level at the point under consideration. A storm surge tions at which tidal floodin- is documented by the reference is defined as an additional increment to the observed tide sources as having occurred; as meteorological factors caus-- the water level to rise above (4) the date and time (to the nearest hour) of the that of the predicted astronomical tide. The specific meteoro- lunar perigee occurring closest in time to (either preceding logical contributions in this case are a strong, sustained, or following) the instance of tidal flooding. For convenience onshore wind and/or decreasing atmospheric pressure. in reference, the times given are uniformly converted from A surge therefore represents the positive residual in the the Greenwich civil time or ephemeris time of astronomical total height of the observed tide in excess of the height ap- tables to 750W.-meridian time (since 1884, designated as pearing in tide tables for that date and time! In order for eastern standard time). If a location on the west coast of coastal flooding to occur, the combined water level from North America is given in col. (3), an additional 3 hours these two causes must be higher than the level of the adjoin- must be subtracted from those given in cols. (4), (5), and (8) ing land. The height of the storm surge above mean sea to'obtain 120'W.-meridian time (Pacific standard time) level must be considered in terms of the elevation of the (5) the date and eastern standard time (spe4ed to the shoreline with respect to this same datum plane in order nearest minute) of the syzygy alignment (either new moon or to establish the possibility for coastal flooding. By the same full moon) closest to the occurrence of the tidal flooding; token, the use of observed (recorded) hourly height data (6) the algebraic difference in time between the oc- for the tides is not meaningful until referenced to the actual currences of perigee and syzygy nearest to the flooding event, flood level for the point in question. All such cases of shore- taken in the sense perigee minus syzygy, and rounded off to line inundation cited in tables 1, 2 are confirmed by pub- the nearest hour; lished eyewitness accounts. (7) the particular phase of syzygy represented-either new moon (NM) or full moon (FM) TABLE 1 (8) the mean epoch of perigee-syzygy, obtained by adding one-half the difference in hours given in col. (6) List of 100 Representative Examples of Major (without regard to algebraic sign) to the time of the earliest Coastal Flooding Along the North American of these two phenomena; and Coastline, 1683-1976 (9) documentary sources of the flooding event, given variously as a citation to a contemporary newspaper (with Explanatory Comments newspaper title coded, plus date, page, and columns) or a Table I consists of a compilation of 100 cases of severe professional journal, book, or other reference in which a coastal flooding caused by the combined action _R perigean more detailed description of the flooding event occurs. The spring tides and near-coincident, strong, persistent, onshore coding numbers used for each reference source are listed at winds. As indicated by the reference sources given in the the end of table 4d. table, almost all of these instances of tidal flooding are of a With the single exception of Case No. 70 (P- S= - 87h), magnitude to warrant mention in contemporary local or all accompanying perigee-syzygy alignments have a separa- regional newspapers and/or to be cited as of considerable tion-interval between the two components not exceeding consequence among historical accounts, monthly and annual _L84' (::L3.5 days). This is the arbitrary limit of separation meteorological reviews, coastal storm summaries, or other established in this study in order to include pseudo-perigean technical sources of marine data. The documented examples spring tides as well as perigean spring and proxig Pan spring of tidal flooding listed are, therefore, semantically distinct tides. Among the data of table 1, a comparative summary is from the more restricted category of meteorological storm available indicative of (1), the possible divergences of the surges. As described in the foregoing section on meteorologi- times of flooding from the mean epochs of perigee-syzygy Conversely, a negative storm surge refers to the depression of within which the special tide-raising influences of this dual local water levels below those predicted from the existing astro- alignment are felt, and (2) the greatest separation-interval nomical forces; it is caused by a strong, persistent, offshore wind between perigeeand syzygy at which the combined gravita- and/or rapidly increasing atmospheric pressure. tional action has a distinct effect. TABLE I.-List of 100 Representative Examples of Major Coastal Flooding Along the North American Coastline, 1683-1976, Related to the Near-Contiguous* Occurrence a) of Perigean Spring Tides Coupled With Strong, Persistent, Onshore Winds (All times given correspond to the meridian of 75*W. longitude) Separation- Ke Nearest Nearest interval: Type of Mean Epoch Notes and Reference Sources for Flood- y Perigee No. Date of Flooding Location of Flooding Perigee syzygy Minus syzygy of Perigee- ing (See key at end of table 4d.) Date Date SyZygy syzygy (h) 1 1683/84 Mar. 22 Boston, Cambridge, Charlestown 1684 Mar. 31 Mar. 30 FM 1684 Mar. 30 (18) p. 25. (O.S.). (Mass.). 0100 2100 +4 2300 1684 Apr. I (N.S.). 2 1693 Oct. 19 From Virginia settlements on the 1693 Oct. 29 Oct. 28 NM 1693 Oct. 29 (15) p. 17. (O.S.). Delmarva peninsula to Long Island 0600 2300 +7 0230 1693 Oct. 29 (N.Y.). Q (N.S.). 3 1704/05 Jan. 15 Boston, Salem (Mass.); Newport 1705 Jan. 25 Jan. 25 NM 1705 Jan. 25 (18) p. 41. (O.S.). (R.I.). 1400 0000 +14 0700 1705 Jan. 26 M (N.S.). 0 4 1722/23 Feb. 24 Boston, Dorchester, Chatham, Ply- 1723 Mar. 6 Mar. 6 NM 1723 Mar. 6 (4) p. 16; (6) pp. 41-42; (48) 2/21- (O.S.). mouth, Marblehead, Cape Cod, 1300 1900 -6 1600 28/1723 (O.S.), p. 2, col. 2; (75) 1723 Mar. 7 Salem, Mass.; Hampton, N.H.; p. 269, fn. 1. M (N.S.). Falmouth, Me, 5 1770 Jan. 8 ....... New England, especially near Boston, 1770 Jan. 10 Jan. .11 FM 1770 Jan. 10 (6) pp. 78-82. Mass. 1500 1200 -21 0130 6 1775 Sept. 9 ....... Halifax, Nova Scotia, and Newfound- 1775 Sept. 8 Sept. 9 FM 1775 Sept. 8 (5) 12/1775, p. 581; (15) p. 27t; land, Sept. 9-11. 0700 1000 -27 2030 (20) v. 2, p. 1261. 7 1786 Dec. 4-5 ..... Boston, Nantucket, Mass.; and New 1786 Dec. 4 Dec. 5 FM 1786 Dec. 4 (6) p. 124; (10) pp. 81-86; (18 pp. England. 1500 0800 -17 2330 70-71; (45) 12/11/1786 (N.S.), No. 1690, p. 3, col. 1. 8 1802 Mar. 1-2.. ... Coast of Massachusetts ............. 1802 Mar. 2 Mar. 4 NM 1802 Mar. 3 (6) pp. 161-167; (18 p. 166, col. 2. 0) CQ 2300 0000 -25 1130 9, 1830 Mar. 26 ...... Portland, Me.; Portsmouth, N.H.; 1830 Mar. 24 Mar. 24 NM 1830 Mar. 24 (6) pp. 249-251; (49) 3/30/1830, p. 2, Newburyport, Gloucester, Beverly, 2000 1000 +10 1500 col. 2. Salem, Danversport, Lynn, Boston, Charlestown, and Cambridge, Mass. 10 1839 Dec. 15 ...... Boston, Newburyport, Plum Island, 1839 Dec. 18 Dec. 20 FM 1839 Dec. 19 (6) pp. 266-272; (19) p. 34, col. 2, Salem, Marblehead, Cohasset, 1400 2100 -55 1730 p. 35, col. 1. Plymouth, and Cape Cod, Mass. 11 1846 Mar. I ...... Bodie's Island and Hatteras Banks, 1846 Feb. 24 Feb 25 NM 1846 Feb. 25 (23) pp. 37, 77. 6.5 N.C. 0900 1432 -30 0000 12 1846 Sept.7-8 .... Bodie's Wand, Hatteras Banks, N.C.; 1846 Sept. 4 Sept. 5 FM 1846 Sept. 5 (0) pp. 138, 282. Possible hurricane; coastline along Pamplico (Pam- 1700 0800 -15 0030 but see tidal backwash attribution lico) Sound; Oregon Inlet. for flooding and breaching of spit associated with q ffshore northwesterly wind in (15) p. 131; see also table 2, and text, part I, ch. 2; (23) pp. 37, 77. 13 1831 Apr. 14-16... Minot's Lighthouse, Cohasset, Scitu- 1851 Apr. 13 Apr. 15 FM 1851 Apr. 14 (6) pp. 302@310; (10) pp. 128-138. ate Harbor, Dorchester, Deer Is- 1300 1800 -53 1530 8 land, Shirley Gut, Winthrop, Pleasant Beach, Salem, Gloucester, and Boston, Mass.; Newcastle, N.H. 14 1861 Nov. 2 ....... New Jersey coast, between Jersey 1861 Nov. 2 Nov. NM 1861 Nov. 2 (51) 11/4/1861, p. 1, cols. 5, 6. City and Newark, N.J., and north- 1200 1100 +1 1130 ward to Boston, Mass. 15 1869 Oct. 5 ....... Cobequid Bay, Burncoat Head, and 1869. Oct. 5 Oct. 5 NM 1869 Oct. 5 (8) pp. 11, 16; (13) pp. 253-259. Noel Bay, Nova Scotia; also 0200 0900 -7 0530 Probably a greatly modified hurri- northern Maine in vicinity of cane; see (16) p. 109, and text, Eastport. (Perigean spring tides part 1, ch. 4; (15) pp. 108-11. amplified by "Saxby's Gale.") 16 1870 Oct. 25 ...... Cumberland Basin, New Brunswick'.. 1870 Oct. 25 Oct. 24 NM 1870 Oct. 24 (8) pp. 15, 28, 30, 31. Q 0000 1100 +13 1730 @? 17 1873 Aug. 9 ....... Pictou, Nova Scotia ................ 1873 Aug. 9 Aug. 8 FM 1873 Aug. 8 (7) 1902, p. 12. 0600 0900 +21 1930 18 1877 Nov. 1-2.. ... North Atlantic coast ............... 1877 Nov. I Nov. 5 NM 1877 Nov. 3 (51) 11/3/1877, p. 3, col. 2. 2042 0348 -79 1230 19 1878 Oct. 23 ...... New York City and Coney Island, 1878 Oct. 25 Oct. 25 NM 1878 Oct. 25 (51) 10/24/1878, p. 1, col. 7; (57) N.Y.; Brighton Beach, Long 0100 1800 -17 0930 10/24/1878, p. 1, cols. 2, 3; (64) Branch, and Sandy Hook, N.J.; 10/24/1878, p. 1, col. 3. Chester, Greenpoint, and Philadel- phia, Pa. 20 1882 Sept. 28 ...... Long Branch, Highland Beach, Sea 1882 Sept. 26 Sept. 27 FM 1882 Sept. 26 (51) 9/29/1882, p. 5, col. 2. Bright, Atlantic Highlands, and 1400 0000 -to 1900 Asbury Park, N.J. 21 1885Nov.24...... Boston, Revere, and Winthrop, Mass.; 1885 Nov. 25 Nov. 22 FM 1885 Nov. 23 (46) 11/25/1885, p. 1, coli. 4-6. ;z- Long Island, Rockaway Beach, 0330 1630 +59 2200 Yonkers, and Peekskill, N.Y.; As- bury Park, Atlantic City, and Rahway, N.J. 22 1887 Oct.12 ...... Moncton, New Brunswick ........... 1887 Oct. 16 Oct. 16 NM 1887 Oct. 16 (7) 1899, p. 5. 1300 1800 - 5 1530 C% 23 1891 Oct. 13 ...... Atlantic City, Long Branch, Asbury 1891 Oct. 16 Oct. 17 FM 1891 Oct. 16 (51) 10/14/1891, p. 1, col. 5. Park, Sea Bright, Cape May, and 1300 0900 -20 2300 Sandy Hook, N.J. C) 24 1894 Jan. 22 ...... Cape Hatteras, N.C ................ 1894 Jan. 20 Jan. 21 FM 1894 Jan. 20 (II)pp.147-148;(54)1/26/1894,p.2, 1000 1000 -24 2200 cols. 3-4. 25 1895 Feb. 8-9 ..... Bangor, Me.; Portsmouth, N.H.; Prov- 1895 Feb. 9 Feb. 9 FM 1895 Feb. 9 (47) 2/9/1895, p. 3, col. 6; 2/11/1895, ;M3 idence and Newport, R.I.; Glouces- 0800 1200 -4 1000 p. 3, cal. 4; (51) 2/9/1895, p. 3, ter, New Bedford, Cape Cod, and cot. 4; 2/10/1895, p. 1, cals. 3-7 Boston, Mass.; Sandy Hook, N.J.; and p. 2, cot. 1. Staten Island, N.Y.; Halifax, Nova Scotia. 1 26 1896 Oct. 8 ....... Between Amherst, Nova Scotia, and 1896 Oct. 7 Oct. 6 NM 1896 Oct. 6 (7) 1899, p. 31, 1901, p. 22. 1 Sackville, New Brunswick. oooo 1700 +7 2030 27 1896 Nov. 6 ....... Pictou, Nova Scotia, and Charlotte- 1896 Nov. 4 Nov. 5 NM 1896 Nov. 4 (7) 1902, pp. 12-13. town, Prince Edward Island. 1200 0300 - 15 1930 See footnotes at end of table. 00 TABLE I.-List of 100 Representative Examples of Major Coastal Flooding Along the North American Coastline, 1683-1976, Related to the iVear-Contiguous* Occurrence of Perigean Spring Tides Coupled With Strong, Persistent, Onshore Winds-Continued (All times given correspond to the meridian of 75'W. longitude) Separation- interval: Key Nearest Nearest Per .gee Type of Mean Epoch Notes and Reference Sources for Flood- No. Date of Flooding Location of Flooding Perigee Syzygy Milnus Syzygy of Perigee- ing (See key at end of table 4d.) Date Date Syzygy syzygy (h) 28 1897 Nov. 27 ...... Pictou, Nova Scotia ................ 1897 Nov. 24 Nov. 24 NM 1897 Nov. 24 (7) 1902, p. 12. 1000 0400 +6 0700 rn 29 1899 Feb. 9 ....... New York, N.Y .................... 1899 Feb. 9 Feb. 9 NM 1899 Feb. 9 (25b) v. 27, no. 2 (2/1899), pp. 41-44; !Z 6.5 0900 0400 -19 1830 (51) 2/9/1899, p. 4, col. 3. 30 1899 Aug. 17 ...... Newport News, Va., and Va. coast.... 1899Aug. 20 Aug. 21 FM 1899 Aug. 20 (59) 8/18/1899, p. 1, col. 7. 1700 0000 -7 2030 31 1900 Oct. 11-12 ... Charlottetown and Summerside, 1900 Oct. 8 Oct. 8 FM 1900 Oct. 8 (7) 1902, pp. 15-16. Q Prince Edward Island. 0100 0800 -7 0430 32 1901 Apr. 20 ...... Between Amherst, Nova Scotia, and 1901 Apr. 18 Apr. 18 NM 1901 Apr. 18 (7) 1901, p. 22. Sackville, New Brunswick. 1600 1700 -37 1630 I min. 33 1901 May 18 ...... Between Amherst, Nova Scotia, and 1901 May 17 May 18 NM May 17 (7) 1901, p. 22. 6.5 Sackville, New Brunswick. 0200 0100 -23 1330 Z:t 31 1901 Nov. 24 ...... Asbury Park, Jersey City, Sandy 1901 Nov. 25 Nov. 25 FM 1901 Nov. 25 (31) 11/25/01, p. 1, col. 7; p. 2, cols. rn Hook, Sea Bright, and Shrews- 1100 2000 -9 1530 3,4. Z. bury, N.J.; Manhattan And Coney GrQ Island, N.Y.; New Haven, Stam- ford, and Greenwich, Conn.; Chatham and Provincetown, Mass. 35 1908 Feb. 3 ....... Port aux Basques, Newfoundland; 1908 Feb. I Feb. 2 NM 1908 Feb. 2 (35) 2/3/08, p. 4, col. 2. Harrington Harbour, Quebec. 2000 0400 -8 0000 36 1909 Dec. 26 ...... Boston, Mass ...................... 1909 Dec. 23 Dec. 26 FM 1909 Dec. 24 (11) pp. 257-258; (25b) v. 38, No. I 0348 1630 -84 2200 (1/10), p. 4; (46) 12/27/09, P. 1, cols. 1-4; p. 2, cols. 2-8, p. 5, cols. Q@ 5-8; (75) p.,269 and fn. 1, p. 270, fn. 4. 1 37 1914 Nov. 20 ...... Quebec, Quebec ................... 1914 Nov. 16 Nov. 17 NM 1914 Nov. 17 (9) p. 14. 1 2300 1100 -12 0500 38 1914 Dec.. 17718... Long Beach, Balboa, and Los Angeles, 1914 Dec. 15 Dec. 16 NM 1914 Dec. 16 (30) 12/18/14, pt. 11, p. 1, cols. 4-5, Calif. 0912 2135 -36 0300 p. 6, cols. 3-5. 39 1915 Apr. 3 ....... Virginia Beach and Cape Henry, Va.; 1915 Apr. 1, Mar. 31 FM 1915 Mar. 31 (11) p. 191; (61) 4/4/15, p. 1, col. 1, Cape Hatteras, N.C. 1848 0038 +42 2200 p. 2, col. 7, p. 4, cols. 2-3, and p. 5, col. 3. 40 1916 July 13 ...... Charleston, S.C ................... 1916 July 14, July 15 FM 1916 July 14 (51) 7/14/16, p. 20, col. 4. 1900 0000 -5 2130 41 1917 Oct. I ....... Moncton and Sackville, New Bruns- 1917 Sept. 29, Sept.30 FM 1917 Sept. 30 (9) p. 95. r I wick; Amherst and Windsor, Nova 1306 1531 -27 0230 Scotia. L42 1917 Oct. 31 ...... Moncton, New Brunswick, and, to 'a 1917 Oct. 27, Oct. 30 FM 1917 Oct. 28 (9) p. 95. lesser degree, at Sackville, New 1748 0119 -55 2130 Brunswick, and Amherst, Nova Scotia. A-43 1918 Apr. 10-12 ... Sea Bright, Atlantic City, N.J.; 1918 Apr. 10, Apr. I I NM 1918 Apr. 10 (51) 4/11/18, p. 15, cols. 5, 6; 4/13/18, 7.5 Staten Island, Rockaway Beach, . 0500 0000 -19 1430 p . H, Col. 3; 4/13/18, p. 11, Col. 3. and southern Long Island, N.Y. 44 1918 Nov. 18 ...... New York, N.Y.; Batiscan, Quebec ... 1918 Nov. 16, Nov. 18 FM 1.918 Nov. 17 (51) 11/19/18, p. 9, Col. 3, p. 22, Col. 2230 0233 -29 1230 3; 11/25/18, p. 12, Col. 6. 45 1919 Nov. 7 ....... Manhattan and Coney Island, N.Y ... 1919 Nov. 81 Nov. 7 FM 1919 Nov. 8 (51) 11/g/19, p. 5, Col. 1; 11/9/19, 0900 1900 +14 0200 P. 10, Col. 6. 46 1922 Jan. I I ...... Sea Bright, Clifton, and Long Branch, 1922 Jan. 14, Jan. 13 FM 1922 Jan. 14 (51) 1/12/22, p. 6, cots. 4-5. N.J. 1848 0936 +33 0230 47 1923 Dec.8 ....... South Bend and Raymond, Wash.... 1923 Dec. 6 Dec. 7 FM 1923 Dec. 7 (63) 12/9/23, p. 16, HH, Col. 3. 2200 2100 -23 0930 .48 1926 Feb. 11-13 ... Los Angeles, Long Beach, San Diego, 1926 Feb. 12 Feb. 12 NM 1926 Feb. 12 (33) 2/14/26, p. 1, Col. 4; (34) 2/14/26, Capistrano Beach, and Ventura, 0700 1200 -5 0930 p. 1, cols. 6-7; (51) 2/14/26, p. 7, Calif. cols. 2-3. 49 1926 June 28 ...... Cape Hatteras, N.C ................ 1926 June 28 June 25 FM 1926 June 26 (12) p. 246. 0448 1613 +61 2300 19 B-50 1927 Mar. 3-4 ..... New England coast ................ 1927 Mar. 4 Mar. 3 NM 1927 Mar. 3 (44) 3/3/27, p. 1, Col. 3; (51) 3/4/27, - 0500 1400 +15 2130 p. 23, Col. 1. C-51 1927 Apr. 2 ....... Atlantic City, N.J." and Delaware. . @ 1927 Apr. I Apr. I NM 1927 Apr. 1 (51) 4/3/27, sec. 1, p. 19, Col. 2; (39) 1700 2300 -6 2000 4/5/27, p. 3, Col. 4. ZS 1 52 1927 Dec. 5 ....... Atlantic City, NJ ................. 1927 Dec. 6 Dec. 8 FM 1927 Dec. 7 (51) 12/5/27, p. 13, cot. 2. 2000 1232 -41 1630 53 1929 Apr. 11-12... Coastal regions of New York and 1929 Apr. 12 Apr. 9, NM 1929 Apr. 11 (51) 4/11/29, p. 60, Col. 8; 4/12/29, New Jersey. 1630 1533 +73 0400 p. 5, Col. 2; 4/13/29, p. 35, Col. 5; ;z- 7.5 4/14/29, p. 1. Col. 5, p. 14, cols. 3-8 54 1929 Nov. 18 ...... Boston and Winthrop, Mass ......... 1929 Nov. 19 Nov. 16 FM 1929 Nov. 17 (51) 11/19/29, p. 20, Col. 3. 0048 1914 +54 2200 55 1930 Aug. 23 ...... From Block Island, N.Y., to Maine ... 1930 Aug. 23 Aug. 23 NM 1930 Aug. 23 (51) 8/24/30, p. 1, Col. 6, p. 16, Col. 1. 1500 2300 -8 1900 Z. 56e 1931 Jan. 6 ........ Boston, Cape Cod, and Peaked Hill, 1931 Jan. 6 Jan. 4 FM 1931 Jan. 5 (51) 1/7/3 1, p. 2, cols. 4-5, p. BQ27, Mass.; Hampton, N.H. 0948 0815 +50 0900 Col. 8 (Last Edition); 1/10/31, p. 17, Col. 5. C) 56w 1931 Jan. 6 ....... Quinault Indian Reservation, Taho- 1931 Jan. 6 Jan. 4 FM 1931 Jan. 5 (51) 1/7/31, p. BQ27, Col. 8 (Last 2 lah, Wash. 0948 0815 +50 0900 Edition). D-57 1931 Mar. 4-5 ..... Halifax, N.S.; Boston, Salem, Win-. 1931 Mar. 4 Mar. 4 FM 1931 Mar. 4 (25b) v. 59, no. 3 (3/31), p. 127; throp, Revere, Gloucester, and 0500 0600 +6 0530 (37) 3/5/31, sec. 1, p. 2, cols. 7, Newburyport, Mass.; Portsmouth, min. 8: 3/6/31, p. 20, Col. 2; (51) 3/6/31, N.H.; Portland, Me.; New Haven P. BQ48, Col. 2; 3/9/31, p. 1, Col. 1, I and Greenwich, Conn.; Atlantic 3/10/31, p. 18, cols. 1, 4; (75) p. City, Jersey City, and Ventnor, 270, fn. 4. N.J.; Rockaway and East Hamp- ton, N.Y. See footnotes at end of table. TABLE L-List of 100 Representative Examples of Major Coastal Flooding Along the North American Coastline, 1683-1976, Related to the Near-Contiguous* Occurrence of Perigean Spring Tides Coupled With Strong, Persistent, Onshore Winds=-Continued (All times given correspond to the meridian of 75*W. longitude) Separation- Ke Nearest Nearest Interval: Type of Mean Epoch Notes and Reference Sources for Flood- y Perigee NO. Date of Flooding Location of Flooding Perigee Syzygy Minus Syzygy of Perigee- ing (See key at end of table 4d.) Date Date syzygy Syzygy (h) E-58 1931 Apr. I ....... Boston, Mass.; Flushing, N.Y.; South- 1931 Apr. I Apr. 2 FM 1931 Apr. 2 (39) 4/1/31, p. 1, col. 4;" (51) 4/2/31, 7.5 ampton, Jersey City, Atlantic City, 1700 1500 -22 0400 p. 2, cols. 2, 3. and Long Branch, N.J. C% 59 1932 Nov. 2 ....... New York, N.Y., and coast of New 1932 Oct. 29 Oct. 29 NM 1932 Oct. 29 (51) 11/2/32, p. 1, col. 3, p. 3, col. 5. 01Q I Jersey. .2200 1000 +12 1600 60 1932 Nov. 30 ...... Boston, Winthrop, Cape Cod, and 1932 Nov. 27 Nov. 27 NM 1932 Nov. 27 (37) 12/l/32, p. 7, cols. 7, 8. Nahant, Mass.; Hampton Beach, 1000 2000 -10 1500 N.H. 61 1933 Jan. 27-28. .. Atlantic City, N.J., to Bar Harbor, 1933 Jan. 22 Jan. 25 NM 1933 Jan. 24 (43) 2/l/33, p. 1, col. 5, p. 6, cols. 3, 6; Me. 2148 1820 -69 0800 (51) 1/26/33, p. 1, coIs. 2-3; 1/27/33, p. 21, cols. 1, 2; 1/29/33, p. 6, cols. 1-3. 62 1933 Apr. 12 ...... Long Island, N.Y .................. 1933 Apr. 12 Apr. 10 F M 1933 Apr. I 1 (51) 4/13/33, p. 3, col. 2. 0612 0838 +46 0800 Z. 63 1933 Dec. 17. Aberdeen, Hoquiam, Cosmopolis, 1933 Dec. 17 Dec. 16 NM 1933 Dec. 17 (55) 12/18/33, p. I, col. 2. ;2 on:1 and Montesano, Wash. 0700 2200 +9 0230 64 1934 Aug. 20-22... Newport Beach, Malibu Beach, La- 1934 Aug. 23 Aug. 24 FM 1934 Aug. 24 (27) Apr. 1935, p, 61, col. 1, par. 2; guna Beach, and Balboa, Calif. 1500 1500 -24 0300 Oct. 1940, p. 113, col. 1, par. 2; (33) 8/22/34, p. 1, col. 4. 65 1934 Dec. 8 ....... Laguna Beach, Newport Beach, and 1934 Dec. 8 Dec. 6 NM 1934 Dec. 7 (27) Apr. 1933, p. 62, col. 1, par. 1; Santa Monica, Calif. 0300 1225 -+39 0800 Oct. 1940, p. 113, col. 1, par. 2; (30) 12/8/34, p. 6, col. 4. 66 1935 July 16 ...... Oak Beach, Long Island, N.Y ....... 1935 July 17 July 16 FM 1935 July 16 (51) 7/17/35, p. 14L+, col. 7. 2142 0000 +46 2300 67 1937 Oct.21-23 ... Boston, Mass., and New York, N.Y ... 1937 Oct. 21 Oct. 19 FM 1937 Oct. 20 (46) 10/21/37, p. 1, col. 8; (51) 1100 1648 +42 1400 10/24/37, sec. 2, p. 1, col. 1. F-68 1939 Jan. 3-5 ..... Aberdeen, Hoquiam, and Neskowin, 1939.Jan. 6 Jan. 5 FM 1939 Jan. 5 (25b) v. 67, No. 1 (1/39), p. 30; (55) Wash.; Marshfield, Astoria, Coos 0600 1600 +14 2306 1/4/39, p. 2, cols. 3-6; 1/5/39, p. 1, Bay, Seaside, Tillamook, Portland, cols. 4, 7; 1/6/39, p. 1, cols. 4, 7, and Delake, Oreg.; Long Beach 15. 6, col. 1; 1/7/39, p. 3, cols. 1-5. and Hermosa Beach, Calif. G-69 1940 Apr. 21 ...... Boston (Deer Island), Cohasset 1940 Apr. 20 Apr. 21 FM I W Apr. 21 (51) 4/22/40, p. 1, col. 2 (Late City (Minot's Light and Bassing's Is- 1400 2337 -34 0700 Ed.); p. 34L, col. 1. land), Hull, Winthrop, Beachmont, and Quincy, Mass. 70 1940 Dec. 25-28... South Bend and Raymond, Wash.; 1940 Dec. 25 Dec. 28 NM 1940 Dec. 26 (55) 12/26/40, p. 1, col. 7 (Fi*al Ed.); Delake and Nelscott, Oreg.; Los 0100 1556 -87 2030 12/27/40, p. 1, cols. 1-4 (Final Ed.); Angeles, San Pedro, Redondo (56) 12/27/40, sec. 1, p. 1, col. 3; Beach, and Point Fermin, Calif. sec. 3, p. 1, col. 8; 12/28/40, p. 3, cols. 1-3; p. 7, cols. 3-5; 12/29/40, p. 6, col. 2. 71 1944 Nov. 30- New Bedford, Cape Cod, Chatham, 1944 Nov. 26 Nov. 29 FM 1944 Nov. 28 (43) 12/7/44, p. 1, col. 1, p. 8, col. 2; Dec. 1. and Provincetown, Mass.; Long 2300 1952 -69 0930 (51) 12/1[44, P. 25L, col. 1; 12/2/44, Island, N.Y.; Jersey City and Sea p. 15, col. 1. Bright, N.J.; Mt. Desert Island, H-72 1945 Nov. 20 ...... Portland, Eastport, and Machias- 1945 Nov. 18 Nov. 19 FM 1945 Nov. 19 (40) 11/21/45, p. 1, col. 8. port, Me. 2100 1000 -13 0330 1 73 1948 Jan. 2 ....... Boston, Mass ...................... 1947 Dec. 28 Dec. 27 FM 1947 Dec. 28 (51) 1/3/48, p. 3, cols. 2-5 (illustra- 1 1800 1527 +27 0430 tion), 6. 74 1948 Jan. 25-26 ... Vicinity of San Francisco, Calif ...... 1948 Jan. 26 Jan. 26 FM 1948 Jan. 26 (30) 1/26/48, p. 8, col. 6; (33) 1/26/48 0600 0200 +4 0400 p. 1, col. 7. 75 1949 Oct. 18 ...... Long Branch and Sea Bright, Nj .... 1949 Oct. 21 Oct. 21 NM, 1949 Oct. 21 (51) 10/19/49, p. 59, col. 1. 1000 1600 -6 1300 76 1951 July 17-18 ... Long Beach, Calif ................. 1951 July 17 July 18 FM 1951 July 18 (30) 7/19/51, p. 1, col. I (Final Ed.). 1800 1400 -20 0400 77 1951 Dec. 3-4 ..... San Francisco and Burlingame, Calif.; 1951 Nov. 30 Nov. 28 NM 1951 Nov. 29 (62) 12/3/51, p. 16, col. 6; p. 13, col. I Duwamish River, Wash. 0800 2000 +36 1400 2; 12/4/51, P. 1, cols. 3-6. 178 195'l Dec. 29 ...... San Francisco and San Rafael, Calif.. 1951 Dec. 28 Dec. 28 NM 1951 Dec. 28 (33) 12/31/51, p. 1, col. 4; (34) 1800 0700 +11 1230 12/29/51, p. 1, cols. 7, 8 (Final Ed.). 79 1953 Oct.22-24 ... Manhattan, Brooklyn, and New Ro- 1953 Oct. 21 Oct. 22 FM 1953 Oct. 21 (51) 10/23/53, p. 1, cols. 1, 2; p. 47, chelle, N.Y.; Wildwood and Ham- 1100 0800 -21 2130 cols. 2, 3; 10/24/53, p. 9, cols. 5, 6. ilton Beach, N.J.; Stamford, Conn.; Boston, Mass. 80 1958 Jan. 7-8 ..... Along Hampton Roads and the cast- 1958 Jan. 8 Jan. 5 FM 1958 Jan. 7 (25a) v. 9, No. 1, p. 9. ern piedmont and tidewater por- 1900 1509 +76 0500 tions of Va.; southern R.I., Cape 1 Cod, and coastal Mass. and N.H.; Wells Beach, Me. -L81 1938 Feb. 3-4 ..... S. San Diego Bay, Imperial Beach, 1958 Feb. 5 Feb. 4 FM 1958 Feb. 4 (30) 2/4/58, pt. 1, p. 1, col. 3; 2/5/58, Santa Paula, Long Beach, Alamitos 1800 0305 +39 2230 pt. 1, p. 1, cols. 4-5. 2 Bay Peninsula, Santa Monica, and Seabright, Calif. C) 82 1958 Apr. 1-2 ..... Boston, Nantucket, Winthrop, Chat- 1958 Apr. 3 Apr. 3 FM 1958 Apr. 3 (46) 4/2/58, p. 1, cols. 6-8 (Late City ham, Lynn, and Revere, Mass.; 1500 2300 -8 1900 Ed.); 4/3/58, p. 1, col. 3 (Late City Portsmouth, N.H. Ed.). 1-83c 1959 Dec. 29 ...... Atlantic City, N.J.; Long Island, 1959 Dec. 28. Dec. 29 NM 1959 Dec. 29 (25a) v. 10, No. 12, pp. 465, 466; - N.Y.; Cape Cod, Gloucester, Rock- 2000 1400 -18 0500 (25b) v. 87, No. 12 (12/59), p. 457; land, and Biddeford, Mass.; Kenne- (25c) v. 1, No. 12, p. 121; (46) bunkport, Me.; Rye, N.H. 12/30/59, p. 3, cols. 6-8; (51) 12/30/59, p. 6, cols. 3-4. 1-83w 1959 Dec. 30 ...... San Francisco Bay area, Calif ....... 1939 Dec. 28 Dec. 29 NM 1959 Dec. 29 (25c) v. 1, No. 12, p. 120; (32) 2000 1400 -18 0500 12/30/59, p. 1, col. 8. See footnotes at end of table. TABLE I.-List of 100 Representative Examples of Major Coastal Flooding Along the North American Coastline, 1683-1976, Related to the Near-Contiguous* Occurrence of Perigean Spring Tides Coupled With Strong, Persistent, Onshore Winds-Continued (All times given correspond to the meridian of - 75*W. longitude) Separation- Key Nearest Nearest Interval: Type of Mean Epoch Notes and Reference Sources for Flood- Perigee No. Date of Flooding Location of Flooding Perigee Syzygy Minus SyZygy of Perigee- ing (See key at end of table 4d.). Date Date Syzygy Sy-ygy (h) 84e 1961 Jan. 15 ...... Atlantic City and Ocean City, NJ.; 1961 Jan. 16 Jan. 16 NM 1961 Jan. 16 (38) 1/16/61, p. 1, Col. 1; (50) 1/16/61, also Delaware. (Strong surface 1800 1700 +1 1730 P. 1, Col. 8. Q winds, together with intensified subsurface currents associated with perigean spring tides, weakened and destroyed a Texas tower ap- proximately 80 nautical miles offshore, S.E. of New York City, in an area of about 180 ft water cl@ depth, on this date as well.) 84w 1961 Jan. 15 ...... San Buenaventura State Park, Ven- 1961 Jan. 16 Jan. 16 NM 1961 Jan. 16 (22) p. 15. tura County, Calif. 1800 1700 +1 1730 -85 1962 Mar. 6-7 ..... Along entire Atlantic coast from 1962 Mar. 6 Mar. 6 -31 NM 1962 Mar. 6 (24) v. 6, No. 3, pp. 79-85; (25a) south of Portland, Me., to South 0400 0500 min, 0430 v. 13, No. 3, pp. 137-139; (25c) Carolina. v. 4, No. 3, pp. 134-139; (26) v. 15, No. 3, June 1962, pp. 117- 120; (27) Oct. 1962, pp. 4--9; (28) Dec. 1962, pp. 860-887; (51) 3/6/62, p. 24, cols. 2-5; 3/7/62, z 5 p. 1, cols. 2, 3 (Late City Ed. ; c,3 p. 24, cols. 2-4, 3/8/62, p. 1, Col . 6-7; p.. 22, cols. 3-8; p. 62, CoIs. @0 2@-5; 3/9/62, p. 17, cols. 3-6; p. 18, cols. 2-4; (71); (72); (73) ch. 41, pp. 617-659. L 86 1962 Oct. 13 ...... Local estuaries and bay locations of 1962 Oct. 12 Oct. 13 FM 1962 Oct. 13 (14) pp. 9, 20, 43, 147; (31) 10/18/62, Wash. (e.g., Union); Oreg. (e.g., 2300 0800 -9 0330 pp. 1-3, 6-8. Coos Bay); northern Calif. (e.g., I Humboldt Bay); and central Calif. (e.g., Pacifica.and Redwood City drainage areas) L K-87 1962 Nov. 10-14... Cape May to Sandy Hook, N.J.; 1962 Nov. 10 Nov. I I FM 1962 Nov. 11 (25c) v. 4, No. 11, pp. 118-119; (5 1) (coastal erosion from Fire Island 0900 1704 -32 0100 11/11/62, see. 1, p. 44, Col. 1; to Montauk Point, L.I.); New 11/15/62, p. 39, Col. 8. York City; Bridgeport, Corm.; Cape Cod and Nantucket Island, Mass.; coastal lowlands, Maine 88 1965 Sept. 26 ...... Capistrano Beach, Calif ............. 1965 Sept. 22 Sept. 24 NM 1965 Sept. 23 (32) 9/27/65, p. A-20, cal. 5. 1800 2218 -52 2000 89 1967 Apr. 27 ...... Atlantic City, Nj .................. 1967 Apr. 23 Apr. 24 FM 1967 Apr. 23 (51) 4/28/67, p. 46-L, cols. 2-4; 1400 0700 -17 2230 4/30/67, p. 85-L, cal. 4. 7.5 90 1967 Nov. 28- Coasts of Massachusetts and southern 1967 Nov. 30 Dec. I NM 1967 Nov. 30 (24) Nov. 1967, p. 208, cal. 2, par. 3. Dec. 3. New England. 0900 1110 -26 2200 91 1969 Dec.4-14 .... Rincon Point, Ventura, Ocean Beach, 1969 Dec.10 Dec. 9 NM 1969 Dec.9 (24) Mar. 1970, p. 104, cal. 2, par. 4; Oceanside, Carlsbad, and Del Mar, 0600 0443 +25 1730 May 1970, p. 149; cols. 1, 2, par. 1; Calif. Sept. 1970, p. 259, cols. 1-2 ' 92 1970 Mar. 5-6 ..... Capistrano Beach and Newport 1970 Mar. 6 Mar. 7 NM 1970 Mar. 6 (30) 3/7/70, p. 1, cols. 1, 2; p. 10, Beach, Calif. 0500 1243 -32 2100 cols. 1, 2. L-93e 1971 Mar. 26 ..... Virginia Beach, Norfolk, and Parts- 1971 Mar. 26 Mar. 26 NM 1971 Mar. 26 (24), Sept. 1971, p. 293, cal. 1; p. 297, mouth, Va. 0400 1400 -10 0900 cal. 1; (60) 3/27/71, p. 1, cols. 2-4. L-93w 1971 Mar. 26 ..... Oxnard Shores, r1ear Oxnard, Calif. 1971 Mar. 26 Mar. 26 NM 1971'Mar. 26 (22) p. 17. 1 0400 1400 -10 0900 94 1971 Apr. 22 ...... Oxnard Shores, Calif. 1971 Apr. 23 Apr. 24 NM 1971 Apr. 24 (22) p. 30; (30) 4/23/71, pt. 1, P. 3, 1300 2302 -34 0600 cols. 1, 4; 4/24/7 1, p. I I cal. 4, 2/26/71, p. 1, cal. 1; (32) 4/23/71, p. 1, cols. 4, 5. 95 1971 Dec. 3 ....... Winyah Bay, Georgetown, and Paw- 1971 Nov. 30 Dec. 2 FM 1971 Dec. 1 (21) p. 6. leys Island, S.C. 0600 0249 -45 0430 96 1972 Feb. 18-20 ... Along Hampton Roads, Va@, to 1972 Feb. 17 Feb. 14 NM 1972 Feb. 16 (24) May 1972, pp. 201-202; (25b) Stamford, Conn.; Old Orchard 1400 1929 +67 0430 v. 101, no. 4 (4/73), pp. 363-370; Beach, Kennebunkport, and (36) 2/20/72, p. A-1, cal. 5; (41) Portland, Me. 2/20/72, p. 1, cal. 3, p. 28A, cols. 1, 2; (42) 2/0/72 (Weather), cal. 7; 2/21/72, p. 1, cols. 6-7, p, 10, cols. 6-7, p. 14, cols. 2-6, p. 20, cols. 4-7. 97 1972 Nov. 20 ...... Rincon to Oxnard, Oxnard Shores, 1972 Nov. 20 Nov. 20 FM Nov. 20 (55) 11/24/72, p. 6, 2M (illustra ion and Hollywood-by-the-Sea, Calif. 1900 1800 + 53 1830 11/28/72, p. 4, J-4M, cols. 6-8. also, on Nov. 25-26: coastal beaches min. of Oregon and Washington; Gulf of Alaska. M-98e 1973 Dec. I I ...... Halifax, Nova Scotia ............... 1973 Dec. 10 Dec. 9 FM 1973Dec. 10 Verbal confirmation from marine 1800 2100 +21 0730 weather forecaster, Boston office, National Weather Service. M-98w 1973 Dec. 11 ...... Tokeland, Raymond, and South 1973 Dec. 10 Dec. 9 FM 1973 Dec. 10 (56) 12/12/73, p. 24 3M, cols. 4, 5; Bend, Wash.; Seaside, Astoria, 1800 2100 +21 0730 (63) 12/12/73, p. 1, cols. 1-4; (69) and Newport, Oreg. P. 1. N-99 1974 Jan. 8 ....... Santa Barbara, Santa Monica, and 1974 Jan. 8 Jan. 8 FM 1974 Jan. 8 (30) 12/26/73, p. 1, cols. 2, 3; 1/7/74, San Clemente; also Newport Beach, 0600 0800 2 0700 sec. 1, p. 3, cal. 3; 1/9/74, pt. 1, Capistrano Beach, and Malibu p. 1, cols. 5-7; p. 29, cols. 1, 2. Beach, Calif. See footnotes at end of table. TABLE I.-List of 100. Representative E@amples of Major Coastal Flooding Along the North American Coastline, 1683-1976, Related to the Near-Contiguous* Occurrence of Perigean Spring Tides Coupled With Strong, Persistent, Onshore Winds-Continued (All times given correspond to the meridian of 75*W. longitude) Separation- Ke Nearest Nearest Interval: Type of Mean Epoch Notes and Reference Sources for Flood- rn y Perigee -i NO. Date of Flooding Location of Flooding Perigee Syzygy Minus Syzygy of Perigee- ing (See key at end of table 4d.) Qk Date Date Syzygy C% Syzygy (h) 0-100 1976 Mar. 16-17... 0gunquit, Cranberry Island, Popham 1976 Mar. 16 Mar. 15 FM 1976 Mar. 16 (25c) v. 18, No. 3, p. 8; (65) 3/19/76, Beach, Saco, and Kennebunkport, 1400 2200 +16 0600 p. 1, coIs. 1-6, (66) 3/17/76, v. 93, S, Me.; New Castle, Rye, Hampton No. 133, p. 1, cols. 1-4; (67) 3/17/76, Beach, and Portsmouth N H v. 12, No. 11, o. 1, col. 1; (68) No. 143, p. 1, col. Marblehead, Provincetown, a. 3/17/76, v. XC, 1. Plum Island, Mass.; Halifax, Nova Scotia. 4@ *The distribution frequency for the intervals of time between each of the observed tidal floodings and the corresponding mean epochs of perigee-syzygy is significant in show- ing a strongly contributing astronomical causal relationship. This distribution in terms of numbers of cases of tidal flooding observed is: For an interval of <ld, 33; � Id, 30; �2d, 18; � V2 12; �4d, 6; � 5d, 1. Fully 81% of the cases of extreme tidal flooding cataloged therefore occur within � 2d of perigee-syzygy, 93% within �3d, and 99% within �4d. This is the basis for the � 3.5-day divergence limit for major perigee-syzygy effectiveness set throughout this volume. From this consideration, it is also obvious that there really is no such thing as a simple per@gean tide, since when the Moon is more than the 3.5-day interval from perigee-syzygy (within which perigean spring tides exist) it is within approximately 3.5 d of quadrature, and the diminished effects of perigean neop tides are felt. In this evaluation, cases in which flooding occurs on both the east and west coasts (even a day apart, as in Nos. 83e, w) are counted as one event, having the largest ofthe two divergences from the mean of perigee-syzygy. Of significance to the analysis of major tidal flooding is the fact that, with only one exception (No. 70) in the preceding table, the separation-interval between perigee and syzygy also is less than, or equal to, � 84b (� 3.5d). For all cases of tidal flooding for which the corresponding perigee-syz'ygy data are obtained from the computer printout of table 16 (those in which P-S= :L24h and syzygy times are rounded off to the nearest hour only), the calendar day of the week may be established, where desired, from the Julian Day given in this printout. (See the Explanatory Com- ments preceding table 16.) tThe storm accompanying this perigean spring tide is of uncertain, but possible hurricane origin. That associated with No. 2 is cited in the Philosophical Transactions, 19, of the Royal Society of London, August 1697, p. 659, only as the "Great Storm at Acomack" (a part of the presently designated Delmarva Peninsula). A similarly debatable situation exists in the case of No. 6, where the observed storm superimposed upon perigean spring tides was far north of the usual region of intensification of tropical storms and hurricanes. (See the Explanatory Comments on historical hurricanes preceding table 2.) Representative Great Tidal Floodings of the North American Coastline 25 Accordingly, although a few of the examples given may California), However, the term hurricane is used in connec- seem to exceed, by a day or so, the tolerance limit in which tion with all such storms occurring in lower latitude por- the influence of perigean spring tides would normally be tions of the North Pacific Ocean, east of the intemationaI expected, a comparison with the circumstances of the astro- dateline. nomical alignment and the predicted daily tidal ranges The word typhoon characterizes similar storms found in around this time reveals that: (1) such apparently more the China Sea and in the North Pacific Ocean, west of the divergent examples are still especially close to perigee, international dateline. The term tropical cyclone properly although possibly several days removed from syzygy; (2) the refers to such storms originating in the Indian Ocean to the predicted tidal level is above that of mean high water springs; south of India, off the southeast coast of Africa, in the Bay or (3) the height predicted is of a magnitude approaching- of Bengal, or the Arabian Sea. Baguio is the expression used and therefore over a 19-year cycle of compilation, contribu- for hurricanes in the Philippine Islands. Although the four tory to-the upper limit of this averaged value of maximum preceding terms are synonymous, it is important to note high tides for the station in question. A representative few that a tropical depression has not yet reached the intensity such more divergent cases are, accordingly, included in the of any of these storms-or, alternatively, after a filling and table for completeness. These serve to show the tidal life- weakening of the low pressure center, has been downgraded span of perigean spring tides in terms of their permissible from hurricane strength. divergence from the epoch of maximum perigee-syzygy in- Gordon E. Dunn and Banner I. Miller in their @book on fluence-particularly in the case of those examples of tidal Atlantic HurricaneS4 (appendix B) have included the fol- flooding that last over several successive days., lowing relative intensity scale for hurricanes, based upon the A significant factor of event correlation between the in- maximum winds and minimum atmospheric pressure as- dividual entries of this table is indicated in col. (2) by- the sociated with them. Since both these quantities are lacking brackets connecting instances of tidal flooding related within in connection with early American hurricanes, the intensity the principal short-range cycles of perigee-syzygy alignment. ratings in these cases have been inferred or extrapolated These relationships may involve the circumstances of suc- from contemporary eye-witness accounts of the apparent cessive floodings coincident with: (1) the approximate 28.5- strength of the storm, judged from observed wind-damage day repetition of perigee-syzygy alignment, once attained and tidal flooding effects, including destruction of property (the average between the anoinalistic and synodic months) ; and any loss of life involved. The Beaufort scale for esti- (2) occasional double or triple multiples of this period; or mating relative wind intensities did not become available (3) the 6.5- to 7.5-month average interval between perigee- until 1806. syzygy occurrences discussed in chapter 6. The contributing role to tidal flooding provided by the heightened astronomi- The Intensity Classification of Hurricanes cal tide-raising influences at times of perigee-syzygy is sub- stantially confirmed by this evidence. Intensity Maximum winds Minimum central classification pressure TABLE 2 Minor ....... < 74 mph (< 64 kn) >29.40 in. (>996 nib) .A Representative List of North American Hurri- Minimal ..... 74 to 100 mph 29.03 to 29.40 in. canes Occurring Nearly Concurrently With (64 to 87 kn) (983 to 996 mb) Perigeari Spring Tides Major ....... 101 to 135 mph 28.01 to 29.00 in. (88 to 117 kn) (949 to 982 nib) Explanatory Comments Extreme ..... 5; 136 mph (5; 118 kn) 28.00 in. (!5 948 mb) In the modern precise definition of the word hurricane, only two principal criteria are involved: (1) that the sur- A list and description of "Hurricanes Affecting the face winds within the intense, low-pressure cyclonic system United States, by Sections," 1635-1963, is contained in ap- forming the hurricane shall, at the time of its being so desig- nated, have a sustained velocity equal to 74 miles per hour pendixes B, C of the aforementioned work, and hurricanes, (64.3 knots) or greater; and (2) that the incipient 'hurri- 1493-1951, are described in chapters XII-XV and ap- cane shall have an origin over tropical or subtropical waters. pendix of Ivan R. Tannehill's book on Hurricanes ". In Ad- The expression hurricane applies to storms possessing the dition, such hurricanes are discussed, and documented with above characteristics and occurring either on the east or west both contemporary and later sources, in David M. Ludlum's Early American Hurricanes, 1492-1870.' coast of North America, in the Gulf of Mexico, or the In the present work, the purpose of table 2 and itern A-2, Caribbean Sea. In all cases, the hurricane originates over "Summary and Conclusions," -chapter 8, is to consider the tropical or subtropical waters. On the east coast 'the hurri- coastal flooding potential added to hurricanes by their coin- cane may penetrate to middle or even high latitude before ci&nce or near-coincidence with perigean spring tides. With recurving eastward, moving inland, or, with a loss of ther- a few uncertain examples, table 1 likewise contains only cases mal energy at high latitudes, dissipating completely. On the of coastal flooding generated by the combination of perigean west coast, the hurricane only infrequently moves out of sub- spring tides and offshore storms. Because of the previously tropical waters to landfall on the California shoreline (usu- mentioned, often completely subjective methods of wind ve- ally not traveling farther north than the Gulf of Lowei locity appraisal, it is difficult to establish with absolute cer- TABLE 2.-A Representative List of North American Hurricanes Occurring Nearly Concurrently With* Perigean Spring Tides Separation- Key Nearest Nearest Interval: Type Mean Epoch Reference Sources for Flooding No. Date of Flooding Location of Flooding Perigee Perigee of of Perigee- (See key at end of table 4d.) Syzygy Minus Date Date Syzygy Syzygy Syzygy (h) 200 1635 Aug. 14-16 Gloucester, Cape Cod, and Boston, 1635 Aug. 29 Aug. 27 FM 1635 Aug. 28 (1) pp. 279-280; (2) entry of 8/16/ (O.S.). Mass., etc.; Buzzard's Bay and 1600 2200 +42 (N.S.) 1900 1635; (3) pp. 102-103; (6) pp. 3-10; Provi ) (10) pp. 34-46; (15) pp. 10-13. Aug. 24-26 dence, R.I.; Connecticut. (N.S.). 202 1638 Aug. 3 Rhode Island, Connecticut, and 1638 Aug. 9 Aug. 9 NM 1638 Aug. 9 (15) p. 13. (O.S.). Massachusetts. 1500 1300 +2 (N.S.) 1400 Aug. 13 (N.S.). 211 1683 Aug. 13 New Hampshire and, by blocking 1683 Aug. 22 Aug. 22 NM 1683 Aug. 22 (15) pp. 16-17. 72, (O.S.). hydrological runoff, in Connecti- 2300 0500 +18 1400 Aug. 23 cut. (N.S.). 215 1693 Oct. 19 Delmarva peninsula, and from Vir- 1693 Oct. 29 Oct. 28 NM 1693 Oct. 29 (15) p. 17. (O.S.). ginia to Long Island, N.Y. 0600 2300 +7 0230 Oct. 29 (N.S.). 238 1743 Oct. 22 Boston, Mass. etc .................. 1743 Nov. 4 Nov. 2 FM 1743 Nov. 3 (15) pp. 22-23. (O.S.). 2300 0300 +68 1300 Nov. 2 (N.S.). 253 1803 Oct. 2-3 ..... Norfolk, Va ....................... 1803 Oct. I Sept.30 FM 1803 Sept. 30 (15) p. 192. 0400 1900 + 9 2330 254 1810 Aug. 12 ...... North Carolina coast ............... 1810 Aug. 13 Aug. 14 FM 1810 Aug. 14 (15) p. 192. 2000 1700 -21 0630 255 1815 Sept. 3-5 ..... New Bern and Beaufort, N.C ........ 1815 Sept. 2 Sept. 3 NM 1815 Sept. 3 (15) pp. 112-113. co 1900 0900 -14 0200 256 1816 Sept. 23 ...... Coastal North Carolina ............. 1816 Sept. 21 Sept. 21 NM 1816 Sept. 21 (15) p. 194. 1600 1000 +6 1300 0) 257 1831 June 10 ...... St. Augustine and Atlantic coast of 1831 June 9 June 10 NM 1831 June 9 (15) p. 194. Florida. 1400 0200 -12 2000 258 1834 Sept. 4 ....... South Carolina (especially George- 1834 Sept. 4 Sept. 3 NM 1834 Sept. 4 (15) pp. 121-122; (25d) National town). 1900 0951 -33 0230 Weather Service No. 16, June 1975, p. 20. 259 1837 Aug. 16-20 .. Between N.E. Florida and North 1837 Aug. 15 Aug. 16 FM 1837 Aug. 15 (15) p. 194. Carolina. 1900 0100 - 6 2200 260 1846 Sept. 7-9. . . . Cape Hatteras Inlet and Outer Banks, 1846 Sept. 4 Sept. 5 FM 1846 Sept. 5 (15) pp. 131-132; see also backwash N.C., especially Nag's Head. 000 0800 -15 0030 tidal flooding aspects due to westerly winds noted in table 1. 261 1854 Sept. 7-8 ..... Savannah, Ga.; Charleston, Port 1854 Sept. 4 Sept.6 FM 1854 Sept.5 (15) pp. 132-134; (25d) National Royal, Beaufort, and Sullivans 1100 1618 -53 1330 Weather Service No. 16, June 1975, Island, S.C.; Sept. 10: Newark, p. 21 (Correction required in N.J. source: should read Sept. 7-8). 262 1861 Nov. 1-3 ..... Cape Hatteras, N.C., northward to 1861 Nov. 2 Nov. 2 NM 1861 Nov. 2 (15) pp. 101-102. Jersey City and Newark, NJ.; 1200 1100 +1 1130 New York City and Long Island, N.Y.; Newport, R.I.; Cape Cod, Boston, and New-Bedford, Mass.; and Portland, Me. 263 1869 Sept. 8 ..... . Cape Cod, Mass.; and southern 1369 Sept. 6 Sept.6 NM 1869 Sept. 6 (15) pp. 101-108, especially p. 104, New England 1500 0100 +14 0800 col. 2. 264 1869 Oct. 3-4 ..... Grand Manan, Campobello, Deer 1869 Oct. 5 Oct. 5 NM 1869 Oct. 5 (15) pp. 108-111, especially P. 110, (15) and Mt. Desert Islands, Eastport, .0200 0900 - 7 0530 col. 2, and p. 111; see also combi- Calais, and St. Andrews, Me.; to nation of extratropical and tropical New Brunswick, Canada. storms in (15) p. 109,, col. 1, and table 1, No. 15. 265 1874 Sept. 28 ...... South Atlantic coast, especially 1874 Sept. 26 Sept.25 FM 1874 Sept. 26 (70) 9/29/1874, p. 3, cols. 4-6, 9/30/ C1% Charleston, S.C., and Savannah, 1300 1700 +20 0300 1874, p. 1, col. 2. Ga. 266 1878 Oct. 23 ...... Richmond, Va.; Washington, D.C.; 1878 Oct. 25 Oct. 25 NM 1878 Oct. 25 (51) 10/24/1878, p. 2; (57) 10/24/1878, Cape May, N.J., and along Dela- 0100 1800 -17 0930 p. 1, cols. 2-3; (64) 10/25/1878, p. 1, ware River; Philadelphia, Pa. col. 3. 267 1894 Sept. 27-28 ... Georgia and the Carolinas .......... 1894 Sept. 26 Sept.29 NM 1894 Sept. 27 (17) p. 312. 0032 0044 -72 1300 268 1899 Aug. 17-2l... Cape Hatteras, N.C., etc ............ 1899 Aug. 20 Aug. 21 FM 1899 Aug. 20 (11) p. 164; (59) 8/18/1899, p. 1, col. 9. 1700 0000 -7 2030 276 1916 July 13-14.. . South Carolina coast ............... 1916 July 14 July 15 FM 1916 July 14 (17) p. 313. 1900 0000 - 5 2130 277 1926 July 25 ...... New Jersey coast, especially Manas- 1926 July 26 July 25 FM 1926 July 25 (51) 7/25/26, p. 1, col. 5, p. 13, cols. quan and Seagirt. 0618 0013 +30 1500 2-3. 281 1938 Sept. 21-22 ... Long Island, N.Y.; Providence, R.I.; 1938 Sept. 20 Sept.23 NM 1938 Sept. 22 (10) pp. 173-181, and illustrations (Became extra- and southern New England coast- 1900 1534 -69 0530 following p. 184; (17) pp. 272-273. tropical storm.) line. 283 1940 Sept. 2 ....... Northern New England coast, Cape 1940 Sept. 3 Sept. I NM 1940 Sept. 2 (46) 9/2/40, p. 1, coIs. 7, 8, p. 11, cols. Cod, Mass. 0100 2315 +26 1200 1-2. 286 1945 Sept. 18-19 ... Atlantic City, Nj ................. 1945 Sept. 22 Sept.21 FM 1945 Sept. 22 (16) pp. 283-284. 2300 1546 +31 0730 288 1954 Sept. 11-12 ... Coastal areas from middle Atlantic 1954 Sept. 14 Sept.12 FM 1954 Sept. 13 (17) pp. 309, 310. (Edna) States to New England, especially 1500 1519 +48 1500 Long Island and southern New England. 289 1954 Oct. 15 ...... Morehead City and Wilmington, 1954 Oct. 12 Oct. 12 FM 1954 Oct. 12 (17) pp. 245-257; (25d) National (Hazel) N.C.; Solomons, Md. 2100 0000 +21 1030 Weather Service No. 16, June 1975, p. 25; (27) April 1958, pp. 29-31; p. 30, col. 1, par. 2; (53) 10/15/54, p. 1, cols. 5-7, 8; 10/16/54, p. 1, cols. 1-3, 3-6, 7-8; p. 2, cols. 4, 7; p. 3, cols. 34. - 290 1961 Sept. 21 ...... Southern New York and New Eng- 1961 Sept. 22 Sept. 24 FM 1961 Sept. 23 (17) pp. 342-343; (25b) Vol. 90, pp. (Esther.) land. 2300 0634 -32 , 1500 107-119. 295 1971 Sept. 30- Aurora, Cherry Point, New Bern, 1971 Oct. 4 Oct. 4 FM 1971 Oct. 4 (25b) vol. 100, No. 4, pp. 256-267; Oct. 1. and Washington, N.C., as well as 1000 0700 + 3 0830 (25c) HYDRO-27 Nov. 1975, p. 8. (Ginger) along Hatteras Banks and Pamlico Sound. *Cases in which the hurricane's principal flooding effects are within 3.5d of the mean epoch of perigee-syzygy. 28 Strategic Role of Perigean Spring tides, 1635-1976 tainty the occurrence of true hurricanes in this early period taneously recorded weather observations on standardized of American history. Six factors contributed to this chart formats. Accordingly, until this time, there were also uncertainty: no means of tracing the origin of a landfalling weather dis- 1. In the 17th and 18th centuries, in which any de- turbance except, after the fact, from the reports of ships finitive scientific knowledge of the origin and nature of which had traversed the area during the period of its hurricanes was lacking, it was a common practice to label formation. as a hurricane, almost indiscriminately, any storm system 5. A frequent tendency therefore existed to consider accompanied by violent winds, inflooding tides from the sea, a disproportionately large number of such cases of extremely and catastrophic damage. A tendency toward flamboyancy active coastal storms to be of "tuffoon" nature, and to label and some exaggeration also occurs in the publication of early them unqualifiedly as hurricanes. An unfortunate inclination eye-witness accounts of these storms, which are characterized also continued, in the case of those storms which had been by a too frequent repetition of words describing each suc- wrongly described as hurricanes in earlier literature, to let ceeding coastal flooding as "the greatest tide ever beheld in these initial designations stand. the memory of man," or a close paraphrase. 6. Often, in this early period, such intense storm systems Accordingly, the use of the term "huriicane" in such may have been ai@bitrarily defined as hurricanes because of early accounts-extending even into the mid-nineteenth their severe coastal flooding effects. The designation was century-is not necessarily reliable. This fact is especially given without any allowance for the perigean spring or obvious when, for example, it is stated in these contempo- ordinary spring tides which might have been present. And, of rary records that an east coast hurricane occurred in course, such early terminology was assigned without any mid- or high latitudes during the month of January, well out consideration to a minimum wind velocity requirement in of the ordinary North Atlantic hurricane season running accordance with the modern classification of a hurricane. from June through October-although occasionally extend- With these nomenclatural aspects of hurricanes thus his- ing into May or November. (Some few examples of known. torically evaluated, it should be clearly stated that there is deviations from this normal hurricane season are on record, no intention, in the present work, to discriminate subjectively but any such departures have occurred over tropical waters.) between (1) hurricanes (table 2) or (2) offshore storms 2. While, in this early period, many sailing ships plied (table 1) as contributing causes to coastal flooding when the hurricane-prone waters of the subtropical Atlantic and either of these two weather phenomena occurs in conjunction Caribbean, no expedient means of communication was with perigean spring tides. The emphasis on winter storms available to co'nvey a warning of any hurricane moving in this volume revolves around the fact that the flooding toward the east coast of North America before it hit the aspects of hurricanes already have been more adequately mainland. Meanwhile, an America-bound ship had either treated in other published sources. Under the appropriate met disaster in the storm, had ridden it out, usually with ac- conditions, both types of storms are strongly conducive to companying damage and delay in arrival at its destination, tidal flooding. or had been forced to return to a Caribbean port. Hence, in However, as confirmed in the accompanying bibliographic the relatively short period of time spanning the hurricane's search (see part I, chapter 4) and the bibliography at the landfall, subsequent onshore movement, and alongshore or end of this work, the effects of a coincidence between either offshore passage, there was no real way of establishing its of these wind-intensifying situations and the astronomical tropical origin. A very intense extratropical. storm formed tide-enhancing phenomenon of perigee-syzygy have not been offshore within a deepening low pressure center, or associ- discussed definitively anywhere in the scientific literature. Further, the greater length of time a winter storm is active ated with a traveling wave along a cold front just off the near any one coastal location due to a generally slower coast, and, affecting the coastal regions successively from velocity of forward movement compared with that of a hur- Cape Hatteras north, might easily have been called a hurri- ricane actually provides, in the average case, a greater poten- cane in this early period. The high-velocity winds common tial for tidal flooding. The hurricane center's movement over to the type of storm system today known as a noreaster, the sea surface is, in general, relatively fast, and the flooding which frequently invades all parts of New England from influence more transient. off the coast, likewise could have been confused with the similar winds characteristic of a hurricane. TABLE 3 3. Whether various of those early storms designated as hurricanes on the basis of apparent wind velocity and Representative Cases of Coastal Flooding Occur- damage produced actually possessed winds of the sustained ring Near the Times of Ordinary (Syzygian) 74 mph required according to the present-day classification Spring Tides, Coexistent With Strong, Sustained, system is a matter of open conjecture. A revolving-cup wind Onshore Winds instrument (anemometer) capable of recording continuous wind velocities (but still relatively inaccurate, and breaking Explanatory Comments down at 'extreme velocities) was not designed, in practical form, until 1846 (by T. R. Robinson). As described later in the text (part II, chapter 7), a con- 4. No method was available in this country prior to siderably greater statistical probability exists at ordinary January 1, 1871 (the date of the first U.S. synoptic weather spring tides than at the times of perigean sp@ ing tides for map) to represent regional weather data by compiling simul- the coincidence therewith of strong, persistent, onshore TABLE 3.-Representative Cases of Coastal Flooding Associated* With Ordinary Spring Tides, Coupled With Strong, Persistent, Onshore Winds Key Nearest Perigee Nearest Type of Reference Sources for Flooding (See key at end No. Date of Flooding Location of Flooding Date syzygy Syzygy of table 4d.) Date 319 1878 Sept. 11 ...... Along tidewaters of Savannah and Ogeechee Rivers, 1878 Sept. 26 Sept. I I FM (52) 9/12/1878, p. 3, cot. 3. Ga. 1500 1437 321 1885 Feb. 16 ....... New York, N.Y .................................. 1885 Feb. 26 Feb. 15 NM (51) 2/17/1885, p. 1, cot. 7; p. 2, cot. 1. 0624 0912 322 1889 Sept. 10 ...... New York, Rockaway Beach, Seaside, and Coney 1889 Sept. 5 Sept. 9 FM (51) 2/11/1889, p. 1, cols. 5-7. Island, N.Y. 2006 0842 338 1914 Dec. 7 ........ Atlantic City, N.J., and New Jersey coastline; Far 1918 Dec. 15 Dec. 2 FM (51) 12/8/14, p. 1, cot. 1; p. 7, cols. 3-6. Q Rockaway, Coney Island, Arverne, and Sea Gate, 0912 1321 Long Island, N.Y. 348 1925 Dec. 2-3 ...... Coasts of New Jersey and New York; Long Island 1925 Nov. 19 Nov. 30 FM (51) 12/4/25, p. 1, cot. 6; p. 2, cols, 2-3. Sound; Coney Island, Bath Beach, Brighton Beach, 1436 0311 and the Rockaways, Long Island, N.Y. 349 1926 Oct. 25 ...... New York, N.Y ............ ..... 1926 Oct. 19 Oct, 21 FM (51) ) 0/26/26, p. 1, cols. 2-4; p. 3, cols. 2-3; p. 16, 1000 0015 cols. 2-5. 350 1927 Feb. 19-20. ... Cape May, N.J., to Cape Cod, Mass.; Atlantic City, 1927 Mar. 4 Feb. 16 FM (51) 2/21/27, p. 1, cot. 8; p. 2, cols. 1-6; 2/22/27, Perth Amboy, South Amboy, Morgan, and Long 0512 1118 p. 1, cot. 5; p. 3, cols. 2-3. Beach, N.J.; New York City and Long Island Sound, N.Y. 354 1929 Oct. 2 ........ Barnegat lighthouse near Barnegat City, N.J.; coast 1929 Sept. 27 Oct. 2 NM (51) 10/3/29, p. 1, cot. 1; p. 2, cols. 3-6. of New York; along Long Island Sound. 1942 1719 359 1932 Oct. 19 ....... Boston, Mass .................................... 1932 Oct. 30 Oct. 14 FM (51) 10/20/32, p. 44BQ, cols. 5, 6. 0918 0818 361 1933 Feb. 9 ........ Sandy Point, Newfoundland ....................... 1933 Feb. 18 Feb. 10 FM (51) 2/10/33, p. 1, cot. 1. a 0542 0800 367 1937 Apr. 27 ....... Ocean City and north coast of N.J.; Far Rockaway 1937 May 10 Apr. 25 FM (51) 4/28/37, p. 14, cot.. 4. and south coast of Long Island, N.Y. 1300 1024 368 1938 Oct. 28. West Wildwood, NJ ............................. 1938 Oct. 16 Oct. 23 NM (51) 10/29/38, p. 21, cot. 4. C1 0300 0342 369 -1939 Sept. 26 ....... Long Beach, Long Island, N.Y .................... 1939 Sept. 12 Sept.28 FM (51) 9/27/39, p. 20, cots. 1-4. 1300 0927 370 1939 Nov. 25 ....... Bay Shore, Fire Island Beach, Point o'Woods, Sal taire, 1939 Dec. 3 Nov. 26 FM (51) 11/27/39, p. 1, cot. 2. Long Island N.Y. 0200 1654 373 1947 Nov. 12 ....... Cape Cod, Mass ............. I.................... 1947 Nov. 3 Nov. 12 NM (51) 11/13/47, p. 29, cot. 7; 11/14/47, p. 46, cot. 2. 0900 1501 375 1949 Feb. 25 ....... Redondo Beach, Calif ............................ 1949 Feb. 14 Feb. 27 NM (51) 21/25/49, p. 47, cot. 5; 2/26/49, p. 8, cot. 5. 0500 1555 376 1950 Nov. 26 ....... Boston and Winthrop, Mass ....................... 1950 Dec. 8 Nov. 24 FM (25e) HYDRO-32, pp. 8-9; (51) 11/27/50, p. 16, 2000 1014 cols. 2-6. 378 1953 Nov. 7.. Southern New Jersey; Oakland Beach, Staten Island, 1953 Nov. 18 Nov. 6 NM (51) 11/8/53, p. 1, cols. 2-8; p-. 40, col. 1; p. 42, N.Y.; Southport Beach, Conn.; and south coast of 1800 1258 cols. 1-4. New England. See footnotes at end of tabIe. TABLE 3.-Representative Cases of Coastal Flooding Associated* With Ordinary Spring Tides, Coupled With Strong, Persistent, Onshore Winds-Continued Key Nearest Perigee Nearest Type of Reference Sources for Flooding (See key at end No. Date of Flooding Location of Flooding Date Syzygy Syzygy of table 4d. Date 379 1955 Oct. 14 ....... Lowland coastal regions from Cape Hatteras to Maine, 1955 Oct. 5 Oct. 15 NM (51) 10/15/55, p. 1, col. 1; p. 34, cols. 2-4. including Staten Island, N.Y.; and entire Connecti- 0600 1432 cut shoreline. 380 1956 Jan. 10 ....... Cape May, Atlantic City, and along north shore and 1955 Dec. 28 1956 NM (51) 1/11/56, p. 33, cols. 2-4. Raritan Bay, N.J. 1900 Jan. 12 2201 381 1956 Apr. I I ....... Norfolk and Hampton Roads, Va .................. 1956 Apr. 15 Apr. 10 N M (25e) HYDRO-32, p. 8. 1700 2139 398 1973 Oct. 29 ....... Monmouth Beach, N.J., to northern New Jersey and 1973 Oct. 15 Oct. 25 NM (51) 10/30/73, p. 1, cols. 5-7; p. 47, cols. 3-6. the Rockaways, N.Y. 2000 2217 Spring Tides, Plus Hurricane: 351 1927 Aug. 25 ....... From Delaware Breakwater to Cape Cod ............ 1927 Aug. 15 Aug. 27 NM (51) 8/25/27, p. 3, col. 1. 1042 0146 372 1947 Oct.15 ....... Savannah and Savannah Beach areas, Ga.; Georgia 1947 Oct. 9 Oct. 14 NM (51) 10j16/47, p. 31, col. 1. and South Carolina coast. 1300 0110 *Tidal flooding occurring within � 2d Of SyZygy (difference taken in sense Fl.-S.) or-for those cases of greater separation-always following and (allowing for phase lag), within +3.5d of the time of the highest semimonthly spring tide. For all cases noted, the perigee-syzygy interval also is >84h (3.5d), the upper limit for even pseudo-perigean spring tides. @Actually, a case of pseudo-perigean spring tides (P-S= -38h) but with the flooding occurring 5 cl@ys after the mean epoch of perigee-syzygy, and closer (+4d) to the time ofsyzygy. Representative Great Tidal Floodings of the North American Coastline 31 winds and their contribution to coastal flooding. The reason occurr ed on April 10 at 2244' e.s.t. (the additional lag due is that the phenomenon of syzygy occurs twice in each synodic to parallax age before the peak of the high waters was month (new moon and full moon) or approximately 25 reached being approximately 1.5 days). The first-quarter times in each calendar year. This frequency of disposition moon occurred on April 12 at 1933h e.S.t. Under the force of must be compared with the usual occurrence of only 2 cases a strong, northeasterly gale, tidal flooding was experienced at of perigee-syzygy in each year which possess separation- such locations 'as New Brighton, South Beach, and St. intervals of � 12 hours or less (or, at most, 5 cases which George, Staten Island, and at Riverhead and Babylon on have separation-intervals of up to _L24 hours. The possible Long Island, N.Y. range of opportunity for securing the coincidence of a sustained, strong, onshore wind is proportionately greater at TABLEs 4a-4d syzygy alone than at perigee-syzygy. Despite this fact, the number of cases actually recorded Miscellaneous Factors of Dynamic Influence Asso- involving severd tidal flooding at times of ordinary spring ciated With Perigean Spring Tides, in Cases tides is far less in terms of justified proportion to those pro- Variously Lacking, or Reinforced by, the Pres- duced at times of perigee-syzygy. This is because of the ence of Strong, Persistent, Onshore Winds greater tidal amplification occurring from the combined Explanatory Comments alignment of perigee-syzygy, and the resulting increased potential for tidal flooding if the necessary supporting mete- Tables 4a-4d quantitatively depict four supplementary orological conditions are also present. A representative group but revealing tidal phenomena associated with the predic- of examples of coastal flooding accompanying ordinary spring tion of perigean spring tides. These are: tides is given in table 3. (a) the 'attainment of water levels of record-establish- One further lunisolar configuration is deserving of com- ing height for astronomically produced tides (the corre- ment in connection with its relative tide-raising forces. This spondingly named highest astronomical tide for the locality) is the situation in which the Moon, while located at its perigee at the times of perigee-syzygy; and closest monthly approach to the Earth, is simultaneously (b) The creation of extreme low waters of record, pro- at its greatest possible orbital angular distance from either duced by the same amplified gravitational forces at the low- of the two syzygies (i.e., at one of its two positions of quad- water phases of these tides; rature). The resulting tides produced (called perigean neap (c) The occurrence of cases in which extraordinarily tides) are always of much smaller amplitude and range than high waters are raised near the times of perigee-syzygy, but perigean spring tides. do not actually produce flooding of themselves because of Thus, even in the presence of strong, persistent, onshore insufficiently strong supporting winds. However, at high- winds, it is an uncommon circumstance in which major tidal water phase, they effectively block the hydrological runoff flooding accompanies pengean neap tides. Instances of created by heavy precipitation, ice and snow melt, or simi- coastal inundation at such times are correspondingly rare lar freshets on the land. The result is a greatly augmented throughout history, unless extraordinarily high winds asso- flooding of the coastal regions. The same type of flooding ciated with an active coastal storm or a severe landfalling situation may occur as the result of tidal blocking of storm hurricane have prevaile@. drairis or elevated sewerage outfalls-even those supposedly However, for the record, a typical prototype of one such remote from the land; and flooding tide uplifted by an unusually strong, onshore wind (d) The production of conditions unmarked by severe was that which took place on 1894 April 11 along the coast- flooding of the coast, but accompanied by extreme scouring line of New York State (as recorded on page 1, col. 2 of the and erosion of beaches, berms, estuaries, and inlets along New York Times for April 12). In this month, perigee wide stretches of the shoreline. 32 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 4a.-Representative Cases of the Highest High Waters of Record Observed at Various Tidal Stations, Within 2 Days of Perigee-Syzygy (Resulting from astronomically induced perigean or pseudo-perigean spring tides, without coincident strong onshore winds or significant coastal flooding.* See table I for wind-supported cases of tidal flooding.) Extreme Mean High Perigee Epoch Date Place Water Minus of (ft Syzygy Perigee- >MHW) (h) Syzygy (75- W.) ATLANTIC COAST 1932 Mar. 24 ..... Clarks Point, Mass... . ...... ...... 2.1 +21 Mar. 22 1730 1932 Apr. 21...... Rockland, Me ........................... 2.4 - I Apr. 20 1530 1940 May 20 ..... Boston Light, Lighthouse Island, Mass.. 2.3 -67 May 19 2330 1942 May 31 ..... Bath, Me ............................... 1.9 +9 May 30 0530 1942june29..... Bath,Me ............................... 1.9 -11 June 28 0130 1952 Aug. 5 ...... Boston Light, Lighthouse Island, Mass ...... 2.3 +20 Aug. 5 min. 1530 1953 Feb. 15 ..... Bar Harbor, Me ......................... 3.9 +9 Feb. 14 0030 1953 Apr. 13 ..... Deer Island (Fort Dawes), Mass ........... 3.3 -37 Apr. 12 2030 1954 June 2 ...... Port Clyde, Me .......................... 3.0 -39 May 31 0330 Extreme Perigee Mean High Minus Epoch Of Date Place Water Syzygy Perigee- (ft (h) Syzygy >MHHW) (75-W.) PACIFIC COAST 1927 Oct. 13 ..... Seward, Alaska .......................... 4.1 +7 Oct. 10 1930 1936 Dec. 27 ..... Santa Monica, Calif ...................... 2.3 -55 Dec. 26 1930 1945 Oct. 22 ..... Skagway, Alaska ......................... 5.8 +8 Oct. 21 0500 1948 Jan. 23-26. . Los Angeles, Calif ....................... 2.2 +4 Jan. 26 0400 1951 Jan. 5-6 .... Sweeper Cove, Adak Island, Alaska ........ 2.6 -31 Jan. 6 2330 1951 Nov. 30 ..... Neah Bay, Wash ......................... 4.0 +36 Nov. 29 1400 1951 Dec. 29 ..... . Crescent City, Calif ...................... 3.1 +11 Dec. 28 1230 *Note: The cast coast cases cited also occurred prior to the great n-lid-Atlantic coastal storm of March 6-7, 1962. This event, in the combination of meteorological and astronomical effects, set many new tidal height records and was accompanied by major coastal flooding (see table I and chapter 7). Note the cyclical perigee-syzygy relationship between four pairs of these maximum high tides, bracketed above. Representative Great Tidal Floodings of the North American Coastline 33 TABLE 4b.-Representative Cases of the Lowest Low Waters of Record Observed at Various Tidal Stations, Within 2 Days of Perigee-Syzvgy Extreme Perigee Mean Low Minus Epoch of Date Place Water Syzygy Perigee- (ft (h) syzygy <MLW) (75-W.) ATLANTIC COAST 1908 Feb. 2 ...... Port Hamilton, MY ...................... -4.1 -8 Feb. 2 0000 1928 Mar. 23..... Solomons, Md ........................... -2.2 +39 Mar. 22 1030 1934 June 28.... . Southport, N.C .......................... -1.9 +20 June 27 1000 1936 Mar. 24 ..... Miami Beach, Fla ....................... -1.4 +5 Mar. 23 0130 1940 Jan. 24 ..... Fernandina Beach, Fla ................... -3.7 -36 Jan. 25 1200 1940 Mar. 24 ..... Willets Point, MY ....................... -3.8 -10 Mar. 23 Boston, Mass ............................ -3.5 1000 1943 Jan. 7 ...... Eastport, Me ............................ -4.2 -37 Jan. 6 min. 0730 1953 Feb. 15 ..... Charleston, S.C ......................... -2.8 +9 Feb. 14 0030 1954 Dec. 11 ..... Morehead City, N.C ..................... -1.7 -23 Dec. 9 0830 1935 Nov. 30 ..... Portland, Me ........................... -3.5 +19 Nov. 29 Portsmouth, N.H ........................ -3.2 2130 1959 May 23 ..... Eastport, Me ............................ -4.2 -8 May 22 0400 202-509 0 - 78 - 5 34 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 4b.-Representative Cases of the Lowest Low Waters of Record Observed at Various Tidal Stations, Within 2 Days of Perigee-Syzygy-Continued Extreme Perigee Mean Low Minus Epoch of Date Place Water Syzygy Perigee- (ft (h) syzygy <MLLW) (75-W.) PACIFIC COAST 1916 Jan. 4 ...... Seattle Wash ............................ -4.6 -15 Jan. 4 1630 1919 Dec. 8 ...... Ketchikan, Alaska ....................... -5.2 -7 Dec. 7 0130 1930 Jan. 14. . Seward, Alaska .......................... -4.3 +2 Jan. 14 1800 1930jan. 16.. Astoria, Oreg ........................... -2.8 +2 Jan. 14 1800 1932 Dec. 26 ..... Los Angeles, Calif ....................... -2.6 -33 Dec. 26 San Francisco, Calif ................. ; .... -2.5 1330 1933 Dec.17 ..... San Diego, Calif ......................... -2.6 +9 Dec. 17 La Jolla, Calif ........................... -2.5 0230 Los Angeles, Calif ........................ -2.6 Santa Monica, Calif ...................... -2.5 San Francisco, Calif ...................... -2.5 1936 Nov. 29 ..... Neah Bay, Wash ......................... -3.6 -26 Nov. 27 2200 1937 Dec. 17 ..... San Diego, Calif ......................... -2.6 -5 Dec. 17 1130 1947 Jan. 7 ...... Friday Harbor, Wash .................... -3.9 -16 Jan. 6 1600 1950 Nov. 11 ..... Sweeper Cove, Adak Island, Alaska ........ -2.9 + 14 Nov. 10 0100 Nov. 1.2 .... Massacre Bay, Attu Island, Alaska ......... -2.5 +14 Nov. 10 0100 1951 June 19..... Sitka, Alaska ............................ -4.0 +1 June 19 0800 1951 Dec. 29 ..... Yakutat, Alaska .......................... -4.3 +11 Dec. 28 1230 1955 May 22..... Crescent City, Calif ...................... -2.7 +7 May 21 1930 1957 Jan. 16. . Ketchikan, Alaska ....................... -5.2 + 16 Jan. 16 Sitka, Alaska ............................ -4.0 0900 Skagway, Alaska ......................... -6.7 Juneau, Alaska .......................... -6.6 Yakutat, Alaska ......................... -4.3 1959 Dec.30 ..... Ketchikan, Alaska ....................... -5.2 18 Dec. 29 0500 TABLE 4c.-Examples of Perigean Spring Tides Resulting in, or Conhibuting to, Coastal Flooding Through Impaired Hydrological Runoff Separation- Interval: Ke Nearest Nearest Type of Mcan Epoch Reference Sources for Flooding (See Date of Flooding Location of Flooding Perigee Yerigee Syzygy Minus Syzygy of Perigee- key following table 4d.) Date Date Syzygy Syzygy (h) 458 1932 Mar. 24 ...... Boston, Mass.; New York, MY 1932 Mar. 23 Mar. 22 FM 1932 Mar. 22 (46) 3/29/32, p. 1, cols. 6-8, p. 6, cols. 0400 0700 +21 1730 2-5; (51) 3/29/32, p. 1, cols. 4-5, p. 4, cols. 2-5. 466 1936 Mar. 21 ...... Newburyport and tidewaters of Mer- 1936 Mar. 23 Mar. 22 NM 1936 Mar. 23 (40) 3/19/36, p. 1, cols. 7-8; Pictorial rimack River, Mass.; also, on 0400 2300 +5 0130 Review (14 pp.); (74) MKR-I, March 19: Kennebec and Augusta, XIII, pp. 89-93. Me. 469 1940 May 22 ...... Norfolk, Va ....................... 1940 May 18 May 21 FM 1940 May 19 (58) 5/23/40, p. 13, col. 5. 1400 0833 -67 2330 478 1952 Aug. 5 ....... Boston, Mass ...................... 1952 Aug. 5 Aug. 5 FM 1952 Aug. 5 (46) 8/6/52, p. 1, cols. 2-6; p. 24 ;i 1500 1440 +20 1500 (illustrations). min. 86 1962 Oct. 13 ...... Pacifica, Calif ..................... 1962 Oct. 12 Oct. 13 FM 1962 Oct., 13 (31) 10/18/62, pp. 1-3, 6-8. 2300 0800 -9 0330 ZI C) a) TABLE 4d.-Illustrative Cases of Coastal Erosion Produced at Times of Perigean Spring Tides Coincident With Strong, Persistent, Onshore Winds Gn Separation- Nearest Nearest Interval: Type of Mean Epoch Reference Sources for Erosion (See Key Date of Erosion Location of Erosion Perigee Date Syzygy Perigee Syzygy of Perigee- key following table 4d.) No. Date Minus Syzygy Syzygy (h) K-87 1962 Nov. 10-14... Fire Island to Montauk Point, Long 1962 Nov. 10 Nov. I I FM 1962 Nov. 11 (51) 11/15/62, p. 39, col. 8. - Island, MY 0900 1704 -32 0100 489 1967 Jan. 27-28. .. East side of Plum Island, Mass ...... 1967 Jan. 28 Jan. 26 FM 1967 Jan. 27 (29) pp. 52, 250, 256, 259. 1000 0141 +56 0600 490 1967 May 25-26 ... East side of Plum Island, Mass ...... 1967 May 21 May 23 FM 1967 May 22 (29) pp. 248, 251. 2100 1523 -42 1800 491 1969 Feb. 15-16 ... South spit of Pawleys Island, S.C .... 1969 Feb. 13 Feb. 16 NM 1969 Feb. 15 (21) p. 6. orc, 2300 1126 -60 0500 492 1969 July 29 ...... Closure of existing south inlet of Paw- 1969 July 28 July 28 FM 1969 July 28 (21) p. 6. leys Island, S.C., by erosion, and 0400 2200 -18 1300 creation of a new inlet farther north. CY) N-99 1974 Jan. 8 ....... Recreational beaches at Oceanside, 1974 Jan. 8 Jan. 8 FM 1974 Jan. 8 (32) 1/19/74, local news section. Calif. 0600 0800 -2 -0700 @0 C) Representative Great Tidal Floodings of the North American Coastline 37 Reference Sources for Tidal Flooding Reference Reference Code No. Code No. (1) William Bradford, Of Plymouth Plantation, 1620-1647, (24) National Oceanic and Atmospheric Administration A New Edition, with Notes, Etc., by Eliot Morison, (NOAA), Environmental Data Service, Washington, New York, 1952. D.C.: Mariners Weather Log (2) Governor John Winthrop's journal, entry for August 16 (25) National Oceanic and Atmospheric Administration (O.S.), August 26 (N.S.), 1635, subsequently published (NOAA), National Weather Service (formerly U.S. as History of New Englandfrom 1630 to 1649, James K. Weather Bureau), Silver Spring, Md.: Hosmer, ed., 2 voIs., New York, N.Y., 1908. (a) Climatological Data-National Summarv (3) Nathaniel Morton, New England's Memorial, Cambridge, (b) Monthly Weather Review Mass., 1669. (c) Storm Data (4) Fitz-Henry Smith, Jr., Bostonian Society Publications, (d) NOAA Technical Reports, NWS Series vol. 11, Second Series, "Storms and Shipwrecks in Boston Bay and the Record of the Life Savers of Hull," (e) NOAA Technical Memoranda, NWS Series Boston, Mass., (n.d.). (26) Weatherwise (bimonthly publication for the American (5) The Pennsylvania Magazine, Cambridge, Mass., December Meteorological Society and others), Boston, Mass. 1775. (27) Shore and Beach (periodical publication of the American (6) Sidney Perley, Historic Storms of New England, Salem, Shore and Beach. Preservation Association), Miami, Fla. Mass., 1891. (28) The National Geographic magazine, Washington, D.C. (7) W. Bell Dawson, Survey of Tides and Currents in Canadian (29) Coastal Research Group, Department of Geology, Uni- Waters, Government Printing Bureau, Ottawa, Ont., versity of Massachusetts, Contribution No. 1, Coastal 1896-1903. (Note: The appropriate fiscal year of each Environments, X.E. Massachusetts and New Hampshire, 1972. annual survey listed among the reference sources (30) The Los Angeles Times, Los Angeles, Calif. usually precedes the actual date of publication by 1 (31) The Pacifica Tribune, Pacifica, Calif. year.) (32) The Sate Diego Union, San Diego, Calif. (8) W. Bell Dawson, Tides at the Head of Bay of Fundy, (33) The San Francisco Examiner, San Francisco, Calif. Dept. of the Naval Service, Ottawa' Ont., 1917. (34) The San Francisco Chronicle, San Francisco, Calif. (9) W. Bell Dawson, Tide Levels and Datum Planes in Eastern (35) The Evening Telegram, Saint John's, Newfoundland, Canada, Dept. of the Naval Service, Ottawa, Ont., 1917. Canada (10) Edward Rowe Snow, Great Storms and Famous Shipwrecks (36) Bridgeport Sunday Post, Bridgeport, Conn. of the New England Coast, Boston, Mass., 1943. (37) The New Haven Yournal-Courier, New Haven, Conn. (11) David Stick, Graveyard of the Atlantic: Shipwrecks of (38) Delaware State News, Dover, Del. TheNorth Carolina Coast, Chapel Hill, N.C., 1952. (39) Every Evening, Wilmington, Del. (12) Ben Dixon McNeill, The Hatterasman, Winston-Salem, (40) Daily Kennebec yournal, Augusta, Me. N.C., 1958. (41) Maine Sunday Telegram, Portland, Me. (13) Transactions of the Canadian Institute, vol. IX, University (42) Portland Press-Herald, Portland, Me. of Toronto Press, Toronto, Canada, 1913. (43) The Bar Harbor Times, Bar Harbor, Me. (14) Dorothy Franklin, West Coast Disaster, Columbus Day, (44) The Boston Evening Globe, Boston, Mass, 1962, Gann Publishing Co., Portland, Oreg. (no (45) The Boston Gazette and Country journal, Boston, Mass. publication or copyright date). (46) The Boston Herald, Boston, Mass. (15) David M. Ludlum, Earo American Hurricanes, 1492-1870, (47) The Boston journal, Boston, Mass. Boston, Mass., 1963. (48) The Boston News-Letter, Boston, Mass. (16) Ivan Ray Tannehill, Hurricanes, 9th ed., Princeton, (49) The New Hampshire Gazette, Portsmouth, N.H. N.J., 1956. (50) The Newark Star-Ledger, Newark, N.J. (17) Gordon E. Dunn and Banner 1. Miller, Atlantic Hurricanes (51) The New rork Times, New York, N.Y. (rev. ed.), Baton Rouge, La., 1964. (32) The Savannah Morning News, Savannah, Ga. (18) David M. Ludlum, Early American Winters 1, 1604-1820, (53) The News and Observer, Raleigh, N.C. Boston, Mass., 1966. (54) News-Observer Chronicle, Raleigh, N.C. (19) David M. Ludlum, Earty American Winters 11, 1821-1870, (55) The Oregon Daily journal, Portland, Oreg. Boston, Mass. 1968. (56) The Oregonian, Portland, Oreg. (20) William E. Clark, ed., Naval Documents of the American (57) The Philadelphia Inquirer, Philadelphia, Pa. Revolution, vol. 2, Washington, D.C., 1966@ (58) The Norfolk Virginian-Pilot, Norfolk, Va. (21) U.S. Army Engineer District, Charleston Corps of (59) The Times-Dispatch, Richmond, Va. Engineers, Charleston, South Carolina, Reconnaissance (60) The Virginian Pilot, Norfolk, Va. Report on Beach Erosion, Pawleys Island Beach, George- (61) The Virginian Pilot and the Norfolk Landmark, Norfolk, Va. town County, South Carolina, October 1972. (62) The Seattle Daily Times, Seattle, Wash. (22) Beach Erosion and Damages to the Ventura County Shoreline, (63) The Seattle Post-Intelligencer, Seattle, Wash. Department of Public Works, Ventura County, Calif., (64.) The Evening Star, Washington, D.C. June 1972. (65) Biddeford-Saco journal, Biddeford, Me. (23) Annual Report of the Superintendent of the Coast Surveyfor (66) Evening Express, Portland, Me. 1847, Washington, D'C., 1847. (67) York Couqy Coast Star, York County, Me. 38 Strategic Role of Perigean Spring Tides, 1635-1976 Reference Sources for Tidal Flooding-Continued Reference Reference Code No. 'rode No. (68) The Portsmouth Herald, Portsmouth, N.H. (73) Charles L. Bretschneider, "The Ash Wednesday East (69) Raymond Herald and Advertiser, Raymond, Wash. Coast Storm, March 5-8, 1962; A Hindcast of Events, (70) The Savannah Daily Advertiser, Savannah, Ga. Causes, and Effects," in Proceedings of the Ninth Con- (71) M. P. O'Brien and J. W. Johnson, "The March 1962 ference on Coastal Engineering, Lisbon, Portugal Storm on the Atlantic Coast of the United States," in (1964), 1964. Proceedings, VIIlth Conference on Coastal Engineering, (74) Massachusetts Geodetic Survey, Works Progress Ad- Council on Wave Research, The Engineering Founda- ministration Project No. 165-14-6085, "High Water tion, Richmond, Va. 1963. Data, Flood of March 1936 in Massachusetts," Boston, (72) Civil Works Branch, Construction-Operations Division, Mass., November 1, 1936. North Atlantic Division, Corps of Engineers, U.S. (75) Fitz-Henry Smith, Jr., "Some Old-Fashioned Winters Army, Report on Operation Five-High, March 1962 Storm, in Boston," vol. 65, Proceedings of the Massachusetts August 1963. Historical Society, Boston, 1940. TABLE 5 A Representative Sample of Newspaper Articles Covering Tidal Flooding Events Associated with Perigean Spring Tides, 1723-1974 Explanatory Comments The following reproductions of news articles, covering nomical conditions given in table 1, where the same serial 50 major tidal flooding events that have occurred on both numbers are used. the east and west coasts of North America in association The presence of a capital letter preceding this number with perigean spring tides, comprise one-half of the total indicates that a corresponding synoptic weather map and/ list of representative events listed in the master catalog or tidal curve relating to this event (and carrying the same, (table 1) . In practically all cases, considerable additional alphanumeric descriptor) are to be found in part 11, chap- information was contained in the original full-length news ters 7 and 8, respectively, of the text. Where tidal flooding article. These news accounts have been shortened, and occurred simultaneously on both the east and west coasts, considerable detailed material relating to individual prop- a small letter "e" or "w" following the key number indi- erty losses as the result of tidal flooding has been deleted. cates which coast is represented. The excision of material is indicated by the use of ellipses. The figures printed in the lower left corner following News photos which, in many cases, accompanied the orig- each news article provide information relating to the inal stories and illustrated the considerable extent of flood- perigee-syzygy alignment with which the reported tidal ing damage have been eliminated, for technical reasons. flooding was associated. The first such entry gives the date However, no substantive editing involving any altera- and time of the mean epoch of perigee-syzygy, specified to tion of the original content has been employed@ Every the nearest.hour or half-hour in the respective eastern attempt has been made to preserve all possible information standard time (e.s.t.) or Pacific standard time (P.s.t.) zone on the preceding and concurrent meteorological condi- concerned. All times given are standard times, despite the tions pertinent to the tidal flooding, the observed and occasional historical intervention of daylight time or war recorded heights of the tides, and other factual data. Care time. The number in parentheses is the separation, in also has been exercised to include all newspaper datelines hours, between the times of perigee and syzygy, in the or, where these are lacking, other textual references to the algebraic sense perigee minus syzygy. This grouping of time of the flooding event (the day of the 'week, etc.) data conforms exactly with the data given in similar slant- through which an accurate correlation may be made with lettering on the reproduced synoptic weather maps, tide the corresponding perigee-syzygy data. curves, or other graphical representations throughout the The exact source of each article is identified by news- volume, with which these data may be rigorously com- paper name, day of the week and date of publication (or pared. the period of coverage for weeklies), and the page and The morning-final or evening-final editions of the news- column for each article used. The initials "O.S." stand for papers concerned were used in nearly all cases. Where Old Style Calendar and "N.S." for New Style Calendar, another edition was used and this fact is known, it is so whose exact meanings are explained in a technical note at indicated. Since many of the original newspaper articles the beginning of chapter 1. (References-to columns start were not reproducible in their aged condition, all articles with that at the extreme left hand side of the page as col. I have been uniformly reset, in abridged form. Although and proceed progressively to 'the right.) Although news- some of the earliest news accounts lack headlines, and papers may have changed their titles over subsequent other such heads have been eliminated because of their years, the contemporary title is used in all cases. The arti- multiple-column widths or large point sizes, an effort has cles are chronologically arranged. been made to retain significant headings wherever possible. The boldface number following each newspaper article Additional news articles relating to unusually large is a key number for use in cross-referencing the article to coastal flooding events which are given special attention in the listing of the flooding events and their associated astro- the main body of the text are contained in chapter 7. 39 40 Strategic Role of Perigean Spring Tides, 1635-1976 The Boston News-Letter Islands were submerged by the waves, and The Boston Herald (Now England - Weekly) many docks were so badly shattered that Wed., Nov. 25,1885 Thurs., Feb. 21-Thurs., Feb. 28, 1723 it will be necessary to rebuild them. The Page 1, Cols. 4-6 (O.S.) Harlem flats resembled an inland sea ... Page 2, Col. 2 . . . The tide rose to a great height and Boston, Fehr. 25- Yesterday, being the washed out many manufacturing places Lord's Day, the Water flowed over our . . . A MIGHTY TIDE, Wharff's and into our Streets to a very . . 1. Much damage was done to buildings surprizing height. They say the Tide rose by the wind, and to the docks by the very 20 Inche8 higher than ever known before. high tide, The meadows between Williams- The Storm was very strong at North-ea8t burg and Greenpoint were flooded by the wind backing the water up East river, and Old Neptune Baptizes a number of buildings were inundated ... ... The loss and damage sustained is very great, and the little Image of an Inunda- 1878 Oct. 25 the Sholu. tion which we had, look'd very dread- 9.5h e.s.t. (-17) ful . . . 1722123 Feb. 23 (O.S.) 1723 Mar. 6 (N.S.) An Unprecedented 16h e.s.t. (-6) Rise of Water. 4 The New York Times Fri., Sept. 29, 1882 Picturesque Commingling Page 5, Col. 2 The Boston Gazette and HIGH TIDES AT LONG BRANCH of Wind and Wave. . Country Journal Long Branch, Sept. 28-The storm on Mon., Dec. 11, 1786 (N.S.) the New Jersey coast has increased in in- Great Dami.irua to Property No. 1690, Page 3, Col. 1 tensity since midnight yesterday, the gale Boston, December 1I.-On Monday evening continuing from the north-east ... in New York. last came on, and continued without inter- ... At high tide this morning-8:30 o'clock mission until Tuesday evening, as severe -a terrific sea was coming over the Long a snowstorm as has been experienced here Branch Ocean Pier, the black waves touch- for several years past ... ing the floor of the pier 20 feet above the The Jersey Coast Strewn ... The wind, at cast, and northeast, blew ordinary tide ... with Wreckage. exceeding heavy, and drove in the tide ... The heavy sea washed over the land with such violence on Tuesday, as over- and into the Shrewsbury River, the water ... Yesterday's storm proved one of the flowed the pier several inches, which en- reaching the first floors of the elegant severest that has visited this section of the tering the stores on the lower part thereof, cottages and flooding the stables. Car- country, its effect being most perceptible did much damage to the Sugars, Salt, &e. riages were sent to higher ground on the along the coast and water front of the city. therein-considerable quantities of wood, mainland. The Pennsylvania Railroad was In the upper harbor at noon, when the tide lumber, &e. were carried off the several badly cut at Seaside Park, and passengers was full, the sight was a grand one . . . wharfs ... were sent by way of the New-Jersey Cen- tral to New-York. At Branehport, Little ... At the South city ferry the tide over- 1786 Dec. 4 Silver, and Red Bank at low tide the flowed to the entrance gates on Lewis 23.5h e.s.t. (-17) waters were within eight inches of the street on the East Boston side, and the floors of bridges, and much alarm was felt Eastern-avenue entrance in the city proper 7 as to the effects of the high tide to-night, was all awash for a short time. The ticket This tide is the highest ever known boxes on the East Boston side were sub- here . . . merged to the depth of several inches by the encroaching element. At the North . . .The high tide of yesterday morning ferry the extreme high tide made matters has not been surpassed in several years. unpleasant for the pedestrians, as the The Philadelphia Inquirer Late last evening the tide was rising water worked its way up through the east- Thurs., Oct. 24, 1878 rapidly, and there was 'every indication erly end of the new headhouse on the Bos- Page 1, Cols. 2, 3 that this morning it will reach the same ton side. The ferry employes say that the height as yesterday, if it does not surpass tide was the highest that has been known High Tide at New York and Shattered it ... here for a great many years. The tide at Shipping, Docks and Buildings. midnight was considerably higher, it rising 1882 Sept. 26 11 ft. 7 in., but owing to the decrease of NEw YORK, Oct. 23-The tide which ac- 19h e.s.t. (-10) the wind, its effects were not so severe as companied the eastern gale of today was those of the noon tide ... one of the highest remembered, and caused 20 extensive damage along the city's eastern . . . The waves at noon broke over the front. The sea walls around Ward's, Ran- high wall of the- State dock, South dall's and the upper end of Blackwell's Boston, and sent their spray high in air, Representative Great Tidal Floodings of the North American Coastline 41 the foam from which was blown several no trains are allowed to cross it. The docks all along the New Jersey coast, and par- hundred feet inland. The sea wall between at the different hotels have all been dam- ticularly between Sandy Hook and Point Jeffries point and Wood island, which has aged, and are likely to break up entirely Pleasant. For twelve hours the wind along unless the wind shifts soon. The families the seaboard has blown from forty to fifty Towered Above the Angry Waves living in small houses along the ocean and miles an hour and the sea has been un- since the destructive gale which washed bay have been obliged to move out. The usually high and strong . . . Minot's light away in 1851,-was yester- cellar of the great hotel is flooded. The day overtopped by the briny elements, and wind is blowing a gale,, . . . ... The foundation and platforms of the large sections of it were wholly submerged, Ocean Hotel bathing pavilions, just south while on all parts the sea made heavy ... At Hunter's Point, the tide rose to an of the pier, were this morning smashed breaks at frequent intervals . . . extraordinary height, water to the depth into kindling wood by the high tide and of several feet having covered the docks carried out to sea. Between the Surf Along the North and South Shores. and street for a distance of a hundred House, just north of the pier, and Chelsea yards, rendering foot travel to the ferries Avenue nearly eight feet of sand have been The tides ran unusually high at Lynn. and railroad impossible. Wagons cannot carried away, and the bluff has been badly There was much. damage at some of the get aboard the ferry boats, the latter being washed and inundated . . . wharves. The water nearly reached the several feet above the ferry bridges. The Nahant roadway. The BOStOD, Revere lower parts of Astoria and Ravenswood -Minugh's Hollow, at Seabright, is Beach & Lynn railroad's outward tracks are also flooded. The meadows at Flushing flooded by the high tide in the Shrewsbury were badly washed for a fourth of a mile are under water, and the railroad trestle River. and several small houses there have between the Point of Pines and Oak is covered in places. Several wagons and been badly undermined. The tide there is Island . . . small outhouses have been carried off and so high that the first floors in several are floating in the bay. The cellars and houses are submerged. At Highland Beach The tide was the highest at Salem that first floors in the lower part of the village the tracks of the New-Jersey Southern has been known for years. It filled the are flooded, and the inmates of the houses Railroad are covered with water ... North river canal to the top. have been compelled to move upstairs. The tide at Edgeworth and in the marsh At Atlantic City, N. J., the tide was the ... POINT PLEASANT, N. J., Oct. 13-The on Charles street was the highest ever highest for years. The damage to property high tide this evening cut the beach badly known. A large number of cellars were was considerable. Much of the board walk at Seabright. At this place the large pavil- flooded, and a lot of lumber floated off. along the oceanfront is washed away, and ions of W. T. Streets and Dr. Knox were The water covered the Saugus branch the railroad tracks are washed out near Surrounded by water and both houses were track of the Boston & Maine railroad, the inlet. Many of the streets are flooded. washed away. The seas ran down all At- causing some inconvenience to trains. The Boats are being used to convey residents lantic and Arnold Avenues and the board tide also covered Charles street, making it up and: down some of the streets walks are afloat. At Bayhead 300 feet of impassable. A large number of tons of hay bulkhead and board walks were cut out was floated off on the marshes at Welling- . . . From Barnegat bay to Sandy Hook and went to sea. At Barnegat City the ton, causing a considerable loss. the beach is covered with boards torn from railroad is torn up to the beach and rail- At Cohasset the tide was the highest bulkheads and summer houses. The ocean road communication to the city is cut off. since April 16, 1851, the day of the destrue- promenade and pavilions of James A. At Atlantic City and Ocean City the sea tion of Minot's ledge lighthouse. The Bradley, the founder of Asbury Park, 'is very high, and the railroad from Cape streets and meadows in the vicinity of the were damaged to the amount of $1000. May to Sewell's Point is under water. The harbor were overflowed, and the wharves Several elegant cottages at Elberon have sea came in like a tidal wave. It is the were covered to a depth of 18 inches. been badly damaged. Worst Surf in years. . . . At Bridgeport, Ct., the tide reached the NEW YORK AND VICINITY highest point known in that vicinity for 1891 Oct. 16 many years, wharves, warehouses and cel- 23h e.s.t. (-20) Great Damage to Property-The Highest lars along the water front being over- 23 Tide Ever Known flowed to the depth of several feet, causing much damage . . . NEW YORK, Nov. 24, 1885. Never before has such a high tide rolled in upon the 1885 Nov. 23 city, and incalculable damage has been 22h e.s.t. (+59) (lone along the water front. At 10 o'clock, when the tide was at the full, the water The New York Times ,%vas said by the ferry authorities to be Sat., Feb. 9, 1895 nearly three feet higher thaii it had ever Page 3, Col. 4 been known before. The bridges in the ferry houses on the North river were tilted up toy the tide to an angle of 30*, and the incoming boats Scraped along on the top of The New York Times TREMENDOUS TIDES ON THE COAST the rack guards. When the boats were Wed., Oct. 14,1891 made fast to the (locks, the passengers, in Page 1, Col. 5 Wharves, Streets, and Buildings Flooded many eases, had to be hoisted upon the bridge ... . . . enormous high tides prevailed along the entire coast . . . A telegram from Rockaway Beach says DAMAGE BY HIGH TIDES BIG TIDES ALONG NEW-ENGLAND. "Great dainage has been done all along the beach. The tracks of the New York, Wood- Streets, Wharves, and Buildings haven & Rockaway railroad have been LONG BRANcH, N. J., Oct. 13-The Badly Flooded. washed out, and train,,; cannot. proceed. severe northeast wind and rain storm The spite work across Jamaica bay is which has been raging for the past twenty- BANGOR, Me., Feb. 8-The tide here totally submerged, and, for safety's sake, four hours has done considerable damage today was the highest since the freshet of 42 Strategic Role of Perigean Spring Tides, 1635-1976 1846. There Is from one to three feet of large four-masted steamship Patria of the noon they made trips more regularly. At 4 water in the cellars of stores on Exchange, Hamburg-American Packet Steamship P. M. the tide was so low and the ice on the Brooklyn side became so bad that it Broad, Central, and Front Streets. The Company, while proceeding to sea this was necessary to stop running the boats damage caused is from $15,000 to $20,000. evening, grounded in the main ship chan- The tide is five feet higher than flood. nel, near the southern edge of Palestine . . . The railroad bridge across Kenduskeag Shoal . . . 1895 Feb. 9 stream is weighted down with freight cars and locomotives to prevent it from being 10h e.s.t. (-4) carried away. PORTLAND, Me., Feb. 8.-To-day's tide LOWEST TIDE IN TWENTY YEARS 25 was the highest known here for years. In some cases the water rose to the flooring of the wharves, and it flooded many cel- lars. Ferryboats Blockaded by Ice Few Lines in Operation. BATH, Me., Feb. 8-The tide to-day is The Richmond (Va.) Dispatch the highest ever recorded here, necessitat- A northwest wind, an extremely low Fri., Aug. 18, 1899 Ing the stopping of work in several build- tide-the lowest in twenty years, old boat- Page 1, Col. 7 ings along the wharves. men say-and the heavy ice conspired yesterday to tie up all the ferries on the PROVIDENCE, R. I., Feb. 8-The tide East River from the Battery to Thirty- THE TIDE UNUSUALLY HIGH at this port was the highest since the fam- fourth Street . . . ous storm of September, 1869. The water NEWPORT NEWS, VA., August 17.- ran over docks and wharves and sub- 1895 Feb. 9 (Special.) -James river at this point is merged cellars of warehouses. In some 10h e.s.t. (-4) higher to-night than it has been since the parts of the Narragansett Electric Light- great storm of 1889. It is believed the Ing Company's plant 6 feet of water were 25 tide has risen five feet above average high measured. The damage to the company will water. The water is up in the car-tracks, amount to thousands. in the bottom of the piers, and within a foot of the pier-floors . NEW-BEDFORD, Mass., Feb. 8-The tide here was never known to rise so high The New York Times 1899 Aug. 20 as it did to-day. Water covers the wharves to the depth of two feet. Front Street was Sun., Feb. 10, 1895 20.5h e.s.t. (-7) inundated to the depth of eighteen inches. Page 2, Col. 1 On Water Street the New-Bedford Ma- 30 chine Company and the Smith & Carlton ... The Staten Island ferryboats were all Iron Foundry were obliged to close, and running, but their trips to and from St. several of the mills were forced to close George were eventful. The Southfield had down because of the large amount of a severe encounter with an ice floe at 6 water in the basement. o'clock in the morning. She was on her first trip from Staten Island, and she had HIGHLAND LIGHT, Mass.. Feb. 8- a number of passengers on board. She Such a gale as swept Cape Cod'to-day has came up the bay without much trouble, but The New York Times not happened before since the great bliz- between Governor's Island and the Battery Mon., Nov. 25, 1901 zard of 1888. The wind at 9 A. M. reached she got stuck in a heavy icefield that was Page 1, Col. 7 a velocity of sixty miles an hour. swept by the current around from the The tides in the bay were higher than North River into the East River toward ever known before, washing the banks and the bridge. The Southfield tried hard to Heavy Tide Overflows East and threatening the destruction of twenty fish- escape from the ice, but her wheels were ing houses along the shore. Roads were clogged and she was forced to drift with washed in every direction. the floe . . . West River Fronts. NEWPORT, R. I., Feb. 8.-A tremen- . . . The boats of the Staten Island line . . . The northeast gale, that started to dous high tide, accompanied by great seas ran all day, but late in the afternoon the blow in this neighborhood Saturday even- and heavy ice, is doing great damage tide was so low that the ferry bridges Ing, (lid not abate to any appreciable ex- along the water front to-day. Two barges were far above the decks of the boats, and tent, until well in the afternoon of yester- are ashore. the ascent and descent were so dangerous day. Its maximum velocity was nearly At the beach, a part of the sea wall is that teamsters did not dare to risk their sixty miles an hour. It blew with unabated gone, and the roadway is washed away. horses on the steep planks, and wagon fury all night 4aturday and yesterday At the naval station, several thousand traffic had to be suspended ... morning dollars' damage was done to walls. . . . The Shackamaxon, that plies between . . . Not only the winds inade life miser- 1895 Feb. 9 Ellis Island and the Battery, made several able from a marine standpoint, but the 10h e.s.t. (-4) trips, and every one was eventful. She tides as well. According to veteran marl- encountered immense cakes of ice, through ners long familiar with everything that 25 which she had to plow her way, and the had to do with New York Harbor, a tide northwest winds that swept in gales across such as has not been seen in these parts the bay helped to impede her progress ... in nearly a -,core of years washed upon the The New York Times shores of the city and nearby islands yes- Sun., Feb. 10, 1895 . . . The Fulton Ferry boats Fulton and terday morning. It swept over the Battery Page 1, Cols. 3, 7 Farragut ran until 4 o'clock yesterday wall. deluged the piers along the river afternoon. From 6 to 9 A. M. they had fronts, finally ending in the cellars under . . .SANDY HOOK, N. J., Feb. 9-The much difficulty in getting across, but after the houses on South, West, and other af- Representative Great Tidal Floodings of the North American Coastline 43 feeted streets, soaking and in many cases The tide nwl wind swelit oyster boats northeast. meeting unusually high tides, so ruining, the merchandise or other things an(] haii0soine sloops in a wrecked mass the waves rose high, worked ' havoc with contained in them . . . upon the shore and ineadows. The Golden the strongest bulkheads, and tossed about Gate. a large sloop oAvned by Capt. boardwalks with a playful madness ren- ... In Manhattan the greatest damage, of William E. Woolley of this place, was dering then) fit only for kindling wood . course. was along the streets fronting on dashed upon the -shore here, and crashed the. river-, and in the subway. On West through :i large. storehouse building owned . . . The flood tide at 5:26 o'clock in the Street produce inerchants were busy bail- by Baner & Hopkins . . . morning came tearing in and tearing ing the water out of their cellars. From up . . . Warren Street to Park Place, on West Storehouses. docks. and bath hou,,,es Street, the shops, saloons, and restaurants were lifted from their foundations and ... The Manhattan Beach Hotel suffered were flooded. A restaurant at 165 West carried away Nvith the, tides . . . severely on its water front. The plank walks Street was so completely surrounded with were torn away, 610 feet being destroyed, water that the proprietor was unable to Thornas Brown'-,, dock at Locklm)rt was and the bathing pavilion was very nearly get to it when he arrived to open up early almost completely wrecked by the tide destroyed. At the Oriental Hotel the board- in the morning. walk Nvas torn to bits. The iron lamp posts The Fall River steamer in arriving at were twisted and bent, and the embank- Pier 18, at the foot of Murray Street, had inent cut into. It will not be possible to fix to keel) her passengers on board owing to the loss until the storm has subsided and the water, which was about two feet deep, MUCH DAMAGE ON THE an examination can be made. The waves that flooded the street outside. . . . breaking over - what was the boardwalk CONNECTICUT COASTS. rolled in ion the lawn and scattered over ... In the East River there was a serious it the debris of its earlier destruction. The amount of damage, due to a tide, which -NEW HAVEN, Conn., Nov. 24-At Shi')_ total loss at Coney Island is estimated at river men insist has never been equalled pan Point, in Stainford, several docks on- $2.1,000 . . . in their experience. The lighthouse ion the nected with Summer residences were car- CHATHAM, Mass., Nov. 24-The life north end of Blackwell's Island, usually ried away by the unusually high tide, and savers along the shore from Monomoy ,high above flood tide, was wrapped in the cellars of a number of buildings near Point to Provincetown report the gale as spray, the platform of the house being but the -water front were completely sub- very severe. -,vith a high tide which has little above the water. The entire north merged. Along the canal the water rose washed away miles of the beaches and side of the island was flooded at 9 o'clock, over the banks and a considerable part of made bad inroads into the headlands. At and several small fraine buildings were the lower end of the city was inundated. South Beach the high tide and heavy seas carried away. The freight offices of the North and East have cut away the sand embankment for In the upper west side the greatest River Steamboat Company were flooded, many years . . . damage was in the rapid transit tunnel, -is were many of the shops on the canal . . . the excavations extending through Lenox I Avenue north fron) One Hundred and . . . Milford probably suffered more than 1901 Nov. 25 Thirty-fourth Street to the Harlem River any other town on the Connecticut shore, 15.5h e.s.t. (-9) . . . and the damage there is estimated at $10 - 34 h _ 000. The seawall at Burwell's Bea( , r . ... This trench is eighteen feet wide and cently built. was completely carried away. forty feet deep, and is to go under the At Fort Trumbull Beach every bathing river at a depth of sixty feet below its house was washed away, and the banks bottom. The contractor had sunk a c0ffer and lawns of the Summer homes were dam at the river bank. This held, but the destroyed . . . water poured over it and into the tunnel, filling it. The banks were softened and . . . At Greenwich the tide.was five feet caved in at many places, but the tunnel is higher this morning than usual, and every- not seriously damaged. The loss to the thing on the low lands was carried away. contractors is about $10,000 . . . Lumber yards were flooded, and huge piles 1901 Nov. 25 of lumber toppled over and floated out. into The Evening Telegram 15.5h e.s.t. (-9) the harbor. At Belle Haven two docks Saint John's, Newfoundland owned by John P. Lafflin and John B. Barrett were swept away and carried on Tues., Feb. 3, 1908 34 to Byram shore, and the macadam roads Page 4, Col. 2 were damaged to such an extent that it The New York Times will take from $3,000 to $4,000 to repair ... The railway track was washed away them. The total damage in this vicinity about eight miles this side of Port aux Mon., Nov. 25, 1901 will reach at least $7,000 . . . Basques so that the Bruce express was Page 2, Cols. 3, 4 not able to leave there this morning. The sea swept in with terrific violence and inundated the track for several hundred HAVOC AT KEYPORT yards. The tide is not expected to subside KEYPORT, N. J., Nov. 24-The tide SCENES OF DESTRUCTION till this afternoon, about 3 o'clock . . . rose until the docks along the water front 1908 Feb. 2 were several feet below the water. More Oh e.s.t. (-8) than a hundred large sloops were in Key- AT OLD CONEY ISLAND port harN)r. besides a large number of smaller cr- Iks 35 aft. Owners of the vessels stood Bulkheads and Boardwa upon the shore this morning and were Smashed Into Kindling Wood. poiverl"s to save their property, as the vessels dragged their anchors and burst Coney Island breezes yesterday were froni*their moorings. of the cyclonic sort, and came from the 44 Strategic Role of Perigean Spring Tides, 1635-1976 The Los Angeles Times The Virginian-Pilot and the Fri., Dec. 18, 1914 Norfolk Landmark Pt. 2, Page 1, Cols. 4, 5 Norfolk, Va. Sun., April 4, 1915 Destructive. Page 5, Col. 3 SEAS LASHED BY GALE STORM SEVERE AT BATTER COAST TOWNS VIRGINIA BEACH . . .More damage was inflicted by the storm at Virginia Beach than that resort has suffered in the past 30 years. Swept by the 75-mile gale of Friday night and Houses Destroyed, Bulkheads Shattered, Se2ver and Gas early yesterday morning, the beach front suffered in a number of places, both from Mains Severed by Pounding Breakers on Crest of High wind and water . . . Tide-More Trouble Feared Today-Loss of Property ... Practically all of the board walk in Many Thousands-No Casualties. front of the site of the old Princess Anne hotel was torn up by the surf which broke over the sea wall 1915 Mar. 31 Lashed to a furi,- by a. heavy on-shore bags of sand and timbers, they cannot bope 22h e.s.t. (+42) gale that lent impetus to an unusually to stem the huge tide expected ... high ti(le@ the sea battered the southern 39 coast early yesterday morning with fury 1914 Dec. 16 and destroyed property worth many thou- Oh P.s.t. (-36) sands of dollars. From all along the shore came the same 38 story. of huge, waves leaping over barriers and carrying destruction with them. At The Los Angeles Times The New York Times Long Beach $80,000 damage was done, Fri., Dec. 18, 1914 Thurs., April 11, 1918 while. at Balboa the loss was als:) heavy. Railway tracks were washed out at the Pt. 2, Page 6, Cols. 3-5 Page 15, Cols. 5, 6 harbor and traffic delayed for hours. One fatality due to the storm was reported PENINSULA INUNDATED. Sixty-Mile Blow from the East from the sea. There were no casualties In the wake of a forty-five mile gale, ashore. the tide rose to unprecedented height at Piles Twelve-Foot Tide Over The off-shore breeze that accompanied Balboa Beach yesterday morning, broke Piers and Streets. the rain of Wednesday night switched to over the bulkheads, cut 100 feet off the tip the southeast early in. the day, and blew end of the peninsula, inundated Collins at places forty-five miles an hour. No Island, damaged or wrecked a score of Beach Hotels. and Bungalows damage was (lone here. residences and receded, leaving many Flooded and New Cement Shore Further trouble at coast points is feared thousands of dollars damage in its wake Walk Undermined for this morning's high-tide period. TERROR AT LONG BEACH. A sixty-mile easterly gale, blowing ... Although the storm was accompanied directly from the sea, pushed a tremen- Washing houses into the sea, tearing up by a gale from the southeast and the high- dous tide against the whole length of the concrete bulkheads and cement promen- est tide in nearly twenty years, there was south shore of Staten Island late yesterday ades, and spreading terror and damage no damage to shipping at the harbor ... afternoon, submerging piers from four to along the ocean front, the wind, aided in six feet, inundating streets and business its work of destruction by an extremely ... The tide at 8:50 a.m. reached 7.5 feet, property, and tearing several small ves- high tide and heavy rain, paid a terrifying and with the storm behind it backed up sels from anchorages and throwing them the water in the channel and the bay to a ashore. It was estimated that the property visit to Long Beach early in the morning. hitherto-unknown height. loss would reach $100,000 . . . Many persons had narrow escapes from drowning in their seaside bungalours, one About 200 feet of the Salt Lake track at of which was completely destroyed, and Ostend was washed out by the high tide, ... All along the waterfront from Simon- four are partially washed away. and train service was demoralized for son Avenue, at Clifton to Fort Wadsworth, Great anxiety is felt along the Nvashed- several hours. Repairs were completed a distance of two miles, the piers were out portions of the beach over this morn- last night and service resumed . . . under water, and the ships which had been ing's high tide, when more buildings and loading or discharging cargo had to be works are expected to go. A tide of 7.3 1914 Dec. 16 moved to outside anchorage last night to feet is expected at 9:15. Many of the Oh P.S.t. (-36) prevent them pounding to pieces. In Clifton houses on the east beach are hanging over the water was four feet deep in the a bluff caused by the waves, and, although streets, and boats were used to move the owners and occupants of these build- about. ings worked feverishly last night with Summer hotels and bungalows at South Representative Great Tidal Floodings of the North American Coastline 45 Beach and Midland Beach were damaged water. Families, fearing the water would makes a difference of, say, a couple of feet severely. The flood swept over the first rise above their living quarters, sought as compared with moon at the quarter. On floors of most of these places. Long refuge in the upper stories. Finucan's the 18th, then, wind and moon favored an stretches of the new concrete walk at Hotel, facing the sea, was so undermined exceptional high tide. both beaches were undermined by the tide by water that it was feared, it would On Nov. 18 my barometer showed a sea- . . . collapse. The boulevard at Edgemere was level reading of approximately 28.7 inches, covered with water and several bungalows perhaps, with one exception, the lowest I . . . At 10 o'clock last night it was said were washed away. have ever happened to observe. When the the tide had reached ele ven feet above barometer is low-that is, when the air normal high tide, the highest for years ... ... According to the city gauge at Pier A, pressure on top of the water is lessened- North River, at 10 o'clock Thursday night the water tends to rise. In support of this . . . SEABRIGHT, N. J., April 10-Row the card registered a height of water of let me quote from William M. Davis's boats were used in Ocean Avenue tonight eight and fifteen-hundredths feet above book 'Whirlwinds, Cyclones, and Torna- at high tide. The crest came at 11:30 after mean low water. This is the highest tide does,' where he speaks of this-phenomenon which it subsided a little after threaten- since the records were established in in the Bay. of Bengal. - -- ing to inundate several buildings ... 1886 ... "The diminished atmospheric pressure about the storm centre allows the heavier 1918 Apr. 10 SEA FLOODS ATLANTIC CITY surrounding air to lift the water, and for 14.5h e.s.t. (-19) every inch that the mercury falls in the ATLANTIC CITY, N. J., April 12.-A barometer the water will rise a foot. . . . A-43 record tide did much damage along the and if a strong tide conspires with these sea front today. For the first time in years other causes a great flood is produced." the sea flooded the lawns of the big hotels, The same rule that works in the Bay of The New York Times smashed doors and flooded cellars, drown- Bengal works in New York Bay, I should ing out fires in some of the apartment think. Sat., April 13, 1918 houses and causing loss of property in CHARLES VEZIN, Jr. Page 11, Col. 3 store rooms. The water put the plant of Yonkers, Nov. 22, 1918. the electric company out of service, and 1918 Nov. 17 Unusually High Tide Drives the entire city was in darkness last night. 12.5h e.s.t. (-29) Water to Station Entrances 1918 Apr. 10 in Jersey City. 14.5h e.s.t. (-19) 44 Homes at Sea Bright Inundated- A-43 $50,000 Damage at Sea Gate. ... The high east wind and the unusually high tide yesterday caused great damage all along the Atlantic Coast . . . The New York Times Sat., Nov. 8, 1919 ... On the waterfront the water piled up Page 5, Col. 1 by the wind flooded streets, undermined The New York Times houses, interfered with ferry traffic, and Mon., Nov. 25, 1918 caused discomfort to thousands of persons. Page 12, Col. 6 In New Jersey the water came up so high HIGH TIDE nows that it flooded the waiting rooms of the Remarkable Tides on Nov. 18 railroad stations and interfered with the To the Editor of The New York Time8: handling of freight In the Erie and Penn- Your issue of Nov. 19 contained this STREETS AT FERRIES sylvania railroad yards. paragraph: When the tide came up water began to "The south wind caused an unusually run down the steps of the entrance to the/ high tide. Many of the ferry bridges were Hudson tunnel in the Lackawanna station lifted until vehicles had to go up a sharp Unusual Rise Causes Delays on in Hoboken. It soon became so bad that incline to make the boats, and in some the Jersey Side for More the entrance had to be closed to the public, cases the water flooded the ferry houses." Than Three Hours and a barricade of boards was hastily Your issue of the 20th reproduced a raised to stop the water from flooding into dispatch from Quebec, dated Nov. 19, the tube and interfering with the traffic. which read in part as follows: As the tide came higher the water rose "The tidal wave . . . swept up the St. UPPER PLATFORMS USED in the ferry houses and more poured into Lawrence last night, causing damage esti- the tunnel . . . mated at $1,000,000. Part of the village of Batiscan was submerged by the flood Pilots Make Slips with Difficulty . . . Wind and tide wrought destruction tide." -Water Enters Cellars on along the shore from Long Beach to Sea The above accounts went on to ascribe New York Side Gate. At Coney Island, Brighton, and Sea the abnormal tides to the south and east Gate the police last night estimated the winds, which, of course, had an effect, but damage at $50,000 . . . there were two otlier unmentioned causes -the moon, and the low barometer pres- ... In the, district around Par Rockaway sure. An extraordinarily high tide on the streets were flooded, small buildings car- The moon was full Nov. 19, and it is a North River yesterday morning, said by ried away, and larger ones damaged. Train familiar phenomenon that, other things the water front experts to have been and trolley service was practically stopped. being equal, tides always run higher and caused by the northeast wind and the full Near Howard Beach parts of the Long run lower at full moon. Frequenters of the moon, flooded the streets and cellars of Island Railrokli-tracks were covered by seashore inay have noticed that this the houses, interfered with the power 46 Strategic Role of Perigean Spring Tides, 1635-1976 'plants of the Grand and Desbrosses The San Francisco Examiner various places attained a velocity of 75 Streets surface car lines, and partially Sun., Feb. 14, 1926 miles an hour, lashed practically the entire tied up the Hudson River ferry services, Page 1, Col. 4 New England Coast line last night and. which caused a good deal of inconvenience this morning, compelling ships to seek to the early morning commuters. shelter, and wharves to be submerged, and The passengers managed to board the causing much damage . . . ferryboats from the upper platforms on COAST TIDES . . . an exceptionally strong, high tide the Jersey shore, but the water was so swept in at 10:46 this morning. The tide deep in the streets below that trucks had M reached such a height that the water was to wait two hours.before it subsided ... on a level with the base of the caplogs of practically all the wharves along Atlantic ... The Brooklyn shore suffered, too, from ATTACK FIL av. the exceptionally high tide, and two men At Long Wharf, T. Wharf and several were marooned all Friday night on a jetty others the water seeped underneath the running from the Municipal Baths . . . caplogs and the floorings, flooding the wharves with water that averaged about The pilots on the Brooklyn ferryboats STARS' HOMES one foot deep . . . had considerable difficulty in making their slips on account of the tide, and many of Ventura Wharf Crumples Tide 13 Feet or Higher the piers along the front were flooded. In Under Battering Newtown Creek the water rose three feet Under normal conditions the tide today in the early forenoon and flooded both Highways and Bridges Blocked; should have,risen 11 feet at its highest, shores. Pilots said these exceptionally high but the indications were that it went to tides come about once every five years, Long Beach Sea Wall Is Washed Out the 13-foot mark or higher. Large, docked and the exact cause has never been deter- ships loomed high above the wharf strue- mined . . . LOS ANGELES, Feb. 13-(AP)-South- tures . . . ern California was slowly emerging tonight 1919 Nov. 8 from the three day raging of elements, in 1927 Mar. 3 2h es.t. (+14) which gales and driving rains vied with al- 21.5h e.s.t. (+15) most unprecedented high tides, leaving in 45 their converging wakes death, injury and B-50 property damage estimated in tens of thou- sands of dollars . . . ... mountainous seas, whipped into fury by off-shore gales, have resulted in three deaths by drowning, one injury and the The New York Times destruction of one wharf, damage to num- Sun., April 3, 1927 Seattle Post-intelligencer erous piers, beaching of many small fish- Page 19, Col. 2 Sun., Dec. 9, 1923 ing craft, and wholesale undermining of Page 16 HH, Col. 3 dwellings, cabins and strand walks on the Atlantic City Streets Flooded- water fronts . . . ATLANTIC CITY, N. J., April 2- The loss of the Ventura wharf ties up Driven up the beach and over the bulk- shipping activity entirely at that city, all heads by a fifty-mile northeaster, a heavy PACIFIC COUNTY ca- r-goes having been discharged on the one sea flooded parts of the Inlet section, at wharf. Six hundred feet of the structure high tide tonight. collapsed . . . Although the high seas did not reach the ... The Coast highway to San Diego was proportions of the February flood. water IS HIT BY TIDE ts stood a foot deep in sections of Maine rendered impassable by washou near Avenue; waves lashed across the trolley San Juan Capistrano and farther south tracks at the Inlet loop and gigantic comb- near Oceanside . . . ers washed over the bulkheads at the SOUTH BEND, Dec. 8.-Pacific County 1926 Feb. 12 ocean ends of Vermont, Rhode Island and is still estimating its losses and trying to 6.5h P.S.t. (-5) Gramercy Avenues . . . repair them after the worst combination storm and tide the Willapa Harbor district 48 1927 Apr. 1 has known for more than fifteen years ... 20h e.s.t. (-6) . . . The long and narrow Willapa Bay 0-51 acted as a gigantic funnel with the wind and tide pushing the water far above the scheduled 10.5 mark and inundating tide- Every Evening lands, the lower lying farms of the co6nty The Boston Evening Globe Wilmington, Del. and portions of South Bend and practically Thurs., March 3, 1927 the entire city of Raymond . . . Page 1, Col. 3 Tues., April 5, 1927 Page 3, Col. 4 1923 Dec. 7 6.5h P.s.t. (-23) Wharves in Boston Under LIGHTHOUSE KEEPER 47 Water Foot Deep MAROONED BY WATER High, rough seas, whipped into fury Due to the heavy tides caused by by a h6avy northeasterly gale, which at unsettled weather conditions of the past Representative Great Tidal Floodings of the North American Coastline 47 few weeks, the river embankment, 300 The flood condition lasted for two hours, The New Haven Journal-Courier yards above the lighthouse, on the gov- an hour before and an hour after the tide Thurs., March 5, 1931 ernment reservation at the junction of the reached its peak. Half the length of Long Sect. 1, Page 2, Cols. 7, 8 Delaware and Christiana rivers, suffered Wharf from Atlantic Avenue was covered a break and the rush of water through the with seven inches of water . . . fissure virtually made the keeper, W. H. Johnson, a prisoner. . . . The Eastern Avenue approach to REVERE HARD The water, at high tide, is two feet deep South Ferry was inundated with more on the reservation than a foot of water and foot passengers unable to board the ferries were taken HIT BY EXTRA 1927 Apr. 1 aboard on trucks. 20h e.s.t. (-6) Winthrop's seaside suffered much dam- age as the big waves battered the break- RISE OF TIDES C-51 water and crashed over the Shore Drive The tide was the highest ever wit- Many Homes Flooded, Forcing nessed at the Boston airport, rolling up 200 Persons To Seek Shelter .over the southern bulkhead and covering Elsewhere. The New York Times about a third of the runway . . . Fri., April 12, 1929 1929 Nov. 17 Revere, Mass., March 4(AP)-The Red Page 5, Col. 2 22h e.s.t. (+54) Cross tonight came to the aid of civic HIGH TIDE CARRIES OFF (See also chapter 7.) authorities in supplying food and shelter A JERSEY BUNGALOW 54 to more than 300 persons left homeless by the battering of a storm tossed ocean. With more than 75 cottages and homes ... Although the southeasterly wind which flooded or demolished, scores of persons prevailed most of the day showed a maxi- sought refuge from the city mum velocity of twenty-four miles an hour in the city, it did considerable damage The New York Times . . . About 25 pupils at the cities schools along the Jersey coast. Accompanied there Wed., Jan. 7, 1931 (Last Ed.) were forced to appeal to police when the by unusually high tides, it drove the sea Page BQ 27, Col. 8 unchecked tide inundated their homes or waters inland for several hundred feet at tore them to wreckage. some places. At Point Pleasant Coast Tides Cause Huge Damage All police and fire reserves were called Guards and volunteer workers put in a on duty and stationed at Revere Beach bu,,y day trying to save bungalow colonies ... Dense fog delayed vehicular traffic and for the purpose of aiding sufferers and threatened by the rising waters. But de- harbor shipping and caused several mis- watching for further damage by the re- spite their efforts one bungalow was carried haps in and near New York yesterday, turn tide. Police believed the midnight tide out to sea, while five others were wallow- while the highest tide in a score of years, would be at least as severe as that of the ing fti shallow water close to shore and stirred up by a full gale which battered (lay ... 600 feet of boardwalk was converted by the New England coast, caused extensive the %vaves into driftwood. The damage damage . . . ... Representatives Augustine Airola and there is estimated at $30,000 ... Thomas F. Carroll told the governor the New England Coast Battered damage here was estimated at $1,000,000 1929 Apr. 11 and that greater loss was anticipated with 4h e.s.t. (+73) ... All along the New England coast the the rising tide ... angry seas pounded wharfs, undermined 53 cottages and flooded storehouses, The As- 1931 Mar. 4 sociated Press reported. Occupants of of- 5.5h e.s.t. (-1) fices along the Boston waterfront were (See also chapter 7.) forced to use ladders to get in and out of their places of busixiess, while those using the harbor ferryboats were forced to use D-57 The New York Times improvised gangplanks. Tues., Nov. 19, 1929 Several cottages were washed from The New York Times Page 20, Col. 3 their foundations at Hampton, N. H., Fri., March 6, 1931 where the tide was the highest known Page 130 48, Col. 2 since 1909, and between thirty and forty 13-FOOT TIDE SWEEPS Summer homes were surrounded by water BOSTON'S WATERFRONT THIRD GREAT TIDE . . .The streets of the Indian village of BOSTON, Mass., Nov. 18.-A record tide, Taholah on the Quinault Reservation in driven four feet beyond its normal height Washington 'were flooded by the highest by the easterly storm, inundated Boston's tide ever known there . . . LASHES BAY STATE waterfront today, causing heavy damage. 1931 Jan. 5 The tide reached its highest point in BOSTON, March 5-Towering seas con- many years with a rise of 13 feet 6 inches 9h e.s.t. (+50) tinued to lash the coast of New England at 11:45 A. M. An unusual rise had been early today despite the fact that the wind expected, but the water rose two feet 56e and snow storm which accompanied'yes- beyond the mark predicted, flooding cellars terday's record-breaking tides had moved and food stores piled up in wharf sheds. off-shore ... 48 Strategic Role of Perigean Spring Tides, 1635-1976 . The waves of the third consecutive The New York Times abnormal tide, though somewhat abated, swept in at noon today and toppled several Boston, March 5, (AP)-The storm Tues., March 10, 1931 beach houses which had been weakened which yesterday lashed the northeast Page 18, Cols. 1, 4 by the previous more savage onslaughts. coast, causing damage estimated in the The loss is expected to run into the millions, blew itself out today. There was PORTLAND, Me., March 9 (AP).-A millions ... no recurrence of the extreme high tide, howling overnight southeaster, bringing which was responsible for the greater part heavy snow, sleet, rain and lightning, to- The finale to the most destructive of the destruction. day had caused some damage along the storm since 1898, today's tide ripped apart As the sea rolled back it left in its wake Maine coast . . . crumbling seawalls, again inundated sev- a shore line streamed with splintered eral communities and tore more cottages dwellings and summer cottages and up- ... An unusually high tide switched the from weakened foundations . . . rooted and undermined seawalls and break- mouth of the Goose Fair River, dividing great swells broke over seawalls an waters. Highways and roadbeds of electric line of Old Orchard and Saco, 100 feet to hour before high tide' . . . and steam railroads were washed out in the south . . . : * . Firemen started pumping out the many places and road gangs labored to re- . . . NEW HAVEN, Conn., March 9- inundated section of Beachmont, where pair the damage. Although the force of the Damage to the Connecticut shorefront water lay from three to seven feet deep, tidal storm was felt all along the North from yesterday's storm will total $1,000,- surrounding scores of houses. The Atlantic states the most destructive blows 000, according to estimates compiled from nearest estimate of the loss is $3,000,000 fell on the Massachusetts and New Hamp- reports received today. The shorefront . . . shire coasts. suffered heavily from Greenwich to Madi. ... HALIFAX, N. S., March 5-Damage Numerous summer cottages were demol- son. Record-break!Dg high tides were re- estimated at a million dollars has been ished at Revere, popular greater Boston corded over this area. In practically every caused by the violent storm and record summer resorts, and at Hampton Beach, colony cottages or bath houses were wash- high tides along the coast of Nova Scotia N. H. ed away and wreckage was strewn over during the last thirty hours . . . Fear that today's tide would approach lawns and roads ... ... Wharves were carried away, at least the record high of yesterday to multiply one deep-sea cable twisted and torn, and the damage already inflicted was found ... For the first time in recorded history bridges were smashed when a peaceful without foundation. The wind that had the Housatonic River overflowed its banks countryside received the worst battering been blowing from the northeast, driving . . . by mountainous seas in the memory of its the sea upon the land, shifted to the north- oldest inhabitants. west, serving to abate the heavy seas. ... Beachfront communities in New York Devil's Island, standing like a sentinel Many sections that were flooded yesterday and -New Jersey were busy repairing the off Halifax Harbor, where the snug homes remained comparatively dry . . . damage done by the tides and gale over the week-end. On Fire Island bar, opposite of its fishermen nestle together, appeared Revere Hard Hit Centre Moriches, the new inlet cut by the to have borne the brunt of the attack. The raging seas seemed to be filling in tide was unusually high and as the spray, The Beaehmorit district of Revere, bat- again . . . borne before the fierce wind, drove clean tered by three successive tides, tonight across the island, the women and children escaped further assault. The after mid- (See also chapter 7.) of the place fearfully watched the island night tide officials believed would be minus men hauling their boats to safety. the fury of its predecessors which left the 1931 Mar. 4 Seas swept over the sheds housing the greater part of the district under water. 5.5h e.s.t. (-1) lifeboats, there being a life-saving station Acre upon acre of land on which homes on the island, and for a time inhabitants or summer cottages rested were covered D-57 of the island feared for their lives as the tonight with black placid water. The land giant seas threatened to carry away the being of the marsh variety failed to soak breakwater . . . up the water . . . N 1931 Mar. 4 Travel by Rafts 5.5h e.s.t. (-1) Those families who declined to leave their water surrounded homes were forced D-57 to go about on rafts or in row boats. The water in some areas reached a depth of The New York Times six feet . . . Thurs., April 2, 1931 The New Haven Journal-Courier ... At Highland Light, Mass., a shift in Page 2, Cols. 2, 3 Fri., March 6, 1931 wind saved the Peaked Hills Coast Guard Page 20, Col. 1 station and four cottages at Ballston Beach from tumbling into the sea. The beach was battered incessantly from Tues- HIGH TIDES MENA CE NEW ENGLAND EASTERN COAST day night until this noon when the change WITH A HEA VY GALE BL OWING in wind was noted. The tide there was higher than anytime during the past ten STORM PASSES years BOSTON, April 1.-April rode in to New England on the crest of a northeaster 1931 Mar. 4 which tonight caused uneasiness along 5.5h e.s.t. (-1) shore for fear of damage by high tides. AF1 ER DAMAGE Three high tides are scheduled in eight- D-57 een hours. The first this noon ran a foot higher than the predicted stage, despite Millions Of Harm Done By High the fact that the wind was only just be- Tides Sweeping Far Ashore ginning to rise. As the day advanced the Upon Towns. gale increased . . . Representative Great Tidal Floodings of the North American Coastline 49 High Tides Wreck Summer waters and piers along the New England trict, Grays Harbor attempted today to coast causing damage estimated at thou- take stock of damage done by a great Home at Southampton sands of dollars. Scores of persons em- storm driven tide which flooded major por- ployed in Boston waterfront offices were tions of Aberdeen, Hoquiam and Cosmo- . . . Blinding sheets of rain swept the marooned during the peak period of the polis Sunday. streets of New York and its vicinity yester- tide and in Winthrop, flooded streets kept A survey of the business district this (lay, while high tides and a strong north- students in a school during the noon lunch morning indicated a loss in merchandise east wind caused damage along the north- period. and fixtures of between $50,000 and $100,- eastern coast of the country . . . At Truro on Cape Cod and along the 000. Flooded homes, street damage and New Hampshire coast in the Hampton road washouts will augment the total loss. . . . The Summer home of William F. Beach area, damage to cottages was re- The port of Grays'Harbor tidal gauge Ladd, member of the New York Stock ported. The summer cottage of Osborne measured the rise at 15.8 feet, four feet Exchange, at Southampton, L. I., was Ball of Boston at Truro tumbled into the above the predicted high tide mark and wrecked when a heavy sea undermined sea when the thundering surf undermined nearly a foot higher than any previous the house, which had been pounded by the eliff on which it stood. tide in history here . . . waves for several weeks. At high water time, about 12:30 p. in., the tide reached a height of 13.66 feet and the chief cause was declared to be . . .All along the Jersey coast bulkheads unofficially was reported to have reached the great tide, supplemented by the 90- were battered and Summer homes dam- a height of more than 15 feet. The normal mile southwest gale aged by the wind and tide . . . tide is 11 feet, four inches . . . ... Eastbound traffic was threatened again ... Trains on the North Shore division of ... In Boston the tide inundated the low this morning when another tide of over the Long Island Railroad were held up for lying piers of the Atlantic avenue section. 11 feet began backing water over the low- eighteen minutes by an open drawbridge The water seeped into the approaches at land road between Aberdeen and Monte- at Main Street, Flushing, which had been many of the famous old wharves, includ- sano. The series of 11-foot tides will con- opened to permit the passage of a tug and ing Central, India, Long and T., and many tinue until Thursday then could not be closed at once because trucks were stranded on piers. Perry boat of the wind and tide . . . slips were flooded and many passengers 1933 Dec.16 were delayed for a short time. until the 23.5h P-s.t. (+9) Tides Shatter Bulkheads. water receded. LONG BRANCH, N. J., April I (AP).- A sight that attracted much attention 63 Pounding waves, driven before a forty- was that of ships lifted almost to street five-mile northeast gale, shattered portions level by the rising waters. Meanwhile, of bulkheads today between here and crews worked vigorously to keep mooring Highlands, threatening hundreds of cot- ropes from snapping under the strain. , tages. A sudden shift of the wind to south All along the north and south Massa- before high tide, saved coast resorts from chusetts shores beach cottages were sur- greater damage . . . rounded with water and in many instances serious damage was done to the structures The San Francisco Examiner 1931 Apr. 2 by the beating of the surf. Wed., Aug. 22, 1 .934 4h e.s.t. (-22) For the first tinie since 1909, the town Page 1, Col. 4 of Nahant was isolated when the waters E-58 of Lynn harbor inundated the narrow pe- ninsula connecting the town with the mainland . . . -0- HUGE MYSTERY 1932 Nov. 27 15h e.s.t. (-10) The New Haven Journal-Courier 60 Thurs., Dec. 1, 1932 WAVES FLOOD Page 7, Cols. 7, 8 Huge Tide In Lo A. BEACHES The Oregon Daily Journal Mon., Dec. 18,1933 Boston Area Page 1, Col. 2 Forty-foot Water Walls Strike; Two-Story Apartment Swept Does Damage Coast Area From Foundations; No Wind Pounded by NEWPORT BEACH, Aug. 21.-(AP)- Water Rushes Over Roads A strangely acting Pacific Ocean, which And Shore Towns Are has been running waves 30 and 40 feet Rains, Tides high during the day, got out of bounds at Partly Submerged. high tide at 6:10 tonight and swept a two-story apartment building from its foundation and damaged other buildings. Boston, Nov. 30 (AP)-The highest tide Aberdeen, Dec. 18.-(AP)-While soggy Part of the city was inundated a few of the season today swept over break- skies continued to pour rain on this dis- feet 202-509 0 - 78 - 6 50 Strategic Role of Perigean Spring Tides, 1635-1976 . . . The waves threatened for a time to backing into Hoquiam streets through Tide gauge readings at Delake during cut a new channel across from the ocean sewers also ... the storm and high tides which ensued, to Newport Bay, ripping out a large cut were 15 feet Wednesday, when most dam- in the sand under the apartment building Storm Floods Neskowin; age was inflicted; 14 feet yesterday, and and across Central avenue . . . 12 feet today. A normal high tide reading Many Homes Damaged of 9.8 had been scheduled for today. . . . Portions of the Central avenue pave- Two lives are known to have been lost ment, the only connecting link between Neskowin, Jan. 4.-A heavy sea follow- in theaugmented. tides which hammered the city and the fashionable residential ing in the wake of a stormy night which the Oregon coast yesterday . . . section on Balboa Peninsula, were torn up, saw the wind reach a 75-mile-an-hour isolating for a time the residents on the velocity, flooded -Neskowin Tuesday morn- Resorts Flooded Again peninsula . . . ing, causing an estimated damage to homes Fog prevailed this morning at Astoria and buildings of from $50,000 to $75,000. and south as far as Wheeler. Nelscott re- ... No wind was reported and no explana- The turbulent sea water, which poured ported the sun shining. There was no wind tion for the unusual waves could be given into the city between 9 and 11:30 a. m., either point ... by weather officials wrecked the community kitchen, restau- at rant and warehouse and undermined the ... Damage Nvas less yesterday than dur. 1934 Aug. 24 Neskowin store. Neskowin apartments and ing Tuesday's storm, the tide being as Oh P.s.t. (-24) about 30 per cent of the homes were high, but not driven by a gale. The Tilla- 64 damaged mook beaches seemed to be harder hit ye- terday. but resorts again were flooded as 1939 Jan. 5 far south as Coos Bay 20h P.s.t. (+14) The Oregon Daily Journal F-68 Fri., Jan. 6, 1939 The New York Times Page 1, Col. 7 Wed., July 17, 1935 Page 14 L+, Col. 7 The Oregon Daily Journal Thurs., Jan. 5, 1939 Highest Seas in Years Page 1, Cols. 4, 7 Sea Unruly, Threaten Oak Beach, LJ ... Four women were injured, one perhaps fatally, Thursday noon near Seaside as ... OAK BEACH, L. I., July 16-One of the northern Oregon coast suffered a re- the highest seas in years, driven by a currence of attacks by huge swells accom- in (alifornia strong southeast wind for two days, pound- panying a high tide. The women were ed this village of twenty homes on the standing on a log when a swell picked it Three Homes Washed Into outer bar tonight, partly undermining the up and slammed it about Pacific; Others Damaged foundations of three cottages ... . . . 'XIarshfield, Jan. 5.-(AP)-A tide so . . . After 10 P. M., when high tide had high that many persons described it as a Long Beach, Cal., Jan. 6-(AP)-Three passed, the danger lessened. An automo- "tidal wave" moved houses, damaged small modest beach homes in the Alamitos pe- bile parking space on the beach was under craft and destroyed cabins in the Coos iiiiisiila area southeast of Belmont shore more than a foot of water. The waves had Bay area Thursday. were washed to sea today as giant break- dashed up within forty feet of the Coast Three houses were shifted on their ers, riding in from the Pacific on high tide Guard station here . . . foundations at Charleston and 15 cabins ground swells. crashed over the low sea wrecked ... wall . . . 1935 July 16 . . . High water forced the International ... The tide also bronght extensive dam- 23h e.s.t. (+46) Cedar Mill to shiat down here ... age to Manhattan and Hermosa beaches, where the highest water in years flowed 66 1939 Jan. 5 as far as 180 feet inland. 20h P.S.t. (+14) But the Alamitos peninsula below Long Beach was hardest hit. F-68 William E. Ross, boat builder there, said the tide was the worst in his 35 years' ex- perience. The Oregon Daily Journal Mrs. D. H. Collins stood by and watched Wed., Jan. 4,1939 The Oregon Daily Journal the tide carry her two-story dwelling into Page 2, Cols. 3-6 Fri., Jan. 6, 1939 the Pacific . . . . . . Aberdeen, Jan. 4.- (AP) -A sudden Page 1, Col. 4 . . . Alore than two feet of water roared halt in the southwest gale and rain del- . . . Apprehension felt regarding, another in at some Santa Monica bay points, uge which had hammered Grays Harbor high tide along the coast today was al- sweeping out the board walk along the for 48 hours until shortly before noon layed when the first community reporting, strand between Manhattan and Hermosa Tuesday temporarily ended a serious flood Nelscott, announced that the Lincoln beaches . . . threat in Aberdeen and Hoquiam. county crest had passed shortly before I Water had backed up through sewers in p. m. and that the extreme height of the (See also chapter 7.) parts of South Aberdeen and had just tide was 12 feet, two feet lower than that 1939 Jan. 5 started over the Chehalis river dikes in of yesterday. 20h P.s.t. (+14) two places, when the rain and wind halted It is believed this relative figure will and the high tide which had been pushed indicate the situation at other points, as F-68 four feet above its predicted 10Y2 foot the tide visitations yesterday were similar peak started to recede. Water had been at all of them. Representative Great Tidal Floodings of the North American Coastline 51 The New York Times who recently refused to let it be dredged ocean rainbows, today estimated damage Mon., April 22, 1940 out because anti-aircraft guns might have of a two-day Christmas beating by wind, Page 1, Col. 2 (Late City Ed.) to be rushed to the island overland in rain and high tides. event of war. Taft had the worst, with damage to the seawall that protects Pacifle street along Tip of Maine Is Isolated Siletz bay. Mountainous waves drenched GIANT WAVES LASH BOSTON. April 21-The northeast tip of that street, littered door yards, dug holes Maine and i6 7,000 residents were isolated in lawns and removed 200 yards of filling tonight as a 50-mile-an-hour northeaster back of the wall. sent a high surf pounding against New Nelseott reported damage to the seawall, NORTHEAST COAST England waterfront roads and property ... removal of stairways to beach from Over- took property and piling of logs on the An incoming tide, driven by the gale, ramp . . . flooded Quincy Shore Boulevard, main Hundreds Marooned in Towns highway between Boston and Cape Cod, Near Boston-Blizzard Hits for three miles and halted automobile Maine and Vermont traffic. Squantum, a Quincy peninsula of 1,500 residents and home of a Naval Reserve Angry Seas air base, was cut off temporarily as the tide swept across its only outgoing high- BOSTON, April 21-Scores of persons way . . . were marooned today and the coast was 1940 Apr. 21 still Batter hammered by mountainous waves whose 7h e.s.t. (-34) spray washed over Minot's Light, 114 feet high, and lifted surf to a height of 130 G-69 feet at Deer Island, as a northeast storm, continuing from yesterday, brought to New England heavy rain, sleet, hail, snow and California a gale blowing fifty-one miles an hour The Oregon Daily Journal LOS ANGELES, Dec. 27.-'(AP)-An Thurs., Dec. 26, 1940 angry ocean continued today to pummel Page 1, Col. 7 (Final Ed.) "a coastline, aim- A family of four and three other per portions of the Californi sons on Bassing's Island off Cohasset Har- ing its severest blows at the little town of bor fled to the mainland in dories when High Tide, Wind Redondo Beach. the sea swept over the island for the first A house and a liquor store, normally, time since the storm of '98, in which the even at highest tide, 50 feet away from the steamer Portland went down ... Create Damage water, were undermined in today's assault. Both collapsed. . . . The sea, lashed by the gale, sur- In Coast Region Two houses which were dropped into the mounted seawalls, undermined streets and surf yesterday by the gnawing action of flooded cellars. . . . A nine-foot tide Wednesday, pushed 25-foot combers and ground swells were Hundreds of persons were temporarily by a 50-mile-an-hour wind, damaged sea- being battered into debris today. , marooned in churches in Winthrop and walls and flooded Tillamook farms and the Damage estimates run as high as $250,- Beachmont by flooded streets, and services Coast highway. 000 . . . had to be called off tonight at one in Hammond, on the Columbia estuary be- Winthrop low Astoria, reported today that the tide 1940 Dec. 26 washed out the approach to the Hammond 17.5 P.s.t. (-87) . . . Several hundred Summer homes at beach road Wednesday, but that there was Hull were damaged by wind and sea. The no other damage 70 tide late tonight was 11 feet 3 inches, six inches higher than. the morning tide and 1940 Dec. 26 the continuing gale increased the floods 17.5h P.s.t. (-87) and coastal damage, driving waves and The Oregonian surf against cottages many yards from the 70 Sun., Dec. 29, 1940 ocean front ... Page 6, Col. 2 1940 Apr. 21 7h e.s.t. (-34) The Oregon Daily Journal Fri., Dec. 27, 1940 Coast Awaits G-69 Page 1, Cols. 1-4 (Final Ed.) New Storms The New York Times HIGH TIDES SAN FRANCISCO, Dec. 28 (AP)- Mon., April 22, 1940 The Pacific seaboard, battered by recent Page 34 L, Col. 1 SPECTACULAR ON storms, braced itself for more onslaughts of wind and rain Saturday night, while Shirley Gut, formerly a strait between OREGON COAST high water flooded many roadways . . . Winthrop and Deer Islands, but long since closed by storms, was nearly reopened by DELAKE, Dec. 27.-North Lincoln resi- Winter tides were at high peak. Salt the sea, to the concern of army engineers dents, under bright skies and a span of water stood so deep on highway 101 south 52 Strategic Role of Perigean Spring Tides, 1635-1976 of San Rafael that many cars were stalled, Thousands of New York commuters were age in Eastport alone was estimated un- and high-wheeled trucks were used to delayed in reaching work when high tides .--officially at $100,000. tow or push them to higher ground . . . stranded them in Long Island and New When the water flooded the Northern Jersey. Long Island Railroad service was Herring Company wharf at Eastport, five 1940 Dec. 26 discontinued between 8:50 and 11:25 A. M. women employes of the U. S. Customs and 17.5 P.s.t. (-87) over Jamaica Bay between Hamilton and Immigration offices in a three-story wharf Howard Beaches when the tides covered building were taken down ladders to 70 the railroad trestle. Trains between Long safety. Beach and Island Park were delayed. Tidewaters of the Machias River wash- The tide backing up into the Erie Rail- ed out the Maine Central railroad tracks road yard in Jersey City covered road at four places between Machias and East approaches to the ferry line with three Machias, interrupting travel from.Bangor feet of water, and for the first time in to Calais. Rails were torn up for a dis- eighteen years ferry service was suspended tance of 600 yards at one place. A paral- at 8:30 A. M., resuming at 10 o'clock. leling highway was damaged but remained Water rose more than two feet above the passable. ferry slips and flooded Pavonia Avenue, Reports of extensive damage to wharves, The New York Times stalling many buses and trucks. fishermen's "shops," and industrial plants Fri., Dec. 1, 1944 While the Central Railroad of New came from Cutler, Camden, Bar Harbor Page 25 L, Col. 1 Jersey said that it had had no difficulty in and other "downcast" points ... loading its ferryboats, high tides north of Sea Bright overflowed tracks at several 1945 Nov. 19 points, resulting in delayed service. 3.5h e.s.t. (-13) HIGH WINDS, TIDES The high tide in Jamaica Bay cut off vehicular traffic o. the C,.ss Bay Park- H-72 way and Rockaway Boulevard routes from LASH THE CITY AREA the peninsula to the mainland, which were flooded from 8 A. M. until noon . . . Third Wettest November Bows 1944 Nov. 28 Out With Gusts Hitting 57 9.5h e.s.t. (-69) The San Francisco Examiner Miles and Snow Flurries 71 Mon., Jan. 26, 1948 Page 1, Col. 7 Commuters Delayed as Tracks, Ferry Slips and Roads Are Tides Flood Flooded-Planes Grounded The Daily Kennebec Journal ... The third wettest November on record Augusta, Me. blustered to a close amid snow flurries Wed., Nov. 21, 1945 yesterday as winds reaching fifty-seven Page 1, Col. 8 Bay Area miles an hour swept the metropolitan area, disrupting railroad, ferry and air services. The tempestuous weather, the Weather Bureau predicted last night, would con- Record Tide, tinue in strong to gale strength until some time today . . . ... The wind velocity started to increase 70 Mph Gale, S.F. BOYDROWNS., about 9 A. M.. when it was measured at R OA DS BL 0 CKED 23 miles an hour, and ranged between 45 Heavy Snow and 50 miles an hour in, the afternoon, with gusts up to 57. It had subsided last night to 32 miles an hour and was expected Portland, Me., Nov. 20--(AP)- to range about there throughout the night A fierce southeast gale whipped An unprecedentedly high tide flooded por- tions of three Bay area counties yesterday . . . the Maine coast today causing and was blamed for the drowning of a . . . The sea was whipped into almost waterfront damage running into San Francisco boy . . . record tides along New England's coast, hundreds of thousands of dollars. causing damage estimated in the millions ... Small craft warnings were hoisted on of dollars. Cape Cod bore the brunt of the Sweeping tip the coast, the gale, which the Bay for northeasterly winds up to storm. Coast Guardsmen evacuated per- recorded wind gusts of 70 miles an hour thirty-five miles per hour due this morning. sons on Nantucket Sound from Falmouth here, drenched southwestern Maine ... to Chatham, and dozens of homes that FLOODS ROADS have withstood the September hurricane . . . In Machiasport, numerous sardine were wrecked. Provincetown reported boats, hauled up for the winter, were set The tide spilled onto several Marizi eleven-foot tides inland, the worst in forty adrift by the high tide. County roads, including Highway No. 1 at years. In New Bedford, floods crippled An estimated 28-foot tide at Eastport, Dolans Corner, south of Mill Valley, and several industrial plants. In many coastal on Passamaquoddy Bay, exceeded a preii- a service road between San Quentin and communities electric and telephone lines ous high there of 27.1 feet, moving build- San Rafael. Some autos stalled on the were down. Fishermen suffered large ings from their foundations and Wrecking latter. The water almost overlapped High- losses in gear. wharves and waterfront bulkheads. Dam- way 101 just south of San Rafael. Representative Great Tidal Floodings of the North American Coastline 53 In San Francisco, sewers backed up in ... A battery of pumps.worked throughout The Seattle Daily Times the south of Market area, flooding several the day yesterday to eliminate sea water Mon., Dec. 3,,1951 streets which rushed into the area affected by Page 13, Col. 2 the earth's subsidence. ... The tide rise, six feet eight inches, was More than 100 homes in a six-block- described by the Coast Guard as the high- square area of the district were flooded SP ills est due this year, although today's high following the third record high tide in Tide tide, at 10:52 a. m., will reach six feet three nights. seven inches . . . Tides of 7.2 feet swept through harbor area storm drain systems Tuesday night Over Bank Of 1948 Jan. 26 and sent water gushing through streets to 1h P.s.t. (-@-4) flood small homes with as much as 14 Duwami*sh inches of water . . . 74 Some automobiles were left in the A high tide of 12.7 feet spilled over the flooded streets and others were pushed or west bank of the Duwamish River about towed out of the path of the water. 9 o'clock this forenoon. Water inundated Each day since Monday, residents said, lawns of three residences in Riverside the tides sent water into the area between Drive, a foot deep near Webster Street. Seaside Blvd. and Water St. . . . Occupants said little damage resulted, and the water receded by noon. Another ... The piers at Berth 32 and Berth 33 on 12.6-foot tide is due about the same time The New York Times the harbor waterfront also were flooded tomorrow Wed., Oct. 19, 1949 by sea water during the high point of the Page 59, Col. 1 tide. 1951 Nov. 29 The flooding is basically due to the land 11h P.s.t. (+36) Jersey Shore Streets Flooded subsidence in the harbor area, although failure of some sandbag dikes and the 77 LONG BRANCH, N. I., Oct. 18 (AP)- plugging of pumps in the area also are Rising tides and high waves pounded blamed for the condition ... beaches and flooded some streets in the Shore area tonight. 1951 July 18 Thirty-foot-bigh waves were reported at 1h P.s.f. (-20) The San Francisco Chronicle Seabright, where water inundated parts of Sat., Dec. 29, 1951 Ocean Avenue six to eight inches deep. 76 Page 1, Cols. 7, 8 (Final Ed.) Police said that not much damage was done but that Ocean Avenue was expected to be closed to traffic for about twenty- Bay Area Gets a Soaking four hours. 1949 Oct. 21 13h e.s.t. (-6) High-Tides Flood Marin; 75 The Seattle Daily Times Valley Situation Eases Mon., Dec. 3, 1951 Page 16, Col. 6 Except for I the few dozen Bay Area families, whose homes have been flooded, New Storm Causes this will be a wonderful week end to stay home. Flood Damage In The storm so far has been persistent, The Los Angeles Times but relatively benign. Heavy rainfall has Thurs., July 19, 1951 North California been general, but temperatures have been Page 1, Col. 1 (Final Ed.) mild for this time of year, even in the mountains, and there have been no de- SAN FRANCISCO, Dec. 3.-(AP)-A structive winds. new storm, on the heels of one which Tide Floods closed the Golden Gate Bridge Saturday High tides and a break in the dike north for three hours, caused flood damage in of San Rafael flooded Railroad avenue Northern California today . . . which leads to fhe San Francisco Bay Airport. The tide rose 6.9 feet above mean Water stood three feet deep in sections low tide. Long Beach; of -Sonoma, 35 miles north of San Fran- The road to Mill Valley was under water eisco, A dozen ra.,hes 1. Sonoma County at Dlan's Corners, So was Highway 101 were isolated. Eight schools were closed. South of Richardson's Bridge during the Flood waters entered Burlingame, 15 miles high tide. Boat Saves 9 South of San Francisco, and marooned people in stores . . . 1951 Dec, 28 ... Two expectant mothers and five chil- 9.5h P.s.t. (+11) dren were among a number of persons 1951 Nov. 29 evacuated by lifeguard boats from homes 11h P.s.t. (+36) 78 flooded by sea water at record high tide last night in the Long Beach Harbor area. 77 54 Strategic Role of Perigean Spring Tides, 1635-1976 The New York Times ramps, while the rejected cars went to Fri., Oct. 23, 1953 Manhattan by bridges and tunnels. High Page 1, Cots. 1, 2 (Late Ed.) water also hampered commuters on the Lackawanna ferryboats and Hudson and Manhattan tube trains in Hoboken. Lower Manhattan Wetted by Tide 150 in Jersey Evacuated The police and Coast Guardsmen evacu- ated a dozen residents and 150 employees As Full Moon Pays Us Close Call of oyster-shucking sheds when the surf invaded Wildwood, N. J. Two schools in Union Beach, N. J., and one in At- lantic City were closed for part of yester- Early commuters in downtown New incidence of perigee with the beginning day by flood conditions. Five square blocks York found the water curb-deep in a few of a full moon-the moment when the of Atlantic City were flooded by Absecon spots off South and West Streets yesterday earth, the sun and the moon are in a Inlet backing up in storm sewers and morning. A high perigee tide, possibly straight line so both the sun's and the trolley service was disrupted there. aided by the winds, had pushed sea water moon's gravitational pulls work together Artists living in converted sail-lofts on up into lower -Manhattan storm sewers on the oceans---occurs twice each year, the Boston wharves had to evacuate yes- and out into the streets ... Joseph M. Chamberlain of the Hayden terday morning with hip boots or in row- Planetarium explained boats as salt water came over the sea wall. A few cellars were flooded downtown There were overflowing tides all along the and in coastal Brooklyn, and traffic was ... The Coast and Geodetic Survey which Maine coast, but that is an old story there. delayed by deep water in several New calculates for each day a tide forecast, The United States Coast and Geodetic Jersey points. But there was no report of had placed the tide yesterday morning at Survey predicted that the great tides damage from the unusual tide . . . the Battery at 5.9 feet above the mean would taper off today. This part of the low water level, which is the "normal" coast was spared much damage, the ocean- ... The high tide at 7:34 yesterday morn- low water level for the day. Low water ographers said, because we did not have ing coincided with the full moon at 7:56 yesterday was 0.8 feet below normal, so strong east winds A. M. and came only a few hours after the range of the tide yesterday morning the moment when the moon was in perigee was 6.7 feet, a figure far above average, 1953 Oct. 21 -its closest approach to the earth. the agency reported . . . 21.5h e.s.t. (-21) The moon travels an irregular path as it 1953 Oct. 21 79 moves around the earth. At perigee, the 21.5h e.s.t. (-21) closest point, when the moon's gravita- tional pull on the oceans exerts its great- est influence, the tides are high. The co- 79 The New York Times Thurs., April 12, 1956 The New York Times strongest gravitational pullon the oceans. Page 63 L+, Col. 2 Sat., Oct. 24, 1953 The full moon entered perigee on Thurs- Page 9, Cots. 5, 6 day morning, while the semimonthly HIGH TIDES CAUSING spring tide occurred yesterday. The Army Corps of Engineers meas- FLOODS IN NORFOLK ured high tide at 8:22 A. M. yesterday off TIDE AGAIN SPILLS Fort Hamilton at the Narrows at 8.2 feet. This was 2 feet above average and I one- NORFOLK, Va., April,11 (AP)-The half foot above high tide on Thursday highest tides in twenty years started flash INTO CITY STREETS morning. floods in low-lying Hampton Roads areas tonight and isolated two communities. Water Backs Up Drains The rising water halted ferry service across Hampton Roads, blocked highways, Floods Caused by a Full Moon High water in the harbor backed up forced closing of the James River Bridge storm drains into Grand Street; West at Newport News and seriously interfered Close to Earth Disrupt Rail Broadway and West and Barclay Streets. with coastal shipping. and Ferryboat Service Between one and two feet of water lay in The towns of Poquoson and Willoughby the cellars of 200 homes along Jamaica were cut off. Bay in Hamilton Beach and Howard The Army dispatched a fleet of amphibi- For the second day, a perigee spring tide Beach in southern Queens. The Long ous vehicles from Fort Eustis on an emer- caused tidal waters to overflow some city Island Rail Road could not run trains to gency mission to restore communications streets and low acres in the suburbs. those stations until 10:20 A. M. because of with them. In addition to a few downtown Man- flooded tracks. The floods were precipitated by strong hattan streets, the water affected areas The Long Beach Bridge to Island Park, northeast winds that raged up to seventy along the New Jersey coast, both shores of L. 1. was closed at 8 A. M. as Reynolds miles per hour in gusts ... Long Island and occasional points along Channel overflowed the northern approach the New England coastline as far as East- road 1956 Apr. 13 port,'Me. 7.5h e.s.t. (+ 115) A perigee spring tide occurs twice every . . . Ferryboats of the Erie Railroad year, when the full or new moon (a spring floated sohigh above their slips in Jersey tide) happens to be nearest to the earth City, N. J. that no automobiles could 80 (Alternate) (the point of perigee). At this time both board until 11:25 A. M. Commuters on sun and moon simultaneously exert their foot, however, embarked by using upper N_ Representative Great Tidal Floodings of the North American Coastline 55 The Los Angeles Times Mayor Cecil Gunthorp telegraphed Gov. N. H., were flooded, but damage was less Tues., Feb. 4, 1958 Knight that "the City Council has declared than feared. Part 1, Page 1, Col. 3 a local emergency, wherein all cash re- Revere street in Winthrop and Wessa- serves have been used and financial as- gussett road in Weymouth were among in- sistance is needed." undated thoroughfares between 8 and 10 Under Knight's proclamation, the State p.m. when the seasonably high tides were Tide, Surf Hit will provide aid ... pushed three feet higher by the storm. 1958 Feb. 4 19.5 P.s;t. (+39) Water on T Wharf 81 During the storm evening tides in Bos- San Diego Bay ton ran several feet higher than normal. More than 50 residents of apartments on T Wharf were marooned when the. tides swept over wharf stringers. Community Fishing boats tied up to the wharf, and The Boston Herald at adjacent wharfs were at doorstep level By a Times Correspondent Wed., April 2, 1958 while the tides were high. Page 1, Cols. 6-8 (Late City Ed.) A number of automobiles parked on the IMPERIAL BEACH, Feb. 3-High tides wharf were also marooned by the excep- and pounding surf smashed at homes and tiona Ily high tides and some of them had the boardwalk at the height of today's Giant Waves, 82-mph their electrical systems soaked as high storm, creating an emergency condition winds swept the water across the wharf that led to proclamation by Gov. Knight of Waves Lash Coast Cape planking . . . a state of disaster in this South San Diego Bay community. 1958 Apr. 3 At least four families -were prepared to A roaring northeast storm at sea sent 19h e.s.t. (-8) evacuate their ocean-front homes. One was wind,,, up to 82 miles an hour through Nan- partly undermined as the boardwalk in tucket last night and pounded waves 82 front collapsed. against the Winthrop sea wall that tow- City crews rushed truck-loads of rock ered 50 to 75 feet into the air. The Boston Herald and sand to the beach front in an effort to Low roads in several coastal communi- Thurs., April 3, 1958 protect property. ties between Chatham and. Portsmouth, Page 1, Col. 3 (Late City Ed.) The Los Angeles Times Wed., Feb. 5, 1958 2 Big Tides Part 1, Page 2, Cols. 4, 5 Rip Walls H*Igh T*1des Batter at Main Roads The 18th northeast storm since Decem- Southland Coast Areas ber kept hammering at New England last night, causing coastal damage from tides four feet above normal that marooned High tides, lashed by the same Pacific caused the flooding. City crews piled sand- communities and smashed waterfront storm that brought heavy rains to the bags atop the seawall in preparation for a property twice in one day. Southland, battered at Southern California similar tide peak this morning. Again at 9 o'clock last night high tides coasts yesterday. In Seal Beach, bulldozers piled up an thrashed exposed locations, casting up At Oxnard Beach, northwest of Port 8-foot sand dike along Seal Way east of more sand, rock, sections of cottages, fish- Hueneme, Navy helicopter and crash-boat Municipal Pier to guard a row of apart- ing and lobster gear and other debris. The crews reported they failed to find the body ment houses. unusually high morning tide was whipped of a 17-year-old Santa Paula girl who was In San Diego County, work crews labor- by 70-mile-an-hour winds. washed into the sea late Monday. The ed in a rainstorm to pile rocks along a teen-ager, Judith Lou Nasalroad, was section of Imperial Beach waterfront Nahant Isolcited caught by a huge wave while walking on where four homes were undermined by I the beach. The tumbling waves swept her high tides Monday. Gov. Knight declared Nahant again was isolated as Lynn into the sea. the beach front a disaster area to make Shore Drive, leading to this town from On the Alamitos Bay Peninsula near -State funds available to work crews . . . Lynn and the only means of getting to Long Beach, two feet of salt water dam- Nahant, was under three feet of water for aged lawns from 56th to 59th Place along 1958 Feb. 4 a second time at 9 p.m. the bayfront. Crews blocked off Ocean 19.5h P.s.t. (+39) . Nearly 100 families were marooned in Blvd. at 50th Place after a high tide their homes on Surfside and Beach roads pushed water over a 30-inch cement sea- 81 in Lynn by last night's high tide. wall. Water again was licking the sides of A U.S. Coast and Geodetic Survey team the Metropolitan Police station and the said a 7.1-foot peak tide at 9:50 a.m. amusement stands on Revere Beach Boule- 56 Strategic Role of Perigean Spring Tides, 1635-1976 vard, which was closed to traffic, and was The New York Times gushing downward into Ocean avenue, in Wed., Mar. 7,1962 the rear of the beach area. Page 1, Cols. 2, 3 (Late City Ed.) Winthrop Shore drive was closed and 400 families in the Point Shirley s ti of Winthrop were marooned, as were more in the Beachmont area of Revermea-Y Snow, Rain,'Gales, Tides 1958 Apr. 3 19h e.s.t. (-8) Lash Mid-Atlantic States 82 The New York Times A savage storm lashed the mid-Atlantic Railroad and ferry travel was hampered Wed., Dec. 30,1959 states with snow, rain, gales and high in New Jersey and Long Island. A Hudson Page 6, Col. 4 tides yesterday from Virginia into New and Manhattan Railroad train with 494 England. At least nine persons were killed passengers, many of them standing, was and six were missing last night. stalled for more than three hours at Flooding forced thousands of persons Kearny, N. J., by the flooding of the NEW ENGLAND HIT out of their homes and electricity was cut Passaic River . . . off from 85,000 users. The damage in the Atlantic City area alone was estimated at 1962 Mar. 6 BY SAVAGE STORM more than $1,000,000 ... 4.5h e.s.t. 31 min.) ... winds up to sixty miles an hour roared in between 2 P. M. and 2:50 P. M. J-85 Near-Record Tides Strand Scores The Weather Bureau warned that high (See also chapter 7.) winds would continue today, bringing tides three to five feet above normal and caus- BOSTON, Dec. 29 (UPI)-A savage ing new flooding of low-lying areas. storm swept into New England from the Midwest today. Carrying snow, sleet and rain, it churned up the highest tides in The Los Angeles Times 108 years and stranded hundreds of per- Fri., March 6, 1970 sons. Page 10, Cols. 1, 2 Boston harbor's tide rose about two and a half feet above normal. Wind-lashed WINDS, HIGH TIDES breakers surged over beaches and seawalls on the highest tide since 1851 when an April storm carried away a stone light- house. The unofficial reading by the Coast and Geodetic Survey was 14.3 feet above mean Two Beach Areas low tide as compared with the 108-year- old record of fifteen feet. Huge seas, born of gale-lashed winds, pounded the coast and inundated low sea- side areas. Roads and cellars were flooded. Pounded by Surf Two bridges in Maine were awash and telephone and power lines were knocked Two sections of the Orange County smashed it into splinters. out. coastline suffered heavy damage Thursday Breakers then chopped away beach sand Boats Rescue 300 morning from a combined attack by high and sloshed against the foundations of tides and storm winds. several residences . . . Three Coast Guard boats rescued 300 Seawalls valued at more than $75,000 men, women and children from flooded were battered down by waves which then Anticipating another high tide of homes in Hull on Massachusetts' south chewed at the foundations of several lux- about 6.4 feet this morning, residents or- shore. ury homes on the shores of Capistrano dered an emergency haul of rocks and The sea surged over two bridges at Beach. boulders to replace the seawall. Kennebunkport, Me., marooning some At Newport Beach, heavy surf again Orange County Weather Central said, eighty families. Two feet of water covered took a mile-long bite of sand from an area however, Thursday's strong winds should the bridges but officials said the families of which the pier is the center, and threat- be diminished by today . . . were in no danger. ened to undermine lifeguard headquarters at the foot of the pier ... 1970 Mar. 6 1959 Dec. 29 18h P.s.t. (-32) 5h e.s.t. (-18) . . . High tide, cresting at 6.3 feet just (See also chapter 7.) before 8 a.m. Thursday, was pushed by 92 westerly winds of 25 to 30 m.p.h. Heavy 1-83e surf at 6pistrano Beach pounded against several hundred feet of wooden seawall protecting homes on Beach Road and Representative Great Tidal Floodings of the North American Coastline 57 The Virginian-Pilot towns before spreading slowly across the water a foot deep throughout town. Norfolk, Va. rest of the state . . . Flooding caused by the tide and winds Sat., March 27, 1971 also was reported at nearby Raymond and ... The famed pier at Old Orchard Beach, South Bend. Police said water reached Page 1, Cols. 2-4 for example, gave way before the rolling depths of four feet in the streets of the ... The season-mocking snowstorm which sea. The large arcade section at the end two communities. No injuries were re- ,ushered in the sixth day of spring for of the pier was torn away and the wreck- ported. much of the Atlantic Seaboard pushed age washed up on the beach. tides above normal and plunged thermom- The touchy period caLe between 2 and eters below average Friday. In Kennebunk, selectmen will seek state 3 p.m. at the peak of the high tide when Tides crested at Sewells Point at 9 p.m. aid for what they describe as a disaster winds of 75 miles per hour were reported at 6 feet, 2.8 feet above normal and the area. at Seaside. highest since the Ash Wednesday storm About 30 families were evacuated along of 1962, the weatherman said. Kennebunk Beach and in the Great Hill The wind-caused flooding at Tokeland High tide at Virginia Beach measured section near the beach. Severe flooding pushed a large trailer house out into a 7.6 feet, or 4 feet above normal. washed out roads, and high seas crushed a street and washed another house off its Willoughby and Ocean View appeared portion of the granite and wood sea wall foundation. hardest hit by the wind-driven tides, al- along the Kennebunk beaches. Waves breaking over the.seawall near though scattered flooding was reported A couple was rescued from their Kenne- the general store and post office threw logs throughout the area from Colonial Place bunk Beach home after surf began pour- against the store and littered the road in Norfolk to Wolfsnare Plantation in ing through the front windows . . . with rocks, driftwood and debris. Virginia Beach. 1972 Feb. 16 1973 Dec. 10 Water was knee-deep in the parking lot 4.5h e.s.t. (+67) 4.5h P.s.t. (+21) of the Quality Court Motel at Willoughby Spit. The wooden pier at Virginia Beach 96 M-98W reportedly suffered damage . . . ... Norfolk police said the worst flooding Friday occurred at Ocean View, on May- flower Road in Colonial Place, Olney Road, West, Main Street, Boush Street, and The Los Angeles Times Mowbray Arch. The 7900 block of Hamp- Wed., Jan. 9,1974 (CC Ed.) ton Boulevard was impassable for a time Part 1, Page 1, Cols. 2, 3 because of high water, police reported ... The Oregonian 1971 Mar. 26 Wed., Dec. 12,1973 9h e.s.t. (-10) Page 24, 3M, Cols. 4, 5 Giant Waves Pound L-93e Tidewaters flood Southland Coast, Maine Sunday Telegram Washington towns; Undermine Beach Homes Portland, Me.-Final Ed. Sandbag Barriers Erected Sun., Feb. 20, 1972 winds to ease off to Ward Off Tidal Assault. Page 1, Col. 3 Giant wind-driven waves riding on surg- A wild northeast blizzard, with snow Strong coastal winds Tuesday blew ing high tides battered the Southern Cali- taking a back seat to high tides and winds, water from a near-record 16-foot tide over fornia coast Tuesday, damaging homes and wreaked havoc on southern Maine coastal the seawall at Tokeland, Wash., leaving flooding nearby areas. Occupants of many beachfront homes from Santa Barbara to San Clemente The Los Angeles Times Fri., April 23, 1971 Part 1, Page 3, Cols. 1, 2 erected sandbag barriers throughout the day in preparation for the next high tide Heavy Surf, Tides and Winds Batter at 10:08 a.m. today. The wave and tidal assault came as Oxnard Shores Homes rainfall from a five-day storm tapered off after dropping 7.69 inches in the Los A combination of unusually high tides, the ocean. Angeles -Civic Center. heavy surf and strong winds Thursday The damage left the six homes, valued caused considerable damage to six expen- at between $60,000 and $80,000, either In Orange County, supervisors proclaim- sive homes along a three block stretch of hanging over a weak, sandy cliff or strand- ed a "local emergency" for wave-battered Mandalay Beach Road at Oxnard Shores, ed on pilings that have "only 5 feet of coastline sections. north of Oxnard Beach. sand to go before there's nothing to hold them up," Police Capt. Jack Snyder said (See also chapter 7.) According to officials, the crescent- . . . 1974 Jan. 8 shaped beach area, which is annually 1971 Apr. 24 4h P.s.t. (-2) pounded by the wind and sea, has been 3h P.s.t. (-34) under its latest, and perhaps greatest, on- N-99 slanght for several days. Thursday, a section of beach 60 feet 94 wide and 12 feet deep disappeared into Chapter 2. The Impact of Perigean Spring Tides Upon Representative Events in American Nautical History Without pragmatically asserting a total and absolute The quantitative information provided by accompany- causality of relationships in any of the following circum- ing eyewitness accounts, when coupled with supporting stances, there is, nevertheless, ample justification for the data from modern tide tables, point realistically to the fact fact that, on certain occasions, perigean spring tides have that occurrences of this particular type involving perigean played a significant role in determining or altering the spring tides do not necessarily require the alignment of course of nautical history. A few episodes researched from perigee and syzygy within the close limits of agreement American naval annals will serve to indicate the strategic in time possessed by the cases of severe coastal flooding importance of these tides. Since the increases in ampli- previously described. tude ' associated with these tides (and winds) may occur in rather widely varying degree, the influences of such The Fate of the Frigate. Trumbull amplitude variations can be either detrimental or desir- At the outset of the Revolutionary War, the American able. colonies had no organized navy, and much of the burden Perigean Spring Tides as an of the war effort was bome by privateers and by ships provided by the individual new States. However, limited Aid to Navigation funds were shortly authorized by the Continental Con- gress for the establishment of a small complement of Numerous cases have been mentioned in the preceding Federal Navy vessels, and existing shipyards, along the chapter in which destructive coastal flooding resulted coast were given the task of constructing these new ships from perigean spring tides that occurred in conjunction of war. with strong onshore winds. Additional instances also can Early in the year 1776, at the Connecticut River be cited in which moderate but navigationally important increments in tidal heights have had a direct impact upon (Brainerd Quarry) shipyard of John Cotton in East Mid- historical events. These lesser increments were provided by dletown, Chatham Township (then consisting of several perigean spring tides reinforced by light but steady on- parishes ranging from present-day Portland to East Hamp- shore winds, generally insufficient to cause flooding. Ap- ton), work was started on the frigate Trumbull of 28 propriate examples are given below. guns. L Iofting was begun near the end of February ' and 'The term "amplitude" is sometimes used in this volume in a the ship was launched on September 5.' The ensuing general physical sense to designate the magnitude of either a positive activity can only be described as involving the ultimate in or negative displacement of the tide with respect to mean water misplanniing as well as a classic blunder in shipbuilding. level, in preference to the more restrictive words "rise" or "fall" of In the lack of present-day information concerning the the tides. The expression "increased amplitude" collectively allows for the algebraic increment in both the high and low waters asso- exact outboard profile of this ship, the body plans used in ciated with perigean spring tides. construction of the Trumbull can only be assumed to be Strictly defined in tidal nomenclature, the value of the amplitude those specified for the official design of a Continental is equivalent to one-half the range (see fig. 6 in appendix), and may differ quantitatively from either the rise or fall (the vertical frigate.' If this conjecture is correct, the Trumbull had a displacement of the surface of the sea respectively above or below full-load draft of IS ft 4 in. which, allowing for an addi- the local chart datum) at times of high or low water. The word tional navigational safety factor of 2-3 ft of keel clear- amplitude is also used as a mathematical coefficient (i.e., "ampli- tude of a constituent") in the harmonic analysis of tides. ance, was still in excess of the minimum water depth at 59 60 Strategic Role of Perigean Spring Tides, 1635-1976 the mouth of the Connecticut River at any ordinary high until the publication date of the chart is given as 5.4 ft. tide. The Trumbull ran aground on a bar b From modem data, the mean range of ordinary spring The original of the accompanying early chart of the tides at Saybrook'jetty at the mouth of the Connecticut mouth of the Connecticut River (fig. 4), titled "Captain River is 4.2 ft, and that at Old Saybrook Point is 3.8 ft. Parker's Chart of Saybrook Barr" [sic], with engraving With consideration to the preceding ship-draft and done by Abel Buell, Connecticut's first engraver, is in the hydrographic sounding figures, together with others to be possession of the Connecticut Historical Society. A helio- discussed later in this same section, the Trumbull obvi- type copy made from a very exact tracing of the fragile ously could not get off the rivermouth bar on which she chart (from which published version fig. 4 was repro- had grounded at any ordinary high waters (including duced) occurs in "The Public Records of the Colony of spring tides). As a result, she was prevented from taking 11 4 Connecticut, May 1768-May 1772. any part in naval actions throughout the entire early por The date printed on Captain Abner Parker's chart is tion of the Revolutionary War. 17 7 1. However, information provided by the Connecticut Although those in,@olved were repeatedly prodded by Historical Society and published in a professional paper admonishments from militarily interested parties in Con- of the society ' dealing with this early chartmaker reveals gress' and in Connecticut,' including an appeal to presi- that the Governor's House shown on the chart was not dent-to-be John Adams (at that time delegate to the actually built until 1784. Accordingly, the chart must have Continental Congress" from Massachusetts and member of been several times revised and updated from its original the Board of War), all efforts to get the Trumbull off the publication date, which the Connecticut Historical Society bar were without success. An indication of the existing states could not have been earlier than 1784.' state of despair and of the fact that the shoalness of the A further search reveals that no earlier British or Amer- water constituted the principal problem to be overcome ican chart exists in the Geography and Map Division of showed in this same letter from William Vernon to John the Library of Congress, and even the contemporary Adams, dated December 17, 1778. The letter quoted the Atlantic Neptune charts do not extend west of Newport, opinion of a New England mariner aspiring to command R.I., in this sectionlof Long Island Sound. the new frigate, one Captain Hinman. This authority With these explanatory comments, it may safely be as- claimed that only by the use of a "camel" (the name sumed that Abner Parker's chart provides an accurate given to a type of special flotation gear) was there appar- and at least very representative contemporary indication ently any hope of clearing the bar.' With the Trumbull of water depths in the vicinity of Saybrook Bar during the a firm captive within the Connecticut River, the vessel period under discussion. On this chart, the shallowest was in danger of "sitting out" the entire Revolutionary water depth in the principal navigation channel at the War. mouth of the Connecticut River is given as 6-8 ft, with On August 11, 1779, an unusually high water occurred that over the closely adjoining bars being only 4-7 ft. associated with a perigean spring tide. The tide was pro- The earliest available nautical chart (fig. 5) for which duced by a close alignment (difference, - 20 hours) be- detailed hydrographic soundings were made of this river tween perigee and syzygy, with the mean incidence of the mouth and its associated ban by the Coast Survey (the two phenomena taking place at approximately 7: 00 a.m., forerunner of the present National Ocean Survey) is 75' W.-meridian time, on that date. The resulting peri- chart No. 360 (1st edition) of the Connecticut River, gean spring tide could, of course, have been enhanced by published in 1853. Soundings on this chart (figs. 6-7) sustained, strong, onshore winds. Although contemporary clearly show that the least depth of water anywhere weather records from this immediate vicinity are lacking, directly along the designated ship channel or over im- a diary account of local weather conditions at New mediately adjacent ban is 5V2-7 ft, which is quite similar Haven, Conn., during the Revolutionary War period, to that shown on Captain Parker's chart 79 years later. preserved in the vault of the National Climatic Center, On-the Coast Survey chart, the height of mean low water NOAA, indicates that the wind conditions were calm above the chart plane of reference is 0.6 ft, and the rise there on this date in 1779. This would tend to indicate the Of highest tide observed above this plane of reference up presence of high atmospheric pressure over the area. Simi- lar contemporary records show that no strong hydrologi- Considerable confusion seems to exist in modern reference cal runoff from recent severe rainfall, or melting snow or sources concerning whether the Trumbull actually grounded or ice, occurred to swell the height of the waters at the river was simply blocked by the rivermouth bar; however, compare the direct contemporary quotations in references 14 and 16 which follow. mouth. _7 7 - ---- ---- Otlic VENOR 'kh HN 14 YN" `7@ "At uw A, N k 4 1_441" It pp, t-, @# , ,2- ir, f'_ I 4 y 4 lk 3F 'WIN'i n, Q, 5 N* MTO I n:0 k", w @@% , .' '- '' -, p K'Q21TRIA I i @3 5Y 6F 'igx C JR, iWr :!2 RI 54V V"@ W'7 NO\, gr Jr, 51 ki I, I- -II - , 31 V, 4 A IF 311 3 @A 61 $p 2F 3F ge W , " - 11 j kons 3r , 5 zi xv j @tll Z, Courtesy of Library of Congress and the Connecticut Historical Society Fic;URE 4.-Captain Abner Parker's chart of Saybrook Barr [sic] at the mouth of the Connecticut River, engraved by Abel Buell and dated 1771, but probably revised to at least 1784 (see text). 62 Strategic Role of Perigean Spring Tides, 1635-1976 Existing historical accounts" reveal that, precisely on A book titled The Record of Connecticut Men in the this day of welling perigean spring tides, the Trumbull Military and Naval Service During the War of the Rev- cleared the bar. In view of Captain Hinman's earlier state- olution, 1775-1783 gives both support as well as several ment, it is quite probable, although only permissible by clues to this supposition that the Trumbull's stranding and inference-lacking any detailed account of the actual resulting shore problems with, and desertions by, the floating-out procedure-that the process of clearing the ship's crew lasted from the latter portions of the year bar was aided by supplementary flotation gear. Of greater 1776 to the early portion of 1779: certainty, with consideration to the exact agreement be- cc * *. Of 109 officers and crew variously assigned to tween the dates of ship flotation and perigee-syzygy, is the the Trurn- bull between Sept. 15, 1776 and Jan. 22, 1778, fact that the sensible increase in tide height produced by some 35 deserted, 'run' or left the ship without liberty this very close alignment between perigee and syzygy was mostly in July 1777, but some in Aug. 1777 and lasting a definite contributing factor in release of the ship. until Feb. 9, 1778. . ." " Due care must be exercised in substantiating this asser- ". . . Its first Captain, Dudley Saltonstall, being trans- tion. Conceding, from the quantitative evidence later to ferred to the Warren, Capt., J. Nicholson of Penn., took be presented, that ordinary spring tides were not adequate command in latter part of 1779. to this purpose (very nearly 60 cases of ordinary spring One official mention of the Trumbull's stranding, and tides having occurred during the total of 1,071 days the activities of the British fleet in the area, occurs in the since ship launching) it must fairly be noted that, in the Colonial Records of Connecticut: cycle of astronomical events, 13 cases of perigean spring ". . . During. 1778, Deshon of the Boston [Navy] tides also had been passed over during that same 3-year Board spent much time in Conn. attending to the naval period. This circumstance requires further evaluation. business of that state. This had to do chiefly with freeing Following the ship's original September 5, 1776 launch- the Trumbull frigate from a sandbar upon which she had ing date, completion of the rigging and top hamper would grounded. During the same year Vernon was for a time undoubtedly have taken some months, and considerable at Providence endeavoring to get to sea the Continental additional fitting time would have been required before vessels which the British had blockaded in that port ' * *" 14 the vessel was ready to proceed to New London for load- Various resolutions passed by the Council of Safety or ing of stores. The continuous slippage of ship-readiness the Board of War during the period 1778-1779 also pro- dates.through delays caused by such factors as nonavail- vide a chronological account of certain postlaunching ability of spars, desertions among the ship's crew, change activities in connection with the frigate Trumbull and in- of command, etc., indicated in the documents quoted dicate that, as of January 1778, the Trumbull had not below, can readily account for the fact that possible other yet been outfitted with spars: opportunities offered by any of these 13 previous perigean "At a Meeting of the Governor and Council of Safety spring tides for a tide-assisted escape from the sandbar Holden at Hartford in and for the State of Conn. on the were not used. 29th day of Jan. A. D. 1778. Voted-That an order be Also at issue is the exact date on which the Trumbull drawn on the committee of Pay-Table to draw an order first made the trip from Chatham down the Connecticut on the Treasurer for the sum of E250, in favour of Capt. River and ran aground on a sandbar at the mouth. Al- John Cotton for procuring spars for the use of this though no discoverable record covering this precise episode State to be in account. exists, experts on C ,onnecticut's history seem to feel that, Ordered delivered Jan. 29, 1778." Same "on the 25th Day of Feb. 1778. because of the pressing need for the frigate's services, the "W Ihereas the Hon"e Congress of the United States journey down river and the subsequent stranding occurred have authorized and requested his Excellency the Gov- during the late autumn of this same year." Of consider- ernor and this Board to cause the *continental frigate able significance in this connecti n is the earliest date on Trumbull, now lying near the mouth of the river Connec- which river ice might interfere with the vessel's passage ticut and there detained by reason of an apprehended downstream. Years of climatological records show that at difficulty of getting over a bar of sand, call'd Say Brook least the upper reaches of the Connecticut River are cus- Bar, to be removed and got over said bar ready to proceed tomarily frozen over during some portions of, and occa- to sea &c. Therefore, sionally most of the time between, November and "'Resolved and ordered by his Excellency the Governor March. and this Board, That Capt. John Cotton of Middletown Impact of Perigean Spring Tides on American Nautical History 63 =Z 'N; 110 t L' ip- - V "k %L W, t Q-1 7" ."Zw. h Ni 11 h4' % Ij 0 M 0 V 11, 11F CONNECTICUT It I NVE R SURVEY OF THE COAST OF THE UNITED STATES v, 0 J FIGURE 5.-U.S. Coast Survey Chart No. 360 (Ist ed.) of the mouth of the Connecticut River, published in 1853, including basic tidal data. Boxed areas are enlarged in figs. 6 and 7. 64 Strategic Role of Perigean Spring Tides, 1635-1976 .......... .... ... . ....... wJil.s ...... 1@2 ........ ... ..... @7: 4 4 . . . . . . . 42 41 '01 4 . ......... ............... 4i ........ .. S 37L F . ..... ..... .. . ....... ....... J q ... .. ..... .-F .. ........... .. ........... . ..... ... 3 3 007 ...... . . . . .. . . . . . ..... .................. ... ..... ... I........ 44,"L@ 7PO . . . . .-- ---- House,: V. e. e -sea tt 811!ryt. V A l* sil I N 57MR: 0. FIGURE 6.-Enlarged section of the U.S. Coast Survey Chart No. 360 (Ist ed.), showing soundings at the mouth of the Connecticut River between Fort Fenwick and Lynde's Point made in 1849 and 185 1. Impact of Perigean Spring Tides on American Nautical History 65 N t.02 . ...... .... TON . ..... iYed. Agbt Ts. 12 the Se.1 Mile* -4 ... 62 ......... ... . .. ........ )4 i4. 7-- 4 CY4 . .... ..... ... . . .......... ............... ..7 .(V4 "S2. ... ......... ...... ..... -42.. ............ 4 7A 1:32, :j q Z 32 31 3:4; m S 3 .14 4@ 3 4 4- -4 3:'t 4 h1d.S- 32&- .4 32 FIGURE 7.-Enlarged portion of U.S. Coast Survey Chart No. 360 (Ist ed.), indicating the hydrography executed along the outer navigation channel at the mouth of the Connecticut River beyond Lynde's Point in 1849 and 185 1. 202-509 0 - 78 - 7 66 Strategic Role of Perigean Spring Tides, 1635-1976 being and he is hereby fully authorized, impowered and "The English at Saybrook Point protected the land directed, forthwith to endeavour by all proper and practi- approach with a palisade drawn across the narrow cable means in his power, to cause the said continental isthmus, which very high tides overflowed and isolated frigate to be remov'd and got over said bar and into the from the main-land. Their corn-field was two miles dis.- Harbour of Newlondon, and for that end to employ such tant from the fort, and skulking Pcquotes were always on help and assistance of men and materials as he shall find the alert to waylay and murder them." and adjudge proper and necessary. And Dudley Salton- And so, likewise, astronomically reinforced high tidal r stall, Esq , commander of said ship, and all other officers waters played an important role on several occasions and men belonging to said ship, are hereby requested, during the Revolutionary War. The impact on history ordered and directed, to afford said Capt. Cotton every of the particular tide-related circumstance under dis- aid, help and assistance in their power, to effect this im- cussion involved not only the subsequent somewhat portant and necessary object and which Congress have so limited naval action of the Trumbull, but also the in- much at heart. And said Capt. Cotton is to use his best triguing question of just what her potential contribution prudence and discretion in prosecuting this important might have been to the small and hard-pressed elements business to prevent said ship falling into the hands of the of the Continental Navy during the earlier phases of the enemy, or any other misfortune; and to make report as Revolutionary War had greater advantage been taken soon as may be to his Excellency the Governor of his doings of the intervening cases of perigean spring tides. in the premises together with the expence attending the Captain James Nicholson was chosen to command the execution thereof that the same may be defrayed and Trumbull on September 20, 1779. Cruising orders were proper information immediately made to said Hon" issued to him on April 17, 1780, and the ship saw active Congress. duty during the remainder of the war." "Same "On the 27th Day of February A.D. 1778. On June 2, 1780, she took up the chase of the Watt, "Resolved, That the Committee of Pay-Table be di- a British vessel serving under letter of marque, with whom rected to draw on the Treasurer in favour of Capt. John she fought a valiant battle. Significantly, in terms of Cotten [sic] from the sum of 100 pounds towards defray- the hypothetical question of her previous untried contri- ing the expence of getting the ship Trumbull over Say- bution 23 to the war effort, it has been authoritatively Brook Bar &c., and charge the same to said Cotten to be stated that, throughout the entire period of the Revolu- in account for the purpose aforesaid. . ." " tion,.this particular conflict ranks a close second in the "Same . . . "On Tuesday [corrected, this should read severity of the battle to the fierce naval encounter between Thursday] the 3rd Day of February 1780. the Bon Homme Richard and the Serapis, a classic, naval "Upon the request of the Board of War, of the 18th engagement. December 1779 for two tuns of powder to supply the two Again, quoting from the Colonial Records of Connecticut: frigates the Trumbull and Burbon now lying at the port "In June, 1780, one of the most hotly contested engage- of New London. . ." 18 ments fought at sea during the Revolution occurred to the It is a well-known historical fact that the blockading northward of the Bermudas between the Trumbull 28, activity of elements of the British Fleet " together with Captain James Nicholson, the ranking officer of the Con- harassing activities by scattered land forces " were for- tinental navy, and the Liverpool privateer Watt 32, Cap- ever present during the war, and recurrent occupancy of tain Coulthard. After a fight of two hours and half both Long Island Sound by British ships could have prevented vessels withdrew seriously disabled, and with difficulty escape of the Trumbull on previous occurrences of favor- made their ways to their respective ports . . . the Trum- able perigean spring tides. However, arguing against any bull to Boston and the Watt to New York.' 1 24 major deployment of land forces, during the period fol- On August 8, 1781, while escorting 28 merchant ships, lowing the evacuation of British troops from Boston to the Trumbull encountered the British Iris, a 32-gun frig- Halifax, the British were primarily concerned with de- ate of sup@rior strength, accompanied by two support fending New York City. vessels. In the ensuing one-sided engagement (fig. 8) she In a 19th century book titled Nooks and Corners of the was compelled to strike her colors. The -engagement as New England Coast, a curiously opposite situation occur- recounted in the Colonial Records of Connecticut reads: ring during the French and Indian War, but also show- "In July, 17 8 1, he [Robert Morris, director of the Con- ing an historical dependence on the tides, is brought out: tinental Fleet] ordered the'Trumbull,' 28, Captain James % V@ JZ"4, - (Z co 0 w cr v it"T- V. CL 0 o -t,j tj .41 lkr tj 100- CD look C-D NO 00 WA CD 0 0 CD '41 > ]4f ri 49 d-iOls?H Iv.?zlnvAT uvouatuV uo sap!j ffuutiy un9guaj jo l9qui, 68 Strategic Role of Perigean Spring Tides, 1635-1976 Nicholson, to proceed to Havana with despatches, letters, tions of Nathaniel Bowditch's American Practical and a cargo of flour, The 'Trumbull' had scarcely cleared Navigator, the generally accepted epitome of navigational the Capes of the Delaware on August 8, when she was knowledge in this country, first published in 1802. How- chased by the frigate 'Iris' 32, Captain George Dawson. ever, the basic principle of these tides is described, together Encountering a storm, the 'Trumbull' was dismasted, and with their practical advantage to navigators in getting thus crippled she was overtaken by the 'Iris'. The 'Trum- in and out of shallow harbors, in John Hamilton Moore's bull's' crew were a sorry lot; some of them were British The New Practical Navigator, a British mariner's hand- deserters, and others were cowardly and disaffected. It book which, although having gone through 12 English was late in the evening when the fight began. Many editions by 1796, was first published in the United States of the crew now put out their battle lanterns and flew only in 1799. Although this work contains errors in its from their quarters. Captain Nicholson and his officers, tables which Bowditch subsequently sought to correct, with a handful of seamen, bravely defended their ship Moore precisely summarizes the nature of perigean spring against . impossible odds for an hour before they tides in the following words which, because of their direct surrendered. application to navigation, are appropriate both to the ". . - A letter from New York dated Aug. 111, 1781, immediately preceding and succeeding examples of the informs us that 'this day arrived the celebrated rebel practical importance of these tides: frigate named the 'Trumbulr." " This terminated'her "When the moon is in her perigaeum, or nearest ap- war service. proach to the earth, the tides rise higher than they do, under the same circumstances, at other times; for, ac- CONTEMPORARY KNOWLEDGE OF cording to the laws of gravitation, the moon must attract PERIGEAN SPRING TIDES most when she is nearest the earth . . . Some of these In considering various other reasons why a possible effects arise from the different distances of the moon frorn practical advantage was not taken of earlier perigean the earth after a period of six months, when she is in the spring tides to accomplish the release of the Trumbull same situation with respect to the sun; for if she be in from Saybrook Bar, it is important to recognize the gen- perigee at the time of the new moon, she will, in about six erally rudimentary knowledge of the tides in this colonial months after, be in perigee about the time of full moon. period. These particulars being well known, a pilot may chuse First and foremost, there should be taken into account [sic] that time which will prove most convenient for con- the almost certain lack of technical awareness of either ducting a ship out of any port, where there is not a suf- the causes or effects of perigean spring tides at this early ficient depth of water on common spnrig-tides." date. To,this must be added a rather limited familiarity Other references indicating an awareness of perigean by navigators with the technical principles underlying spring tides by early philosopher-scientists-although a even ordinary spring tides. This knowledge rarely ex- knowledge not necessarily shared by navigators-are given tended beyond the fact that, in accordance with a well- in a survey of pertinent tidal literature in part 1, chapter known rule-of-thumb, higher (spring) tides were associ- 4 of the present work. The fact remains that, whether the ated with the "full and change of the Moon." Therefore, Trumbull's rescuers knew the exact cause of this tidal any case of perigean spring tides would not likely have phenomenon or not, they took advantage of it, with posi- been regarded as being any different from ord* mary spnng tive results. tides, which already had presented repeated opportunities TIDAL ANALYSIS for floating the ship free, without avail. Whether those It will be observed that the portion of the previously concerned actually knew in advance of the favorable op- mentioned condition of tidal enhancement used occurred portunity presented by this particular perigean spring on exactly the same day as perigee-syzygy. In the light of tide in tenns of a water level considerably above that of subsequent discussions in this volume concerning "phase ordinary spring tides is, accordingly, very much a matter age" and "parallax age" in relation to perigean spring of conjecture. tides (see chapter 8), it is desirable to point out that each In evaluating the comparative dearth of tidal knowl- tidal situation possesses its own local timing response to edge in this early period, it is worthy of note that neither gravitational forces which must always be individually the astronomical phenomenon of perigee-syzygy nor the considered. This circumstance, as will'be repeatedly em- practical effects resulting therefrom in the form of peri- phasized throughout this volume, prevents the application gean spring tides are anywhere mentioned in early edi- of any too positive, all encompassing or generalized rules Impact of Perigean Spring Tides on American Nautical History 69 in connection with even closely adjoining coastal areas high water) at Saybrook Light around the preceding subject to the same tidal action. Such "station differences" 1920 date was pred icted for July 15, 1920 and was 4.8 become a function of harmonic constants (table 19), ft, which is 0.5 ft in excess of the mean spring range, 4.3 which are representative of local tidal responses to astro- ft, for this station. On July 13, 14, 15, 16, 17, and 18 the nomical effects. Additional deviations from the tidal con- predicted maximum daily ranges for this station were 4.5, ditions which prevail at certain standard or "reference" 4.7, 4.8, 4.8, 4.7, and 4.5 ft, respectively-above the mean tide stations, expressed as time and height variations in spring range for 6 successive days, and still in excess of this the high and low waters, also may be either positive or value even 3 days after the occurrence of perigee-syzygy at negative. 5:24 a.m. (e.s.t.) on July 15. Tides at the mouth of the Connecticut River initially It is noteworthy that, in this very comparable case to react more rapidly in their response to the influence of that of 17 79, the perigean spring tidal range not only was perigee-syzygy than do coastal locations farther south predicted to remain above the mean spring range for 3 (compare with the tidal analysis following "The Battle days after perigee-syzygy, but the first case in excess of of Port Royal Sound, S.C.," below). The peak of the this range occurred even 2 days before perigee-syzygry. perigee-syzygy tidal influence at the Connecticut River (Within this series, the first case of such a condition in outlet actually occurs sometime prior to the near-coinci- excess of the mean spring range for Saybrook Light oc- dence of perigee and syzygy. curred at 7:54 p.m., e.s.t., on July 13, approximately I A modern example based on actual data available from 33V2 hours before the mean epoch of perigee-syzygy.) tide tables appropriate to this location for a situation As indicated earlier, the first instance of a maximum daily corresponding to the same time of the year, possessing tidal range in this series was predicted for July 15, or on nearly the same separation in time between perigee and the same day as perigee-syzygy. This situation provides a syzygy, a similar declination of the Moon, and other contrast with the longer phase and parallax ages noted in factors will serve to substantiate this statement. The peri- connection with Port Royal Sound, S.C., on page 84. gean spring tide involved in the'Trumbull's release oc- HYDROGRAPHIC ANALYSIS curred on August 11, 1779, in connection with a near- An additional technical evaluation of the Trumbull's alignment between perigee and syzygy which took place at approximately 8:00 a.m. (75' W.-meridian time) design draft and the actual water depth necessary for this on this date. The time difference between perigee and ship to have crossed the bar at the mouth of the Con- syzygy was -20 hours (with perigee preceding syzygy) necticut River is in order. The previously mentioned 1771 and the Moon, at new phase, was in declination +21.4. chart (fig. 4) of the Connecticut River shows the least A closely similar circumstance existed at the entrance of depth of water along that portion of the channel (indi- the Connecticut River at approximately the same time of cated by anchorage symbols) between the present light- the year, with almost exactly the same interval between house on Lynde's Neck and Fort Fenwick on Saybrook perigee and syzygy (-20 hours), with perigee preceding Point to be 18 ft (3 fathoms). However, the water depths syzygy, and the new moon in nearly the same declination over the bars located just outside the mouth of the river ( + 17.60) at the time of perigee-syzygy on July 15, are much less. To the southeast of the ship anchorage, the 1920-for which date tide tables are, of course, readily water depth averages 10 ft, and over numerous bars out- available. side the entrance it shallows to 4-7 ft. Although shifting bottom sands make the water depth In practice, the predicted tide heights for Saybrook 11) Light, at the entrance to the Connecticut River, and a so- at the river entrance extremely subject to change, possibly called "subordinate" tide station, are referred to the pri- even within a few days, the sounding data given on this mary tide station at New London, Conn., at which regular early chart of 1771 ( 1784) are at least broadly representa- tidal measurements are made. As a further source of data, tive of the situation as it existed on the Connecticut River in 1776. The hydrographic data of this chart, indicating the earliest available hydrographic chart of the Connec- navigational impediments subject to a partial offsetting by ticut River (chart No. 360 of 1853) previously referred high tides, are further reinforced by data on the Coast to (fig. 5) indicates that the rise of the highest tide ob- Survey chart of 1853, which indicate a, similar least depth served above the chart plane of reference prior to the of 7 ft at many places along the outer portions of the chart's publication date was 5.4 ft. channel. From appropriate annual tide tables, the first of two The chart datum for the 1853 chart corresponds to the maximum daily tidal ranges (lower low water to higher mean low water of spring tides which, because of the ad- 70 Strategic Role of Perigean Spring Tides, 1635-1976 ditional depression of the low-water stage produced in but spars, sails, and other heavy gear would subsequently these tides, is a little lower than the mean of all low waters again increase the draft in the sea-ready condition in used in the compilation of present-day nautical charts. which she grounded on the bar. However, this datum is considerably more representative From a consideration of the tidal data specified earlier, in the case of perigean spring tides. The height of mean the maximum depth of water available across the bar at high water with respect to this.spring tide datum plane as the river mouth, even at ordinary spring tides, would be noted on the 1853 chart is 4.5 ft, and the height of mean 12 ft. - low water is 0.6 ft, giving a mean range of 3.9 ft. By con- Assuming a forward trim and negligible pitch move- trast, the mean spring range is listed as 5.0 ft, and, since ment of the ship, it would still be necessary, in these only the mean low water of spring tides has been set as the poorly sounded and as yet basically unsurveyed waters, to arbitrary zero point on this 1853 chart, the rise of ordinary ahow 2 to 3 ft of keel clearance to accommodate local mean high water springs according to these chart data is channel-bottom variations and to ensure a safety precau- 5.0 ft. tion avainst ffroundiDg. Considering the extra buoyancy Thus, realizing that the Trumbull would have to that could have been provided by a "camel," a rudimen- navigate water depths shoaling at the places previously tary calculation shows it would have required more than mentioned to Within 7 ft or less of the latter datum plane, 250 water-tight hogsheads (63-gallon capacity) first par- and allowing for a mean rise of spring tides to 5.0 ft above tially filled with water, and then successively submerged, this datum, only a ship having a draft of 12 ft (7 ft+5 ft) lowered into position beneath the ship, and pumped com- or less could cross these bars even at ordinary spring tides. pletely free of water, to raise the Trumbull by only 1 ft. Although profile plans for the Trumbull have been Even allowing for the buoyancy provided by such an ex- determined by the present writer to be unavailable from tensive flotation gear, therefore, it is evident that the addi- either U.S. Navy or British Admiralty sources (late in the tional water depth created by a perigean spring tide would Revolutionary War, as previously noted, the ship was be necessary to allow the Trumbull to clear the bar-and captured by the 13 'ritish) it is stated in Howard 1. this is, obviously, the opportunity that was utilized in Chapelle's The History of the American Sailing Navy that 1779. it may be assumed she was of the standard design for a 28-gun frigate approved by the Marine Committee of the 0 Continental Congress." A sister ship of this class was the The Second Battle of Charleston Harbor frigate Virginia constructed at the shipyard of George The bar outside the harbor at Charleston, S.C.,-like, Wells in Ba!timore in 1776, and which, after being that of the previous example (and another at the entrance blockaded by the British for more than a year, also ran aground in the Chesapeake Bay in 1778. Outboard pro- to New York Harbor)-was instrumental recurrently files for this vessel are available in Chapelle's previously throughout the Revolutionary War in impeding the sail- mentioned book. Scaling from the waterline on these ing. activities of deep-draft men-of-war. In the case of plans gives a full-load draft (ready for service) of 18 ft Charleston, tidal circumstances connected with the astro- 4 in. Without stores, provisions, or armament, and nomical phenomenon of perigee-syzygy played an im- ,stripped of all extraneous weight other than that neces- portant role in the second siege of this city in 1780. (The sary to make the ship sailable, the draft, in the opinion first British attempt to lay siege to Charleston on July 4, of a NO-AA naval architect, would probably have been 1776 had failed.) Although a matter not directly ac- reduced to a maximum of 14 ft. counted for in history, the second attempt by the British to capture this southern port was undoubtedly aided by a However, in the narrow confines of the upper reaches perigean spring tide. of the Connecticut River, the square-rigged vessel, if Arriving off Charleston Harbor at the beginning of under sail, would not be able to tack, and a following wind March 1780 after needed ship repairs at Savannah, Ga., would also mean an offshore wind which, if strong, would the British found that, because of the deep drafts of their depress the height of the tides at the river entrance. To vessels, the depth of water in the entrance channel (fig. negotiate the narrow, curving portions of the river, she 9) was such that it was impossible to cross the offshore- would have to be towed by small boats. This would pennit bar. They were compelled to stand off the coast for more the ship to be initially stripped of top hamper, rigging, and than 2 weeks, hopefully awaiting a better opportunity at sailing gear (some control ballast would have to be re- the next high water springs. Probably unaware of the tained), and would reduce her draft to about 12 ft 8 in., special nature of the circumstance, but taking advantage Impact of Perigean Spring Tides on American Nautical History 71 of the augmented high waters resulting from a pseudo- we lay in that situation on the open coast in the winter perigean spring tide occurring on March 20, 1780, they season of the year, exposed to the insults of the enemy for succeeded in negotiating the bar with a major naval attack 16 days before an opportunity offered of going into the force, including a 50-gun frigate, two 44's, and four 32's. harbour, which was effected without any accident on the The significant aspects of this naval engagement were 20th of March, not withstanding the enemy's galleys con- told in a subsequent report by Vice-Admiral Marriott tinually attempted to prevent our boats from sounding 11 28 Arbuthnot to the British Admiralty, dated May 14, 1780: the channel . . . 99 - -. Preparations were next made for passing the The perigean spring tides of which use was made on squadron over Charles-town bar, where [at] high water this occasion occurred as a result of a pseudo-perigee- spring tides there is only 19 feet water. [Compare with syzygy situation having a mean date of March 19.65, 1780, actual sounding data appearing on the two charts (figs. with a separation between perigee- and syzygy of approxi- 10 and I I ) compiled by different sources shortly after this mately -37 hours. Significantly, the British had been un- siege.] The guns, provision and water were taken out of ;able to make use of the preceding set of spring tides about the Renown, Roebuck, and Romulus to lighten them, and March 6, which would have occurred near lunar apogee AL- @'7 4, -IN i Srolrr 8 4 /J1, M ..... 5 4 A B 0 U IR k"Z 0 b 4, "R, CIA V 11;@ Al S -4 tv A X A- C 0 It Y Courtesy of William L. Clements Library, University of Michigan FIGURE 9.-Hydrographic chart of Charleston Harbor, S.C., prepared by the British engravers, Sayer and Bennett, as a documentation of the tide-assisted penetration of harbor shoals and second siege of Charleston by the' British, 1780. 72 Strategic Role of Perigean Spring Tides, 1635-1976 and whose high-water levels would, therefore, be even It is noteworthy that even this considerably larger somewhat less than those of ordinary spring tides (the separation-interval (selected purposely, in this early average situation at perigee-quadrature, discussed at chapter, as a test case for the practical range of perigean length in part II, chapter 5). The March 6 tides were also spring tide influence) is still sufficiently small to produce accompanied by quartering offshore winds, as noted significant amplitude increments in the tides. This may below. be seen by comparing the high water and daily range The attendant circumstances were described in editions data of table 6 with the corresponding values for mean of the Pennsylvania Packet for April 25 and May 2, 1780: high water springs and mean spring range in the second "March 19.-The British under General Clinton, now following paragraph. encamped on James Island, seem to wait for the shipping The wider separation-interval in the test case, com- which lay off the bar, dnd have been disappointed at the bined with other dynamic factors is, in turn, responsible last springs by south-west winds, which kept down the for the circumstance that the lunar geocentric horizontal tides so that they cannot get over. This day the springs parallax at the mean epoch of perigee-syzygy on Octo- are at the highest, but the weather so hazy that they will ber 13.88, 1974 was only 59'48.55" compared with scarcely attempt it, and it will probably clear up with 60'43.8" on March 19.65, 1780. unfavorable winds. We begin to hope that Province [Prov- These facts give tacit but demonstrable support to the idence] has interposed a second time to prevent their assumption of yet further increased tide-raising effects getting over until we are ready. If they should get over from the smaller -37" interval which occurred in March either now or hereafter, there will probably be the hottest 1780. As will be established in subsequent chapters, the contest that has happened this war, just off Fort Moultrie. Moon's proximity to the Earth and the astronomical The British ships destined to come in are said to be the factors which lessen this distance are the foremost causes Renown, fifty guns; Ro'ebuck, forty-four; Blond, thirty- for augmentation of tidal heights. The data of table 6 for )) 29 two; Perseus, twenty and Camilla, twenty . . . October 1974 are, therefore, values safely on the small "March 20-This morning the British got their ships side in terms of the enhanced astronomical tidal situation over the bar. They consist of ten vessels of force, from in March 1780. twenty guns to a sixty-four, as some say, others a At Charleston Harbor, the corresponding predicted fifty. . . ." 30 higher high waters (HHW's), lower low waters (LLW's), This successful passage over the Charleston bar and and maximum daily ranges given in the tide tables were: subsequent victorious attack by the British upon the TABLE 6-Comparative Tides at Charleston Harbor, S.C. American fleet confined within the harbor-followed by October 13-19, 1974 the second Siege of Charleston-resulted in the capitula- tion of the American ground forces under General Ben- Maximum jamin Lincoln on May 12, and the capture of the Con- Date Time HHW LLW Daily tinental ships Providence, Boston, and Ranger, compos- Range ing major elements of Commodore Whipple's squadron. American naval vessels destroyed and sunk were the (e.s.t.) October 13 ........ 0542 6.4 -0.2 6.6 Briscole, 44 guns, General Moultrie, 20 guns, and Notre October 14 ........ 0634 6.7 -0.4 7.1 Dame, 16 guns. October 15 ........ 0725 6.8 -0.5 7.3 TIDAL ANALYSIS October 16 ........ 0815 6.8 -0.5 7.3 October 17 ........ 0901 6.7 -0.4 7. 1 A modern 1974 tidal circumstance possessing conditions October 18 ........ 0948 6.4 -0.1 6.5 approximately comparable to those encountered in the October 19 ........ 1034 6.1 +0.2 5.9 second Siege of Charleston will serve to illustrate the tacti- cal importance of the tides in this 1780 occurrence for It will be observed that the first of two maximum which tide tables are not available. heights (HHW's) for these perigean spring tides was pre- Around the date October 13, 1974, a pseudo-perigean dicted for October 15 at 7:25 a.rh. (e.s.t.), approximately spring tide similar to that of March 20, 1780 occurred, 34 hours after the perigee-syzygy that occurred at 9:06 related to a phenomenon of perigee-syzygy whose mean p.m. (e.s.t.) on October 13. This accords very closely alignment took place at 9:06 p.m. (e.s.t.), on October 13, with the circumstances under which the British crossed the with a separation of -68 hours (perigee preceding Charleston bar at HHW on March 20, 1780, the next syzygy by this amount). day after the pseudo-perigee-syzygy on March 19. Impact of Perigean Spring Tides on American Nautical History 73, t;, -4@ N @r V qh A T Q -V h -S: d, 14- (-A, @F Zir X" Qq - 71 CZ. A ".4 J" V n; T4, q A" 4- Courtesy of Library of Congress FIGURE 10.-Hydrographic chart of Charleston Harbor, S.C., published by the House of Fayden in Philadelphia, May 27, 1780, 2 months after the successful navigation of the entrance shoals by British frigates at the time of a perigean spring tide, March 20, 1780. On the chart (fig. 10) published by the House of coast of South Carolina are, consistently, 0.0 ft. The mean Fayden in Philadelphia on May 27, 1780, 2 months after spring tidal range at Charleston is 6.1 ft. the second Siege of Charleston, the datum for mean high In this comparative situation, the predicted higher high water spring tides at Charleston is given as 5.6 ft above water at Charleston Harbor therefore remains in excess the mean low water chart datum. Corroborating this early of the value for mean high water springs-and even above value, the figure given for mean high water springs at that representing mean spring range-for periods of 7 Charleston (Custom House Wharf) in modern tablesis and 6 days respectively, around perigee-syzygy. Likewise, also 5.6 ft above the same chart datum. The corrections the maximum predicted tidal range at Charleston remains to the height of HHW for North jetty, at the entrance above the mean spring range for 5 days after perigee- to Charleston Harbor and nearby points on the outer syzygy, even under these conditions involving a compara- 74 Strategic Role of Perigean Spring Tides, 1635-1976 tively large (-68-hour) separation in time between the confirmed on the same portion of the earliest Coast Survey two components. The separation-interval for the 1780 chart of Charleston Harbor published in 1855* (figs. 12, example was somewhat smaller, approximately -37 13), where the minimum channel depth is shown to be hours, a factor contributing still further in this case toward 3V4 fathoms. Despite the constantly drifting bottom sand, the raising of high tides. both inside and outside the harbor, these charts provide Closely supporting the above analysis is the footnote an interesting comparison of the general bottom config- of tidal information contained on the earliest chart of uration at two epochs 75 years apart. Their general Charleston Harbor prepared by the Coast Survey (Chart similarity is also germane to the assumption of an average No. 432, Ist edition, 1855) where the highest tide of reproducibility of sea-level datums over extended periods record at Castle Pickney on Charleston Harbor up to that of time, necessarily employed throughout these various date is given as 7.32 ft (observed on April 15, 1851- analyses. accompanying another pseudo-perigean spring tide). On To provide the most accurate information possible con- this same Coast Survey chart, the mean daily tidal range cerning the ships involved in this siege, an inquiry was at this location is given as 6.01 ft. The level of mean low directed to the National Maritime Museum in Green- water springs is specified to be - 0. 19 ft below that -of wich, England, relative to the drafts of the ships Renown, mean low water (the chart datum), and the mean range Roebuck, and Romulus. The report indicates that: of spring tides is given as 5.81 ft. Hence, the rise of mean "Unfortunately, the official lists of ships in possession high water springs above mean low water is 5.82 - 0.19 = of the Admiralty do not give the drafts of 1780, but do 5.63 ft. The minimum navigable water depths past the so in the 1790's, by which time the Renown was out of bar outside Charleston Harbor just prior to the second service. Her sister ship, the Portland-, is stated in a list Siege of Charleston can now be correlated with these tidal of 1795 . . . to have a draft of 10'6" forward, 15'7" data. aft. . . . The Roebuck and the Romulus were somewhat HYDROGRAPHIC ANALYSIS similar ships, draft 10'8V2" forward, 141V2" aft. It is not, A second chart (fig. 11 ), of the water depths inside and however, specified exactly what these measurements de-. outside Charleston Harbor, prepared by the British en- scribe, except that they are 'light'." " gravers Sayer and Bennett in 1780, within a few months The latter statement would imply an out-of-service after the second siege of this city, is more specific in its draft, discounting -any load of gunpowder, stores, shot, hydrographic data than is the Fayden chart. According or cannon. The previously quoted memorandum from to a premetric practice in nautical chart representation, Vice-Admiral Arbuthnot indicates that guns, provisions, all water depths up to 18 ft are given on the chart in units and water were taken out of these ships before Charleston of feet; depths in excess of 18 ft (3 fathoms)-and, spe- to lighten them. No mention is made in Admiral Arbuth- cifically, those along designated navigation channels-are not's account relative to the ships making rendezvous to specified in fathoms (1 fathom=6 ft). However, the refit, for example, in the available Five-Fathoms Hole depths of water over shallow bars or submerged reefs after crossing the bar. Inasmuch as a combat status,was (which are indicated on the chart by stippled areas out- resumed immediately on crossing the bar, it is unlikely lined by dotted lines) are also given in feet, printed along- that more than the bare minimum of tactical gear, shot, side the submerged features. Having been prepared long and ordnance was removed, and that the major portion before this standard procedure went into effect, the two of the ship's heavy combat-readiness equipment remained. 1780 charts utilize a slightly different manner of presenta- Certainly it would be impractical, under the contingen- tion. With the exception of a few shoal-water passages cies of time and a hostile environment, to remove more where the water depth is specifically indicated as being than the guns located on the top deck. in feet, all soundings thereon, regardless of location, are It is, therefore, clearly mandatory that (in a directly given in fathoms. opposite case to that of the Trumbull) an additional 1 to . Thus, the shallowest Iwater depths between two bars 2 ft must be added to the previously specified light drafts bracketing the designated Ship Channel (which the of the Renown, Roebuck, and Romulus under such con- British used) leading into Charleston Harbor are seen ditions of near-combat readiness, to compensate for their to range from 2 to 3 fathoms (12.0 to 18.0 ft), with considerably stripped-down conditions when out of serv- the water depths over the bars being only 8 ft. The first ice. A minimum operational draft for the Renown before values appear on the chart shown in fig. 10; the second Charleston of 16V2 to 17 ft aft can, therefore, safely be value is given in fig. 11. These quantities are also generally assigned. Impact of Perigean Spring Tides on American Nautical History 75 h' CK 1P, @A X1 9 '2 @5 IL A' B 0,-U b 6' r T ..... rts n... .3, _* ............... 7 96 N 7-7 T 44, & 6 -N _7 '7 Courtesy of William L. Clements Library, University of Michigan FIGURE I I.-Enlarged portion of Sayer and Bennett chart of Charleston Harbor (fig. 9), emphasizing the shoals at the entrance through uhich the deep-draft British frigates were forced to pass. Comparison of water depths with those of figure 10 shows a close agreement between these charts published respectively in England and America. In addition, subject to the small-boat harassment which opportunity for crossing the bar, in contrast to a permis- Vice-Admiral Arbuthnot mentions, and to prevent anV sible period of waiting for favorable conditions in the further buildup of resistance by American forces, there Connecticut River example. was the necessity for the British to accept those weather Choppy seas coupled with a possible light ground swell and tide conditions which offered the earliest possible might readily be produced by the unfavorable winds men- -El oan&j ui p2jujua ijuqz) QTp jo uoiliod QTp sQvexpui uQjL- pQxoq llems QLjj -s@uejd uinjup puu vlep lepp iuvaglusis SululujuOD lgqRj UT AQAznS ISUOD -S-fl Qql Aq pQqsi n@ (I -oN -pa IlEt -oN ljeiqo S-j-* 0) s;njz)poiddL, sli puu ioqiE*H uois3jmLjo jo ii-eqj Ajuuiuupjj--Zj aunoij .lq T 1 r 5 t i7l '0 A lzw -All 7 8-1 4A ta" f- 45k Z, A A w ILI -4v Z 'T ji 77 1H B8; q Z'. % % vt N"VIS aull.1411 3ul jo IWO 2411 so A141,11AN 71 S'4 H @lv 0 Rd @tv IS1 I U N V, f JIN-F-g- =ii-,R a PIE 9Z61-901 's,9P!.L ?uz-"ig uv-9419cf 10 9109 929,91MIS 9L Impact of Perigean Spring Tides on American Nautical History 77 .@ - "-- ";-..-'-.'-'-: ".' -....... @' Ia..... -.---V.-."'.-.--...: . 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I . . @ I . 78 Strategic Role of Perigean Spring Tides, 1635-1976 tioned in the previously quoted Pennsylvania Packet ar- determined by the Federal Government to have the great- ticle. The movement of this swell over the prominent est possible strategic value in pushing the war against the shoals in this area could cause "blind rollers." These, in South. turn, would cause the entering ships to heave and pitch The armada was peremptorily scattered en route by the and would require additional keel clearance to prevent first lashings of a violent coastal gale (some historical running aground. Thus, in order to ensure a reasonable sources have variously described it as a hurricane)' margin of safety in these little-known waters, the largest which, moving northward, subsequently struck inland and British ship, the Renown (even with a partially lightened caused severe tidal flooding along the New Jersey coast. condition) would have needed a water depth of at least (See the list of historic tidal floodings of North America 20 ft to negotiate the channel. in table 1 under the date November 2, 1861.) Choosing, for the sake of impartiality, that contempo- The date of mean perigee-syzygy upon this particular rary British chart which shows even the greater of the two occasion (with only I hour separating the two compo- values (2V4 fathoms or 13.5 ft) for the shoal-water depth nents) was November 2, 11.5 hours, 75' W.-meridian in the channel, the required tidal height above mean low time (eastern standard time not yet being in use). This water for safe navigation must, therefore, have been very near-coincidence of perigee and syzygy was com- 20 - 13.5 = 6.5 ft. This is a condition which, according to bined with an extremely close proximity in the distance of the data appearing on the 1855 Coast Survey chart, is the Moon from the Earth at the time, represented by the not attained even at ordinary -spring tides, whose mean large geocentric horizontal parallax of 6 F2 7.6" (see table height at Castle Pickney on Folly Island is given as 5.63 ft. 16) -yielding a proxigean spring tide. Modem tide tables indicate that the difference in high As explained in the subsequent tidal analysis of this waters between Folly Island and Sullivans (Sulivan's) event, because of the normal "phase age" and "parallax Island on the outer coast is 0.0 ft. The necessary additional age" between the close alignment of perigee and syzygy rise in tide height to provide a navigable water level and the associated increased tidal effects in these southern of 6.5 ft (or 8.0 ft, according to the second British chart) coastal waters, the maximum augmented tidal effects above mean low water could have been provided only by could be expected approximately 1 day after perigee- the perigean spring tide at this second Siege of Charleston. syzygy-or in the early morning hours of November 3. As further confirmed by data taken from modern tide tables Two further episodes in U.S. naval history, the one available for this location, the accompanying increased similar, the other involving a different operational appli- tidal ranges caused by the perigee-syzygy alignment cation, but both related to the amplitude-increasing as- would also continue for several days thereafter, through pects of perigean spring tides, occurred during the Civil November 4, 5, and 6. War. Thus, paradoxically, the same perigean spring tides The Battle of Port Royal Sound, S.C. which, in conjunction with strong onshore winds, resulted in tidal flooding and severe coastal damage in New Jer- This third instance in which perigean spring tides un- sey, served an advantageous purpose in the attack on questionably exercised an important influence upon an Forts Walker and Beauregard, commanding Port Royal event in American history forms a desirable technical ex- Sound. This advantage resulted from the relatively high tension of the preceding example. It is characteristic of navigational waters associated with these perigean spring a tidal property derivable from table 19 that, on the south Atlantic coast of the United States, perigean spring tides tend to follow, by I to 1 Y2 days in time, the near- In the interests of scientific objectiveness, reference should be coincidence between perigee and syzygy which produces made to the discussion concerning the necessary uncertainty in desig- nation of early North American hurricanes-and the often more-or- them. less arbitrary classification thereof by experts (among whom opin- On October 29, 186 1, a contingent of the Union Fleet, ions . differ)-th.at precedes table 2. it is not the purpose of this known as the South Atlantic Blockading Squadron, sailed treatise to exercise any partiality. The disturbance in question had moved on northward from the southward from Norfolk, Va., subject to sealed orders. scene of action in the present case. Hence, the exact type of storm This largest naval armada ever constituted in American earlier represented has no direct bearing upon the navigational im- history, up to that time, consisted of 50 fighting ships portance of the astronomically produced perigean spring tides. These alone aided the tactical circumstance at Port Royal Sound described under the command of Flag Officer Samuel Francis Du above. Remotely produced swell or waves were not a contributing Pont. Its destination, Port Royal Sound, S.C., had been factor. Impact of Perigean Spring Tides on American Nautical History 79 tides as approximately 40 ships 'which were not too badly The R.B. Forbes came to me [on Monday, No- scattered or disabled by this same storm off Cape Hatteras vember 4] to say that the Augusta and Dale, steam made rendezvous some 10 miles off Port Royal Sound gunboat and sloop-of-war, were outside. I reported the early on Monday morning, November 4." (Several other- fact to the commodore, and he expressed so earnest a wise reputable historical reference sources give this date wish to get them in before the attack that I determined as November 5 and the date of crossing the bar as Novem- to bring them in at once, though night had already come ber 7, both of which are incorrect.) All artificial aids to on. The Augusta draws 15 and the Dale 16 feet. We navigation (position-fixing targets, buoys, lighthouses, ran down about 8:00 p.m., and anchored a boat, with etc.) already had been removed by the rebel forces and, a Fresnel lantern in it, at the entrance of the channel. on this low coastline, no significant features of natural I then went to the two vess& and communicated the topography were available, to serve as identifying navi- commodore's orders. Both captains were ready to go in gational landmarks. if I would take the responsibility of leading them. The Much battered by the gale, the remnants of the original Augusta took the Dale in tow, and we passed in without fleet assembled one by one, and anchored outside Port trouble, having no cast less than 19 feet [the evening Royal Sound (fig. 14), where the passage of these deep- lower high water associated with the perigean spring draft ves'sels across the bar at the entrance now posed a tide would have been about 9:25'p.m. on this date], serious operational problem. In the months of prepara- and I had the satisfaction of reporting to the flag-officer tion that had preceded this great combined deployment their arrival at half past eleven p.m. Running outside of naval and army forces to the south, it obviously had again I anchored the Vixen at the entrance in readiness been planned to arrive and enter the harbor at the time to bring in the Ericcson and the Baltic, drawing 20 and of the spring tides associated with the new moon of No- 22 feet vember 2. It is questionable whether, in the existing state ". . . At sunrise [Tuesday, November 5] we anchored of knowledge, it was recognized, or definitely brought into a large, spar buoy at the, entrance of the south channel. consideration, that this date also represented an occasion Mr. Platt and Mr. Jones, Ist and 2d officers of this of perigean spring tides. vessel, were then sent on board of the Baltic and Ericcson, The storm had delayed the mission by 2 days. Al- respectively, and I led in with the Vixen at half flood rthe morning higher high water for the perigean spring ready the lifespan of the presumed ordinary spring tide L (which normally reaches a maximum and declines within tide of this date would have been about 9:50 a.m.]. a day or two) was fast disappearing. This undoubtedly We had no cast less than 27 feet, and I can say with explains the sense of urgency for immediate passage across certainty that vessels drawing 25 feet may come in at all ordinary tides [an oblique reference to the fact that, at the bar indicated in the eyewitness account given below. 27 feet and more, the existing tides were in excess of However, as shown in the subsequent tidal analysis of "ordinary" (including spring) high tides-see be- this episode, perigean spring tides last considerably longer. low] . . . The hydrographic survey vessel Vixen, a side-wheel ". . . The Wabash started for the batteries at 8:30 steamer which had been obtained by the Union Navy a.m. 33 from the Coast Survey for inshore sounding operations, As recounted above, during the lower high water in was ordered into action. It had been brought along to the late evening of Monday, November 4, the Vixen Port Royal Sound (then known as Port Royal Bay or guided two smaller ships over the bar. On the morning simply Royal Bay) for just such a contingency as they of Tuesday, November 5 (with higher high water about now faced. During the ensuing activities of making sound- 9:50 a.m.), aided by the effects of the perigean spring ings by leadline, buoying the channel, and leading the tide, she led the remainder of the large-draft vessels of fighting ships across the bar, the influence of the perigean the fleet, with the flagship Wabash (fig. 15) second in spring tide soon became known, as is referred to obliquely line, across the bar, "with only a foot or two to spare." 34 and without elaboration in the official reports of the ex- ". . . As they ran past vessels that already had crossed, pedition. Charles 0. Boutelle, Assistant, U.S. Coast Sur- cheers rang out over the water. After this came some vey, was in charge of these sounding activities and, in delay until buoys could be placed around the dangerous a letter dated November 8 from Port Royal Bay, he shoal. . . Even then, as the next succeeding low tide wrote to the Superintendent of the Coast Survey [deepened by the effect of perigean springs] ap- as follows: proached . . . the Wabash, trying to fix the outlines of .80 Strategic Role of Perigean Spring Tides, 1635-1976 Ai .1 P., fj "0 0 to GO 0. *% AAM t 0 FT WALKER, < W Z@ FTBEADRIGARD 20 G A. t nbprrta Tr& j fell" 4 0, -4 % Sketch, of PortHoyaz, S.C, sent to theNavyTep! from,thcFlut. Mov.186 11. Autoyrapht& Copy by RLtndertkda, Coast S@ey ONUe. Fic;URE 14.-Sketch of Port Royal Sound, S.C., and the Union naval maneuvers before Fort Walker, prepared by a Coast Survey technician aboard the hydrographic survey ship Vixen during this Civil War engagement in November 1861. The chart shows the location of the entrance channel between Gaskin's Bank and Martin's Industry depicted in greater detail in figure 16. 8 OL 0 609-WE a_vXv 4 0 t'j C_n 4A z o j, C) Af@ A 0 --'4 A @'v A W N, R .1 0 CD 0 4., r I (D 4w, -@@kk- 2@ A4 0 (D 71 P .:Z -A CC cr 0 A p Rt (D0 0 Cfq 0 0 0 to P aq to f"D @l 0 M, ev 5tlm I(.10MH Ivo,zlnvN Uv-')z.'9u'y uo sgp?l ful4s uVagpod 10 lqv4wj 82 Strategic Role of Perigean Spring Tides, 1635-1976 the fort before dark, pushed on too rapidly and grounded. spring tide would provide only 19.5 + 6.4 = 25.9 ft at By the time she was free again, Du Pont decided it was mean high water springs. too late to proceed, and the squadron was signaled to with- As before, actual tide data for Port Royal will be taken draw out of gunshot for the night. from available modern sources for a situation having ex- Although the planned attack was delayed on the next actly the same time difference between perigee and syzygy day by bad weather, on November 7 Fort Walker 'was as occurred on November 2, 1861. A comparison of the captured, and later, Forts Royal and Beauregard. data for Port Royal and Saybrook Light will reveal, for Through this success at Port Royal, the Federal Navy these respective cases, a basis for individual analysis of ( 1) secured access to, and control of, all inland waterways the lag-time influence between perigee-syzygy and the oc- between Savannah and Charleston. The naval blockade currence of the maximum influence of perigean spnng of the South was thereby greatly enhanced. tides, and (2) the total duration of time over which the TIDAL ANALYSIS effects of these perigean spring tides are felt. These two factors are the combined result of geographic location, The depths of the actual soundings made on Novem- hydrography, and astronomy. ber 4-5 empirically confirm that a pengean spring tide In order to establish tides at Martin's Industry at the was present and that its effects extended several days after mouth of Royal Bay which are similar to those of Novem- the time of mean perigee-syzygy at this particular loca- ber 2, 1861, a closely comparable perigee-syzygy situa- tion on the east coast of the United States. tion occurring on January 8, 1974, has been chosen. On Supplementary tidal data contained on the contempo- this date, perigee-syzygy had a separation of - 2 hours, the rary nautical charts mentioned in the next section sup- geocentric horizontal parallax was 61'30.0", and the dec- port this statement. Descriptive notes accompanying the lination of the Moon was + 20.4'. Very closely spaced preliminary chart, of which fig. 16 "is an enlarged section, timesbetween perigee and syzygy and close proximities of indicate that the mean rise and fall (i.e., the mean range) the Moon to the Earth, among other factors, are seen to be of high water springs in Port Royal Sound is 7.3 ft. The common to both the 1861 and 1974 instances. Both will average fall of low waters associated with spring tides later be described as proxigean spring tides. below the chart datum (plane of reference) of mean low Daily high- and low-water predictions for Martin's In- water i's - 0.9 ft. This gives a reduced value for mean high dustry are calculated by re 'ference to Savannah River En- water springs of 7.3 - 0.9 or 6.4 ft above the chart datum trance'the most representative tidal station at which reg- of mean low water. The rise of the highest observed high ular measurements are made. From the tide tables, the water above the chart datum prior to the date of the mean spring range at Martin's Industry is 7.6 ft. However, chart is given as 8.6 ft, and the fall of the lowest tide responding to the effect of the close perigee-syzygy which observed below this same plane of reference is -2.0 ft, took place on January 8 at 6:48 a,m. (e.s.t.), the predict- indicating arise of 8.6-2.0 or 6.6 ft above mean low ed maximum daily ranges for the perigean spring tide occurring at Martin's Industry on January 8, 9, 10, 11, water. The latter values provide an ess@ntially accurate 12, and 13 were, respectively, 9.6, 9.8, 9.6, 9.1, 8.3, and means of determining the incremental variations (8.6- 7.3 ft. The corresponding predicted high waters for these 6.4 = 2.2 ft) and ( - 2.0 - ( - ) 0.9 = - 1. 1 ft) caused by dates were, respectively, 8.0, 8.0, 7.8, 7.5, 7.0, and 6.5 ft. perigean spring tides. These differences were probably The value of mean high water springs previously given is supplemented in the extreme instances noted above by the 6.4 f t. effects of onshore and offshore winds, respectively. Therefore, for this almost exactly comparable situation Based on the sounding data provided for mean low to that of 1861, the higher high water would have re- wateron the aforementioned preliminary chart, the sum mained in excess of mean high water springs on, and for of this low water depth and the height of the high water, fully 5 days after, the date of perigee-syzygy. This accounts both subject to the effects of a perigean spring tide (i.e., for'the fact that the necessary height of waters required 19.5 + 8.6 @ 28.1 ft) is, in fact, necessary to account for for navigation over the bar at Port Royal still existed on the water depth measured by the Vixen at Royal Bay near November 5, 1861, a full 3 days after perigee-syzygy, a the time of higher high water on the morning of November situation which would not have occurred in the case of an 5. The statement contained in the hydrographic report ordinary spring tide. C4 nowhere less than 27 feet" also conforrns with, and con- Similarly, at Martin's Industry, the maximum response firms the existence of, a perigean spring tide. An ordinary in tidal range to the phenomenon of perigee-syzygy took Impact of Perigean Spring Tides on American Nautical History 83 7- A 777,777777 *41 T15, 31 Jil 3A % A r 34 -34 ..4 -17 1 '00 *Ivor t7p 34 -A 3 r+ 47 C/o 4z 15 -73* L j, 41 34 16 34, '17 3 ,10 '34. '16 0 7 "V-` 47 @ @:,h . 0" 4 U -34 4., 14- -15 34 `4 0, 14 k. JA ? r+ -17 :- Ot ;A FiGURE 16.-Enlarged section of aPreliminary Chart of Port Royal Entrance .(Sketch No. 26 in the annual Report of the Superintendent of the Coast Survey for 1862 based on soundings executed in M5, 1856, and 1862. The area represented is in the South Channel lying between Gaskin's Bank and Martin's Industry. 84 Strategic Role of Perigean Spring Tides, 1635-1976 place, a day later, on January 9, 1974. The first of two to the keel was then given " as 22 ft 9 in., which is maximum higher high waters in this series occurred on matched by statistical data on Civil War ships contained January 8, at 7:04 a.m. (e.s.t.), approximately V4 in Official Records of the Union and Confederate Navies hour after perigee-syzygy-whose mean epoch was 6:48 in the War of the Rebellion." Here the draft figures are a.m. (e.s.t.) on January 8. Even this small delay is in given as "loaded, forward, 22"6"; aft, 23'." These values contrast with the situation at the mouth of the Connect- are obviously low, however, when the weight of guns icut River in the previous example, where the first maxi- and armorplate is considered. Top hamper also would mum higher high water occurred 33V2 hours earlier than have added considerable displacement, bringing the full- the mean epoch of perigee-syzygy. The fact that the pre- load draft of the Wabash certainly somewhere more ne .ar- dicted high tides at Port Royal Sound remained in ex- ly in the range of 24 to 26 ft. cess of the value of mean high water springs (6.4 ft) for The South Channel traversed by the Union Fleet is 10 a full 5 days after perigee-syzygy also illustrates the effect miles to sea from the entrance to Royal Bay. In intensified of perigee-syzygy in extending the duration of spring swell at such offshore distances, the heave and pitch of tides, and corroborates the similar 5-day extension at the vessel alone would require a safety margin of several Saybrook Light, Conn. (MHWS = 3.8 ft). feet for keel clearance. Thus the total depth of water HYDROGRAPHIC ANALYSIS required for safe passage of the Wabash over the bar A Preliminary Chart of Port Royal Entrance published would have been at least 28 ft. With the exception of hurricane-lifted seas, this water depth is available only in 1862 by the U.S. Coast Survey and based upon sound- as the result of the perigean spring tide conditions de- ings executed in 1855, 1856, and 1862 (of which fig. 16 scribed in the section on "Tidal Analysis," together with is an enlarged portion) shows the least depth of water favorable onshore winds. (for a chart datum corresponding to mean low water) along both the South Channel and the Southeast Chan- nel at the entrance to Port Royal Sound to be 3 Y4 The Perigean Spring Tide as an fathoms (or 19.5 ft). The South Channel was used by the attacking fleet. The Southeast Channel is somewhat Agent of Coastal Erosion narrower and contains contiguous shoals shallowing to. 3 fathoms. Because of the added onslaught against the land pro- The bar itself is about 10 miles from the headlands duced both by increased current velocity and greater forming the entrance to Royal Bay. A major shoal just to range in water level associated with perigean spring tides, the east of the South Channel and lying between it and low-lying and potentially submersible coastlines are sub- the Southeast Channel forms the most seaward part of ject to greater erosional influences under these circum- the bar, and is called Martin's Industry. The water shoals stances. The actions of strong onshore winds, high waves, to a depth of 6 ft here at mean low water (even less, if and swell may likewise tear at coastlines wherever these offshore winds prevail) and, because of the effects of in- meteorologically produced factors are present. When creased range, falls to 4 ft at low water associated with such wind-induced conditions also reinforce a higher- ordinary spring tides. To the west of the South Channel than-usual tide, a greatly increased erosional influence is lie the Gaskins Banks, with depths as shallow as 14 ft, almost certain to occur. Marked coastline attrition may decreasing to 11 ft (at mean low water) further north then result from both astronomical- and wind-accelerated where the two entrance channels converge. tidal current velocities, larger sedimentary particles main- DATA CONCERNING THE DRAFT tained in suspension in the water, and enhanced transport OF THE WABASH of eroded sediment away from the shoreline. The effects of tidal erosion also are related to more Precise figures on either the full-load or lightened drafts forceful water impact against the shoreline, and wave of the ship Wabash, flagship and largest in the fleet which scouring at greater heights and distances onshore than us- crossed the bar on the morning of November 5, are not ual. These influences may be combined, during each re- directly available. The only draft figures obtainable in duced stage of the tides, with foreshore-undercutting at connection with this vessel are those established in 1897 points which are lower, farther offshore, less compacted when the ship was stripped down and housed over as a through constant shifting, and herice less resistant to ero- receiving ship in the Boston Navy Yard, with her gun sion. Because the same intensified astronomical forces as- batteries and deck armament removed. The mean draft sociated with perigean spring tides act upon both the low - Impact of Perigean Spring Tides on American Nautical History 1 85 and high waters, this phenomenon is characterized by ex- commanded by Lt. George M. Bache, brother of the sec- ceptionally low tides as well as exceptionally high tides. ond superintendent of the Coast Survey, together with 10 When these are combined with powerful wind action, the seamen, were lost in this storm off the coast. Although re- erosional effects of such an alternation of extreme high and ferred to in some historical sources as a hurricane, neither low waters may be highly destructive, or even catastrophic, Ivan R. Tannehill in his book Hurricanes (8th ed., 1952) in contrast with the steady, degradational action of the nor Gordon E. Dunn and Banner 1. Miller in their work sea which occurs continuously on all coastlines during or- Atlantic Hurricanes (rev. ed., 1964) include this storm dinary tides. If perigean spring tides are accompanied among their comprehensive catalogs of true hurricanes and by strong, onshore winds and swell, large portions of tropical storms.' The accompanying gale swept the coast- beachline, as well as sections of the foreshore, may be line, adding its effects to a perigean spring tide whose max- gouged and torn away. imum rise on this occasion had occurred less than I day An interesting example of the effect of coastal erosion before, as a result of a perigee-syzygy alignment having upon an important episode in history occurred during the a mean date of September 5.0 (with components sepa- Civil War. rated by only - 15 hours). A sustained gale-force wind from the northwest on the 7th and 8th, coupled with high The Hatteras Campaign perigean spring tides, lifted the waters of Pamlico (then Both the bold planning and ultimate success of the spelled "Pamplico") Sound to a height of 2 or 3 ft over Hatteras Campaign undertaken by Union forces at the almost the whole of Bodie's Island." In consequence of very outset of the Civil War are a matter of detailed his- this violent flooding action, Oregon Inlet was forrned. torical record. It is not generally known, however, that This inlet is still called "New Inlet" in the first edition certain definite portions of this planning, as well as a con- of a nautical chart of Pamplico Sound, compiled by the siderable degree of success in the operational aspects of U.S. Coast and Geodetic Survey in 1883 (fig. 17). the campaign, were the indirect consequence of two earlier Portions of the barrier spit to the south similarly were astronomical occurrences of perigee-syzygy and their as- breached at a point where a comparison map of North sociated perigean spring tides. These precursory factors Carolina prepared by Brazier and MacRae in 1833 (fig. will be briefly reviewed. 18) shows no previous permanent passage. Near Hatteras On March 1, 1846, as documented in the annual Re- village, a variably inundattd tidewater area was rendered port of the Superintendent of the Coast Survey for 1847," navigationally passable overnight by the force of the ram- a severe coastal storm swept the vicinity of Bodie's Island, paging waters washing back from Pamplico Sound. Still N.C., and the resulting tidal flooding produced several another severe coastal storm occurred during October, breaches on the seaward side of this narrow spit-one of further scouring this southern inlet. Previously, the waters a line of barrier islands composing the Hatteras Outer forming this narrow channel had been too shallow to per- Banks. mit the passage.of deep-draft vessels. The larger inlet The sea piled onto the land and inundated numerous formed now possessed a sufficient depth of water to ac- portions of the Hatteras Banks. This first of a series of commodate rather sizable vessels, a circumstance condu- three severe coastal storms in the same year followed some cive to the development of active maritime commerce. 3 days after the maximum influence of a perigean spring Hatteras village provided a port for the transshipment of tide centered around February 26 (allowing for a 1-day goods to smaller intracoastal craft more suited to ply the phase- and parallax-age at this location, as normally ex- coastal waterways and rivers. Accordingly, Hatteras Inlet, perienced). This tide was associated with a condition, of as it was called, gradually came to outrank Ocracoke In- perigee-syzygy having an approximate alignment very let and its commercially declining town of Portsmouth in early in the morning of February 25, and a difference in shipping importance. The least depth of water at the en- time between its astronomical components of just over trance to this newly created inlet (which persisted, despite -30 hours. Because of at least a 3-day separation in time shifting sands, over the intervening 15 years until the Civil from the maximum of the perigean spring tides, the flood- War and thereafter) was 14-16 ft. Fig. 19 is an enlarged ing produced on March I only started to form the pre- portion of the U.S. Coast and Geodetic chart of 1883. viously mentioned breaches in the land. However, a second major coastal storm occurred on Again, with objective awareness that the defining conditions and September 7-8, 1846, as mentioned also in the Coast Sur- criteria for hurricanes have varied widely over history, see the Ex- planatory Comments preceding table 2. Cf. also David M. Ludlum's vey annual report." The Coast Survey brig Washington, Early American Hurricanes, 1492-1870, pp. 131-132. 86 Strategic Role of Perigean Spring Tides, 1635-1976 R -nr . -4 -D P'.A'Mpl@lco Sou'N NORTH CAROLINA v,% A ON WR R@ 7 T :j ji 7 FiGURE 17.-Coast and'Geodetic Survey Chart No. -142 (ed. 1) of Pamplico Sound (now known as Pamlico Sound), N.C., published in 1883. The small boxed area indicates the location of the present Hatteras Inlet, enlarged in much greater detail in figure 19. Impact of Perigean Spring Tides on American Nautical History 87 14 Jig 4 g V 6, N A 9Em -_3 - - - - - - - -Al -j& "M x A '4 Courtesy of Library of Congress FiGURE 18.-Enlarged portion of a "New Map of the State of North Carolina" drawn by Brazier and MacRae in 1833. At this time, although Ocracock (Ocracoke) Inlet is clearly present, there was no breach in the Outer Banks at the present location (indicated by the curved arrow) of Hatteras Inlet. Compare with figure 19. As acknowledged in various historical reference ing artery of communication which made possible a con- sources .... .. Hatteras Inlet had, through this single for- siderable flow of needed supplies through Virginia, North mative process of Nature occurring a decade and a half Carolina, and other States of the South in almost com- earlier, achieved a tactical significance which would en- plete defiance of the Union naval blockade. able it to play a definite role in the Civil War. With ready Toward the end of August 1861, the Union forces access to the open sea provided for privateers and block- were in need of a bold maneuver to counteract the in- ade runners through this inlet, Pamplico Sound became glorious defeat suffered at Bull Run some 5 weeks earlier. an integral part of a network of inland waterways main- In an active planning stage was the first major offensive tained. by the South to transport supplies to the Confed- by the Federal Navy in the Civil War. Hatteras Inlet erate Army. These waterways, in turn, formed a connect- became a key element in a coordinated plan to invade this 88 Strategic Role of Perigean Spring Tides, 1635-1976 A:, d ,:M d V* ... ...... ... N ID .4W: .......... b a 4. q. p MA: . .... . Q7. P.. .3 F b4 it. S I Olt On t FIGURE 19.-Enlarged section of C &GS Chart No. 142, ed. No. I (fig. 17), showing the hydrography of Hatteras Inlet in 1883. Breaching of the barrier spit was caused by the combination of strong eshore winds and severe backwash flooding from Pamlico Sound on September 7-8, 1846, accompanying perigean spring tides. Impact of Perigean Spring Tides on American Nautical History 89 Southern center of commerce by both land and sea. This manded by John P. Gilliss, tortuously warped into Hat- decision by Northern planners had been reinforced from teras Inlet." Through the combined efforts of the fleet a strategic standpoint through information provided by and land forces, and the expedient access provided by the captains of several Union brigs which, earlier in the this inlet, Fort Hatteras, Fort -Clark, and the waters of war, had been captured by the Confederate forces. Im- Pamplico Sound, were secured by the Northern forces prisoned near Hatteras Inlet, and subsequently escaping (fig. 20). through the assistance of privateers, they had confirmed This daring entry into the shoal-infested waters of to the Northern forces the existence of the new Hatteras Hatteras Inlet, subject to continuous fire from Southern access channel, and reported that as many as 100 blockade guns, provided a strong moral victory for the Nor-them runners were escaping through it each month. forces. The immediate consequence of the capture of The Federal Navy Department concluded that a land- these Confederate forts also gave -the North a strong base ing of troops from the sea on the beach near Hatteras of operations in Southern waters and a supply depot for Inlet, followed by a penetration of this inlet by ships to their blockading vessels. InsecuAng the principal means secure the two key forts which guarded it, was a move of ingress to Pamplico Sound, the North had blocked a demanding the highest priority and worthy of the first tactical lifeline vital to the war efforts of the Confederacy. major naval expedition into Confederate waters. The perigean spring tide which had, in conjunction with On Monday, August 26, 1861, the Union fleet set sail from Hampton Roads, Va., under the command of Flag strong winds, created Hatteras Inlet, also made possible Officer Silas H. Stringharn. Troops were landed on shore, an event of considerable importance to the Civil War in as planned, although under very adverse conditions of sea the subsequent passage of the Burnside Expedition and weather. On August 28, the screw steamer Monti- through this inlet (fig. 21), leading to the Battle of Roa- cello, of 655 tons, drawing 12 ft of water and com- noke Island on January 22-26, 1862. oil Xv Jf- Qrq 0 GQ ci 1 0 49-1 rt po CM ilt A, crq 10 z MI-ScOl 's'9P!.L Du'.4S' uvdD'I-IL9c[ 10 9109 Ozffdlv-'IS' 06 M0 CD 0 V1 C fe L qJ 4 CD C'D J, 0 U61 0 t7 0 0 71, FL 0 n ::j No muq @c 2 U14 k -0 0 "A"TAL.% W A, 0 0 G'Q IN C(Q Nj@ C) gs Id ;z CD d, P.-L yiv 4ilt, 4ilt, 46t, 46@ Z5 p IS 0 -45 1A T6 kzoj@zH jv9.zjnvN uv.?!'Iazuv UO S.,gp!,L @U.U@S' UV922.0d 10 JOV4JUl Chapter 3. The Practical, Economic, and Ecological Aspects of Perigean Spring Tides In addition to the previously demonstrated potential desirable, and will serve to emphasize their far-reaching for coastal flooding, many outstanding examples exist in importance. Such examples of international nature in- which the production of perigean spring tides or their cluded among the following may readily be extended by accompanying phenomena (such as strong tidal currents) analogy to the coastal waters of North America. has exerted a prominent influence upon projects in coastal engineering, shoreline reclamation, seawall or groin con- The Effects of Extremely Low Waters struction, and other functions, activities, or events of a technological nature. In the historical development and The same augmentation of astronomical tide-raising continuing application of both marine and maritime forces which, at times of perigee-syzygy, produces above- technology, in particular, as well as in various phases of average high tides is responsible-in the low-water stages intracoastal and harbor navigation, numerous circum- approximately 4-8 hours preceding and following-for stances have arisen in which the occurrence of perigean the production of tides which are exceptionally low. In spring tides has exerted a special impact. Typical of such the first case, enhanced tractive forces amass additional an historical tidal influence upon engineering projects quantities of water near the sublunar point on the surface was the complete destruction of Guglielmo Marconi's of the Earth (and its antipodal position) to create the in- experimental transatlantic radio tower by th6 combination creased high waters of perigean spring tides. At the same of a windstorm and perigean spring tide in 1915. This time, these increased forces draw additional quantities of incident occurred as the result of erosion and unden-nin- water from source regions along a great circle approx- ing of the tower by tidal flooding at Cape Hatteras, N.C., imately 90' from the common meridian of the first two on April 4 of this year (see table 1, chapter 1). positions. All points on this second great circle are sub- Although the role of these tides may have been ob- scured in the details attendant upon a particular activ- Ject to low tides. Because of the rotation of the Earth, these ity-or the tides may have affected only a partial phase exceptionally high and low waters alternate, some 4-8 thereof-their practical contribution to the ultimate suc- hours apart, at the same location during appropriate por- cess or failure of the activity can only be described as of tions of the tidal cycle. I major significance. Among the wide range of available Dangers of Explosive Decompression in examples, a representative few will suffice, and these are Submarine Environments given below. As in all previous instances cited of relationships de- The building of bridges across bays, inlets, or tidewater pendent upon the existence of perigean spring tides, it estuaries and rivers connecting to the sea is an activity must be remembered that the astronomical forces respon- much affected by such possible alternations of extreme sible for their production are worldwide in scope. Accord- high and extreme low waters, and as such constitutes an ingly, although the present work deals geographically area of extreme practical importance in connection with with the influence of perigean spring tides in North pengean spring tides. In the construction of large bridges, America, the addition of a few appropriate examples supported by piers whose foundations extend deep into to retain these tides in their proper global perspective is the soil beneath and along the water channel in order to 93 94 Strategic Role of Perigean Spring Tides, 1635-1976 reach bedrock, an engineering procedure is used which is another mechanical hazard exists which relates to the op- particularly sensitive to tidal changes. eration of the caisson itself. This is the possibility of "blow- In these projects, a device known as a pneumatic cais- outs," or violent reductions of air pressure in the caisson son is customarily employed to provide a pressurized at- caused by an improper seal and the sudden escape of the mospheric environment in which bridge construction air contained therein to the surrounding environment. workers, familiarly called "sandhogs," can work at nec- The open bottom of the caisson must at all times be kept essary depths below the waterline without being flooded immersed in the underlying soil to provide such an air seal. out by infiltration of water through the soil and into the Ordinarily, the buoyancy provided to the caisson by open bottom of the caisson. The pressure of the water is the contained air is balanced by the weight of the caisson. exerted equally in all directions, and increases directly (The hydrostatic pressure of the overlying water to which with depth according to the hydrostatic formula Pd - Ps the caisson is subject at any depth is noneffective in this =PgAd, where P., and Pd are the existing pressures at the surface of the water and at any depth "d" below the sur- regard since it is exerted equally in all directions.) How- face; "p" is the density of the water; "g" is the accelera- ever, should the hydrostatic pressure undergo sudden tion of gravity; and Ad is the change in depth involved. fluctuations due to marked changes in tide level, and be Since hydrostatic pressure is a function principally of "d", uncompensated by corresponding adjustments in caisson an identical pressure exists at any uniform depth in the air pressure, bubbles of air may escape beneath the bottom water, as well as throughout any water-satu Irated earth edge of the caisson and ensuing erosion of the soil may materials situated at this same depth. Thus, as a simple break the air seal. An overpressurized and overbuoyant example, an increase of but 16 in. in the height of the wa- caisson may lift free from the bottom and tilt hazardously, ter overlying a point (easily possible in the case of perigean or possibly float toward the surface.' As compressed air spring tides) results in an increase in hydrostatic pressure escapes from the caisson and is replaced by water, buoy- of 0.58lb/in' at all levels beneath. Even this compara- ancy is reduced and the caisson plunges downward again tively small rise in water level thus represents an increase under its own weight, embedding itself in the mud. Since in hydrostatic pressure amounting to nearly 8.5 times that caissons, like the pontoons used to float bridge beams into of the value of standard atmospheric pressure (0.068 place, also are buoyed into position on the tides, yet lb/in'). It is evident that such an increase (or decrease) another possibility exists for a mishap resulting from in hydrostatic pressureis possible through a corresponding marked tidal variation at times of perigee springs. rise or fall in any estuarine water level which is subject to Such an accident happened during the construction of the action of a strong tidal influence. the Firth of Forth Bridge, in Scotland, in consequence of To compensate for the increased hydrostatic pressure a perigean spring tide associated with a perigee-syzygy caused by additional amounts of overlying water (and to alignment of January 1, 1885 (at 5: 00 a.m. Greenwich- prevent water from 6ooding into the caisson) the work- meridian time, with a separation between perigee and men must breathe air which is compressed in excess of syzygy of - 13 hours). As is usual in the case of perigean the standard atmospheric pressure by an amount propor- spring tides, the occurrence of an extremely high tide was tional to the depth of the caisson. At a depth of 30 ft, the followed by an extremely low tide. As a result, as the water water pressure has increased to 13 lb/in', equivalent to a level fell rapidly, the massive caisson being maneuvered pressure 191.2 times that of the atmosphere. The atmos- into place for the northwest comer of the Queensferry pier pheric pressure within the caisson must, therefore, be in- dropped too suddenly and imbedded itself deep in the creased to allow for the extra pressure produced by a rise mud. Construction of this great bridge was delayed for 10 in water level at times of ordinary high tides and requires months since, despite extensive engineering efforts, the caisson could not be freed from the bottom until Octo- a still greater increment, of the magnitude indicated above, to offset the additional height of perigean spring ber 19, 1885.' tides. In SCUBA diving operations by NOAA, small adjust- Aside from the ever-present danger of a physiological ments in scheduled underwater activity and decompres- syndrome described as the "bends" produced by too rapid sion times are now made to permit adequate periods of depressurization (decompression) of the workmen's decompression for divers operating beneath the increased breathing air (with consequent excruciatingly painful re- depths (or incrementally changing depths) associated lease of inert nitrogen gas bubbles into the bloodstream), with perigean spring tides. Practical, Economic, and Ecological Aspects of Perigean Spring Tides 95 Ship Grounding I It must be emphasized again that extreme perigean Ship groundings and strandings likewise may be spring tides do not occur often enough in any one year affected by the unusually low water accompanying peri- that their influence becomes anything like a controlling gean spring tides. Although ships ordinarily do not enter one in ship groundings. Certainly, there is no intention, or leave ports during low water, in coastwise traffic they in presenting this factual record, to imply that ship often cruise just offshore where shoals and sandbars groundings occur only at perigean spring tides or subject exist-especially at the mouths of.bays and outside en- only to the conditions occurring around these times. Of trance channels. In such locations, unless proper precau- the extremely large number of strandings which have tions are taken, an active possibility exists for unexpect- occurred along the 86,000 mi of American coastline dur- ing the past 300 years, those mentioned are but an insig- edly running aground subject to the exceptionally low- nificant sample. However, should even one stranding have water conditions associated with the minimum stages of been caused, or be caused in the f ture, by a lack of perigean spring tides. The danger is amplified by the u strong ebb currents also present around these times. Un- awareness of this particular tidal phenomenon, it is a mat- questionably, a considerable number of ship strandings ter of concern to maritime commerce.' Because of a po- have occurred throughout American history which are tential loss of life, or the vessel and its cargo, a knowledge attributable to such circumstances. Representative in- of the inherent dangers becomes vitally important, par- stances of ship grouLadings occurring almost exactly at ticularly in an era of increasingly larger supertankers and the times of perigean spring tides, and which are, there- other deep-draft vessels. fore, at least suspect as to their probable or contributing An interesting historical example illustrating a side cause, are given in part II, chapter 8. effect of the extremely low waters associated with peri- The special significance of perigean spring tides for gean spring tides is contained in the facsimile (page modern supertankers and other deep-draft vessels will be 42) of an article from the New York Times of February considered in this same chapter. 10, 1895, relating to the considerable difficulty in loading It would be a somewhat fatuous effort to attempt to and offloading cargo from a ship at dock due to the isolate those cases . in which . the existence of perigean sharply inclined gangplank made necessary under such spring tides might be held to be totally responsible for the conditions. These circumstances still continue today in grounding of ships, because often so many other attendant connection with automatic loading ramps or conveyor and possibly contributory causes (such as fog, navigator's belts, and are of special consequence where the daily tidal error, mechanical failure, etc.) exist at the times of such range is exceptionally high, such as at Eastport, Me. strandings. However, the inclusion, in chapter 8, of some previous cases in which ships are definitely known to have The Effects of Accelerated Currents stranded around the times of penigean spring tides will As will be described in greater detail in part II, chapter serve to point up the special dangers both for nonpowered, 8, a corollary phenomenon resulting from, the perigee- deep-keeled sailing vessels and ships which, through their syzygy relationship is an increase in the velocity of hor- very ponderous nature or deep-draft design, are of cum- izontal (tidally induced) water currents. This is directly ,bersome maneuverability. related to the enhanced vertical rise and fall in water level Whether, in the cases documented, a navigational or produced by pcrigean spring tides. Such strengthened piloting error may have existed, coincidentally-whether currents pose a special problem because of their retarding a possible overlooking of updated nautical chart informa- influences (when opposed to the direction of a vessel's tion may have occurred-or an adverse condition of motion) on the headway of small, slow-speed, and cum * weather or other cause may have contributed-the fact bersomely towed craft, such as barges. Through their remains that the extreme low waters and strong currents accelerating or deflecting influences (when moving in known to be present in each case claimed their ultimate the same direction as, or across the course of an underway toll where the grounding otherwise might not have hap- craft) they likewise impair navigational control and, in pened. These accidents obviously took place at times and all cases, may engender a threat to the grounding of ves- locations where, had not low-water tidal conditions pre- vailed which were more severe than those ordinarily antic- 'An an .alysis of U.S. Coast Guard statistics covering ship ground- ipated, the shipmasters involved never would have ings over a period of 10 years reveals a total of 892 casualties to dreamed of running their ships aground, commercial vessels in which the cause was reported as "a water depth less than expected." 96 Strategic Role of Perigean Spring Tides, 1635-1976 sels, large or small. They also strongly influence marine may occur in these special areas in the case of tropical engineering operations which necessitate work at or below hurricanes.) the waterline., Even in these low latitudes, however, tidal currents run strongly and swiftly subject to the same increase in gravi- Impact Upon Marine Engineering tational forces responsible for the heightened perigean Projects spring tides. Current-produced groundings of ships are Typical examples of this kind exist in the laying of common, for example, in the near-shore waters of both foundations, cofferdams, and caisson supports for the Florida and the Gulf coast. piers of the large bridges which cross estuaries, bays, or Since the accompanying purely horizontal movement inlets affected by tidal waters. A noteworthy exampl e of of water involves both a time-related inertial buildup and the special problems presented by perigean spring tides frictional drag different from these same factors asso- during such a construction project is illustrated in the ciated with tides, the occurrence of the peak of tidal cur- difficulties encountered during the building of the Britan- rents can either precede or follow the peak of perigean nia (Railroad) Bridge across the Menai Straits between spring tides by several days. Periods of ebb currents Anglesey and Caemarvonshire Counties in nor-them usually last longer than periods of flood currents. As will Wales, Great Britain. Here the daily range of the tides be seen on page 98, the times of ebb and flood tidal varies from 2.6 to 24.3 ft, even at ordinary spring tides.. currents often differ considerably with respect to the times The same increased gravitational forces responsible for of high and low tidal waters. this large daily rise and fall in water level become the A typical example of an ocean liner breaking its moor- basis for a further strongly activated current flow accom- ings due to the strength of currents associated with peri- panying (but not a function of) the increased range of gean spring tides is given in the following excerpt from the perigean spring tides, New York Times of August 6,1925: On June 20, 1849, this tube-type railroad bridge was "The strong flood tide in the North River last night ready for the installation of its first span. The span was caught the stern of the White Star liner Olympic at Pier floated into place on pontoons, secured by lines to a 59 as the passengers were starting to go down the gang- giant capstan on shore. But the builders had not allowed ways with such force that the bow rope parted with a loud for the tremendous forces involved in the fast-moving report and the ship slid back about 13 feet. No one was stream associated with perigean spring tides on this date hurt. [The] captain who had given a whistle to make fast perigee-syzygy had to direct towboats again to push the big liner back in- at 9:30 a.m. Greenwich-meridian time, with a separation between components of -9 hours). to her former position." The current caught the pontoons, and the entire span The Influence of Improvements in was in imminent danger of being tom away from the Navigation Aids flailing capstan. Only the prompt and spontaneous action of the viewing bystanders, who applied their combined Alternate possibilities have been cited above, both of strength to the restraining lines, prevented this bridge strandings in the extraordinary shallow waters associated tube from floating out to sea.' with the low-water stage of perigean spring tides, and of ships drifting ashore or aground subject to the strong cur- Dangers to Navigation and Docking rents accompanying these tides. The preponderance of The effects of augmented tidal current flow around the such cases which occur in an early period of American time of perigee-syzygy are also evidenced in active dan- history is, of course, the result of several factors: gers to navigation. It is here important to emphasize (I) The common use, in these early times, of square- that the intensity of tidal currents is not necessarily directly rigged ships which, because of their unwieldiness, were in- related to the magnitude of the local tidal range. It will be capable of working readily against the wind; subject to seen in part II, chapter 7, that almost universally at low- strong onshore winds, these square-rigged vessels were latitude-and at certain mid-latitude stations along the often helpless against being driven into shallow waters and east coast of the United States-as well as in the Gulf of aground by the force of the wind. Mexico, the tidal ranges are very small. In general, these (2) The subsequent development, in an evolution- limited tidal ranges will not support extensive coastal ary process, of fore-and-aft rigged vessels such as schooners flooding where strong onshore winds prevail at the same and ketches-and the combined forms represented by time as perigean spring tides. (Although coastal flooding barks, barkentines, brigs, and brigantines-involving sig- Practical, Economic, and Ecological Aspects of Perigean Spring Tides 97 nificant refinements in hull and sail design; these vessels and whirlpools in the presence of strong currents, render- were capable of beating against the wind, and this, im- ing passage extremely dangerous to smaller craft and a proved maneuverability made them less liable to being matter of close concern to larger vessels. driven aground on bars or reefs, or ashore. The presence of this rock had been known ever since (3) The innovation of steam-driven vessels provided the voyage of Captain George Vancouver in HMS Dis- the necessary power to make sea room even in the face of covery in the year 1786, and is recorded in his journal. adverse conditions of wind and current and thus reduce The first reported major ship disaster attributed to this the possibility of grounding. (Although, even today, die- rock involved the U.S. Navy ship Saranac, a 1,484-ton sel-driven but ponderous and only slowly maneuverable paddlewheel steamer which struck the rock on June 15, supertankers may be forced aground by strong tidal cur- 1875, and became a total loss. Subsequently, and before rents.) the rock was destroyed in 1958, some 25 large vessels and (4) The invention of echo-sounding devices pro- several times as many smaller vessels collided with the vided navigators with a means of securing expedient, ad- rock, with damage ranging from 'Partial to total loss, and vance knowledge of approaching shoals, and submerged at a cost of 114 lives. Included among these ship losses ,bars or reefs. was the stranding of the U.S. cable ship Burnside, which (5) When a vessel is subject to the influences of occasioned a formal memorandum from the American strong tidal currents at night, or under conditions of fog to the Canadian Government recommending, on the or impaired atmospheric visibility, the availability of mod- strength of the cumulative record of disasters, the elimina- em shipbome radar reduces the danger of collision with tion of this hazard to navigation. other vessels, manmade structures, or natural features Technical studies were made in the years 1921 and above the waterline. 1931, and the first attempt at removing the rock was begun in 1942 as part of the war effort in connection with The Optimum Dispersal of Engineering militaxy shipping to Alaska. However, the extremely Demolition Products strong currents present in the passage prevented attempts Seymour Narrows, B.C., is a narrow strait, approxi- to destroy the rock which were made both in this year and mately 2.4 km (1.5 mi) in length, which lies on the east- in 1945. These currents tore away, or caused excessive ern side of Vancouver Island in that portion of the vibration in, the equipment and facilities used in an at- shipping route from Vancouver to Alaska known as the tempt to bore into the rock and to set explosive charges Inland Passage. Through this passage, barely 660-1,100 from a barge anchored above the obstruction. m (2,200-3,600 ft) wide, and flowing between Maud Such preliminary tests revealed the impracticability of Island on the east and Wilfred Point on the west, are either drilling holes or retaining a position in the vicinity some of the swiftest currents in the world. Even at neap of the rock for any extended period of time because of tides, the usual surface velocity is some 14.8 km/h (8 kt) the very high current velocities attained even at ordinary while, at the times of ordinary spring tides, the velocity spring tides. Similar attempts to work from a barge moored increases to 18.5-22.2 krn/h (10-12 kt), making normal to two strong steel cables running from one side of the pas- handling of a ship very difficult against the current flow. sage to the other and anchored to heavy bolts secured At times of perigean spring tides, the flow of water is ac- in the rocks ashore also met with failure as the cables celerated even more, and becomes a real hazard to the pulled loose under the intense strains to which they were maneuvering of ships. subjected by the forces of the currents upon the barge. Compounding the navigation problems, from the very Finally, it was determined that a procedure for drilling earliest days of sail between Vancouver and Alaska until into the rock from below by means of a shore-based access the year 1958, there existed, nearly centrally within this shaft and horizontal tunnel connecting to two further passage, a very distinct hazard to shipping known as vertical approach shafts extending upward to the individ- Ripple Rock. Oriented in a generally north-south direc- ual parts of the rock would be necessary.' / tion, and a little closer to the western shore of the passage, Such a project was inaugurated late in the year 1955 this rock originally constituted a hogback-shaped, under- and, the drilling work was completed early in 1958. The water obstruction whose two peaks rose to within 2.74 m time chosen for the exp losion of the charges imbedded (9 ft) and 6. 10 rn (20 ft), respectively, of the sea surface in the rock pinnacles was April 5, 1958, at 9:31 a.m., at mean low water. Because of this proximity to the sur- Pacific standard time (P.s.t.) - The reasoning behind this face, the submerged formations created both turbulence choice of time is a factor of direct importance to the preS- 202-509 0 - 78 - 9 98 Strategic Role of Perigean Spring Tides, 1635-1976 ent discussion. In order to obtain the highest current ve- A previous, somewhat lower tide (1.6 ft) on January locities possible and to ensure a quick dispersal of the ex- 6 (aided by the Earth's proximity to perihelion) oc- plosion products, a favorable compromise in circum- curred at 2116 P.s.t. But this was a nighttime extreme stances was selected. This included both extremely low low water, unsuited to the project-as were those asso- tides to permit increased rock dispersal (rather than lift- ciated with similar lunisolar alignments in the next follow- ing a huge mass of overlying water), and a strong ebb- ing perigee-syzygy series, October 14-November 12-De- tide to carry the detonation products northward and cember 11, averaging 7 months later. The only other lower thus avoid possible wave damage from the blast at docks tides in the year also followed after the April 5 date, and to the south. formed a part of the same perigee-syzygy series, 1.0 ft at The compromise plan involved the optimum use of 0900 on May 4, 0.9 ft at 0846 on June 2, and 1.6 ft at several specific tide and cur-rent factors close to the time 0831 on July 1. of the explosion. These were predetermined, and the proj- Finally, to the above conditions was added: ect scheduling was ostensibly adjusted to achieve a balance (3) One of the highest tides, although not actually of the most favorable tidal conditions as well as appropri- the highest tide, of the year. The time chosen for the ate weather and other operational factors. The tidally explosion followed a higher high water of 15.3 ft at 0401 contributing factors were: on April 6, with an immediately preceding lower high (1) A condition following, within some 26 hours, water of 13.9 ft at 1648 on April 5. The combination of the strongest ebb current predicted for Seymour Narrows these above-average high and low waters provided a during the entire year. This current of 26.5 km/h (14.3 greater hydrostatic head and a resulting hydraulic action kt) was predicted for 0805 P.s.t. on April 4, 1958. At contributing to a more efficient flushing of the naviga- 0846 on April 5, the predicted current was still 26.1 tion passage after the detonation. The mean higher high km/h ( 14.1 kt). Its strong northerly set acted to carry the water at this location is 14.3 ft; the mean lower low water wave front propagated from the blast, as well as the is 4.4 ft. waterborne products of the explosion, in a direction away The principal tidal advantage sought for this project from the nearest port facilities to the south. obviously related to the strong current flow. The some- Allowing for phase- and parallax-ages, the time chosen what less-than-maximum high- and low-water conditions for detonation was 41 hours after a perigee-syzygy situa- utilized, compared with the annual extremes, represented tion whose mean epoch occurred on April 3 at 1622 P.s.t., a compromise between the various requirements. with a separation between perigee and syzygy of only - 7 Although the- tides in the Inland Passage are of a mixed hours. and highly complex nature, extremely sensitive to solar The only other 26.1-km/h (14.1 kt) ebb current in and lunar declinational influences, and not as sharply the year was predicted for 2022 P.s.t. on October 13, responsive to the perigee-syzygy effect as are those on the 1958. This followed by 29 hours, and was similarly asso- northeast coast of North America, tidal currents in the ciated with, a perigee-syzygy situation having a mean channel obviously are subject to this latter effect. epoch of 1526 P.s.t. an October 12, with a perigee-syzygy The example given is illustrative of yet another case separation of +5 hours. The relationship between these .0 astronomical and perigean spring tidal circumstances *in where perigean spring tides have been used for a practical producing the highest current velocities of the year is purpose and with successful results. This largest non- clearly established. nuclear explosion on historic record was safely detonated at a propitious time, and the hazardous obstruction to This strong current situation was combined with: navigation represented by Ripple Rock was removed to (2) The selection of the first early morning tide of the great benefit of intracoastal navigation in this area. the year predicted for Canoe Pass, Seymour Narrows, which, at its low stage, was only 1.8 ft above the stand- Ecological Influences of Perigean ard datum Plane for the area. (Chosen timewise for its Spring Tides convenience in connection with the operational aspects of the explosion, this low-water level was also a feature Numerous of the physical, chemical, and biological particularly sought after in the project; with a very shal- properties of inshore waters which form a part of bays, .low depth of water overlying the rock, a more effective harbors, and inlets, and estuaries discharging thereto, are dispersal of the products of the explosion would be pos- especially subject to change as the result of both the,ex- sible.) tremely high and extremely low waters produced at the Practical, Economic, and Ecological Aspects of Perigean Spring Tides 99 time,of perigean spring tides. These changes, in turn, may key factor in the growth of many species of diatoms is the have a pronounced impact on the ecology of the estua- establishment of an appropriate rate of osmosis between rine environments contiguous to these coastal water the body fluids of these basic organisms and the water in bodies. Representative effects upon various of these pa- which these organisms live. It is known that the salinity of rameters as the result of the greater rise and fall of the seawater plays a significant role in providing the necessary tides, and the intrusion of seawater to greater distances partial pressure for osmosis to occur, and in the continued into the tidewater zone (and especially into regimes which preservation of this osmotic relationship. normally consist of freshwater) around the time of peri- Some species of (stenohaline) marine animals-usual- gee-syzygy will now be considered. ly, but not always, residents of the deep sea-are extreme- Variations ,In Salinity ly sensitive to changes in salinity. Other (euryhaline) ani- mals display a wide tolerance to saline variations, or can Because of (1) the continuous (and sometimes flood- make necessary adjustments thereto-but not under ex- level) discharge of freshwater from coastal rivers into treme conditions. estuaries, and its possible retention therein by a backup A phenomenon known as entrainment in estuarine of unusually high tides: (2) occasional very heavy rains waters is also a function of changing relative salinity with combined with very low tides; (3) inshore intrusion of, depth. Entrainment is that process by which the fresh- seawater as the result of unusually high tides; and (4) water outpouring from streams into an estuary, being less the evaporation of water in the shallow capture basins dense than saltwater, overrides the latter, and moves off- of tidelands and wetlands, estuarine regions are espe- shore through the estuary at a level near the water sur- cially vulnerable to significant changes in salt content, or face. At the same time, in compensation, more dense salt- salinity. All of. the foregoing conditions may occur in water moves into the estuary from the ocean to form the direct consequence of perigean spring tides. These changes bottom waters of the estuary, the so-called "saltwater may seriously affect the marine inhabitants of such in- wedge." The direction of currents may thus differ by as shore waters. Through associated changes in the density much as 180' between the surface and bottom water in and specific gravity of seawater, salinity is also of con-, the estuary. sequence in altering its relative buoyancy. This factor, A characteristic accompaniment of the estuarine en- in turn, may influence the depth to which marine life vironment is the production of "saltflats," "marshlands," forms (including eggs and larvae) sink-sometimes out and "tidelands" by the tidally induced inflow and out- of their life-sustaining environments. flow of saltwater. The biological regimen is usually quite In this same consideration of factors conducive to the closely controlled by the saltwater, in which, among plants, preservation and development of desirable forms of ma- only marshgrasses will grow. Extreme high tides such as rine life, various types of marine animals used for human those produced at times of perigee springs, with conse- consumption have been shown to be reduced in size and quent isolation of water in shallow pools, cancause evap- maturation in habitats of lesser salinity. Fish respiration is oration basins to develop. The local salinity increases, easier in saltwater than in freshwater, and greater schools marine life is choked out, and waterfowl and seashore of fish are usually found in waters of increased salinity. On wildlife. are affected, Pollution and noxious odors aJso the other hand, decreased salinities may support the exist- result from the decaying grass and fauna. ence of marine shipworms such as.Teredo navalis. Marine life is ordinarily protected against any quick From a marine biological standpoint, the zoo-plankton- change in salinity in a closed-basin environment by the phytoplankton relationship is an inverse one; where min- high latent heat of evaporation, which also means that an ute marine animals are reduced in numbers by low salin- existing low-saline water mixture does not suddenly chill ity, marine plants which often serve as their food source as evaporation occurs from its surface. However, such may proportionately increase to the point of fon-ning marine life is not protected against marked increases in a dense, navigation-fouling mass, particularly where nu- the relative salt concentration of the water such as may tritional salts are available from sewerage waste materials. occur by sudden intrusion in the case of windblown and Water contamination inevitably results. flood-producing perigean spring tides. Thus, specifically, a class of algae known to marine biol- Increased salinity of seawater may also variously act to: ogists as diatoms may either serve beneficially as good (I) exert a greater corrosive influence on ship hulls (with grazing (herbivorous) marine animals, or may destruc- an accompanying increase in the production of rust) ; (2) tively foul estuaries by their too prolific development. A discourage the growth of green algae in coastal waterways 100 Strategic Role of Perigean Spring Tides, 1635-1976 along docks, piles, and piers; and (3) provide a source of- through a colder -surrounding environment. As the tem- incrustations and vegetation-killing salt_qcposits wherever Perature. rises, the capacity of the water for absorbing evaporation occurs in shallow marshland pools. In this oxygen from the air also decreases, starving the fish of latter respect, "increased salinity may also have an effect needed oxygen. The production of temperature extremes on the use of estuarine water husbanded in the tidewater is not frequent in the case of the encroachment of peri- zone for irrigation projects. gean spring tides from the open sea. However, the pro- duction of their associated strong currents may change the Variations in Carbon Dioxide Content temperature of the surface water considerably by horizon- The presence of carbon dioxide in seawater is vital to tal advection of warm water, or replacement of warm sur- both marine flora and fauna because of the necessity for face water by cold water from below if upwelling or over- these marine lifeforms to absorb quantities of carbon into turning and mixing, produced by -density differences, their systems and, through synthesis, to convert carbon, should occur simultaft-e-ously with the intensified flood or oxygen, and hydrogen into carbohydrates. In the case of ebb currents. marine flora, this is accomplished through the process of As will be seen in chapter 7 of part 11, the dynamic photosynthesis; in the case of marine fauna, the action is impact of the unusually high water levels and strong accomplished through respiration and metabolism. The currents associated with perigean spring tides is a pow- necessary source of carbon in each case exists in the abun- erful one when these tides are accompanied by strong, dant carbon dioxide found in seawater. persistent, onshore winds. Often resulting in major struc- On the other hand, the presence of plantlife, absorbing tural damage along the coastline, the physical effects of certain limited quantities of carbon dioxide and leaving these two concurrent factors are also of importance in the seawater slightly alkaline, favors the synthesization of connection with: (I) the diffusion or turbulent dispersion carbonates by hard-shell animals dependent upon the of pollutant wastes as a function of concentration (den- building up of their shells by absorption of these carbon- sity) ; (2 ) the resulting relative buoyancy within the water ates. A balanced ecobiological condition is thus main- environment; and (3) the presence or absence of ver- tained which is very sensitive to -changes in carbon dioxide tical currents. content of the seawater. The-stability of the carbon diox- Estuarine pollutants of comparatively high density ide content is a necessary aspect in the -Cxistence of many with respect to the water will normally sink to the bottom forms of marine life, and the existence of an exact carbon because of their weight. Here they can become trapped in dioxide-oxygen balance is extremely important to all, ma- the cold and dense water below a thermocline surface rine life'forms. (possibly accompanying a "saltwater wedge") in the es- The quantities of carbon dioxide dissolved in seawater tuary in the same general manner that smog pollution is held down beneath a temperature inversion in the atmos- can be increased as the result of strong evaporation, or by an increase in salinity. In an action opposite to that of phere-but with different effects. A temperature inversion most gases dissolved in a water solution, the amount of in the atmosphere (warm air above cold) is a stable con- carbon dioxide absorbed by the water also increases as the dition which prevents mixing and supports pollution of temperature decreases. Any of these properties of the vol- the atmosphere by ground smoke. Conversely, a situation ume of seawater associated with, or resulting from, the in- of warm water above cold (while also a stable one) holds cursion of perigean spring tides far up into the tidewater heavy pollutants near the floor of estuaries where they are area may produce the variations noted, with consequent least bothersome. effects on the ecobiology. However, the presence of a sharp temperature gradient Variations in Water Temperature between cold water near the surface and warm water below a thermocline can result in turbulent mixing and Many forms of marine life are extremely sensitive to lifting of the pollutants to the surface. The altered thermal temperature variations, are incapable of adjusting rapidly conditions produced by the strong influx of cold water in to marked changes in the temperature of the water en- a wind-driven perigean spring tide can give rise to this vironment, and may expire if these temperatures are al- situation. tered suddenly or if temperature extremes are imposed The Effect Upon Grunion Runs upon their habitats. Increased water temperature, through the resultant expansion of the water, is associated Along the southern coast of California, from southern with reduced densities which can cause water to rise Baja California to Monterey Bay, a familiar source of Practical, Economic, and Ecological Aspects of Perigean Spring Tides 101 nighttime sport fishing on the beaches (and, to a limited and at new moon when perigee lies nearest to this alternate extent, commercial fishing from near-shore boats) is the position of syzygy. member of the silverside family (resembling smelt) @ The perigee position (representing the closest prox- known popularly as grunion. These fish, which are gifted imity of the Moon to the Earth) provides an extra grav- with a very remarkable "biological clock," are found itational force lifting each such set of reinforced spring nowhere else in the world. tides to an even greater height. As a further consequence, During their regular spawning season, from February the uplift of this one spring tide in each monthly pair is through August of each year, thousands of these fish ride greater the smaller is the separation in tirne (and hence the crests of incoming waves which occur less than an hour the closer is the geometrical alignment) between perigee after the maximum high-water stage of ordinary spring and syzygy, culminating in the condition known as tides (i.e., tides associated with either the new or full perigee-syzygy. phase of the Moon). The fish are washed ashore by the In addition, the greater of these two monthly peaks breaking waves. As each female fish is carried well up alternates between new moon and full moon once in each onto the beach, she lays her eggs in the sand just below 6.0-6.5 to 7.0-7.5 months (see chapter 6). This maxi- the maximum high watermark reached in the current mum tidal peak also rotates with respect to the seasons cycle of high tides. Here the eggs are simultaneously fer- during successive years as a function of the net forward tilized by the males.' motion of perigee in the lunar orbit (see chapter 4). A The eggs remain in the soft, moist sand during the complete reversal from a maximum tidal peak at full period of time required for hatching@which corresponds moon to a maximum peak at new moon during a given almost exactly with the one-half lunar month required month of the year takes place in a period equal to one- for the Moon to reach the opposite phase of syzygy (i.e., half the time (8.85 years) required for perigee, subject to from new moon to full moon or the reverse). If the eggs solar perturbations, to rotate once around its orbit. (Com- were laid even a short time after the crest of higher high pare, for example, in west coast tide tables the greater of water, they might easily be reached and gouged out by the the two higher high water (nighttime) syzygian tides at higher high water of very nearly the same height occur- San Diego, Calif. at full moon during the spring of 1976 ring slightly more than 24 hours thereafter, or by the next and those at new moon during the spring of 1972, ap-, succeeding lower high water some 12 hours later-in proximately one-half perigean cycle earlier.) either case far too early in their 2-week hatching cycle. If As a general rule, grunion tend to avoid the higher of the eggs were laid too soon, before the crest of higher high the two syzygian tides in each lunar month in favor of water, they might be gouged out again at the peak of this either the immediately preceding or following smaller HHW stage. Ile same principle applies to the necessity spring tide. Were the fish to deposit their eggs at the for spawning at the highest of the two daily high tides, higher peak of the two spring tide maxima in each luna- since if eggs were laid at lower high water, they would be tion, it would mean the lapse of a full month before the washed out to sea again during the higher high water of tide reaches the height of the eggs once again. the same 24-hour day. The exact moment selected for Laying of the eggs at the time of the lesser maximum spawning is, therefore, very critical, and the grunion ob- in each cycle ensures the certainty that the following viously possess some undetermined sensory ability to higher maximum at syzygy some 2 weeks later will isolate an interval of time occurring immediately. follow- reach them again and wash them back out to sea. Ten ing the downward turn of an appropriately selected spring days to 2 weeks is the normal hatching period for grunion high tide. eggs and represents the optimum time at which they During the peak of the grunion spawning season, should be returned to the sea for continuing existence. March through June, spring tides produced at full moon For various reasons, any extension of this period reduces may be either. slightly higher or slightly lower than those their probability for survival. produced at new moon. The particular syzygy configura- Similarly, readily granting the ability of grunion to tion associated with the highest tides depends upon which sense, in advance, the differences between growing tidal of these two lunisolar alignments agrees most closely in heights, these fish would be expected to avoid egg laying time with that of perigee. Thus, the highest tidal peak in at the peaks of perigean spring tides. This is because it any one month occurs at full moon on those occasions would be 6 or 7 months before sufficiently high tides once when the time of perigee is closest to this lunar phrase, again reached the spawning grounds to return the eggs 102 Strategic Role of Perigean Spring Tides, 1635-1976 to the sea (and possibly not then-depending upon the of each 'tidal cycle. Ordinarily, such ice floes require sev- relative heights of the two tides). eral days and successive tidal cycles to make the down- In fact, among the limited available data tabulating stream journey leading to the point of outflow to the grunion runs by actual dates,-it has not been possible to open sea. The collision of ships with these ice floes is pos- find such runs occurring at the maximum crests of peri- sible anywhere en route. gean spring tides. However, they do occur in the lesser 3. In navigational channels and at dockside facilities high waters of syzygies preceding or following a peak located above the normal tidewater mark, the increase perigean spring tide-or in the declining stage of this tide, in water level resulting from perigean spring tides is also as happened at Ocean Beach, Calif., on February 8, 1978. combined with an increased buoyancy caused by the salt- water intrusion and its greater density in comparison Miscellaneous Environmental Influences with freshwater. As a result, any vessel will ride propor- An historic ancillary effect of perigean spring tides tionately higher in the water. This fact may add to the steepness of the more conventional run-out angles be- which is no longer of any consequence was the influence of tween gangplanks or cargo conveyor belts and piers (see these tides in causing the penetration of saltwater up tidal pp. 42, 54, arts. N.Y. Times 2/10/1895, 10/24/1953). rivers alternately for several days, sufficient either to cause Waterline or load-line readings likewise must be obtained the breakup, or prevent the formation and cutting of, from the saltwater Plimsoll marks rather than the fresh- blocks of ice for storage and sale at ice houses alongside water Plimsoll marks. - the river. However, this same influence continues today 4. The relative freedom from po Ilution of an estuary as then in the action of such tides in bringing saltwater into which waste products and sewage arc regularly dis- .far up coastal rivers to points well beyond the normal charged is, in part, a function of the amount of flushing tidewater mark. Numerous related effects may result from which occurs within the estuary subject to the action of the intrusion of these tongues of saltwater variously into successive high and low tides. As a consequence of the agricultural, sports fishing, or ecobiological environments higher HHW, lower LLW, and stronger currents asso- unsuited to receive them. Adverse effects also may result ciated with a perigean spring tide, the flushing action is from the overflowing of river banks not built to withstand increased, resulting in an improved dispersal of pollutant the accompanying tidal increase in water level-or floods wastes. produced by blocking of the downstream hydrological 5. A sample instance of the practical impact of peri- runoff resulting from any coincident, excessively heavy geari spring tides upon fishing activities involved the oc-' precipitation. Some of these effects are described below: currence of this type of tide on July 19, 1974. The case 1. Because the presence of salt in water lowers the reported related to the failure of a small commercial fish- freezing point of the solution compared with that of ing enterprise to find any schools of flounder in their freshwater, the incursion of such saltwater tongues is customary deepwater haunts in Chesapeake Bay on this very effective in preventing the freezing of a river at points particular day-threatening to negate the entire day's upstream which would normally be covered with ice at catch. (Flounder customarily f avor the sidewalls or comparable temperatures. For example, under such hard- ledges of deeper channels and prefer sandy, rather than freeze conditions, portions of the Hudson River, usually muddy, estuarine bottoms.) The fish were finally ac- icebound, would remain open to navigation for the same cidentally discovered, movirg upstream in the shallower reason that the saltwater of New York Harbor remains and quieter waters close to the extreme outer banks of free of ice c'over. the bay, a location which they chose in order to avoid 2. Subject to the influence of perigean spring tides, fighting their way against the unusually strong down- the subsequent breakup of a sheet of river ice already stream currents in the deeper parts of the channel, caused formed can also create a navigational hazard as the ice by the perigean spring tide. floes are propelled by much stronger surface currents 6. Vacationers are also apt to find beaches on which associated with perigean spring tides. A danger of ship they are accustomed to sunbathe-and which are gen- collision with these ice floes occurs as falling tides and erally dry and sufficiently broad above the- waterline to their outgoing (ebb) currents carry the ice blocks down- accommodate crowds even at high tides-completely stream and the return (flood) currents created by rising covered with water and unusable during times of in- tides carry them partially back, in the respective portions creased perigean spring tides. Practical, Economic, and Ecological Aspects of Perigean Spring Tides 103 Recapitulation of the Practical (2) Elevation of high-water level above that Influences of Perigean Spring Tides of sewerage outfalls, causing impairment T and improper distribution of pollution A fairly representative listing of the practical and eco- runoff (Pacifica, Calif., December 20, nomic effects of perigean spring tides, both adverse and 1972.) beneficial, is summarized below. These influences are (3) Retardation of hydrological runoff (re- grouped by category, with prototype examples being given sulting from intense rainfall, snowmelt, in all cases where substantiating evidence is available. freshets, etc.) to the sea, thereby increasing In addition, to provide proper balance, there are included the coastal flooding potential from these a select number of instances of the contributions made to sources; this blocking of runoff at high scientific research in related geophysical projects by the T water adds further to the flooding impact enhanced gravitational forces associated with perigee- of landfalling hurricanes (including syzygy. typhoons, tropical cyclones, or baguios), and both tropical and extratropical coastal Influences of Perigean Spring Tides for storms, if perigean spring tides occur Which Substantiating Evidence Is Available coincidentally therewith (Boston, Mass., (Representative examples, by date and locality, are March 21, 1936.) given in parentheses following the description of each (4) Buoyant uplifting of small craft (or their mooring buoys) to the limits of their influence which has been corToborated in one or more anchor lines. This may result in a dragging instances to date. In those cases preceded by the letter of anchors and/or shearing, of mooring "W," the effects noted are made possible only when the W cables, with loosing and dispersal of the astronomical high and low waters, amplified by the coin- small craft to the forces of wind and sea. cidence of lunar perigee and syzygy, are also accompanied (Severe threat at Avalon Harbor, Catalina by strong, persistent, onshore (or offshore) winds, respec- Island, Calif., January 8, 1974.) tively. As the winds increase in velocity, the indicated (5) Subject to the exceptional tide rise, a effects are increased in proportion. In those cases preceded possible buoyant uplifting of sailboat@ by a "T," the intensified astronomical high or low waters docked in boathouses to the point of alone are sufficient to produce the observed effects.) W impact of nonretractable mastheads with 1. Increased Tidal Rise, at High Water the roof overhang. a. Adverse Effects (Avalon Harbor, Catalina Island, Calif., (1) Coastal flooding, with damage to beach January 8, 1974.) homes and condominiums, shoreline struc- (6) With the same marked rise in water level, tures, wharves, docks, and -marinas; occur- a potential inability for the mastheads of rence of shore and beach erosion, wave tall, lightly loaded (and nonballasted) gouging, scouring, of berms, scarps, and W vessels to pass beneath the nonraisable foreshore; breakover and undercutting of or nonrotable trusses of bridges spanning seawalls, bulkheads, and waterfront road- bays, sounds, straits, or estuaries. ways; inundation of saltflats, drainage (7) Inundation and concealment of bars, swamps, and tidewater marshes; destruc- sunken wrecks, rocks, or pinnacles usually tion of marine fauna and flora in the exposed under high tide conditions and W intertidal zone; ravaging of waterfowl T at ordinary spring tides but, with the refuges, coastal wildlife sanctuaries, and high waters of perigean spring tides, national seashore parks; damage to inshore posing a potential navigational hazard. fishing grounds, and to oyster, mussel, and (Execution Rocks, Long Island Sound, other hardshell beds; disturbance of the N.Y.-numerous occasions.) natural ecological balance. (More than 100 (8) In implanting the pneurilatic-type cais- representative instances of severe tidal sons used in the construction of piers for flooding occurring along both the Atlantic bridges across estuaries, coastal embay- and Pacific coasts of North America over ments, etc., an increase of only 16 inches a period of 341 years are listed in tables,l -2.) in the depth of the overlying, or the sat- 104 Strategic Role of Perigean Spring Tides, 1635-1976 urated interstitial ground waters requires T Connecticut River, August 11, 1779; an increase of approximately 8.5 times Second Siege of Charleston, S.C., March the atmospheric pressure within the cais- 20, 1780; Battle of Port Royal Sound, S.C., T son in order to prevent water infiltration. November 5, 1861.) A definite danger exists for serious seepage (2) Breaching of new inlets or channels, into, or flooding of, the caisson if the permitting ship passage through previously ambient pressure in the caisson is not W impassable offshore barrier spits. increased to compensate for the additional (Hatteras Inlet, N.C., September 8, 1846.) hydrostatic head of water associated with (3) Increased flushing of bays, harbors, and perigean spring tides. estuaries as the result of the greater (See also the opposite, occasionally en- water-intermixing and mass-transporting countered "blowouts" under 2a(4).) capabilities of perigean spring tides and (9) A small but quantitatively significant T their associated stronger tidal currents; adjustment must be made in decompres- this causes a greater dispersal of the sion and/or bottom times of divers engaged effluent pollutants which are discharged in activities which entail a close observ- into these water bodies and an optimum ance of the operational parameters of diffusion and attenuation of water depth and time. Because of the increased contaminants. hydrostatic pressure to which the divers (4) Provision of necessary test conditions T have been subjected at all depths, the for pursuit of quantitative investigations extra height of perigean spring tides in the field of physical oceanography (and the sensible variation in the column and for enhancement of knowledge of of overlying water from low to high T the ocean environment; e.g., the observed tide) may necessitate going to a new destabilization, destratification, and decay diving schedule. influences produced in internal waves by (Considered in NOAA/MUST diving pro- excessively high tidal waters. grams since the perigean spring tide of (Meteor Expedition, April 13-16, 1937, January 8, 1974.) Pioneer Expedition, June 12, 1964.) (10) Extraneous influences may be induced in (5) A means for possible updating and refine- Earth-tide measurements. These take the ment of classical geophysical experiments, form of tilting or deformation of the such as: Earth's crust (together with possible short- (a) Empirical checks on the mass of the period subsidence effects) caused by tran- Moon (although this method as orig- sient but appreciably increased tidal inally used is not very accurate) loading along the coast, Leveling obser- (William Ferrell, Boston Harbor, T vations conducted around the times of 1871). these extraordinarily high tides, as well (b) Determination of the rigidity of the as deflection of the vertical in astronomic T Earth from varying attraction of the observations, and systematic gravity anom- Moon. aly measurements, all may be affected (Albert A. Michelson, Yerkes Observ- thereby. atory, University of Chicago, March (See part 11, chapter 8.) 1914.) b. Beneficial Effects (c) Isohaline undulations in the deep- water layer (the "Moon-waves of (1) Possibility for navigation over otherwise the Gullmar fiord" directly related too shallow and impassable bars, reefs, or to extensive herring catches along other underwater features. (Release of the Scandinavian coasts). frigate Trumbull from the mouth of the (Otto Pettersson, Denmark, 1912.) Practical, Economic, and Ecological Aspects of Perigean Spring Tides 105 2. Decreased Low Tides, at Low Water (the effects 3. Strong Tidal Currents thereof are intensified where the existing astronom- a. Adverse Effects ical low tides are accompanied by strong, persistent, (1) Difficulty in maneuvering heavily loaded offshore winds). cargo ships, tankers, and barges, or tugs a. Adverse Effects and ferries; danger of collision with bridge (1) Causing supertankers and other deep-draft supports, pier pilings, and docking vessels (especially those engaged in coast- facilities, as well as intercollision with wise traffic) to strand as the result of T other boats; accompanying threat of en- W unusual and unexpectedly low water in virODmental pollution by oilspills, etc. shoals and shallows, or because of sharply (2) Increased transport of bottom sands and reduced water levels over bars and reefs; sediment; shifting of bottom features and poses an associated danger of oilspills and T alteration of hydrography through silting, other environmental pollution. deposition, or scouring. (2) Causing boats at dockside or moored to (3) Accelerated diffusion of oilspills, waste buoys in estuaries which are normally products, sludge, and other contaminants, subject to a large tidal range to settle T and possible shoreline pollution before T aground on their keels-necessitating a appropriate protective measures can be special scaffolding or "mattress" at some taken. locations to prevent them from cap:.izing. (4) Danger to boats, both channel-moored (A frequent occurrence in the tidewaters and underway-and to bridge supports, of the Bay of Fundy.) piers, moles, and shoreline bulkheads, (3) Requirement for unusual and difficult T from rapidly drifting ice floes ("harbor T adjustments in gangplanks, offloading masters.") (New York Harbor, February 9, belts, etc., at low tide (and high water.) 1895.) (New York Harbor, February 9, 1895; (5) Difficulty in emplacing caissons, in floating Jersey City, N.J., October 23, 1953.) bridge trusses into place, and in con- (4) A potential hazard from "blowouts" in T summating other marine engineering or connection with pneumatic caissons used diving operations subject to the strong current flow. in construction of bridge piers across (6) Maneuvering difficulties experienced in T tidal estuaries, etc., if suitable atmos- deepwater diving operations involving pheric pressure adjustments are not made lightweight one- and two-man submers- for the lower hydrostatic pressure resulting T ibles;, perigee-syzygy as a possible con- from the lesser weight of overlying water tributing cause of "turbidity currents." at extreme low tide. (NOAA two-man submersible operations b. Beneficial Effects in Oceanographer Canyon, July 17, 1974; (1) Exposing of portions of the seafloor encounter with turbidity current.) ordinarily covered by water-a boon to (7) Formation of "tide rips" (as distinguished marine biologists, marine archeologists, from "rip currents") offshore. In the shipwreck hunters, beachcombers, etc. formative process, the progress of ocean T (Pacifica, Calif., December 20, 1972; waves is slowed down and their height is Dunwich, Suffolk, England, January 11, increased by encounter with an oppositely 1974.) flowing current of considerable strength T (4-5 kt). The wave slopes are steepened, (2) Opportunity to undertake repairs to fixed and the formerly smaller waves develop T marine structures at low levels not usually into larger, breaking waves of short permitted, but now accessible above the wavelength,' offering considerable resist- waterline. ance to, and retarding the passage of, 106 Strategic Role of Perigean Spring Tides, 1635-1976 small vessels. The strengthened tidal cur- uary 15, 1961, nearly coincided with a rents associated with perigean spring very close perigee-syzygy situation of tides may provide the adverse currents January 16 (17.5b e.s.t.). producing such "tide rips." b. Beneficial Effects (Tide rip and internal wave observed (1) Strong currents Associated with perigean aboard US &GS Ship Pioneer in Andaman spring tides may act as a deterrent to Sea area off northwest coast of Sumatra the formation of sheet ice in extremely on June 12, 1964.) T frigid weather. This function will tend 3. a. (8) Disturbance of the thermohaline balance to keep narrows and other navigational usually present in estuaries. When an channels open and clear of solid ice when inmoving tidal current is large in com- such passage (for transportation of fuel parison with the outgoing flow resulting and supplies, etc.) is essential. from discharge of rivers, etc., an increased (2) These same currents can also cause solid mixing of fresh- and saltwater occurs. shields of ice, formed during protracted This action destroys the stabilizing effect cold spells and impairing all navigation, T of an existing wedge of heavier saltwater T to break up mechanically before more along the bottom, tapering upstream, favorable weather arrives which is with overlying freshwater flowing down- sufficiently warm to produce thawing. stream. Such mixing can both overturn (Documented case, February 13, 1687. See the stabilizing entrapment of cold bottom table 1, Ludlum Is p. 25.) water-bringing this colder water to the (3) A contribution to oceanographic and surface-and eliminate the existing geophysical knowledge (e.g., more precise thermocline. quantitative investigations of the electrical (9) Production of dangerous navigational cur- T current flow generated by the motion of rents due to hydraulic gradients formed strong tidal currents through the Earth's within basins interconnected by a narrow magnetic field). channel or strait, where the exceptionally 4. Other Potentially Correlatable Geophysical In- T high perigean spring tides occur at differ- fluences ent times at opposite ends of the channel Establishment of a possible gravitational (e.g., in Deception Pass, Puget Sound, relationship between the astronomical con- Wash., or in Seymour Narrows, east of ditions responsible for oceanic perigean Vancouver Island, B.C.). spring tides and any similar reinforcement .(10) Creation of extremely intense erosional of atmospheric tides-e.g., a conceivable currents by the "resurgent" action of correlation between the astronomical con- perigean spring tides as the high water dition of perigee-syzygy and the property breaks over offshore spits and low barrier of dynamic convergence in atmospheric islands. The accumulating head of water pressure systems producing low-pressure is trapped in lagoons, shallow bays, or centers. Only such low-pressure cells sounds and, as the external tide lowers, possess sufficiently tight pressure gradients attempts to discharge again to the sea to produce the strong, persistent, onshore through existing narrow channels or by winds -necessary for active coastal flooding resurgence over the barrier spit. Exten- in connection with perigean spring tides. T sive scouring and breaching may result. A tantalizing but statistically uncertain Oceari-floor erosion may also occur in zone of agreement exists between these the shallow waters of the Continental two phenomena throughout the more Shelf, due to accelerated ocean currents than 100 years of joint tidal and meteoro- associated with a condition of perigee- T logical records intercompared in the pres@ syzygy. It is noteworthy that the entirely ent study. wind-attributed destruction of a U.S. (From the meteorological viewpoint, an Air Force radar (Texas) tower 60 mi off analytic study made in the Meteoro- the coast from New York City on Jan- logical Statistics Group, ERL, involving Practical, Economic, and Ecological Aspects of Perigean Spring Tides 107 62 years of record, shows an apparent nomena. All of these studies involve positive correlation between U.S. pre- tidally induced effects, in one form or cipitation-generally associated with low- another. pressure centers-and the times of lunar (Cf. Nature, May 28, 1966, p. 893; syzygy.) Nature, November 10, 1972, p. 91; A significant and increasing Dumber of Irish Astronomical journal, December 1972, scientific investigations are now being p. 298; journal of Geophysical Research, undertaken into the possible interrelation- November 10, 1973, p. 7709; New ships between various gravitational force Scientist, January 10, 1974, p. 54, Geo- influences acting throughout the solar physical journal of the Royal Astronomical system and terrestrial weather, earthquake Socie@y, May 1976, p. 245; also part H. production, and other geophysical phe- chapter 8.) Chapter 4. Survey of the Scientific Literature on Perigean Spring Tides In tracing the earliest beginnings of knowledge con- est fere duplum ejus, quod ex variata diametro superius cerning perigean spring tides, it is noteworthy that a erat inventum." clear awareness of the concepts of lunar perigee and Consistent etymological, if somewhat inadequate sci- syzygy (conjunction or new moon, and opposition or full entific descriptions of perigee and syzygy also appear moon) -as well as the possibility of their near-coincidence variously in ancient Arabic, Hindu, and Greek treatises in time-existed even in a very ancient period of astron- on the heavenly bodies. References to these specific terms omy. Such empirically deduced lunar orbital positions are 'contained, for example, in such classic works as have been documented in various primary reference Mey&X77 o-@P7-a@t@ 7-j@ ALTrpovojulfa@ (Great System of As- sources, as noted below. tronomy) or Almagest of Claudius Ptolemaeus, Alex- andrian astronomer (c. A.D. 100-170). The principles Historical Origin of the Concepts of Perigee- enumerated in this magnum Opus a were disseminated Syzygy and Perigean Spring (Perigee- widely in subsequent Latin translations (e.g., in Theorica Spring) Tides planetarum, by Camparrus of Navara, 13th century and The Greek astronomer Hipparchus (c. 125 B.C.), later, Section IV, Theory of the Moon),' and other from observations of the apparent angular size of the eclectic sources. Moon as a measure of its distance from the Earth, pos- Mention of these same orbital configurations further occurs in several medieval lunar treatises (e.g., those of sessed a basic knowledge of the variability of the lunar distance during the course of the month. From these same Johannes de Sacrobosco and Robert Grosseteste)-al- data, he was also aware of the effect of the near-coinci- though perigee is incorrectly defined in those works which dence between perigee and syzygy in bringing the Moon carried over the Ptolemaic theory of epicenters. Among closer to the Earth, as described in part II, chapters 4-5 early contributors to a knowledge of,varying lunar dis- of the present volume. This closer distance of the Moon tances and gravitational force influences as they affect the becomes one of the causes contributing to the greater tides was Johann Kepler, German astronomer (1571- heights of perigean spring tides. 1630). With reference to the specification of lunar posi- This early knowledge of changing lunar distances is tions in orbit according to a- s ystern repeatedly used clearly brought out, for example, in Johann Kepler's throughout the present volume, it was he who first estab- Astronomia Nova (1609),' in his discussion of Hippar- lished the relationships between the position of perigee chus' rudimentary determination of the,distance of the and the anornalistic angle (of the Moon) in orbit. The Moon, specified in units of the Earth's semidiameter. The anornalistic angle is, in this case, defined as the angular considerably closer distance of the Moon (expressed as a distance of the Moon from perigee. smaller number of Earth-radii) at the position of perigee- Despite such early, a priori manifestations of astronom- syzygy compared with that at apogee, and at the Moon's ical knowledge, the increased gravitational forces result- mean distance is indicated in the words: ing from the simultaneous occurrence of perigee-syzygy- "Hoc itaque pacto Hipparchus. (ut habes Cap. VIII, and the effect of this concurrent astronomical alignment Opt. page 313) Lunae distantiam in syzygiis perigaearn upon the Earth's tidal waters-did not become a matter of particular notice until, with the development of naviga- exhibuit 71 semidiametrorurn Terrae, apogaeam 83, mediocrern 77, igitur eccentricitatern 6, hoc est, qualium '@ut cf., R. R. Newton, "The Authenticity of PtoIerny's . . . radius orbis 100000, talem eccentricitatern 7792, quod Data'." Q. J. R. astr. Soc. (1973), 14,'367-388; 15, 7-27, 107-12 1. 109 110 Strategic Role of Perigean Spring Tides, 1635-1976 tion and commerce, actual tide observations were made. resentative, using the tidal situation at Bristol, England. Significantly, the discovery of the special nature of peri- The analysis is based upon a previous example involving gean spring tides took place only when the increased only the solar component of spring tides, in which Newton tide-raising influences of these coinciding lunisolar posi- derives (Proposition XXXVI, Problem XVII) the height .tions were observed in mid-latitude regions removed from to which the tidal waters will rise acted on by the Sun the Mediterranean-since, in the latter regions, tidal alone (at points both directly beneath and on the oppo- ranges exhibited but minor daily variations. The mathe- site side of the Earth from the Sun) in excess of that at matical development of tidal theory during the 18th cen- places which are 90' removed from the Sun. tury further substantiated the relationship between peri- [Note: In this connection, an important, but uncor- gean spring (or perigee-spring) tides and the astronom- rected typographical error (for "113%0 inches" read ical occurrence of perigee-syzygy. " 1 11/3o inches") occurs in the numerical value given on The earliest discoverable published reference in the page 479 in the 1729 edition of the Principia translated English language to the phenomenon of perigean spring from the Latin by Andrew Motte, as extensively revised tides and their potentially destructive capacity when as- by Florian Cajori (1946).' A comparison between the sociated with strong, persistent, onshore winds is a pub- 1803 edition of Motte's English-language translation ("as lished letter of 1@70 transmitted to the Royal Society of carefully revised and corrected by W. Davis") and the London, titled "Arrimadversions on Dr. [John] Wallis' primary Latin source reveals that this error has been car- Hypothesis of Tides." Dr. Wallis' "Essay About the Flux ried forward, both unrectified and unannotated, and de- and Reflux of the Sea" had been communicated and read spite several successive editings, for 143 years into the to the Society in- 1666. After requesting a copy of this es- Cajori text.] Newton's original, true. comparison (the say from Henry Oldenburg, member of the Society, original is in Latin) is (page 48 1 ) : Joshua Childrey, rector of Upwey, England, and an ar- "Cor. 1. Since the waters attracted by the sun's force dent observer of natural phenomena, commented on the rise to the height of t foot and, 11 %0 inches, the moon's essay in the above-mentioned letter relayed through force will raise the same to the height of 8 feet and 7%2 Bishop Seth Ward, in which he refers to an earlier pub- inches; and the joint forces of both [syzygies] will raise the lication of 1653, by himself, as follows: same to the height of 10 Y2 feet; and when the moon is in "There is yet another thing, which seems to have (at its perigee [perigee-syzygy] to the height of 12 Y2 feet, and least) some influence on the Tydes, and to make them more, especially when the wind sets the same way as the swell higher than else they would do, to wit the Perigaeo- [incoming] tide." ' sis of the Moon. And this hath been my opinion (taken The additional effect of perigean spring tides (pro- up first upon the consideration of the Moons coming duced near the time of perigee-syzygy) compared with nearer the Earth) ever since 1652, when living at Fever- ordinary spring tides (occurring at syzygies apart from sham in Kent near the Sea, I found by observing the tydes, perigee) is clearly specified, and the reinforcing influ- (as often I had leisure), that there might be some truth ence of wind action on such perigean spring tides is also in my Conjecture; and therefore in a little Pamphlet, pub- indicated. lished in 1653, by the name of Syzygiasticon instauratum, In the year 1764, the British astronomer Roger Long I desired, that others would observe that year, whether published a five-volume work on Astronomy in which, the Spring-Tydes after those Fulls and Changes, when the in chapters 4 and 5 of volume 2, book 4., he discusses Moon was in Perigaeo (the wind together considered), various aspects of perigee and syzygy-and their relation- were not higher than usual. And since that time I have ship to tidal heights-at some length. found several high Tydes and Inundations (though I In Vol. I of the first edition of Encyclopaedia Britan- must not say all,) to happen upon the Moons being in, nica, published in 1771, a fundamental article by James or very near her Perigaeum." ' Ferguson, Scottish astronomer and inventor of a tide log, In his monumental PhIlosophiae naturalls principia includes the following concise statement: mathematica of 1687, Sir Isaac Newton acknowledged "The moon goes round the earth in an elliptic orbit, the effect of perigean spring tides (without designating and therefore she approaches nearer to the earth than them by name) through illustration in a practical exam- her mean distance, and recedes farther from it, in every ple contained in Corollary I to Proposition XXXVII, lunar month. When she is nearest, she attacks strongest, Problem XVIII, Book III: The System of the World. and so raises the tides most; the contrary happens when The data presented in this sample problem are purely rep- she is farthest, because of her weaker attraction. When Survey of the Scientific Literature on Perigean Spring Tides both luminaries are in the equator, and the moon in 18th Century Tidal Literature Perigeo, or at her least distance from the earth, she raises During the 18th century, the astronomical origin of the tides highest of all, especially at her conjunction and the tides occupied the attention of some of the foremost opposition; both because the equatoreal parts have the scientists of the period, who approached the matter largely greatest centrifugal force from their describing the largest circle, and from the concurring actions of the sun and from the standpoint of dynamic theory. Axnong such out- moon.@l standing contributors to the theory of the tides were: Daniel Bernoulli, Swiss mathematician, author of the John Hamilton Moore's The New Practical Navigator, essay Trait! sur le flux et reflux de la mer (1738); Colin the first U.S. edition of which was published in 1799, Maclaurin, Scottish mathematician, whose essay De shows a practical seaman's knowledge of the independ- causa physica fluxus et refluxus maris ( 1738) also appears ent effects of both perigee and syzygy and their combined in his classic work A Treatise on Fluxions ( 1742) ; Leon- effects in producing high water levels higher than those hard Euler, Swiss mathematician and physicist, who wrote associated with common spring tides. In the light of a Inquisitio Physica in causam fluxus ac refluxus maris subsequent discussion in the present volume relating the (1738); and Marquis Pierre Simon de Laplace, French rate of tide growth to the resulting height of the tide astronomer and mathematician, whose monumental (chapter 8), Moore's early mention of this factor is also Trait! de micanique cileste published in five volumes, of interest: 1799-1825, contained much of the groundwork of tidal "When the moon is in her perigaeum, or nearest ap- theory. The three mays of Bermoulli, Maclaurin, and proach to the earth, the tides rise higher than they do, Euler mentioned above were all submitted in a competi- under the same circumstit'nces, at other times; for, ac- tion held by the Academy of Sciences of Paris in 1738, cording to the laws of gravitation, the moon must attract and all won prizes. Because of the theoretical nature of most, when she is nearest the earth. The spring-tides are these three papers dealing with tidal forces in general, no greater about the time of the equinoxes, that is about the special treatment was given therein to the dynamic origin latter end of March and September, than at other times of perigean spring tides. of the year; and the neap-tidcs are then less; because the The extensive multivolume work of Laplace cannot longer diameter of the spheroid, or the two opposite floods, being then in the earth's equator, will describe be as lightly dismissed, since the author treats so exten- a great circle of the earth; by the diurnal rotation of which sively all of the problems of celestial mechanics, including those floods will move swifter, describing a great circle the complexities of lunar theory. He devotes the entire in the same time they used to -describe a less one, parallel fourth book of his treatise, titled "On the Oscillation of to the equator; and consequently the waters being thrown the Sea and Atmosphere" to the subject of tides, and in- more forcibly against the shores, must cause them to rise cludes selected empirical examples of tide heights as pro- higher." 7 duced by various positions of the Moon and Sun. Finally, a statement previously quoted in connection Laplace perhaps comes the closest, in this period of with the navigational value of the additional heights of the development of tidal theory by mathematical scien- perigean spring tides (page 68) is given again, since it tists, in considering the combined tidal force effects of also indicates, in appropriate historical perspective, an perigee andsyzygy. For example, he compared the actual early knowledge of the recurring cycles of perigee-syzygy measured heights of 12 apogean tides with those of 12 alignments. The extra rise of perigean spring tides above perigean tides (both being observed sim'ultaneously at one ordinary spring tides is clearly stated: of the syzygies) and discovered that these values were in ". . . Some of these effects arise from the different, accord with existing prediction theory-discounting the distances of the moon from the earth after a period of considerable difference in the Moon's motion in celestial six months, when she is in the same situation with respect longitude between the times of apogee and perigee. (See to the sun; for, if she be in perigee at the time of the table 21 of the present work.) new moon, she will, in about six months after, be in In a section titled "Du flux et du reflux de la mer" in perigee about the time of full moon. These particulars, his three-volume work on Astronomie (1771), the French being well known, a pilot may chuse [sic] that time which scientist Joseph J6rome le Fran�ois de Laland presents a will prove most convenient for conducting a ship out purely descriptive account of tidal forces and actions. In of any port, where there is not a sufficient depth of water this, he includes a brief quantitative summary of actual on common spring-tides." tide heights observed at Brest subject to the combined ac- 112 Strategic Role of Perigean Spring Tides, 1635-1976 tion of the Moon and Sun at syzygy, and witli the Moon foregoing writers to the specialized type of tide forming also at perigee, but the data are fragmentary and entirely the subject of the present investigation. selective. A classic article on "Tides and Waves" was written by the British astronomer, Sir George Biddell Airy, for the Early 19th Century Tidal Literature Encylopaedia Metropolitana in 1845 and was repub- Perigean tides as well as ordinary spring tides-but lished in The Encyclopedia of Astronomy 3 years later. not the combination of the two to yield perigean spring In this, only a general discussion is included concerning tides-are described by Nathaniel Bowditch, American the concepts of heightened tides resulting from increased mathematician, in the classic mariner's manual The New forces occurring separately (or simultaneously) at perigee American Practical Navigator, published under his name and syzygy. He does recapitulate Laplace's empirical in 10 editions from 1802 until his death in 1838, and data previously mentioned, and compares some of these under that of his son, Jonathan Ingersoll Bowditch, earlier and subsequent observations in the light of new through 25 additional editions between 1838 and 1867. theory. Since 1869, this work, redesignated American Practical However, this relatively scanty attention paid to peri- Navigator, has been continuously revised and reissued as gean spring tides as summarized in the preceding three Publication No. 9 of the U.S. Navy Hydrographic Office sections was soon to change its focus as the result of (since July 10, 1962, the U.S. Naval Oceanographic Of- Nature's own intervention. fice). In his original volume Bowditch under-took to cor- The "Saxby Tide" of October 5, 1869 rect more than 8,000 tabular errors appearing in John Hamilton Moore's earlier work titled The New Practical The destructive effects of this particular perigean spring Navigator. However, the previously quoted concept from tide which, driven additionally by a strong onshore wind, Moore's book, outlining the special value of perigee devastated an entire section of the eastern Maritime Prov- spring tides to navigators in negotiating a passage across inces of Canada in 1869 were extolled for many years offshore bars, did not find its way into Bowditch's work thereafter by the local residents. An interesting, but sci- in anv form. entifically unacceptable "prediction," which directed public attention to the special vulnerability of perigean The 19th century also brought new investigations and spring tides in terms of coastal flooding preceded this contributions to tidal theory by: the Englishman Thomas particular onslaught of Nature. The individual involved Young, variously physician, physicist, and Egyptologist, in connection with this advance warning was a Lieuten- superintendent of The Nautical Almanac and secretary ant. S. M. Saxby of the Royal British Navy, whose only of the Board of Longitude, who wrote a comprehensive other contribution to technical literature appears to have article on "Tides" in the Suppler nent to the 4th, 5th, and been the publication in 1868 and 1869, in the Transac- 6th editions of Encyclopaedia Britannica (1815-1824) ; tions of the Institution of Naval Architects, of several en- Sir John William Lubbock, , English astronomer and gineering papers dealing with the properties of metals mathematician, who wrote Elementary Treatise on the used in ships. However, in his naval activities, he un- Tides (1839); William Whewell, English philosopher doubtedly also had ready access to The Nautical Almanac and mathematician, who rationalized extensively on vari- (published since 1767) and, by close scrutiny thereof, he ous natural phenomena, including a "Treatise on Tides" made a bold deduction. in the Admiralty Manual of Scientific Enquiry (1849); In November of 1868, he sent a letter to the London Rear Admiral Robert Fitzroy, British naval officer and press warning,-1 I months in advance of the tidal flood- meteorologist, who as commander of the Beagle on the ing subsequently experienced--of the potential flooding famous biological exploring expedition, had the opportu- dangers to be expected on October 5, 1869 from a special nity of observing worldwide tides at firsthand and who, case of astronomical perigee-syzygy occurring near that accordingly, wrote such articles as "Notice of Tidal Ob- date. This particular phenomenon, he noted, was coupled servations" ( 186 1 ) ; and Sir William Thomson, 1 st Baron with a situation in which the Moon would simultaneously Kelvin, British mathematician and physicist, who devised be very near to the Earth's Equator (declination -0.6') an apparatus for taking oceanographic soundings, in- and the Earth would also be approaching perihelion. In vented a tide predictor and an harmonic analyzer, and consequence of the necessarily magnified tide-raising discoursed on tides in Thomson and Tait's Natural Phi- forces and the extreme high tides that would result, he losophy (1883). No special attention was paid by the stipulated-rather too broadly and all too sensationally- Survey of the Scientific Literature on Perigean Spring Tides 113 the certainty that this condition would be accompanied occurs without marked atmospheric disturbance, and at by definite coastal flooding. 2 p.m. of the same day lines drawn from the Earth's centre In his prediction, he included no restriction of the flood- would cut the Sun and Moon in the same arc of right ing to lowland coastal regions nor to latitudinal and hydro- ascension (the Moon's attraction and the Sun's attrac- graphic circumstances capable of providing a sufficient tion will therefore be acting in the same direction) in other ordinary tidal range to make the amplified perigean spring words the new moon will be on the Earth's equator when tides a hazard. Neither did he consider seasonal and clima- in perigee, and nothing more threatening can, I say, occur tological conditions at various latitudes and locations without miracle. The Earth it is true will not be in peri- which could either contribute to, or effectively nullify, the helion by some 16 or 17 seconds of semidiameter. likelihood of strong, persistent, onshore winds. He did not "With your permission I will during September next make use of either the exact Greenwich times of the in- 1869) for the safety of mariners briefly remind your dividual components of perigee-syzygy, nor the mean time readers of this warning. In the meantime there will be time of occurrence of the combined phenomena. He further for the repair of unsafe sea walls, and for the circulation did not allow for longitudinal time differences or tidal of this notice throughout the world." ' delays caused by local hydrographic factors, phase- and It is noteworthy that nothing at all was said in this parallax-ages, etc., at various locations around the globe. letter concerning specific local conditions of weather on Instead, he categorically stated that the morning tide this date. The warning was predicated entirely from astro- of 7: 00 a.m. on this date would be marked by a rise to nomical and tidal considerations, combined with a com- extreme higk waters. He also extrapolated the significant pletely unexplained, all-pervasive atmospheric disturb- impact of his warning beyond the certain, astronomically ance whose exact location is left unspecified. predictable conditions of the, tide. Through a nebulous A subsequent, even less scientific letter, sent to the Hali- assertion of a relationship between "atmospheric disturb- fax, Nova Scotia, press by a local citizen, was probably ances and [the position of] the moon on the equator," he motivated, as often happens, by the desire to derive pub- also included a prediction for an atmospheric storm of licity from the inter'est achieved by an original news story. exceptional severity on this same date. There is, as a matter of record, a completely charlatanistic On the other hand, he did not indicate that, in this attempt by one Frederick Allison of Halifax, who wrote particular instance of perigee-syzygy, the Moon and Sun to the Halifax Citizen about a week before the forthcom- were within -7 hours of direct alignment in longitude ing tidal phenomenon, predicting a heavy gale in this and, as a result (pt. 11, ch. 4), the Moon would also un- city between October 4-5, precisely at the same time as dergo an unusually close perigee approach to the Earth that of the predicted extreme tide. The forecast was based (with a relatively large geocentric horizontal parallax of on a "theory of the Moon's attraction as applied to 61'24.0"). Astronomically, therefore, the condition was Meteorology" which, in the vagueness of its detail, is not one conducive to the production of exceptionally large deserving of further mention. Suffice it to say, as in all tide-raising forces, and would create a perigean spring cases of unqualified release of sensational information, tide offering a natural "setup" for wind attack. As the these two disclosures aroused considerable public concern. subsequent content of the present work will reveal, the In the light of the actual extreme coastal flooding re- sulting from the combination of a winter storm whose extremely high tides resulting were, indeed, susceptible to onshore winds arrived coincidentally with the close ful- flooding conditions in lowlying coastal regions where fillment of Saxby's prediction for augmented high tides, strong, persistent, onshore winds might occur. Albeit, the an air of prophetic hocus-pocus was, unfortunately, given absolute necessity for such an accompanying meteorolog- to this case which weakened the scientific value'to be ical condition (not possible to predict I I months in ad- derived from its occurrence. vance) to occur in order to cause flooding was not even The exact meteorological conditions existing along the brought out in Lieutenant Saxby's communication. The eastern coast of the United States and the Maritime'Prov- significant technical portions of his letter to the press inces of Canada on October 5, 1869 are summarized in follow: a paper on this storm and attendant tidal flooding read "I now beg to state with regard to 1869 at 7 a.m. Octo- by D. L. Hutchinson, Canadian meteorologist, before The ber 5th, the Moon will be at the part of her orbit which Canadian Institute some years later." These conditions is nearest to Earth. Her attraction will be therefore at its are further discussed in David M. Ludlum's Early Amer- maximum force. At noon of the same day the Moon will ican Hurricanes, 1492-1870 (in this latter connection, see be on the Earth's equator, a circumstance which never also the Explanatory Comments preceding table 2). 202-509 0 - 78 - 10 114 Strategic Role of Perigean Spring Tides, 1635-1976 A partial description of the damage created by tidal "In the Bay of Chaleur the water was much above nor- flooding in this area, as presented by Hutchinson in the mal and at Dalhousie, Restigouche County, bordering on aforementioned paper, is as follows: the bay, the lower portion of the town was inundated and ". . . On the day of the storm (Monday, Oct. 4th) boats used to remove property and people from the lower the early morning was foggy, then part clouded and by levels. 7 a.m. fine and warm, in the afternoon assumed a dull "At the head of the Bay of Fundy, in the Basin of leaden colour becoming completely clouded by 5 p.m. As Minas, in and about Cumberland, Hants, Kings and Col- the afternoon advanced the wind blew in fitful angry chester Counties, N.S., the gale was not severe, but rain squalls and the rising tide was-noticed to be coming in fell heavily. The chief damage was caused by the tide, unusually early. At 5 p.m. the wind had increased to a dykes were broken away in all directions, in some places gale and rain began falling at 6 p.m. The gale continued the water was two feet above the second floor dwelling to increase, about 8:30 p.m. it was blowing with hurri- houses, many hundreds of cattle, sheep, etc., drowned, cane force from S. by E. reaching its maximum velocity large quantities of hay destroyed, great stretches of rail- about 9 p.m. when the rain almost ceased. About 10 p.m. road carried away and travel made impracticable in any the wind began to subside shifting to S.W. direction. The wind itself did not do much injury, except "The night is said to have been exceptionally dark with to the fruit crop. At Windsor, N.S. wharves were dam- shingles, slates and other debris blown about in a most aged and churches, dwepings and business places dangerous manner. When the gale was at its height flooded. (about 9 p.m.) the tide was much above any preceding mark, was rising rapidly and had an hour and half to Hutchinson summarizes the meteorological conditions come. In St. John harbour and along the water front the producing the accompanying storm and wind as follows: waves were coming in from the Bay of Fundy to a tremen- "In all probability the storm was one of tropical or dous height dashing over every wharf along the whole har- semi-tropical origin characterized to the southwest by bour line, while the vessels moored at them seemed as if extremely heavy precipitation and greatly increasing in they must be rolled over upon the wharves by the next energy as it moved towards Eastern Maine and the west- swell. Vessels broke away from moorings, some were ern portion of New Brunswick." " driven ashore and many badly damaged. However circumstantial the coincidence of meteor- "Buildings near the water front were flooded in lower ological andastronomical conditions which produced this floors, warehouses were destroyed, everywhere signs of extensive coastal flooding through the cause-and-effect destruction met the eye, slips, coves and beaches were relationship which is clearly beyond the scope of Lieu- filled with debris from the wreckage. . . tenant Saxby's prediction, this event was for years there- cc. . . The high tide at St. John backed up the river after known among the local residents of the area as to'such an extent that it rose upwards of three feet at "Saxby's Tide" or "Saxby's Gale" and has also been dis- Fredericton. On the St. John River near Gagetown in cussed in the scientific literature of this period under this Sunbury County a river steamer had her upper work same designation. carried away by the gale. "In Albert County the damage from wind and tide Late 19th Century Tidal Literature was excessive and at that time estimated at nearly a William Ferrell, American meteorologist, and a tides quarter of a million dollars. expert with the U.S. Coast and Geodetic Survey from "Westmoreland had a terrific gale and the highest tide 1867 to 1882, touched upon various aspects of pexigean ever known, tons of hay destroyed on the marshes, cattle spring tides in such papers as "On the Moon's Mass as drowned in great numbers, whole barns and their con- Deduced from a Discussion of the Tides of Boston Har- tents carried away, telegraph lines destroyed and the roads made impassable. From 'Tide Levels and Datum Planes bor," and "Tidal Researches." These were published in in Eastern Canada'by Dr. W. Bell Dawson, it may be seen the annual Report of the Superintendent of the Coast that the water level at Moncton was nearly six and a half Survey for 1870 (Appendix No. 20) and 1874 (Appen- feet above former or subsequent records. dix), respectively. His "Report of Meteorological Effects "At Moncton the tempest and tide was most disastrous, on Tides," published in the same annual volume for 1871 while, at Shediac, and Point Du Cherie on the gulf not (Appendix No. 6) is especially germane to the present eighteen miles distant, no damage of any description was monograph and includes a mention of tidal reinforcement done. by meteorological effects when these occur at a time of Survey of the Scientific Literature on Perigean Spring Tides 115 perigee-syzygy (without naming the corresponding tides tant part in the similar delay of perigean spring tides fre- as perigee springs), as follows: quently observed on the east coast of the United States. Sketch No. 38 contains a graphic representation (See text in re table 19.) Lamb's analysis was based upon of the heights of the tides and of the lunitidal intervals earlier theoretical approaches to the same problem in given by the tables and by observations, and of the effects William Thomson's and P. G. Tait's Natural Philoso- of, the winds and changes of atmospheric pressure, for the phy," in G. B. Airy's encyclopedia axticle on "Tides and month of July, 1858. This is the time when the obliquity Waves," " and by Hermann L. F. von Helmholtz in of the moon's orbit to the equator is greater than in any Lehre von den Tonemfindungen." other part of the whole series, and, consequently, when Other important investigations relating in whole or in the diurnal tide is the greatest. This. causes the alternate part to the tides which were published in this same period heights of high and low waters to be greater and less, as include: Hydrography and Maritime Meteorology, by represented in the sketch, near the times of the greatest Carl Borgen (1886); Les m@thodes nouvelles de la declinations of the moon, the maximum of the lunar and m&anique Meste, by Jules Henri Poincar6 (1892-99) ; principal part of this effect occurring two days after the "On the Application of Haxmonic Analysis to the Dy- greatest declination. At this time, also, the moon's perigee namical Theory of the Tides," by Sydney S. Hough, in occurs near the time of one syzigy [sic] and its apogee Philosophical Transactions, A, vol. 191 (1898) ; Leqons near the time of the other. Hence the predominating in- sur la th@orie des marjes by Maurice L6vy (1895-98) ; fluence of the lunar parallactic inequality over that of.the and numerous contributions such as "On Waves," by solar, or half-monthly, is well represented by the sketch. At Lord Rayleigh in Philosophical Magazine, 1 (1876). the time of the new moon and the moon's perigee these A new empirical approach to tidal knowledge which two inequalities combine and make the tides unusually would include some of the quantitative aspects of perigean large, but at the time of full moon and the moon's apogee spring tides was to come principally at the start of the the parallactic inequality more than counteracts the half- next century. monthly inequality, so that when in European ports there is a second maximum, though smaller, in Boston Harbor 20th Century Tidal Literature this second maximum is entirely destroyed by the predom- The pursuit of knowledge, like the recurring varia- inating effect ofithe lunar parallactic inequality, and the tions of the tides, seems to move in cycles. The turn of the magnitude of the tides do not come up to the mean century was marked by a very considerable, increase of tide . . . " 13 interest in the practical aspects of perigean spring tides, A basically theoretical article on "Tides" was pre- to be followed, incongruously, by an almost complete pared by the British astronomer Sir George Howard disregard thereof throughout the ensuing period of almost Darwin for the Encyclopaedia Britannica, 9th edition, 23 50 years. (1880), and later republished separately as "The Tides" In the Bay of Fundy inNova Scotia, and in certain (1898). In this article, the subject of perigean spring other localities, the tide is of the so-called anomalistic tides escapes any specific mention. The same lack of any type (i.e., clcsely related to the Moon's anomalistic particular discussion of this type of tides occurs in Volume period-or the time from perigee to perigee). Here, fluc- I, "Ocean Tides and Lunar Disturbances of Gravity," in tuations in tidal range with the Moon's changing dis- Darwin's collected Scientific Papers (1907). tance from perigee to apogee are the largest variations In his prodigious five-volume work, titled Manual of experienced. In such cases, even the difference in range Tides (parts 1-5, 1894-1907), Rollin Arthur Harris, from neap to spring tide may be of lesser consequence then chief mathematician of the U.S. Coast and Geodetic than that caused by the perigee-apogee variation. Survey, developed a wave theory of the tides, and includes The previously mentioned "Saxby Tide" represented numerous individual references to perigean tides as well a case of perigee occurring nearly coincidentally with as to spring tides, but does not evaluate their combined syzygy, while the Moon was located at an extremely effects. close perigee distance from the Earth. Its anomalistic In his outstanding treatise on Hydrodynamics, pub- effects were, accordingly, very strongly felt in the Bay lished in 1895, the English fluid dynamicist, Horace of Fundy region and might very likely have generated Lamb, included an analytic explanation of the retardation the ensuing spark of interest in perigean spring tides. In of the maximum effects of spring tides following times of any event, numerous Canadian Government reports re- new or full moon," a phenomenon which plays an impor- lating to the survey of tides and currents in Canadian 116 Strategic Role of Perigean Spring Tides, 1635-1976 waters-especially in the years from 1902 to 1907-are in the daily range of the tides produced by the combina- replete, with comparisons of extreme tidal ranges, excep- tion of the phenomena of perigean tide and syzygian tionally large current velocities, and cases of coastal flood- (spring) tide, but does not actually define the resultant ing and damage produced at times of perigee springs. perigee-spring tides by name. These reports were variously published by the Depart- Reference sources and glossaries published in the 1940s ment of Marine Fisheries, the Department of the Naval to, 1970's relating to oceanography and tides show a Service, and the Royal Society of Canada. similar inexplicable lack of mention of the phenomenon The same topical emphasis on empirically derived data of perigee springs, for example: led to the development of A Practical Manual of Tides The Manual of Harmonic Analysis and Prediction of and Waves, by W. W. Wheeler, published in 1906. Tides, U. S. Coast and Geodetic Survey (National Ocean In 1913, the causes of long-period variations in astro- Survey) Special Publication No. 98, revised (1911) nomical cycles-and their commensurate interrelation- edition includes no mention of this type of tide. ships-formed the basis for a lengthy article by a Danish The Admiralty Manual of Tides, by A. T. Doodson scientist, Hans Pettersson, in Publications de Circonstance and H. D. Warburg, London (1941) likewise does not (published by the Counseil Permanent Intemational pour contain any reference to this term. I'Exploration de la Mer). He called upon such com- A similar omission occurs in Waves, Tides, Currents mensurable periodicities to explain various astronomical and Beaches: Glossary of Terms and List of Standard alignments which create the maximum possible tide- Symbols, by Robert L. Wiegel, published by the Council raising forces. The influence of perigean spring tides is on Wave Research, The Engineering Foundation (1953). among the topics treated. The author includes a consider- The Glossary of Oceanographic Terms, Special Pub- able discussion of the particularly strong tide-generating lication No. 35 of the U.S. Naval Oceanographic Office force produced by the coincidence of perigee-syzygy and (1966) lists perigean tide and spring tide, but does not perihelion, especially when combined with a simultaneous include the combined designation, perigee springs. positioning of the Moon on the ecliptic at either of its The Tide and Current Glossary, U. S. Coast and nodes. He also brings out the influence toward the pro- Geodetic Survey (National Ocean Survey) Special Pub- duction of extreme tides provided by an unusually close lication No. 228, revised (1975) edition, included a proximity of the Moon to the Earth (involving an excep- definition of perigean tides and tidal currents, as well as tionally small perigee distance and corresponding large spring tides, but did not list the combining form, perigean value of geocentric horizontal parallax which will later spring tides. (The term is to be included in a forthcom- be described as "proxigee" in the present monograph) - ing new edition.) The reduced lunar distance and increased geocentric . Other glossaries and basic reference sources published parallax are, in turn, caused by an exceedingly close prior to very recent years reveal the same basic oversight. perigee-syzygy alignment. As a notable exception, in. a book, Coasts, Waves, and In a book titled Houle, rides, seiches, et marjes (Swells, Weather (1945), by an astronomer-meteorologist, Ripples, Seiches, and Tides) published in 1924, Henri John Q. Stewart, late of Princeton University, he gives P.M. Bouasse of the University of Toulouse, France, dis- specific graphical examples of the exceptional heights and cusses several empirical aspects of the heightened tides depths attained by the high and low phases, respectively. resulting from the near-coincidence of perigee and syzygy. of perigean spring tides. He also mentions the possible A considerable discussion is also included relative to the practical utilization of the flood stage of'such tides in maximized tidal effects produced by the occurrence of navigation over coastal bars. perigee-syzygy while the Sun and Moon are over the Since that time, a noticeable gap seems to exist in any Equator, a phenomenon which the French call la grande more recent literature which deals specifically with the marge d' 9quinoxe. An approximate example of this type topic of perigean spring tides. A computerized literature which is cited is that occurring near March 13, 1918. search through title, abstract, and other bibliographic In his semipopular work The Tides, published in 1926, data banks available in NOAA's OASIS (Oceanic and H. A. Marmer, an outstanding tide expert with the Atmospheric Science Information System), covering the former U. S. Coast and Geodetic Survey, presents several general period from the 1960's to the present, reveals a examples of both the separate and combined influences singular absence of pertinent source literature, and not of perigean spring tides in increasing the tidal range. He one article bearing the words "perigee springs," or describes, in quantitative terms, the percentage increase "coastal flooding" in the title. The considerable bank of Survey of the Scientific Literature on Perigean Spring Tides 117 bibliographic sources (data bases) in the OASIS system the establishment of a practical statistical measure (or searched for relevant citations, and their available periods coefficient) indicating the potential for, and probable of coverage, are: Oceanic Abstracts ( 1964-present), severity of, tidal flooding subject to the foregoing astro- Meteorological and Geoastrophysical Abstracts (1972- nomical circumstances, should strong, persistent, onshore present), Geophysical Abstracts ( 1966-70), Selected coastal winds also prevail at the time. As will be taken up Water Resources Abstracts (1968-present), Defense variously in the following chapters, it is these topics, Documentation Center (1953-present), NASA Informa- together with supporting evidence and newly derived data tion Bank (I 962-present), and Government Reports An- relative to the hypotheses and theories advanced, which nouncements (1964-present). constitute the justification for the present research Following Stewart's work, the subject of perigean spring monograph. tides seems to have fallen almost into oblivion for 20 years. In recapitulation, it is evident from the foregoing sum- With the rapid advances of knowledge made possible mary that the causal connection between perigean spring during and after the International Geophysical Year tides and the astronomical phenomenon of perigee-syzygy (1959-60)-and through orbiting artificial satellites- was a topic of early, although in no sense definitive scien- there came a new interest in astronomically induced tific recognition. Moreover, a strange and inexplicable cyclical events, including the gravitational and tidal in- dearth of investigations has existed historically, in con- fluences of the other bodies of the solar system upon vari- nection with the tidal flooding consequences resulting from ous solar and terrestrial phenomena. Among the books of a coincidence of this gravitational-force concentrating this new body of literature which are related to tides. astronomical configuration and a reinforcing wind from three of the modern sernitechnical references (of British the sea. This lapse has taken place also at a time marked and German origin) listed in the bibliography at the end by a great proliferation in real estate and recreational de- of this volume contain a brief mention of perigean spring velopment along the North American coastline. An tides. equally inexplicable hiatus has occurred in the applica- The great tidal flooding of March 6-7, 1962, although tion of ongoing research technology to the practical an outstanding example of a wind-induced coastal inun- implications of this problem. dation associated with a perigean spring tide (chapter 7, With consideration both to the number of years and Case 4), is designated in nearly all published sources only the frequency of cases of coastal flooding represented as a "spring tide." among the newspaper accounts in chapter 1, it is obvious Continuing and expanding on the vein of the previously that the significance of this astronomically induced tidal cited article by Hans Pettersson, an article on "Earth phenomenon, when combined with adverse wind effects, Motions" by Clyde Stacey in The Encyclopedia of Atmos- has not received the attention it deserves. The increased Pheric Sciences and Astrogeology (1967) describes the potential for major coastal flooding associated with this various special combinations of gravitational forces which particular type of tide has never been adequately brought produce maximum perigean spring tides. out in the literature. Nor, in this same enhanced possi- None of the sources previously listed discusses the re- bility for coastal erosion, inundation, and structural dam- curring short-range potential for tidal flooding associated age, have its impacts upon coastal geography and upon with perigean spring tides in terms of: (I ) the accelerated various marine-engineering, economic, and ecological growth (and relaxation) rate of the tide curve around the phases of the coastal environment been duly emphasized. Particularly is this true as the result of today's rapidly time of perigee-syzygy: (2) the lengthening of the tidal . I day which extends the period of time during which tidal burgeoning real estate development, involving extensive waters are subject to increased gravitational forces at the housing and condominium expansion along the coast- time of perigee-syzygy; (3) the corresponding increase line. A case-study investigation is long overdue on the in velocity of tidal currents, following an analogous pat- cause-and-effect relationships underlying examples of tern of increase in horizontal flow rate at time of perigee- major tidal flooding (both associated with winter storms syzygy; (4) the possibility of an enhanced coupling action and induced by hurricanes) on the North American of sea-surface winds with the inmoving tidal currents un- coastline during the more than 340-years over which his- der these conditions of accelerated water flow; and (5) torical records exist. Such a study is offered here. Part 11-Scientific Analysis I I Chapter General Background Consideration of Astronomical Posi-, tions and Motions Important in the Evaluation of Peri- gean Spring Tides The regular and obviously harmonic astronomical rela- Astronomical Positions tionships which make possible the "equilibrium theory" Although the positions of astronomical bodies are given of the tides are summarized in the appendix to this vol- in as many as five different reference systems, only three ume. Only -those supplementary'aspects pertaining to the of these have any direct application to the tides. These creation, augmentation, and ultimate maximization of are: the horizon system, involving azimuth and altitude; perigean spring tides will, therefore, be included as a de- the equatorial system in which right ascension and declina- scriptive adjunct in the technical portion of this text. In tion are the basic coordinates; and the ecliptic system, following this plan of presentation, the present introduc- utilizing coordinates of celestial longitude and latitude. A tory chapter will serve to clarify the text usage of specific detailed explanation of these systems can be obtained in astronomical terms used in the discussion of perigean any astronomical textbook, and they will not be described spring tides, and also assist in the interpretation of the further here beyond their immediate application to tidal corresponding tidal terms of reference. In succeeding problems. chapters, the discussion will narrow-in by increasingly more specialized stages to consider, in turn, various dy- COORDINATE SYSTEMS namic factors which produce ' the precise astronomical 1. Equatorial System alignments, close lunar distances, and combinations of In the equatorial system, the basic reference circle is gravitational forces responsible for the increased ampli- the Equator of the Earth projected upon the celestial tudes of perigean spring tides. sphere. An axis projected through the north and south geographic poles of the Earth and extended in either Astronomical Factors Significant direction beyond to the two points of intersection with the to Tidal Nomenclature celestial sphere locates the north and south celestial poles. Similarly, the Earth's Equator extended outward to inter- The tides in the Earth's oceans are caused entirely by section with the celestial sphere becomes the celestial the gravitational attraction of the Sun and Moon acting equator. The celestial equator is at all points 90' removed upon these water masses and, in determining and pre- from either of the celestial poles. The astronomical dec- dicting the rise and fall of tidal waters, only the changing lination (8) of a body is measured in degrees, minutes, interrelationships of these three celestial bodies need be and seconds of arc perpendicularly north or south from the celestial equator through 90' to the north or south considered. In discussing the distances, motions, and geo- celestial poles, in the same way that geographic latitude metric relationships of the Moon and Sun as they affect is measured on the Earth's surface. the tides, the exact positions of these two bodies upon the In contrast to geographic longitude which is measured celestial 'sphere are of primary significance. A brief sum- both cast and west from Greenwich through 180' of arc, mary of the alternative methods of defining these positions the corresponding astronomical coordinate of right ascen- is, consequently, desirable. sion (a) in the equatorial system is measured only from 121 122 Strategic Role of Perigean Spring Tides, 1635-1976 west to east and usually in hours, minutes, and seconds of tion of the meridian between the north and south celestial time through 24 hours, rather than in units of arc. It is poles which contains the zenith is called the upper branch, measured around the corTesponding 360' of the celestial and a celestial body which transits this portion is said to sphere from a fixed position back to that same position be in upper transit. The portion of the meridian contain- again. The astronomical position chosen to become that ing the nadir is the lower branch, and the passage of a of 0 or 24 hours is the point of intersection of the celestial celestial body over this portion is termed lower transit. equator with the ecliptic on the celestial sphere. The Successive hour angles are measured from the celestial ecliptic is the apparent path of the Sun around the celes- meridian along the celestial equator through 360', in a tial sphere as the Earth pursues its annual motion of revo- direction opposite to that of right ascension (i.e., from cast lution around the Sun, causing the Sun to appear to to west, or clockwise as viewed from the north celestial revolve around the Earth in the same direction. pole). Hour angles are also designated in units of degrees Since these two great circles, the celestial equator ('), minutes ('), and seconds (") of arc rather than and the ecliptic, intersect at two points, known as hours ('), minutes (m), and seconds (") of time as in the the vernal equinox and autumnal equinox, the origin case of right ascension. Each location on the surface of for the coordinate of right ascension is defined as the Earth has its own local meridian or origin for the that intersection corresponding to the vernal equinox, measurement of hour angle. This subsystem is thus tied or ascending node of the Earth's orbit, where the to the Earth itself and rotates with it, while the coordinate Sun in its apparent annual motion crosses the celestial of right ascension (except for very small perturbational equator from south to north about March 21. This variations) remains essentially fixed with respect to the position is known both as the vernal equinox and stars. First Point of Aries (T). In the same fashion that A series of great circles passing perpendicularly through geographic longitude is measured on Earth-but the celestial equator, each separated by 15' or I hour in now proceeding continuously from west to cast mean solar time from that next to it, and converging on through 360'-right ascension is measured along the celestial poles, are known as hour circles. A different the celestial equator at right angles to any hour system of hour circles exists for every longitudinal position circle on which a celestial object lies. on Earth, and likewise rotates with the Earth. Angular A second method of positional representation in the differences between various 'local meridians and the equatorial system is known as the hour-angle subsystem. Greenwich prime meridian in England, the origin for This subsystem uses ', in place of right ascension and dec- geographic longitude, are specified as the Greenwich hour lination, the coordinates of hour angle (h) and declina- angle (GHA) of the place. The GHA is given in degrees, tion (8). The coordinate of declination is defined exactly minutes, and seconds of arc in the same manner that geo- as before, and its usage is the same in both cases. How- graphic longitude on the Earth's surface is commonly ever, the origin for the Placement of zero hour angle is expressed. different. In the right ascension subsystem, the vernal An important distinction is thus evident between the equinox establishes the great circle corresponding to 0' right ascension and hour-angle subsystems: Subject to (the equinoctial colure). In the hour-angle subsystem, the the rotation of the Earth (i.e., the diurnal motion) the 0' origin is located where (in the Northern Hemisphere) positions of all celestial bodies will continuously vary a great circle from the south point on the celestial sphere through 360' in hour angle during one complete rotation intersects the celestial equator beforr- passing respectively of the Earth from 0' on the celestial meridian to 0' again. through the zenith of the place, the north celestial pole, However, the right ascension of a celestial object will not the north point on the celestial,sphere, the nadir, and the vary as the result of the Earth's rotation, but only if the south celestial pole. object possesses its own motion in right ascension, or a This same- great circle becomes the celestial meridian component thereof. for the place of observation. The celestial meridian, which Thus, the hour-angle subsystem becomes especially use- corresponds with a vertical circle of 0' azimuth, is also ful in evaluating the various effects of the Earth's daily used in connection with the horizon system of coordinates rotation upon the tides. Since the position of the vernal later to be described, since it passes through the zenith, equinox apparently moves through the same angle but in nadir, and principal cardinal points of the latter system as an opposite direction to the Earth at each rotation thereof, well as through the celestial poles of the present system. just as the Moon and Sun do in their apparent diurnal The celestial meridian consists of two branches. That por- motions, the right ascension system is not useful for ex- Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 123 pressing the relative motions of these two bodies, when the ecliptic, at that position where the Moon crosses this plane rotation of the Earth must be considered. from south to north.) The hour-angle subsystem does permit measurement to The advantage of the ecliptic system is that it eliminates be made with respect to the rotating Earth. As the Earth the inclination of the Earth's axis of rotation with respect rotates on its axis once in each 24 hours, in a west-to- to the e-cliptic, and it is particularly useful when the Sun's cast direction, the celestial object will describe a cor- apparent annual motion and the motions of the Moon responding circle on the celestial sphere, but in the with reference to it are concerned. opposite direction, from east to west. Depending upon 3. Horizon System whether the object is located at a position directly on the The horizon system is localized in that it involves the celestial equator (declination = 0') or at some angular position of a celestial body as seen from a given point of distance in declination either north or south of the celes- tial equator, the circle thus described will be a great cir- observation on the Surface of the Earth. The celestial cle or small circle, respectively. body's coordinates of azimuth and altitude as used in This apparent motion of the celestial object along a this system are, therefore, topocentric rather than geo- circle either coincident with, or,parallel to, the celestial centric as in the two previous instances. equator as the Earth rotates will prove to be a sizable The astronomical horizon is a plane perpendicular to advantage in tidal analysis where, for example, as a func- the local direction of gravity; the zenith is the point tion of the Earth's diurnal rotation, the necessary catch-up where this local direction of gravity intersects the celestial time between a point on the surface of the Earth and the sphere. The coordinate of azimuth (Z), is measured in orbiting Moon is required. the plane of the horizon, in degrees, minutes, and seconds 2. Ecliptic System of arc through 360' in a clockwise (westerly) direction as viewed from the local zenith of the place. In various The ecliptic system uses for its fundamental plane the usages in astronomy, geodesy, navigation, and oceanogra- plane of the Earth's annual revolution around the Sun. phy, the point of reference for 0' azimuth may be either As in the right ascension subsystem, the coordinate of the north or south point on the horizon. In calculations celestial longitude (A) is measured eastward through 360c' employed in connection with tides, the azimuths of tide- from the vernal equinox, but in the plane of, or parallel producing bodies are usually measured from the south to, the ecliptic rather than the celestial equator, and in through the west. However, the azimuth or "set" of a degrees, minutes, and seconds of arc rather than time. (As tidal current is that direction toward which it is flowing, viewed from the north pole of the ecliptic, celestial longi- commonly reckoned from the north point on the horizon. tude is measured in a direct, or counterclockwise sense of In this system, vertical angular distances are measured rotation.) (in one direction only) above the astronomical horizon The coordinate of celestial latitude (9) similarly is through 90' toward the astronomical zenith. The meas- measured in degrees, minutes, and seconds of arc directly urement is in degrees, minutes, and seconds of arc. This north or south of (i.e., along ecliptic meridians at right positional coordinate representing angular distance above angles to) the plane of the ecliptic. It reaches 90* at the the horizon is known as astronomical altitude (H). Small north'or south poles of the ecliptic. Subject to perturba- circles of equal altitude parallel to the horizon are termed tions, P for the Moon ranges only from about 40561 to almucantars; great circles perpendicular to the horizon 5020. and passing through the zenith are vertical circles. Because the orbit of the Moon does not lie exactly in The vertical circle passing through the north and south the plane of the ecliptic, but is inclined at a very small points on the horizon, plus the zenith, nadir, and north angle averaging 509' to it, an acceptable artifice will and south celestial poles, is called the celestial meridian. later be used (pt. II, ch. 4) in defining either the true or The horizon system is especially valuable for measuring mean longitude of the position of lunar perigee. Here the times and circumstances of rising and setting of celes- the longitude of the perigee of the Moon's orbit, referred tial objects with respect to the astronomical horizon, since to either the mean or the true equinox of date, is measured this plane is the basic reference plane for the system. It from the vernal equinox along the ecliptic to the mean is also valuable in determining positions in terms of the (or true) ascending node, and then along the Moon's cardinal points of the compass, and for making compari- orbit. (The ascending node of the Moon's orbit is the sons with other local geographic or geodetic positions on point of intersection of the Moon's orbital plane with the the Earth's surface. 124 Strategic Role of Perigean Spring Tides, 1635-1976 Since the Moon is relatively close to the Earth compared ment (ranging from an almost inconsequential to a major with other celestial bodies, and the figure of the Earth is amount) in the positions of bodies in space. These motions that of an irregular spheroid (or geoid), the Moon's are: , ( 1 ) the diurnal rotation of the Earth; (2) the parallax and distance from the surface of the Earth vary annual revolution of the Earth around the Sun; (3) the considerably at any angular altitude above the horizon. precession of the equinoxes; (4) the nutational motion This system therefore has a particular usefulness in con- of the polar axis; (5) the space motion of the Earth with nection with tides in establishing the local zenith distance the Sun toward the apex of the Sun's way; (6) the rota- of the Moon. The latter function enters into the computa- tion of the galaxy around its center; and (7) the irregular tion of parallax as a measure of distance of the Moon from shifting of the Earth's crust, as the geographic pole of the the surface of the Earth, as well as in the lunar augmenta- Earth is displaced at a nonuniform rate, and for a yet tion (see figs. 41, 25A, pt. II, chs. 4, 2). uncertain complex of dynamic reasons, with respect to its pole of figure-a motion responsible for the phenomenon GENERAL EQUATIONS FOR TRANSFOR- of "variation of latitude." MATION OF COORDINATES FROM THE In terms of the tides, only two of the above motions arc EQUATORIAL TO THE ECLIPTIC SYS- of consequence. These are the diurnal rotation of the TEM OR THE REVERSE Earth and the annual revolution of the Earth around the Where a and 8 are the apparent right ascension and Sun. In addition, it is necessary to consider the monthly declination, respectively, of a celestial body; A and 8 rep- revolution of the Moon around the Earth. The effect of resent its corresponding celestial longitude and latitude; the Moon's position in declination upon its rate of change in right ascension must also receive attention. and E is the obliquity of the ecliptic, or angle of inclination between the celestial equator and the ecliptic: THE DIURNAL ROTATION OF THE EARTH sin# = sin bcos e-cos 6sinasin a Although all four of the motions mentioned in the cos 0 sin X = sin 6sin c+cos 6sinacosb immediately preceding paragraph are physical and real, Cos Cos X = Cos 3 Cos a the effective measurement of each is made in terms of an and apparent change in position, or the displacement of the Moon and Sun'on the celestial sphere produced thereby. sin 6 = sin 0 cos e + cos 0 sin X sin c The diurnal rotation of the Earth will be considered first. cos sin a = cos g sin X cos c - sin g sin e The actual daily rotation of the Earth results in a phe- Cos 6 Cos a = Cos # Cos X nomenon similar to that observed as a moving car or GENERAL EQUATIONS FOR TRANSFOR- vehicle catches up on another object and passes it. In MATION OF COORDINATES FROM THE what is a purely fictitious or unreal motion, the object EQUATORIAL TO THE HORIZON SYS- thus passed, although stationary or moving at a slower TEM OR THE REVERSE rate in the same direction as the passing body, drops be- Where z is the zenith distance, A is the azimuth, H is hind it and seems to move in a direction opposite to that the altitude, and 8 is the declination of a celestial body; of the latter. and 0 is the latitude of the place of observation: In the same fashion, the Earth rotates daily on its axis against the background of stars which, because of their sin z sin A = cos a sin H enormous distances, may be assumed to be "fixed." As a COS Z @ sin 6 sin 0 + cos 6 cos H cos .0 result, these objects drop back and appear to move in a sin z cos A = sin 6 coso-cos 5 cos Hsino direction opposite to that of the rotating Earth ' and at and exactly the same angular speed. Since any point of ob- servation on the Earth's surface is moving in a circle cos 3 sin H = sin z sin A around the Earth's axis of rotation, each object on the sin a = cos z sin 0 + sin z cos A cos .0 celestial sphere likewise appears to move in a circle. Both Cos a Cos H = cos z cos 0 - sin z cos A sin 0 the radius of the circle projected perpendicularly to this Astronomical Motions axis of rotation and the object's consequent apparent speed of rotation become successively less as the object's The Earth is constantly undergoing no less than seven position is located farther from the celestial equator. Sub- astronomical motions, each of which causes a displace- ject to the diurnal rotation of the Earth, all celestial ob- Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 125 jects (except meteors) appear to rise in the east, move 365.25 days, or approximately 1'/day, on the average, in across the sky, and set on the western horizon. The inde- celestial longitude (fig. 22). pendent motions of the Moon, Sun, and planets among The period of time between two successive alignments the stars will be discussed separately. in longitude of the Sun, Earth, and a given star (the At the vast distances of the stars, any individual mo- sidereal year) is 365-25636042 days; between similar suc- tions which the stars possess are detectable only through cessive alignments with the vernal equinox (the tropical precise measurements, and even over centuries of time the year), 365.24219879 days; between successive solar peri- configurations and relative positions of these objects as gees (the anomalistic year), 365.25964134 days; and- seen from the Earth are subject only to the minute cross- between successive passages of the Earth through the motion components of proper motion. As the stars appear ascending node of its orbit (the eclipse year), 346.620031 to rise and set, subject to the Earth's diurnal rotation, they days. may be thougl;t of as attached to the surface of a vast As the Earth moves physically in a counterclockwise or sphere, which itself rotates daily around the Earth from "direct" sense of motion axound the Sun, the Sun appears east to west as a reflection of the Earth's rotation from (in a purely fictitious manner) to move in the same direct west. to east. sense of revolution as seen from the north pole of the Thus, any given star crosses the hour angle of the vernal ecliptic. This apparent easterly motion must be subtracted equinox (the origin of right ascension) at approximately from the apparent daily westerly motion of rising and the same time in each 24-hour period (actually, because setting caused by the Earth's rotation. The Sun (if its of the Earth's annual revolution, about 4 minutes earlier image could be observed for 24 hours a day, 365V4 days at each transit thereof). The coordinate positions of the in the year) from a nonrotating Earth would move east- stars-except for certain long-period changes-thus re- erly across the sky, completing one full revolution in 3 65 V4 main essentially unaltered. This makes it possible to com- days. Its average easterly movement is 360' (equivalent pile star catalogs in which the right ascensions and declina- to 24 hours or 1,440 minutes of time) divided by 365V4 tions vary only in small units or decimal portions of sec- days, or slightly less than 4'/day. onds of time and arc (due to the common-motion phe- From this cause alone, the Sun's right ascension should nomena of precession, nutation, and aberration, as well increase by close to this same amount during each day. as proper motion, etc.) over long periods of time. Actually, however, as a result of other circumstances, The Moon and Sun likewise rise and set in accordance namely, the elliptical shape of the Earth's orbit and the with the diurnal rotation of the Earth but have, in addi- inclination of the celestial equator to the ecliptic (causing tion, both real and apparent motions of their own which a continuously changing declination of the Sun), the considerably modify their diurnal motions as induced by observed change in right ascension follows a pattern re- the rotating. Earth. The Sun's apparent motion will be lated directly to these factors. The daily increase in the discussed first. Sun's right ascension is least at the equinoxes and greatest at the solstices, the maximum annual increase,@being at the THE EARTH'S ANNUAL REVOLUTION AROUND THE SUN winter solstice since this is also close to perihelion. (See ch. 2, table 9.) The annual revolution of the Earth is responsible for To establish a,uniform. basis for timckeeping, the con- a second instance of an apparent, fictitious motion-that cept of a purely fictitious or mean sun is resorted to, in of the Sun. As the Earth revolves around the Sun in a which this hypothetical celestial body is assumed to move direction which is counterclockwise as viewed from the at all 'times along the celestial equator rather than the north pole of the ecliptic (i.e., in the same direction as ecliptic, and at constant angular velocity. Thus, whereas the Earth's rotation), the object around which it re- the average value of the true sidereal day is 23' 56- volves will itself seem to revolve around the Earth, in this 04.09054' of mean solar time, the mean solar day has a case moving in the same direction as that of the Earth's length of exactly 24' 00' 008 mean solar time, which iis revolution. The Moon is, of course, bound to the Earth equivalent to 24 h 03- 56-555366 of mean sidereal time. by gravitational attraction, and partakes of the Earth's revolution around the Sun, while at the same time it in- THE MOON'S REVOLUTION AROUND dividually revolves around the Earth. The Moon, there- THE EARTH fore, does not appear to revolve counterclockwise, or east- Finally, the Moon revolves around the Earth (fig. 22) ward in the sky, from this particular cause as does the Sun. in the same direction and sense of revolution (i.e., counter- The apparent annual solar motion is equivalent to 360'/ clockwise viewed from the north pole of the ecliptic) in 126 Strategic Role of Perigean Spring Tides, 1635-1976 CATCH-UP MOTION OF EARTH'S ROTATION UPON THE REAL MOTION OF THE MOON AND APPARENT MOTION OF THE SUN THE DIAGRAM IS NOT DRAWN TO ACTUAL SCALE. ll,,%S29.5 ... . ..... ...... .. SUN'S APPARENTI DAILY MOTION M1 MOON'S ALONG MAX. 1E MIN. RBITAL IS2 15.40 io ------7 --------------------- --- 11.80/DAY IREVOLU- THE I /DAY i 2 i CELESTIAL! M2 EARTH'S T I ON,,o SPHERE,1 DIURNAL I ROTAT ION, APPROX. It I 360*/DAY 1*/ DAY J' 3 . ..... ....... . ...... .. loll, --' DURING THE TIME THE EARTH ROTATES FROM T, TO T2, THE MOON REVOLVES FROM Mi TO EARTH'S ORBIT 0 'k E29.5 M2,AND THE SUN APPARENTLY REVOLUTION % MOVES FROM S1 TO S2- APPROX. 10/DAY PLANE OF PAPER IS THAT OF THE ECLIPTIC, SEEN FROM ITS NORTH POLE. FIGuRE 22 which the Earth revolves around the Sun. This results month is shortened by 0.000079 day with respect to the in an apparent motion of the Moon in the same direction sidereal month. as that of the Sun, but of greater magnitude -because the The draconitic or nodical month (measured by two Moon is both closer to the Earth and moving faster. It successive transits of the Moon through the longitude of must also be remembered that the basic revolutionary the Moon's ascending node-or position of intersection motion of the Moon is a real one rather than an apparent between the northward-inclined lunar orbit and the eclip- one conjugate to the annual motion of the Earth as in the tic) is equal to 27.212220 days. It is likewise shortened case of the Sun. with respect to the sidereal month by the regression of the The true revolution of the Moon around the Earth in lunar nodes subject to gravitational perturbations induced a period of one sidereal month, from alignment with a by the Sun. given star to-alignment with that same star again, requires The synodic month is the period of time between align- 27.321661 days. ment of the Moon and Sun in identical longitudes (or right ascensions) and the next succeeding occurrence of The tropical month (the period between two successive this same syzygy position. It is thus equivalent to the inter- alignments of the Moon's position with the longitude of val between two successive conjunctions (new moons) or the vernal equinox) is 27.321582 days. Because of the oppositions (full moons) and is equal to 29.530589 days. slow westward (retrograde) movement- of the vernal This considerable lengthening of the synodic month T A equinox caused by the precession of the equinoxes, this over the period of the sidereal month is explained by the Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 127 fact that, at the same time the Moon revolves around the tions of the Moon and Sun. The corresponding influence Earth, the Earth revolves around the Sun, carrying the of the apparent eastward drift of the Moon in the sky, Moon with it, bound together by their mutual gravita- causing it to transit the celestial meridian some 50 minutes tional de. later each day, will be discussed in an ensuing section on As the Earth physically revolves around the Sun in its the lunar retardation. annual motion, the Sun appears to revolve around the THE MOTIONS OF THE EARTH AND Earth in the same period, at the same angular velocity, MOON IN ELLIPTICAL ORBITS and in the same easterly direction. Accordingly, the ap- It previously has been indicated that the orbit of the parent annual motion of revolution of the Sun occurs in the same direction as the actual monthly revolution of the Earth around the Sun is not circular, but elliptical in Moon around the Earth. Although the velocity of the shape, with the Sun occupying one of the two foci of the Moon in its orbit is much faster than the apparent motion ellipse. (See fig. 4 in the appendix.) It may be noted by of the Sun along the ecliptic, the Moon must each month direct analogy that the Moon also revolves around the travel somewhat farther in its orbit to catch up with the Earth in an elliptical orbit, with the Earth at the occupied motion of the Sun and achieve alignment with it at posi- focus of the ellipse (fig. 23). The dynamic principles of tion of syzygy. orbital motion are exactly the same in each instance, and The extra period of time required in this catch-up a single discussion of the general forces involved will suf- motion is 2.208928 days longer than the sidereal period, fice for both. which accounts for the longer synodic month of 29.530589 By definition, an ellipse is a geometric section con- days. structed by passing a plane obliquely through a cone. The If one were to consider only the motion of the Moon linear circumference of the resulting figure has an "out- of-round" configuration whose greatest diameter is de- with respect to the stars and the length of the sidereal scribed as the Jor axi.s and the least diameter (bisecting, month as previously defined, the Moon would appear to ma drop back in its daily westward motion of rising and and at right angles to, the first) is designated as the minor setting (i.e., drift slowly eastward in the sky). by approxi- axis. By definition, the mean distance of any celestial ob- mately 360'/27.321661 days, or 13.176396'/day-later ject moving in an ellipse is equivalent to the sernimajor defined as the lunar mean daily motion. However, as will axis. The extent of out-of-roundness is described as the be seen, factors exist to alter this average angular velocity eccentricity, whose value varies from 0 for a true circle, through very high values for a thin, very greatly extended of the Moon, both with respect to the Sun and relative to ellipse, to infinity for a straight line. The eccentri'city is any point on the surface of the rotating Earth. defined by the ratio OCIOA in figure 23. The so-called Because of the Earth's motion in orbit around the Sun, anale of eccentricity is represented by the angle OBC in and the Sun's consequent apparent easterly motion in the this same figure, and the sine of this angle is often used same direction as the Moon, the Moon appears to move in astronomical computations. at the somewhat reduced average angular velocity with Kepler's First Law of Planetary Motion states that all respect to the Sun given by 360'/29.530589 days, or, planets (and satellites) in the solar system move in ellip- 12.190749'/day. It is this apparent motion of the Moon tical orbits, with the less massive or secondary object in catching up and passing, and thus moving respectively revolving around its more massive or primary object. toward and away from the Sun in angular elongation, Kepler's Second Law states that the distance of the that produces the continuously changing lunar phase relationships. secondary object from its primary is always such that the radius vector or line drawn from the primary object to It is important to note that the apparent motions of its secondary will describe equal areas in equal intervals both the Moon and the Sun in the sky (the former caused of time. It is clear. from figure 24 that, no matter where by the Moon's orbital motion, the latter by the Earth's in the ellipse a body is located, an area is defined between annual revolution) are in a direction opposite to the mo- two radius vectors drawn to different positions of the ob- tion of rising and setting which results from the rotation of the Earth. The apparent daily motions of the Sun and ject in orbit and the arc of the orbit along which this Moon caused by these respective two factors are, how- secondary object travels. The area circumscribed by these ever, in the same direction as that of the rotating Earth. two lines, and the arc joining the two positions of the This fact is very significant in connection with a further object will always be the same. For example, in figure 24, daily catch-up motion of the rotating Earth with the posi- Ai = A2- 128 Strategic Role of Perigean Spring Tides, 1635-1976 T 0 S SUN PERIGEE-SYZYGY DIRECTION OF M \. ........................ N M........................................................... DIRECTION SUN'S APPARENT OF MOON 9S MOTION ON P ORBITAL MOTION CELESTIAL SPHERE DIRECTION OF EARTH'S E REVOLUTION . .............................. AROUND SUN FQ ....... ......................................................................... . .... EARTH ............................................................................. ..... LO C PERIGEE-SYZYGY RECURS AT NEW MOON EITHER 6-1/2 OR 7-1/2 SEMIMINOR AXIS B ------------------------------- 0.#' SYNODIC MONTHS AFTER PERIGEE-SYZYGY AT FULL MOON MAXIMUM DIAMETER ACROSS THE LUNAR ORBIT IS I C- 763,109 KM 10 =474,173 MI 1> Ix Cn A FM APOGEE-SYZYGY FIGURE 23 Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 129 TO SUN S APOGEE-SYZYGY D I R E C T IION OF NM SLOWER ANGULAR SUN'S APPARENT T VELOCITY AND MOTION ON APC 3 SMALLER ORBITAL CELESTIAL MOTION OF MOON SPHERE AT APOGEE 'All THE MOON'S k ORBITAL VELOCITY IS DETERMINED BY ITS DISTANCE FROM Ik THE EARTH AND ItI KEPLER'S LAW OF EQUAL AREAS. DIRECTION OF EARTH'S ............................... . . . .............. REVOLUTION A TH ................. ........................... FO E,-----o . ............................ .................................................................... LO AROUN D SUN A2 DIRECTION k111 ItI FASTER ANGULAR II VELOCITY AND OF MOON'S PERIGEE GREATER ORBITAL ORBITAL MOTION MOTION OF MOON M 0 FM AT PERIGEE PERIGE,E-SYZYGY NOTE: FOR CLARITY OF PRESENTATION, BOTH THE ORBITAL ECCENTRICITY AND DAILY MOTIONOFTHEMOON AREEXAGGERATED IN SOME DIAGRAMS OFITHIS WORK. FIGURE 24 202-509 0 - 78 -11 RT @H 130 Strategic Role of Perigean Spring Tides, 1635-1976 Kepler's Third Law states that the period of revolution With these new concepts in mind, it is necessary to of the secondary object revolving around its primary (or return to the previously mentioned elliptical motions of of two secondary bodies revolving around their individual the Moon around the Earth and the Earth around the primaries) will vary according to the relationship: Sun. The next step is to discover how such continuously P,2/FO,2 - d13 Id 3 (corrective terms for changing, rather than constant, apparent angular motions ' the masses are omitted) of both the Moon and Sun, together with their positions In words, the square of the period of revolution varies of cl.osest approach to the Earth, affect various astro- Domical configurations and alignments, and the mean or from one time to another (or one object to another) as the cube of the mean distance between the object and its average time intervals between successive such alignments. pr .imary during the interval concerned. The procedures by which these different intervals are The direct implication of these three astronomical laws quantitatively evaluated also Iwill be indicated. is that, as the Moon revolves around the Earth in its 1. The Anornalistic Month monthly orbit, at one position in its orbit known as perigee The period of time between two successive passages of it will reach its closest monthly approach to the Earth the Moon through the position of perigee is known as an and, approximately one-half month later, will reach its ano.malistic month. greatest monthly distance from the Earth known as Determination of the mean length of this month is apogee. analytically complicated by the fact that the perigee posi- Similarly, in the Earth's annual motion around the tion of the Moon's orbit oscillates periodically, but by Sun, about January 2-4 it will pass through a position of closest a Ipproach to the Sun known-as perihelion and, unequal amounts, in a direct and retrograde sense, due to around July 3-6, 6 months later, will pass through a posi- perturbations produced by the Sun. A simplified repre- tion of greatest distance from the Sun known as aphelion. sentation of the length of the mean anomalistic month may, however, be achieved from the arbitrary assumptions Since, in each case of closest approach (perigee or that: ( I ) the perigee position is moving constantly and perihelion) of the less massive object to its primary, the uniformly around the lunar orbit in the same direction as gravitational force of attraction exerted between the pri- the Moon; and (2) this average daily forward motion of mary and secondary is greater, the secondary object will the lunar perigee along the Moon's orbit is + 0. 1114040 also "fall" faster toward its primary at this point. With day. this increased inwardly directed gravitational or centrip- Since the perigee completes one revolution around the etal force being balanced by a correspondingly enhanced lunar orbit in a period of 3,231.48 days (as calculated outwardly directed centrifugal force, the secondary object from observations secured over many years), this corre- remains constrained to move in a closed elliptical orbit. sponds with the average rate of 360'/3,231.48 days, or Because of the in-creased gravitational force involved at this closer distance of approach, the speed of the second- 0. 11 1404'/day specified above. The Moon revolves in its ary object in its orbit also will be greater, and the resulting orbit at a mean sidereal rate (see below) of 13.176396'/ angular distance the object will travel in any unit of time day, a much faster angular velocity. In a recurring catch- will be larger (fig. 24). up motion, which is not a part of the Earth's diurnal just the opposite is true at apogee or aphelion, with rotation, the Moon as seen from the Earth therefore moves the secondary object revolving at a considerably slower once each month from a position to the west of (follow- speed in orbit and covering a much smaller distance (this ing) the lunar perigee, successively overtakes, draws in line applies in either a linear or angular sense). with, and passes this position, and then advances to the The maximum and minimum daily angular velocities east thereof. of the Moon are about 15.4' and 11.8', respectively; The mean daily motion of the Moon in its orbital revo- those of the Sun are approximately 1.016' and 0.983'. lution around the Earth, as measured with respect to the The length of the anornalistic month (from perigee to "fixed" stars is given by: perigee) is 27.554551 days, and that of the anomalistic 3600 3600 year (from perihelion to perihelion) is 365.25964134 sidereal month -_ 27.321661 days 13.176396'/day days. The differences between both these values and the corresponding sidereal periods are the result of perturba- This means that, with respect to the previously assumed, tions which cause a net for-ward motion of perigee and a steadily advancing position of perigee, the Moon moves retrograde motion of perihelion, respectively. at a relative angular speed of: Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 131 13.176396'/day - 0. 11 14040/day = 13.064992"/day accelerations can be obtained simply by taking successive By means of the latter value, the mean anomalistic daily differences in the longitudes of the Sun. Subse- period of revolution (from perigee to perigee) may be quently, in,applying the meaning of these differ&nt veloc- calculated as: ities of motion to tidal phenomena, allowance also will be 3600 made for the daily catch-up motion of the rotating Earth 13.0649920/day = 27.554551 days with the Sun. It will then be necessary in place of these motions in apparent or true (as distinct from mean) longi- However, as previously indicated, this average figure is tude to consider the corresponding motions in right ascen- derived from the dual assumptions of: ( 1 ) a perigee posi- sion (thereby referring them to the equatorial plane of tion which moves continuously in a forward direction, the Earth's rotation). and at a uniform speed, along the lunar orbit; and (2) a The apparent daily motion of the Sun does not vary hypothetical or mean moon, which is moving constantly widely from year to year and, to the order of accuracy at the same speed in its orbit. required for the present purpose, may be obtained from At the times of a close penigee-syzygy alignment, very The American Ephemeris and Nautical Almanac for any different conditions actually hold true. At such times year. Thus, the average daily motions of the Sun in degrees (later to be described as proxigee-syzygy), the perturbed of are in celestial longitude and in seconds of time in right motion of perigee is considerably different in both magni- ascension, bracketing the perihelion of 1975 January 2 tude and direction from the mean value of +0. 111404'/ and the aphelion of July 6, as well as at the two solstices day given above. (See "The Special Motion of Perigee and two equinoxes, are given in table 7. Close to the Position of Perigee-Syzygy Alignment" in pt. II, ch. 4.) At such times also, the orbital angular velocity TABLE 7.-Apparent Daily Motion of the True Sun in Right of the Moon may attain an actual value as high as 15.4'/ Ascension and Lotzgitude for Selected Dates in 1975 day. True distance Apparent daily of sun, 2. Effect of the Solar Parallactic Inequality Nearest motion averaged inclusive for ecliptic The quantity known in tidal theory as the solar paral- Circumstance tabular of inclusive dates Ina (a) In X tabular lactic inequality is that associated with the elliptical shape dates (mean of the Earth's orbit. It arises from the fact that, revolving distance, in this elliptical orbit, once in each half-year the Earth (D= 1) reaches its respective positions of closest annual approach Perihelion: Jan. 3-2 .... 264.60 1.0190 0.9832890 to, and greatest distance from, the Sun, previously defined Jan. 2. as perihelion and aphelion. As also noted eaxlier, the Earth Aphelion: July 6-5 .... 247.16 0.9536 1.0167433 is traveling at a considerably greater.orbital velocity at July 6. 17.44 0.0634 perihelion, and a correspondingly diminished velocity at Winter solstice: Dec. 23-22. 266.36 1.0182 0.9836583 aphelion. Dec. 22.5. The fact that the actual orbital motion of the Earth Summer solstice: June 23-22. 249.49 0.9537 1.0163006 results in a precisely similar, apparent motion of the Sun June U. 16.87 0.0645 in the sky makes it possible empirically to evaluate the Vernal equinox: Mar. 22-21. 218.67 0.9931 0.9961315 changing magnitude of this apparent solar motion by Mar. 21. means of data tabulated in The American Ephemeris and Autumnal Sept.24-23. 215.45 0.9785 1.0033977 equinox: Nautical Almanac. These data give the daily apparent Sept. 23.5. 3.22 0.0146 positions of the Sun throughout the year. If the reflection of the Earth's own orbital motion were the only factor in- volved in the apparent velocity of the Sun's movement, It is apparent from the preceding table that the greatest the angular distance covered by the Sun in its apparent difference in the apparent daily motions of the Sun occurs daily motion would be greatest near the time of perihelion when comparing the respective angular velocities at peri- and least near aphelion. It will be seen (table 7) that, helion and aphelion. This is due to the greater orbital in terms of right ascension, this is not entirely true. speed of the Earth and increased apparent motion of the Since the apparent daily motion of the Sun along the Sun when the Earth reaches its closest annual approach ecliptic is sufficiently representative to illustrate such ef- to this massive body, and the corresponding decrease in fects of the Earth's position in orbit, the changing angular apparent velocity of the Sun at aphelion. 132 Strategic Role of Perigean Spring Tides, 1635-1976 However, as seen also from the second pair of examples, the Moon (due to its large parallax) and, to a lesser-ex- the difference in the Sun's apparent daily motions be- tent, for the Sun, the paths of their movements in declina- tween the summer and winter solstices runs a very close tion have their greatest inclinations to the Equator and the second-since these dates occur within less than 2 weeks differences in declination change the most rapidly. This of aphelion and perihelion, respectively. Moreover, and situation is especially marked in terms of topocentric even more important in terms of the subsequent descrip- motions as the Moon reaches its extreme declinational tion of solstitial tidal peaks (pt. 11, ch. 2), the individual values in the 18.6-year nodical cycle (see pt. II, ch. 4, values of the daily apparent angular motions of the Sun "Eff ects of Extreme Lunar Declination . . . " ). at the times of the summer and winter solstices are higher DECLINATIONAL EFFECTS ON THE AP- than those at aphelion and perihelion, respectively. This PARENT MOTIONS OF THE MOON AND indicates the effect of minimum daily motion in declina- SUN tion and a maximum motion in right ascension, as will be In dealing with the changing tidal forces resulting from discussed in detail in various subsequent sections-with the varying positions and motions of the Moon and Sun. an introductory explanation under the immediately fol- one factor is noteworthy as accelerating the apparent mo- lowing heading. tions of these two bodies in right ascension. This, in turn, Finally, the daily motion of the Sun at the times of increases the Earth's necessa.ry rotational catch-up time, either of the equinoxes is seen to be the least of all- lengthens the tidal day, and provides a greater opportunity evidence of a minimum motion in right ascension and for enhanced tide-raising forces to operate. The effect in maximum motion in declination. In the third set of data question is that of a maximum lunar (or solar) declina- representing the apparent motions of the Sun at the times tion angle in contributing to an increased motion of these of the vernal and autumnal equinoxes, the small differ- respective bodies parallel to the celestial equator. Each ence between the respective daily solar motions on these of the apparent .motions represented, when declination is dates results from several possible causes: (I ) an asym- plotted against increasing right ascension (or the passage r netry in the Earth's orbit produced by a slow regression of time) as in the top of figure 44, reveals a series of curve of the ascending and descending nodes along the ecliptic- maxima and minima in declination. such that the equinoxes are not necessarily symmetrically Any such near-maximum value in declination means arranged with respect to the line of apsides joining peri- that the Moon or Sun, in attaining its greatest angular helion and aphelion; (2) the recognized slow progression distance north or south of the celestial equator, is at a of the Earth's line of apsides along the ecliptic will have point where the slope of the curve is very nearly zero. a similar effect; and (3) the date of the vernal equinox, Practically all of the movement of the body is in right around March 21, is closer to the perihelion date, about ascension and very little, if any, is in declination. As the January 4 (and its effect in increasing the orbital velocity slope becomes zero at the peak of the curve, the daily of the Earth), than the autumnal equinox, approximately differences in declination contrastingly become the small- September 23, is to this same perihelion date. est and, as they pass through zero, change their sign. In consequence, within a day or two of the summer and winter solstices, as the positive and negative solar declina- tion angles reach their respective max .imum annual values, Auxiliary Influences Affecting the the daily differences in right ascension of the Sun also Daily Rate of Lunar Motion in attain their greatest values and the daily differences in declination their least values for the year, as confirmed Right Ascension in table 7. Similarly, at those times, twice each lunar In the interests of completeness, it must be noted that month, when the Moon reaches its maximum declination, several counterproductive astronomical forces exist, capa- either north or south of the celestial equator, the daily ble of altering the extra tide-raising potential created by difference in the lunar declination becomes zero. Within a situations in which the relative motions between Earth, few days of this same date, the daily change in the right Moon, and Sun are slowed down. As will subsequently ascension of the Moon approaches a maximum value for be demonstrated, it is subject to this latter condition that that lunation. augmented gravitational forces produced by the mutual Conversely, as the Moon and Sun in their apparent alignment of these three bodies are exerted over a greater motions cross the Earth's Equator, their declinations be- period of time in a lengthened tidal day, and enhanced come zercy and change sign. At such times, especially for tides result. Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 133 The Effect of Parallax on the of coordinates,, a function of two quantities which serve Moon's Apparent Motion to relate the lunar position to this particular point of In addition to the effects upon lunar motion associated observation. These quantities are the geocentric latitude with the two solstitial and two equinoctial positions previ- (0) of the place and the hour angle (h) of the Moon. ously described, another astronomical factor contributes The latter value represents the angular distance of a ce- to the respective circumstances that: (1) the Moon's ap- lestial object east or west of the local meridian, measured parent motion in right ascension often attains its largest at right angles thereto and, in this usage, expressed in equivalent units of time. Its value is positive when the value and the declinational motion reaches a minimum object is west, and negative when it is east of the meridian. when the Moon is at or near its greatest declination (either An additional parameter which is necessary to transfer north or south of the celestial equator) ; and (2) the the lunar position from a geocentric to a topocentric refer- Moon's greatest motion in declination and least motion in ence system is the distance of the Moon from the center right ascension occurs when it is on or near the celestial of the Earth (given by ir, the geocentric horizontal paral- equator. (All such comparisons of extreme motions refer lax at the time of observation). specifically to the lunation in which the Moon is at the. The first two of the above quantities are different for moment.) each location on the Earth's surface, and the third changes This second contributing factor involves the consider- continuously with time. The two remaining astronomical able difference in the Moon's motiorY as calculated in (1) variables involved are denoted by Aa (the hourly rate of geocentric and (2) topocentric coordinates (i.e., as this change of 4le Moon's position in right ascension) and 8 motion would be observed respectively from the center (the instantaneous value of the Moon's declination). of the Earth and from a point on its surface). The differ- The geometric relationships between these various ence in apparent motion is caused by the relatively close quantities are expressed approximately by the formula distance to the Earth and large parallax angle (see figs. given below. This represents the geocentric motion im- 41, 25A) of the Moon. Two other factors which must be posed on the Moon by the Earth's diurnal rotation, plus considered as an integral part of the present discussion topocentric corrections to this motion introduced by: ( 1 ), are (1) the apparent diurnal motion of the Moon, as a the hour angle and parallax of the Moon; (2) its altered reflection of the rotation of the Earth, and (2) the indi- declination as seen'from the Earth's surface rather than vidual or actual motion of the Moon in its own orbit, its center; and (3) the latitude of the observer. creating a positional displacement which is only vec- toiially related to the motion of the rotating Earth. Aa (topocentric) = Aa (geocentric) + - T" Cos 0 cos h Changes in Right Ascension Associated With 57.3'/radian cos 5 the Apparent Diurnal Motion of the Moon The analytic evaluation of Aa (geocentric) is given by The first of these two motions will now be discussed, Aa (geocentric) = [@h] Fdh-1 employing the equatorial system of coordinates for refer- dt LTUT ence, in order to illustrate the particular influence of lunar declination upon one of several possible variable At this point, a substantial technical digression is de- motions of the Moon in right ascension-that is, the di- sirable, as a supplement to the main text, to explain the urnal motion as seen from a topocentric position. (The alternative method of positional representation in the diurnal motion of the Moon as used for purpose of com- equatorial system of coordinates, and at the same time paiison in the present connection has been defined as that quantitatively to evaluate the unknown analytic terrns in occurring in a diurnal circle and resulting purely from the the above equation. rotation of the Earth. In this usage, it does not contain In the equatorial system of coordinates, the Earth's axis the daily component of the Moon's own orbital motion. is the primary reference, and its extension to the points of The term topocentric-referring to measurements made intersection with the celestial sphere demarcates the north from the surface of a planetary body-also has been dif- and south celestial poles. The celestial equator lies in a ferentiated from the expression geocentric, referring to plane perpendicular to this rotational axis and midway the Earth's center.) between the poles. It is around this axis that the diurnal The apparent diurnal motion of the Moon as seen from motion constituting the immediate topic of discussion any given location on the surface of the Earth is, in topo- occurs. The apparent "rising and setting" motion caused centric terms, and as expressed in the equatorial system by the rotating Earth changes the Moon's position with 134 Strategic Role of Perigean Spring Tides, 1635-1976 respect to the local meridian and hence its hour angle (see difference is of some consequence in the case of the Moon, next paragraph), but does not alter its right ascension, whose apparent motion results from a combination of the since the established origin of this coordinate is, as far as Earth's diurnal motion and the Moon's own orbital the diurnal motion is concerned, also moving at the same motion. angular rate. If the effect of the Earth's rotational motion Whereas anychange in the Moon's position caused by were alone to be considered and the Moon's own actual the diurnal rotation of the Earth alone would occur in a motion due to its revolution in orbit disregarded, the lunar path which, over a short period of time, would remain body would appear to move across the sky in a circle very parallel to the celestial equator, the lunar body actually nearly parallel to the celestial equator. appears to move along a track on the celestial sphere These small circles in which most celestial objects which is a composite of the Moon's own orbital path and (other than those located directly on the celestial equator) the diurnal circle produced by the Earth's rotation. It appear to move, subject only to the diurnal rotation of the is often found to be more convenient to measure such Earth, are called parallels of declination. Great circles apparent motion by means of an available alternate in perpendicular to the plane@of the celestial equator, spaced the equatorial coordinate system. This variation employs I hour apart, and passing through the celestial poles, are the celestial meridian rather than the vernal equinox as a designated as hour circles. That hour circle which co- point of reference and thereby becomes more meaningful incides with the vertical circle of the horizon system, of in establishing the effects, upon motion in right ascension, coordinates, and passes through the zenith, nadir, north of topocentric position on the Earth. The corresponding and south celestial poles, as well as the north and south adaptation of the equatorial system is termed the hour- points on the horizon, is termed the meridian. angle subsystem. That component of the Moon's apparent And it is here that the first distinction is found affecting movement which is parallel to a declination circle and the motions of relatively close astronomical bodies such as takes place between successive hour circles or fractional the Moon and Sun, because of the different positions in parts thereof in a standard unit of time is termed, in the which these would be seen from the center of the Earth discussion which follows, the rate of change in hour angle. and from its surface. The difference is a direct function The specification of apparent motion in either geocentric of the geocentric parallax. A changing parallax angle of or topocentric systems is denoted by adding a subscript the Moon relative to the Earth occurs as the Moon suc- "C' or "T," respectively. cessively regresses toward, transits, and falls behind the The value of the mean diurnal geocentric motion of in 'eridian due to the Earth's faster rotation in the same the Moon in hour angle h and time t, resulting from the direction as that of the Moon's orbital revolution. rotation of the Earth, is given by the differential function At any particular latitude of observation on the Earth's surface, a greater distance is involved in the side of the Fdh-J = 15.04100*/h parallax triangle joining the Moon and an observing posi- L11, tion on the far side of the meridian than in the case of an This figure is derived by a transformation from time to observing position on its near side. When the Moon is west angular systems of measurement. It represents the slight of the meridian, the effect of parallax is, therefore, to excess (3,609.856473") over the length of the mean solar increase the hour angle; when the Moon is east of the hour (i.e., l"=60'X60'=3,600'Xl.003) resulting from meridian, the effect of parallax is to reduce the.hour angle. an average decrease, by atmospheric refraction, of the The coordinate of right ascension is measured in the rate of change in hour angle. The corresponding value plane of the celestial equator and, although it is subject to when converted into radian measure is geocentric and topocentric differences in the same manner dh as the hour angle, the right ascension of a body does not ITJG = 0.26252"' vary with the geographic longitude of th 'e observing posi- Similarly, the value df the mean diurnal topocentric tion on Earth, while the hour angle of the object does. motion of the Moon in hour angle, exclusive of the Moon's Because the change in parallax with position in hour angle is different from the change of parallax with right ascen- own orbital motion, is sion, the diurnal motions in hour angle and in right dh t] = 14.49208*/h ascension of a close celestial body are not the same. The [Ld T Astronomical Positions and Motions Important in the Evaluation of Perigean Spring Tides 135 which is equivalent to The Relationship of the Moon's Motion in rdhJ rad/h Right Ascension to Its Declination = 0.25294 L_dtJT In the basic equation evaluated above, involving only It will be seen that when the next-to-the-last value is the effect of the Earth's diurnal rotation upon the change multiplied by 2,P/d, giving 347.808', it is less than the in right ascension of the Moon, it will be observed that 360' defining one rotation of the Earth, since it contains the cosine of the declination occurs in the denominator. the effects of the Moon's eastward drift resulting from the Hence, as the declination increases from 0' to 90', the Earth's orbital revolution described a few sections earlier. influence of this factor upon the change in right ascension If the additional 50.415- (0.84025') of the mean daily varies from (1) the minimum value produced by the lunar retardation (see pt. II, ch. 2) is multiplied by the other parameters h, 7r, and 0, through (2) larger values same rate of lunar motion, it gives 12.177', and if this is introduced by the presence of a decimal fraction in the denominator, to (3) infinity at 90' (any motion in right added to the rotation during 24", the full 360' comprising ascension is indeterminate at the celestial poles). the daily angular rotation of the Earth from one lunar From an analysis of the spherical trigonometry rela- transit to the next is obtained. tionships in figure 25B, it is also obvious that the ap- Substituting these quantities (in radian measure) in the parent motion of the Moon along any.portion of a paxallel second of the preceding equations: circle of declination (whose radius must @ecrease toward the poles) will likewise vary from a maximum on the Aoe (geocentric) =0.26252rad/h _ 0.25924 raalh celestial equator to zero at the poles. That is, the ap- =0.00958 1dJh ; 0.00958 rad/l/0.0 174511/* parent change in right ascension ( Aa ) P, along any paral- =0.54900*/'= 134.7s/h. lel circle will, as caused by the Earth's diurnal rotation Assuming, by way of example, that the Moon is alone, be approximately equivalent to the change in right on the celestial equator (B=O') and is just transiting ascension at the equator multiplied by the cosine the local meridian (h=O') at the latitude of the U.S. of the declination of the Moon (i.e., (Aa)p= (Aa)B cos Naval Observatory in Washington, D.C. (0 a). =38-55'14.0" N.) and, for simplicity, that ir At the Equator, all of the Moon's apparent diurnal mo- = 60'= 3,600". tion occurs in the coordinate of right ascension, and hence Then: the length of the lunar day is increased a greater amount. 3600" cos 38'55'14.0" cos 00 The precise relationships which variously modified Aa = 134.7'1' + 57.3""1 cos 0' lunar motions in right ascension have with respect to the Moon's declination actually are quite complex. Further- 2,800.9 s1h more, the significance of the declination-induced magni- @ 134.7'/' + 57.3 183.6 tudes of these apparent motions in right ascension result- The effect of the Moon's additional component of motion ing from the Earth's diurnal rotation as they influence the@ltide-raising potential should not be confused with in right ascension resulting from its own orbital motion other effects associated with the Moon's own orbital mo- will be discussed in connection with the extreme lunar tion. Those purely dynamic aspects of the tide-raising displacement caused by the lunar nodical cycle, as shown forces which are related to lunar declination will be in fig. 36 (pt. II, ch.. 4). described in part 11, chapter 4. Chapter 2. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces The preceding chapter describes the continuously lunar transit times, and (2) the necessary "catch-up" changing positions and motions of the Moon, Earth, and times between a point on the rotating Earth and various Sun which, taken together, result in correspondingly apparent motions of both the Moon and Sun in the same varying astronomical forces responsible for the produc- direction. Other dynamic factors of consequence to the tion of the tides. In the present chapter, attention will be period of application of augmented gravitational forces focused upon certain closely related factors operating to involve the instantaneous geometric figure and varying increase both the magnitude and duration of these tide- rotational motion of the orbit of the Moon. These are both raising influences. subject to small disturbances known as "perturbations" caused by the changing gravitational attraction of the Principal Effects Sun, and such perturbations may, in turn, give rise to corresponding variations in the length of the tidal day. Various alignments and combinations of the gravita- The perturbations produced in the lunar orbit will form tional forces acting, as well as the relative distances be- one of the principal topics for discussion in part II, chap- tween Earth, Moon, and Sun, and the angular positioning ter 3, and the further description of their associated effects of the latter two bodies with respect to any observing posi- will be reserved until then. However, with consideration tion on the Earth's surface, collectively exercise a very to the duration of time in which augmented tide-raising important influence in producing tides of considerably forces can act, it is desirable to provide an immediate increased amplitude and/or range. Similarly, the relative introduction to the close connection between lunar transit speeds of motion of these same three bodies, the inclina- times and the length of the lunar day (as loosely desig- tions of the apparent paths of the Moon and Sun to the nated, before various modifications and differences indi- celestial equator, and the lengths of their arcs of move- cated in the present chapter cause it to become the tidal ment across the sky, affect the period of time during which day). Significantly, certain changes in the length of the such augmented tides exist. tidal day may also cause variations in the catch-up times In general, the enhanced astronomical forces creating of the rotating Earth. perigean spring tides are of relatively short duration. Plots Foremost among the variable quantities affecting the of these tides are marked by more steeply sloping curves length of the lunar day and, through it, the tidal day, is of tidal growth and decline (see part 11, chapter 8) asso- the daily lunar retardation. The actual magnitude of the ciated with the transient reinforcement of the tidal forces. daily lunar retardation also bears a very close relationship These amplified crests and troughs occur at appropriate to the daily differences in motion of the Moon in right times of high and low water during the tidal day. As a ascension, introduced in the preceding chapter and con- result, a very important factor of determination in connec- tinued in the present one. tion with the relative intensity of perigean spring tides involves the changing lengths of the tidal day within which The Daily Lunar Retardation such transitorily increased tidal forces are exerted. . Two important concepts affecting the duration of the As has been previously noted, the period of revolution tidal forces acting which will appear repeatedly in future of the Moon in its orbit around the Earth from conjunc- analytic discussions throughout the text are those of (1) tion or alignment with a star to conjunction with that 137 138 Strategic Role of Perigean Spring Tides, 1635-1976 same star again is known as the sidereal month. Its mean actually revolves around the Earth. Thus, the Moon must, value is 27.321661 days. This figure represents the average during each month, catch up with the current position of the period of revolution, obtained from the individual, real Sun to achieve a direct alignment between Earth, Moon, and Sun at times of either new moon or full moon. motion of the Moon in space. It is independent of either the Moon's combined revolution with the Earth around the Sun (annual orbital motion) or the rotation of the The mean period of time, in days, between two such Earth on its axis (diurnal motion) which causes the Moon successive occurrences of either new moon or full moon to rise and set, and to move daily across the sky with has been defined as the synodic month Wun)- respect to any location except one in extreme polar lati- The rhean daily gain of the Moon on the Sun is given tudes on the surface of the Earth. Both of the motions by th e equation: I named above in parentheses, and others as well, do, how- 3600/M,,Id-3600/y,,id=3600/M,,.. ever, introduce modifications in the apparent speed of Therefore 1/M,,,,,=1,127.321661-1/365.25636042 movement of the Moon. Through corresponding altera- =0.036600996-0.002737803 tions in the length of the lunar day, they also affect the =0.033863193 length of the tidal day and, with this, the magnitude of or M.,,=29.530589 days. the tides. With respect to the Sun, the Moon advances in one Thus, continuing from the sidereal or true month, the mean solar day through the previously mentioned average average period of time between two successive conjunc- angular distance of 360'/29.530589d=12.190749'. In tions (or oppositions) of the Moon withthe Sun (i.e., at terms of its times of transiting the celestial meridian, the new moon or full moon, respectively) is termed the synod- Moon is retarded daily through this angle, on the average, ic month. Because the Earth's own mean (orbital) motion throughout the year. Because the apparent angular motion around the Sun carries the Moon with it approximately of the mean sun is only 0.985647'/day and that of the 0.985647' eastward each day and this same amount Moon with respect to the Sun many times greater, the farther away from the next succeeding alignment between Moon is constantly gaining on, and passing the Sun. Earth, Moon, and Sun at time of syzygy, a necessary At the same time that the Moon and the Earth are catch-up motion is required. The synodic month is, there- revolving in their separate orbits, at mean angular veloci- fore, 2.208928 days longer than the sidereal month, or ties of 0.549'/mean solar hour and 0.041'/-", respec- 29-530589 davs. tively, the Earth is rotating on its axis and at a very much faster angular rate given by 360'/24'= 15.0'/-". In con- In the following equation M@W = the length of the trast with the Earth's revolutionary motion around the sidereal month, in mean solar days (measured by the revolu- Sun, this results in an apparent motion of the Sun in a tion of the Moon through 360' from alignment with one direction opposite to that in which the Earth is rotating. star to alignment with that same star again). In one day, the Accordingly, as a reflection of the Earth's daily axial rota- Moon will, therefore, move through 36011M,,,. Similarly, tion'but subject to a small eastward component of motion Y@Id@ the length of the ordinary (sidereal) year, in mean equal to the daily portion of the Earth's eastward revolu- solar days. In one day, the Earth will move through tion around the Sun, the Sun appears to move westward 360'/Y@Id. As the Earth revolves in its annual orbit around the Sun, the Sun appears to move forward in the same in the sky and transits the upper meridiaxi of any place direction in the sky. Accordingly, the quantity 360'/Yid once each apparent solar day. The period of time between also represents the apparent daily motion of the Sun, caused two successive transits of the true Sun is extremely variable by the Earth's revolution. throughout the year. However, at a very early time, this Since the average (mean) orbital motion of the Moon is 12.1907490/day and the mean apparent motion of the Sun apparent motion of the true Sun became the basis for (the equivalent of the Earth's mean orbital motion) is timekeeping by means of sundials. only 0.985647'/day, the Moon appears to move much faster Later, for purpose of convenience, the motion of an in its daily eastward motion in the sky than does the Sun. (This motion is not to be confused with the daily rising and hypothetical or fictitious mean sun was chosen, and this setting motions of both the Sun and Moon in a westward concept has persisted, although the method of determining direction across the sky, an apparent motion caused by the extremely precise clo ck time has changed. The mean sun oppositely directed rotation of the Earth.) In its fictitious is assumed to move uniformly with a constant, average eastward motion with respect to the Earth, the Sun appears to be moving in the same direction in which the Moon rate of motion along the celestial equator instead of along Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 139 its appaxent true path, the ecliptic-and without any the local meridian, the length of the mean lunar day at variation due to the Earth's changing velocity in orbit the Equator is, therefore, 24' 50'@ 24.98. The amount around the Sun. The time between two successive upper above 24 hours is known as the mean daily lunar retarda- transits of, this mean sun across the local meridian of any tion. place is defined as the mean solar day of 24 mean solar hours.. 2. The Tidal Day 1. The Lunar Day It must be noted that the angular velocity of the Moon from which the above value of the mean lunar day is The Moon is likewise caused to transit the upper merid- derived is steadily changing. These changes are caused by ian of any place on the Earth's surface once each day the elliptical shape of the Moon's orbit, its inclination to as a result of the Earth's axial rotation. However, the the celestial equator-with consequent continuously vary- Moon is revolving in its orbit in the same direction as that ing declinations-and by perturbations produced within in which the Earth is rotating on its axis, and this results the lunar orbit. Other local fluctuations in the Moon's in an extra amount of time required for a position on the apparent angular velocity across the sky result from the Earth's surface, subject to its rotational motion, to catch latitude of the position of observation and the Moon's up with the Moon's changing position. In relating the varying zenith distance. The average value of the daily daily apparent gain in position of the Moon to the corre- lunar retardation in transit times may, accordingly, range spondingly delayed time at which the Moon reaches the from 38 to 66 minutes, but may be quite different from tipper meridian of a place, and hence the amount of this the corresponding retardation times in the Moon's rising delay, the following reduction is used: or setting. Various factors-notably the seasonal changes Daily mean synodic motion of the Moon in orbit in the inclination of the ecliptic to the celestial equator = 12.190749'. and the continuously varying angle between the Moon's Mean solar day = 24 mean solar hours. orbit and the local horizon-cause the lunar retardation Thus, the mean synodic motion of the Moon per times in these respective positions to be different. Sim- hour is ilarly, only in transiting the meridian are the Moon's 12.190749' per day/24 hours per day angular motions in right ascension, hour angle, and azi- =0.507948' per mean solar hour. muth the same. At increasingly larger angles from the meridian, greater divergences appear among these three Since the Earth rotates through 15' in one mean solar motions. hour, the preceding hourly motion of the Moon in its The mean lunar day has been defined above. For cer- orbit (or, when the Moon is on the celestial equator, the tain general purposes, and where only average values are instantaneous motion in right ascension) involves a time- concerned, the mean tidal day may be regarded as synon- delay factor of: =0.507948' per mean solar hour. ymous with, and equivalent in length to, the mean lunar -0.033863X60 minutes/hourX24 hours/day day. This does not apply where considerable deviations =:48.73008 minutes 48m45.8'. in the length of the tidal day, dependent upon tidal re- sponses to reinforcing astronomical conditions, are a mat- However, as the Earth rotates through 360' on its axis, ter of immediate concern. the Moon moves through 12.190749' in its own orbit By contrast, a more exacting interpretation of the ac- around the Earth. Allowing for this catch-up motion of tual tidal day (see appendix, fig. 6), as used generally the Earth's rotation upon the changing position of the throughout this volume, involves the period of time be- Moon, the average daily delay between two successive tween the larger maxima (or minima) of two tid6 of the transits of the Moon across the celestial meridian of a same type (ordinarily measured between one higher high place on the Earth's Equator is water and the next) . 360- +12.190749 - =372.190749- The differences between any specific lunar day and the 48.762996-X 372.1907490 /3600 =50.414267- corresponding tidal day are obvious: Lunar transit times -50- 24.9'. used in the determination of the lunar day consider only Since the lunar day is defined as the period of time be- the instant of passage of the Moon across the upper or tween two successive upper transits of the Moon across lower branch of the meridian, and are, therefore, re- 140 Strategic Role of Perigean Spring Tides, 1635-1976 stricted to the meridian altitude of the Moon a; large succeeding upper transits) of the Moon occurs when the numbers of intermediate occurrences of tidal peaks, with difference between successive hourly right ascensions at- the Moon being at different altitudes and azimuths, would tains a minimum value. Other possible correlations, par- not be included under this definition of the tidal day, ticularly any sought between the motions, of the Moon in since the times of lunar transit and those of the maximum either right ascension or declination and the correspond- rise of the tide do not bear a one-to-one correlation. ing length of the tidal day (as distinct from the lunar day) Moreover, the length of the tidal day as used in the are not as well defined. second and more restrictive sense involves numerous addi- . The greatest and least values of the hourly differences tional variable quantities. These -are associated with the in right ascension usually occur, in a directly opposite relative positions, motions, and forces of both the Moon relationship, at times very close to those of the least -and and Sun, perturbations of the Moon's orbit by the Sun, greatest values, respectively, of hourly change in declina- and other specific circumstances relating both to hydrog- -tion. However (since other factors also affect the two raphy and dynamic oceanography. (See pt. 11, chs. 4, 6.) coordinates), these opposing maximum and minimum This more exact usage is especially applicable in the com- values of hourly change in right ascension and declination parison of tidal actions at localized observing stations do not necessarily occur even on exactly the same day. which are subject to (1) different high-water lunitidal Similarly, the time of maximum retardation in transit of intervals (i.e., specific time intervals between lunar transit the Moon does not necessarily agree exactly with an and the highest rise of the tide, attributable to hydro- increase in the length of the tidal day as defined in the graphic and other causes), and (2) varying delays in second concept given above and determined from tide attaining a maximum tide rise after transit of the Moon tables. This is because various other astronomical circum- (associated with unequal phase and parallax lags at the stances, including the gravitational influence of the Sun, individual stations). These effects are discussed further are also effective in altering the period of time between in part II, chapter 6. successive high waters, and hence the length of the tidal day. Relationship of the Tidal Day to Lunar Among those circumstances which tend to increase the Transit 'Times, Hourly Differences'in Moon's apparent motion in right ascension as seen from Right Ascension of the Moon, and Other the Earth are: (1) proximity of the Moon to the position Factors of perigee-syzygy, causing an acceleration of the Moon's A comparison of data tabulated in The American direct motion in orbit; and (2) proximity of the Moon to Ephemeris and Nautical Almanac shows that the greatest its largest values in declination, positive or negative, re- difference in time between successive upper and lower sulting in a maximum forward motion in right ascension. transits of the Moon occurs when the difference between Circumstances which tend to decrease the Moon's ap- successive hourly right ascensions also reaches a maximum parent motion in right ascension include: (1) proximity value (i.e., the Moon is moving eastward in right ascen- of the Moon to the position of apogee-syzygy, with the sion by its greatest amount). The agreement between decreased gravitational force of the Earth causing a re- these two factors is ver-y close. An increase in the differ- duction in the Moon's forward velocity in orbit; and (2) ences between the values of hourly right ascension and an creation of the maximum possible angle of inclination increase in the differences between the retardation times between lunar orbit and the celestial equator (_L28.5') affecting the transit of the Moon are, in fact, directly during the appropriate phase of the 18.6-year lunar nodi- correlatable. cal cycle (pt. 11, ch. 4), thus markedly increasing the incli- Conversely, the least difference in time between im- nation of the Moon's topocentric path in declination, mediately succeeding upper and lower transits (or two augmenting its apparent motion in this coordinate and, to a certain extent, decreasing its apparent motion in right It should be noted at this point also that a small distinction ascension; this effect is in addition to the greater inclina- exists between the meanings of "culmination" and "meridian tion between the declinational motion of the Moon and transit" due to variations between the angles at which parallels the celestial equator, and the relatively reduced motion of declination (equatorial system) and almucantars (horizon sys- tem) cross the celestial meridian. Thus the Moon may transit the in right ascension which occurs when the Moon is near meridian, yet not be exactly at its maximum angular altitude above to, or crossing, the celestial equator compared to that the horizon, as implied by the word "culmination." In the Northern when it is near its semimonthly position of maximum Hemisphere, as the Moon moves toward greater declinations, it culminates following its transit of the meridian. declination. Factors A�ecting the Magnitude and Duration of the Tide-Raising Forces 141 Apparent Diurnal Motion of a Body circle) during the entire period of one rotation of the "Fixed" in Space Earth, as in the case of a "fixed" star, a trigonometric When a very distant and hence, in terms of its actual reduction' is necessary to obtain the object's individual space motion, essentially stationary celestial object such motion in, or parallel to, the celestial equator. Although as a star is subject to the Earth's diurnal rotation, it will the Sun is a star, its distance from the Earth is relatively apparently move through the same distance in hour angle so close that it also exhibits the simulation of the Earth's in the same period of time, no matter at what declination annual orbital motion previously described. it is situated. The reason is a geometric one. Although Only for a short period of time around the equinoxes hour circles converge toward the poles, a point on any where the ecliptic crosses the celestial equator and the given hour circle is located exactly one hour in time from Sun's declination is zero is its motion in longitude very its counterpart position (i.e., one located at the same nearly equal to its motion in right ascension. Hence, only declination) on an immediately adjacent hour circle. In in these positions is the Sun's westerly displacement in hour viewing, from a suitable position on the surface of the angle (caused by the Earth's diurnal rotation) in the same Earth, any such celestial objects having declinations rang- plane as the Sun's easterly motion in longitude, produced ing from 0' to 90', those objects located at greater decli- by the Earth's annual revolution. At all other times and nations will appear to move more slowly (in linear veloc- positions, the daily angular difference in the Sun's longi- ity) across the celestial sphere than those on or near the tude must be converted to a corresponding daily motion celestial equator, but their angular velocities are the same. in right ascension by the use of transformation equations or, more simply, can be obtained directly from tables of Apparent Diurnal Motion of a Body Pos- right ascension of the Sun. The tabulated daily difference sessing Its Own Motion in Right Ascension in the Sun's apparent motion in right ascension (caused In the case of a relatively nearby celestial object such as by the annual revolution of the Earth) is then subtracted the Moon, which also possesses its own orbital motion' from the oppositely directed component of apparent positional displacements result that are quite different motion in hour angle, measured in the same equatorial from those of the preceding section. Where, as in the plane, and caused by the diurnal rotation of the Earth. example of the actual motion of the Moon and the ap- The resulting difference indicates the necessary additional parent motion of the Sun, the movement of these bodies time required for a given point on the Earth's surface to is. in the same direction as that of the Earth's rotation catch up to a position of alignment with (i.e., a meridian (i.e., a direction eastward, or counterclockwise as viewed transit of) the Sun. from the respective poles of revolution and rotation), a Similarly, except at the two positions each month where special catch-up motion is involved which will be exten- the Moon crosses the Earth's Equator, the changing lunar sively discussed in subsequent chapters. (The only excep- longitudes must be converted to a daily difference in right tions to this statement occur in the cases of a few asteroids ascension, or the necessary equatorial coordinate values and comets that revolve around the Sun in a retrograde can be obtained from tables of lunar right ascension. The direction, as well as those planets of the, solar system that daily difference in right ascension caused by the Moon's are relatively close to the Earth and may, on occasion, motion in orbit is then subtracted from the amount of the exhibit apparent retrograde motions.) Moon's motion in hour angle produced by the Earth's Following upon the meridian transit of a celestial body rotation to determine the necessary catch-up time for a having its own direct motion, as observed from a par- given point on the Earth to regain a meridian transit posi- ticular location on the Earth's surface, the Earth must tion with the Moon. The principle of this catch-up time rotate through more than one complete rotation to bring will be extensively elaborated upon in the next chapter. this body into direct alignment over this same point on Variations in the Tide-Raising Force its surface again. Associated With Lunar Parallax Any nonpolar point on Earth rotates in a plane either in, or parallel to, the celestial equator. In considering the It has been specified previously that, in accordance motion of any other body relative to this plane, the body's with Sir Isaac Newton's Universal Law of Gravitation, apparent daily displacement must be converted to an the gravitational attraction between two celestial bodies equivalent component of motion in the equatorial plane. varies directly as the product of their masses and inversely Unless the body remains in the plane of, or parallel to, as the square of the distance between them (i.e., the closer the celestial equator (i.e., exhibits motion only in a diurnal the two bodies are to each other the greater is the interact- 142 Strategic Role of Perigean Spring Tides, 1635-1976 ing gravitational force; as they draw farther apart, this diameter of the Earth as it would be seen from the force decreases as the second power of the distance seFF- Moon-thus in a position very nearly on the local hori- arating them. However, as noted in the appendix ("The zon. b This is equivalent to the angle (viewed at the center Effect of Gravitational Force"), tide-raising forces vary of gravity of the Moon)'between a line drawn from the inversely as the third power of the distance. center of the Moon to a semidiarnetrical position on the In the motion of the Moon in its orbit around the surface of the Earth and another line drawn from the Earth, the gravitational force of the Earth is at all times center of the Moon to the center of the. Earth (fig. 41 ). directed at right angles to the lunar ' orbit, causing the It is also equal to the apparent angular difference in the Moon to fall constantly toward the Earth. However, an Moon's direction in the sky as it would be seen from these equal and oppositely directed centrifugal force resulting two positions on the Earth. This angle-larger when the from the revolution of the Moon in orbit resists the infall- Moon is closer and smaller when it is farther away-is ing motion and keeps the Moon from plunging toward termed the equatorial geocentric horizontal parallax. the Earth. Although the Moon's own gravitational force Hence, the effect of the changing distances of the Moon in upon the Earth is directed along a line connecting their altering the tides, as well as in producing variations in the centers, two components of this total force exerted upon daily retardation of the tidal day from this cause, is termed the Earth's surface, and known as the horizontal (or the parallactic inequality. tractive) component and the vertical component, respec- Table 8 shows a comparison between the continuously tively, act to produce tides in the Earth's waters. varying values of the geocentric horizontal parallax (7r ) Variations in the Moon's tide-raising force as a result and the distance (p, in Earth-radii) of the Moon from the of its changing distances from the Earth form the basis center of the Earth during an ordinary lunation in the for the phenomenon of parallactic inequality. year 1974 (i.e., a period of one synodic month including Because the Moon revolves in an elliptical orbit around all lunar phases, but containing no close perigee-syzygy the Earth with the Earth located at one focus of the alignment). These data may be contrasted with the data ellipse (fig. 23), once each lunar month the Moon comes of table 15, which show the values of P for various to its closest approach to the Earth at perigee and, approx- alignments of perigee-syzygy, perigee-quadrature, and imately 2 weeks later, reaches its greatest monthly dis- apogee-syzygy during 1973 and 1974. The geocentric dis- tance from the Earth at apogee. tance p is related to the value of the geocentric horizontal As was seen in connection with the earlier discussion of parallax 7r through the relationship p=cosec -,r--Ilsin 7r. Kepler's Second Law of Planetary Motions, the radius TABLE 8.-Comparison of Geocentric Horizontal Parallax and vector-or center-to-center axis joining the Moon and the True Geocentric Distance of the Moon for a Case of Wide@@ Earth-sweeps out equal areas at any portion of the lunar Separated Perigee-Syzygy orbit within equal intervals of time (fig. 24). The lunar distances delineated by the two sides of the elliptical sector Horizontal so formed are continuously varying. In order that the Parallax True distance, Date 1974 Earth-radii radius vector may describe equal areas in the same period of time, the angular velocity of the Moon also must be variable at different portions of the orbit. Apr. 14.0 54 19.3409 63.286 841 14.5 54 15.9150 63.353 427 In that half of the lunar orbit between apogee and 15.0 54 15.1045 63. a69 201 perigee, as the Moon nears its position of closest monthly 15.5 54 16.9068 63.334 137 approach to the Earth, it speeds up in response to the 16.0 54 21.2810 63.249 196 increased gravitational force of the Earth which results 16.5 54 28. 1483 63.116 302 17.o 54 37.3921 62.938 300 from the diminished lunar distance. Conversely, between 17.5 54 48.8577 62.718 903 perigee and apogee, the Moon's angular velocity becomes 18.0 55 02.3534 62.462 612 less. Near the exact position of perigee, the Moon is mov- ing at its maximum angular velocity; at apogee, it is Where a sernidiameter of the Earth perpendicular to any local horizon is considered, a variation in geocentric parallax occurs with moving the slowest. Each of these latter two positions in altitude of the Moon above the horizon. This "parallax in altitude" the lunar orbit is called an apse, and the axis connecting is zero in the zenith and maximum on the horizon. Because the them is correspondingly termed the line of apsides. Earth is neither a true sphere nor an oblate spheroid (possessing an The changing distance of the Moon from the Earth is irregular figure known as a geoid), for astronomical purposes the equatorial semidiameter is chosen and adjustments are made, as measured by the angle subtended by the equatorial semi- necessary, for the Moon's altitude and the latitude of observation. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 143 TABLE 8.-Comparlson of Geocentric Horizontal Parallax and perihelion and closest to the Sun in its annual motion, True Geocentric Distance of the Moon for a Case of Widely the Moon is also nearly so, and is then subject to the maxi- Separated Perigee-Syzygy-Continued mum gravitational influence of the Sun, including those forces producing perturbations in the lunar orbit. This Horizontal relationship is, therefore, often referred to as solar perigee Parallax True distance, Date 1974 Earth-radii (i.e., the Sun reaches a position near solar perigee or I I /I apogee as the Earth reaches its position of perihelion or Apr. 18.5 55 17.6508 62.174 627 aphelion, respectively).(! 19.0 55 34.4869 61.860 729 In order quantitatively to illustrate these combined 19.5 55 52.5668 61.527 153 lunisolar effects, the next-to-the-last column in table 9 20.0 56 11.5681 61. 180 433 shows the relative geocentric distances of the Sun from 20.5 56 31. 1469 60.827.238 the Earth corresponding to an astronomical circumstance 21.0 56 50.9457 60.474 199 21.5 57 10.6026 60. 127 721 chosen to accord with the close perigee-syzygy of 1974 22.0 57 29.7624 59. 793 806 January 8. The values are expressed in terms of the mean 22.5 57 48.0878 59.477 884 distance of the Sun from the Earth (equal to the semi- 23.0 58 05.2716 59. 184 663 23.5 58 21.0468 58.918 010 major axis of the Earth's orbit) considered as unity. 24.0 58 35. 1964 58.680 873 24.5 58 47.5589 58.415 242 The Effect of the Parallax Inequality Upon 25.0 58 58.0316 58.302 170 25.5 59 06.5696 58.161 827 the Comparative Lengths of the Tidal Day 26.0 59 13.1813 58.053 612 26.5 59 17.9206 57.976 289 The average speed of the Moon in its orbit is about 27.0 59 20.8770 57.928 159 12.2',/day. However, for the reasons given in the previous 27.5 59 22.1638 57.907 235 section and as partly evident in tables 10, 20, the lunar 28.0 59 21.9064 57.911 420 28.5 59 20.2310 57.938 670 angular velocity increases to an extreme maximum of 29.0 59 17.2549 57.987 138 approximately 14.2' - 15.4'/day ' at very close perigee- 29.5 59 13.0796 58.055 274 syzygies, diminishes to about 14.1'-14.2'/day at perigee- 30.0 59 07.7856 58.141 895 quadrature, and to 11.8'-12.0'/day at apogee-syzygy or 30.5 59 01.4311 58.246 210 May 1.0 58 54.0530 58.367 799 apogee-quadrature. Sensible differences are introduced 1.5 58 45.6704 58.506 561 both in the daily lunar retardation and in the length of 2.0 58 36.2901 58.662 622 the tidal day as the result of these changing lunar veloc- 2.5 58 25.9142 58.836 220 3.0 58 14.5475 59.027 578 itieg. 3.5 58 02.2061 59.236 760 An interesting comparison can be made between the 4.0 57 48.9244 59.463 541 considerably increased daily lunar retardation produced 4.5 57 34.7619 59.707 284 5.0 57 19.8070 59.966 844 as the result of such accelerated lunar velocities at the 5.5 57 04.1801 60.240 488 time of perigee-syzygy and the lesser retardation produced 6.0 56 48.0338 60.525 864 subject to the previously computed mean orbital velocity 6.5 56 31.5511 60.819 988 7.o 56 14.9420 61.119 275 of the Moon (pt. 11, ch. 2, "The Daily Lunar Retarda- 7.5 55 58.4383 61.419 595 tion"). 8.0 55 42.2877 61.716 360 Using the same calculation procedure as in the earlier 8.5 55 26.7474 62.004 632 9.0 55 12.0776 62.279 239 example, involving the mean synodic motion of the Moon: 9.5 54 58.5348 62.534 916 Maximum daily angular velocity of the Moon in orbit 10.0 54 46.3669 62.766 435 (at the representative close perigee-syzygies of May 10.5 54 35.8074 62.968 744 11.0 54 27.0717 63.137 100 2.5 and'Nov. 10.5, 1950) =15.28'/day. 11.5 54 20.3533 63.267 191 12.0 54 15.8210 63.355 255 However, the fact that the Earth is at perihelion does not neces- 12.5 54 13.6163 63.398 183 sarily imply that the Moon is at its absolute minimum distance from 13.0 54 13.8510 63.393 611 the Sun. In order for this condition to be achieved rigorously, the 13.5 54 16.6051 63.340 003 Moon must also be located at its position of apogee (with respect to 14.0 54 21.9245 63.236 719 the Earth) at this time. See chapter 5. ' At an occurrence of proxigee-syzygy having a mean epoch of It is also important to note that, because the Moon is 1918 March 12.39 G.m.t. (P-S=+29h, 8=1.560@ 7rmax=6l'27.- 08"), the Moon's average daily motion between March 12.0-13.0 bound gravitationally to the Earth, when the Earth is at was 15.3566*. 144 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 9.-The Changing True Distance of the Earth From the Sun (Expressed as a Decimal Portion of the Mean Astronomical Distance of the Earth From the Sun-i.e., the Length of the Semimajor Axis of the@ Earth's Orbit-Gonsidered as Unity) These distances are chosen to accord with the period of time around the close perigee-syzygy alignment of 1974 January 8, and indicate the Earth's least annual distance from the Sun at perihelion on 1974 January 4. The table also shows the corresponding increase izj solar semidiameter at perihelion, together with the effect of the Sun's slow daily change in declination and rapid change in right ascension at the winter solstice (1973 December 22). Date Apparent right ascension Apparent declination True distance of the Earth Semi- from the Sun diameter 1973 h in s As 0 1 if All (a.u.=I) A it Dec. 20 17 51 05.47 23 25 37.0 .983 8173 16 16.99 266.41 42.4 652 21 17 55 31.88 -23 26 19.4 0.983 7521 16 17.06 266.50 - 14.2 -614 22 17 59 58.38 23 26 33.6 .983 69b7 16 17.12 266.54 + 14.1 574 23 18 04 24.92 23 26 19.5 .983 65333 16 17. 17 266.55 42.4 536 24 .18 08 51.47 23 25 37. 1 .983 5797 16 17.23 266.51 70.7 498 25 18 13 17.98 23 24 26.4 .983 5299 16 17.28 266.43 98.9 460 26 18 17 44.43 23 22 47.5 0.983 4839 16 17.32 266.33 +127. 1 -421 27 18 22 10.76 23 20 40.4 .983. 4418 16 17.36 266.19 155.1 381 28 18 26 36.95 23 18 05.3 .983 4037 16 17.40 266.00 183.3 340 29 18 31 02.95 23 15 02.0 .983 3697 16 17.44 265.78 211.2 298 30 18 35 28.73 23 11 30.8 .983 3399 16 17.46 265.53 239.0 254 31 18 39 54.26 -23 07 31.8 0.983 3145 16 17.49 265.24 +266.8 -208 1974 Jan. 1 18 44 19.50 23 03 05.0 .983 2937 16 17.51 264.92 294.4 158 2 18 48 44.42 22 58 10.6 .983 2779 16 17.53 264.57 321.7 107 3 18 53 08.99 22 52 48.9 .983 2672 16 17.54 264.18 349.1 - 52 4 18 37 33.17 22 46 59.8 .983 2620 16 17.54 263.78 376.1 + 6 5 19 01 56.95 -22 40 43.7 0.983 2626 16 17.54 263.35 +403. 1 + 68 6 19 06 20.30 22 34 00.6 .983 2694 16 17.53 262.89 429.8 130 7 19 10 43.19 22 26 50.8 .983 2824 16 17.52 262.40 456.2 197 8 19 15 03.59 22 19 14.6 .983 3021 16 17.50 261.89 482.6 263 9 19 19 27.48 22 11 12.0 .983 3284 16 17.48 261.37 508.6 330 10 19 23 48.85 -22 02 43.4 0.983 3614 16 17.44 260.82 +334.5 +396 11 19 28 09.67 21 53 48.9 .983 4010 16 17.40 260.25 560.1 460 12 19 32 29.92 21 44 28.8 .983 4470 16 17.36 259.66 585.5 519 13 19 36 49.58 21 34 43.3 .983 4989 16 17.31 259.06 610.7 577 Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 145 TABLE 9.-The Changing True Distance of theEarth From the Sun etc.-Continued, Date Apparent right ascension Apparent declination True distance of the Earth Semi- from the Sun diameter 1974 h m s As 0 1 It Aft (a.u.=]) A t f/ Jan. 14 19 41 08.64 21 24 32.6 .983 5566 16 17.25 258.45 635.5 631 15 19 45 27.09 -21 13 57. 1 0.983 6197 16 17.19 257.80 +660.0 +682 16 19 49 44.89 21 02 57.1 .983 6879 16 17.12 257.15 684.3 729 17 19 54 02.04 20 51 32.8 .983 7608 16 17.05 256.47 708.2 775 18 19 58 18.51 20 39 44.6 .983 8383 16 16.97 255.77 731.8 817 19 20 02 34.28 20 27 32.8 .983 9200 16 16.89 255.07 755.0 858 20 20 06 49.35 -20 14 57.8 0.983 0058 16 16.80 Mean solar day==24 mean solar hours. Moon will have moved eastward across the sky during the Hence, the mean hourly motion of the Moon at its lunar day may range from 11.8'-15.4', depending upon maximum orbital velocity is the Moon's position in its orbit. 15.28' per day/24 hours per day=0.6367' per hour. Although the tides, in general, quite closely follow the Since the Earth rotates through 15' in one hour, this motions of the Moon, it will be seen in chapter 6 (cf., represents a corresponding time delay factor of "The Phase Age and Parallax Age") that, under certain 0.6367' perhour/150 perhour astronomical and hydrographic situations, their maximum =0.0424X60 minutes/hour X24 hours/day amplitudes may occur either before or after lunar transits. =61.1232 minutes=61m 7.39". While the time of lunar transit is not, therefore, an ac- Since the Moon revolves through 15.28' in its own orbit curate indicator of the time of high water, any change while the Earth rotates through 360' on its axis, the which affects the apparent transit time of the Moon will. Moon's right ascension increases by this same amount. in one way or another, affect the times of the tides. 360'+15.28'=375.28- When the Moon is traveling faster in its orbit at times 61.1232X375.28'/360'=63.7175'=63m 43.0s. of perigee-syzygy, the value of the daily lunar retardation is greater, and, the interval required for the Earth's rota- Thus, subject to these maximized conditions in the Moon's tion (in the same direction) to catch up with the position orbital velocity at the time of a very close perigee-syzygy, of the Moon is longer. The interval between two successive the actual daily lunar retardation has increased from its higher high waters (the second definition of the tidal day) mean value of 50- 24.9-9 to 63- 43.0', a gain of more is increased in proportion. Conversely, when the Moon's than 13 minutes. orbital velocity is reduced, as it approaches apogee, the The increase in the value of the daily lunar retardation daily lunar retardation is decreased and the tidal day is and corresponding extension of the tidal day 'also result shortened. in an increase in the time required for a point on the Repeating the previous computations, but substituting rotating Earth to catch up with the additional advance- the data for a near-minimum velocity of the Moon in ment of the Moon in its orbit made possible in this length- orbit ( 11.82' per day) at a situation of apogee-quadra- ened interval and at the Moon's greater orbital velocity. ture on April 13, 1974 gives: As before, the revolution of the Moon around the Earth 11.82' per day/24 hours per day==0.4925' per hour in the same direction as the Earth rotates on its axis means 0.4925' per hour/ 15' per hour that, for the Moon to undergo two successive transits over =0.0328X60 minutes/hourX24 hours/day any one location on the Earth's surface (in the first defini- =47.2320 minutes=:47m 13.9' tion of the lunar day) the rotating Earth must catch up 360'+ 1 1.82'=371.82' through the angle the Moon has moved in the sky during 47.232OmX371.82-/360-=48.7828m=48m 47.0'. the time the Earth has rotated once through 360' with respect to the Sun (i.e., the mean solar day). As seen The effect of parallactic inequality thus results in a earlier, this extra angular distance through which the difference of more than 15 minutes, on the average, be- 202-609 0 - 78 - 12 146 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 10.-Approximate Orbital Angular Velocity of the Moon, Expressed as a Difference in Celestial Longitude, Showing the Variation at Times of Close Perigee-Syzygy (Proxigee-Syzygy), Apogee-Sy.@vgy (Exogee-Syzygy), and Perigee-Quadrature Apparent Average Apparent Average Alignment Date lunar daily Alignment Date lunar daily longitude motion in longitude motion in longitude longitude 1974 0 0 1974 o 0 Jan. 1.0 1.2803 Jan. 27.0 345.7534 12.8622 12.4004 2.0 14.1425 28.0 358.1538 13.2472 12.6104 3.0 27.3897 29.0 10.7642 13.6763 12.8613 4.0 41.0660 30.0 23.6255 14.1238 13.1566 5.0 55.1898 31.0 36.7821 14.5529 6.0 69.7427 Apr. 24.0 53.5013 14.9174 13.9751 7.0 84.6601 15.1697 25.0 67.4764 14.0916 26.0 81.5680 Proxigee-Syzygy ....................... 8.0 99.8298 14.1590 15.2705 27.0 95.7270 9.0 115.1003 14.1861 15.2006 28.0 109.9131 10.0 130.3009 14.1813 14.9678 29.0 124.0944 11.0 145.2687 Perigee-Quadrature .................................... 14. 1491 14.6046 (Ist quarter) 12.0 159.8733 30.0 138.2435 14.1593 14.0889 13.0 174.0326 May 1.0 152.3324 13.9968 13.6833 2.0 166.3292 - 14.0 187.7159 13.8668 13.2216 3.0 180.1960 15.0 200.9375 13.6949 12.8066 4.0 193.8909 16.0 M.7441 12.4582 Nov. 2.0 63.1558 17.0 226.2023 13.6210 12.1847 3.0 76.7768 18.0 238.3870 13.7851 11.9868 4.0 90.5619 19.0 250.3738 13.9238 11.8588 5.0 104.4857 20.0 262.2326 14.0395 11.7929 6.0 118.5252, 21.0 274.0255 11.7790 7.0 132.6568 14.1316 Perigee-Quadrature .................................... 14.1961 22.0 285.8045 11.8078 (.3d quarter) Exogee-Syzygy ......................... 23.0 297.6123 8.0 146.8529 14.2249 11.8711 9.0 161.0778 24.0 309.4834 14.2076 11-9631 10.0 175.2854 25.0 321.4465 14.1339 12.0811 11.0 189.4193 26.0 333.5276 13.9977 12.2258 12.0 203.4170 Factors A�ecting the Magnitude and Duration of the Tide-Raising Forces 147 tween the respective values of the day tidal retardation of coordinates, it is very obvious that, when the Moon as they occur at perigee-syzygy and at either apogee-syzygy is in the zenith, it is a distance equal to the equatorial or apogee-quadrature. The smaller value of the retarda- radius of the Earth (6,378.388 km or 3,963.530 mi) tion, occurring at apogee-syzygy, averages about 49 min- nearer to the surface of the Earth than when it is on the utes per day. horizon. This amounts to a gravitationally significant This difference of approximately 15 minutes, permit- portion (0.017) of the average distance of the Moon from ting a longer application of the combined gravitational the surface of the Earth (378,000 km or 234,900 mi). forces of the Sun and Moon, and at a time when the Since the tide-raising force increases rapidly as the third latter is exerted from a relatively close distance-together power of any diminished distance of the Moon from the with certain other factors to be developed in ensuing Earth, this quantity is of measurable. importance in deal- chapters-add measurably to the greater tidal,flooding ing with tidal phenomena. The same geometric principle potential at times of perigee-syzygy. is true for the Sun-Earth configuration, but the change in distance here represents but an insignificant portion of Ancillary Effects the mean distance of the Earth.from the Sun (149,500,- 000 km, or 92,900,000 mi). Lunar Augmentation The effect of the lunar augmentation impacts upon In figure 25A, which represents the position of the those aspects of tidal prediction which relate to the instan- Moon on the celestial sphere as seen in the horizon system taneous distance of the Moon from the Earth and it can, LUNAR AUGMENTATION EFFECT LUNAR DECLINATIONAL EFFECT ON MOTION IN RIGHT ASCENSION AND THE LENGTH OF THE TIDAL DAY A. B. Z It u IW A.@ P I I I Af P 0 S L HOR. E 4an 1" P M 637 KM T 0 ,JAVERAGE 3 958M RADIUS 5 4a 0 D C. lly B CL 2,2 Z' /i IN ABOVE, C I: Adp=aae Cos PLANE OF PAPER IS THAT OF &1,60A SEE TEXT THE CELESTIAL MERIDIAN C CL2, 60 FrGuREs 25 A, B 148 Strategic Role of Perigean Spring Tides, 1635-1976 therefore, be considered as a correction to the lunar hori- Therefore: zontal parallax. The computation necessaxy to evaluate S=0.004996058+0.000089373+0.279286111 the quantitative influence of this phenomenon as it affects =0.284371542'=17' 3.7376" the tides follows. = 1023.7376" To the second order, neglecting the flatten 'ing of the 1)023.6577" Earth ewhile assuming that the Earth's semidiameter 7r (topocentric)=@ 0.272453 r= 1, and that the Moon is transiting the local meridian =3,757.1900"=62' 37.1900". (h=O'), the amount of the augmentation in lunar semi- Thus, under these assumed conditions, with the Moon diameter (S-S.) is given approximately by: at one of its closest approaches to the Earth, at its greatest S-S. = S. sin H. cos z'+S. sin' H. (I - V2 sin' z') possible declination, and directly in the zenith of the where (all values are for the Moon) place, the augmentation of the topocentric parallax over the geocentric parallax is V 7.1891". Although this in- S --the observed (topocentric) angular semidiameter crease is relatively small, the concept of lunar augmenta- S. --the geocentric angular semidiameter don is included here in order to consider all possible fac- H. --the equatorial horizontal parallax tors which might have a contributing influence in the Z' --the topocentric zenith distance (from the geodetic production of unusually high tides at the times of perigee- zenith). syzygy. From The American Ephemeris and Nautical Almanac, Since the influence of a closer lunar proximity resulting the value of S is given by: from the phenomenon of lunar augmentation is most strongly exerted when the Moon is in the zenith, S=0.0799"+0.272453 the possible combination of this effect with the augmented or the topocentric parallax is gravitational forces responsible for perigean spring tides would occur: (1) at the Earth's Equator when the Moon S-0.0799" is on the celestial equator; (2) along the Tropic of Cancer 0.272453 and the Tropic of Capricorn near the times of the vernal In order to determine the maximum possible effect of equinox and the autumnal equinox, respectively; (3) at the lunar augmentation arising from a favorable com- geographic latitudes extending farther north and south, bination of circumstances, the extremely close perigee- as the Sun (and with it the Moon) reach higher monthly syzygy situation of 1974 January 8.5 has been selected, declinations, culminating at the times of the summer and having the following ephemeris values: winter solstices, respectively, in the Northern and South- H.=61' 30.0009"=1.025000250' ern Hemispheres; and (4) during those particular por- S.=16'45.43" =0.279286111' tions of the lunar nodical cycle (fig. 36) in which a _LY increase in lunar declination occurs; the maximum aug- Assuming that these large geocentric values had oc- mentation effect on the tides would be felt at these same curred simultaneously at a time in the lunar nodical cycle angular distances (--#5') farther north and south in lati- at which the Moon had reached its maximum declination tude on the Earth's surface. of _L28.5', and selecting also the geographic latitude 0=28.5' north or south, respectively, where the Moon Regional and Latitudinal Effects on the Tides would be seen in the zenith: Resulting From Changing Lunar and Z'=O'; cos z'=-I; sin z=:O Solar Declinations Since: Because of the numerically commensurable relations sin Ho=0.017888675 between the times of occurrence of the semimonthly ex- sin' H.=0.000320005 cursions of the Moon from zero to maximum declination and the semiannual passage of the Sun through the same The exact equation for determining the topocentric parallax 7r from the equatorial horizontal parallax Ho, at any latitude 0, taking extremes, both temporal and regional variations in tidal into account the flattening / of the Earth is: actron result from the combination of the lunar and solar 7r=Ho (1-t sin' 0+5/8 r sin' 20+ declinational motions. Factors Affecting the Magnitude and Duration of the Tide-Raising Forces 149 Where. a([= the right ascension of the Moon Finally, at full moon, the right ascension of the 3([= the declination of the Moon Moon is always 180' or 12h from the Sun. Therefore, a= the mean longitude of the ascending to achieve a maximum lunar declination from the node of the lunar orbit third and fourth terms, the position of a must be the relationship between lunar declination and lunar right 180' when a(c=270', and always 270' or an odd- ascension is given by the expression integer multiple thereof from the Moon itself. If the sin 6(r = 0.406 sin a(c + 0.008 sin 3 ac: Moon is 270" away from its ascending node, it .is at * 0. 090 sin (a([ - a) its greatest negative value of #. * 0.006 sin (3aq: - a). At either new moon or full moon, and with a right As far as the first and largest term on the right-hand ascension which is equal to, or an odd multiple of 90', the side of this equation is concerned, it implies that the Moon will reach its normally largest declination for the largest lunar declinations occur when the Moon has year. a right ascension equal to, or an odd multiple of 900 h (i.e., if converted to hours of right ascension, at a=6 , 1. Solstitial Tides 18h). Because the second term on the right contains An increase in the combined lunisolar diurnal forces by an odd-number multiplier, 3, the same conditions about 33 percent near the summer and winter solstices contributing to the maximization of ac apply to this results in tides of greater diurnal inequality, amplitude, term as have been established for the first term. and range known as solstitial tides. Greater tidal ampli- The two previously specified values of right ascension, tudes at the solstices also are added to by an increase in the 6' and 18", correspond to the positions where the Sun, in Sun's component of motion in right ascension, an exten- its apparent annual motion in. the sky, passes through the sion of the necessary catch-up time between the rotating summer and winter solstices (its positions of greatest Earth and the Sun, and a corresponding lengthening of northern and greatest southern declination, respectively). the period of solar force application. At the present astronomical epoch, the Sun reaches these The Sun, in its apparent annual motion on the celestial positions within a day or two of the dates June 21 and sphere, moves from a declination of approximately December 22. From the first two terms in the above equa- -23.5' at the winter solstice to a declination near +23.5' tion, the largest declinations of the Moon also should at the summer solstice. The Moon's orbit, on the average, occur around these two dates. However, the effect of the attains a maximum inclination to the ecliptic of only 5'9'. Moon's celestial latitude 8 (perpendicular angular dis- The Moon must, therefore, in general quite closely tance north or south of the ecliptic) has not yet been follow the path of the Sun (although not necessarily the considered. timing of the Sun itself) in its motions from maximum On these two dates, the new moon-if at conjunction negative to maximum positive declinations and the re- in right ascension-will have the same c, as the Sun. Since verse. Accordingly, each half-month, the Moon's position the solar declination at the times of either of the solstices will change through declination values whose maximum has its maximum value, the, lunar declination (always range is from --L28.5' and whose minimum range is within 5'9' of the Sun) also will be at a maximum if the z!:: 18.5'. The: effect of the nodical cycle in increasing (or Moon's celestial latitude is simultaneously at its greatest decreasing) the maximum lunar declination attained in possible value. any one year is described in part 11, chapter 3. All terms in the previous equations are sine func- 2. Tropic Tides tions. Hence, the greatest value of lunar declination resulting from the last two terms will occur when the In tropic regions, around latitudes 18.5'-28.5', north differences between (aq:-a) and (3ac-a) are or south, the maximum meridian altitudes of the Moon also 90' or odd multiples thereof. But to give a value accompanying such maximum lunar declinations can of 90' or an odd multiple of 900 in the third term of reach 90' or nearly so, with the zenith distance of the the equation, a itself must always be separated by Moon becoming 0' or a very small value. It will be shown 90' or an odd multiple of 90' from the Moon. If the (pt. 11, ch. 5) that the tide-raising force of the Moon in- Moon is 90' distant from its ascending node, it is also creases as the Moon reaches a position in the zenith. geometrically at its greatest positive value of #, which Hence, tides of greater amplitude and range, known as conforms to the previous requirement. As before, the tropic tides, are produced in these low-latitude regions, same relationship applies to the odd multiple of a([ and are felt as diurnal tides (table 19) even in high lati- occurring in the fourth term of the equation. tude regions of the Pacific Ocean. t50 Strategic Role of Perigean Spring Tides, 1635-19M 3. Equinoctial Tides 1. Solar Declinational Effects The Moon crosses the ecliptic twice each month, once When the Sun is on the celestial equator, the lengths of from north to south, and once from south to north, and the day and night are very nearly equal at the Equator is never more than 5'20' from the ecliptic (its maximum' (although the length of the day increases slightly with possible inclination, due to perturbations). geographic latitude). With the Sun at the summer solstice, The Sun, moving in the ecliptic, crosses the celestial the lengths of day and night remain approximately the equator twice each year at the vernal and autumnal equi- same at the Equator, but the length of the day is as much noxes, about March 2t and September 23, respectively. as 6 hours longer at latitude +60'. The same situation When the Moon comes close to the true equinox positions, applies in the Southern Hemisphere at the winter solstice. it must also lie very nearly in the plane of the celestial As the Sun moves away from the celestial equator, its equator, at a time when the Sun is crossing this same maximum (meridian) altitude above the horizon also great circle. becomes greater. In consequence, since the Sun must move Thus, at times close to the equinoxes, the Sun and over a longer daylight path from horizon to horizon- Moon are in almost the same declination plane (i.e., although its apparent daily motion in right ascension is approximately 0') as the Earth's Equator. The Sun's larger-the duration of daylight is extended. semidiurnal component of gravitational force will then add an extra 27 percent to the lunar force to provide a 2. Effects Due to Changing Parallax and the greater amplification of the Earth's tides. The tides result- Obliquity of the Ecliptic ing are known as equinoctial tides. Because of the effects of the Earth's orbital eccentricity The effect of adding a close perigee-syzygy alignment and inclination on its daily motion, the apparent solar to this already gravitationally reinforced tidal situation day may be approximately 15 minutes longer or shorter will be discussed in connection with high equinoctial than the mean solar day (this constantly changing differ- spring tides in chapter 5, in describing those astronomical ence is designated as the "equation of time'). The simi- factors which lead to the maximization of perigean spring larity between this "equation of time" (caused by the tides. difference between the Sun's actual and mean motions) and a second tide-influential pattern existing between the 4. Latitudinal Effects of the Diurnal Inequality motions of the true and mean moons will be described in The more common Isituation involving, for example, a part II, chapter 3. differing height between higher h *igh water and lower 3. Lunar Declinational Effects high water-and referred to as the diurnal inequality- The same influences specified in connection with the is described in the appendix. Briefly, this phenomenon is Sun in (1) above hold approximately true for the Moon's created by a high declination of the Moon. The diurnal position with respect to the celestial equator, although not inequality also renders unequal the period of time between to such a close degree, since the effects of large parallax higher high water (HHW) and lower low water (LLW) and other factors are of greater consequence in altering compared with that between lower high water (LHW) the apparent orbital motion of the Moon. As the declina- and higher low water (HLW), and hence affects the tion of the Moon increases, the period between moonrise duration of each. The effects of diurnal inequality usually and moonset remains approximately the same at the increase with latitude and, to a greater degree, in the Equator, but this interval increases very significantly at hemisphere to which the Moon's declinational motion I \ carries it alternately during each half-month. However, higher latitudes. The lunar (and tidal) days are length- ened in proportion. the absence of any diurnal inequality when the Moon is over the Equator is general for all latitudes. 4. Effect of the Moon's Orbital Inclination to the Horizon Subordinate Factors Influencing Near the time of the autumnal equinox, with the full the Length of the Tidal Day moon at the vernal equinox opposite the Sun, the Moon's Certain definite relationships exist between the chang- orbit is inclined at a very small angle with respect to the ing lengths of the apparent solar day and those of the horizon at middle and high latitudes in the Northern lunar (and tidal) days which are a direct function of the Hemisphere (particularly, if the Moon's ascending node positional changes of the Sun and Moon. also coincides with the vernal equinox). This circum- Factors A�ecting the Magnitude and Duration of the Tide-Raising Forces 151 stance results in the fact that the full moon rises above any other hydrographic, oceanographic, or meteorological the horizon very slowly and with only a slight daily re- influences. tardation for several successive nights. By rising at essen- The inclination of the North Pole toward the Moon tially the same time and hanging low in the sky for an not only puts the Moon in the zenith at latitudes farther extended period of time on consecutive evenings, it pro- north, but renders the line of the Moon's gravitational vides extra illumination for fall harvesting. Accordingly, force action shorter and more nearly perpendicular for this phenomenon has been given the name "harvest Northern Hemisphere positions on the side of the Earth moon," and the full moon following a month later under turned toward the Moon. The new moon, in line with the nearly the same circumstances has been designated Sun, will cross any local meridian about noon, local ap- "hunter's moon." parent time, and, located centrally in the sky, will exercise From a tidal point of view, theslowly moving Moon its maximum influence in the Northern Hemisphere only possessing but a small daily lunar retardation implies an during these midday hours. accompanying fast catch-up time between a point on the During the full phase of the Moon, just the opposite of rotating Earth and the orbiting Moon. This results, in the above situation is true, with nighttime tides higher, turn, in a relatively short tidal day, and a reduced period and daytime tides lower, in the Northern Hemisphere. of application of any amplified tidal forces. Since the Earth's axis is inclined away from the Sun (and toward the full moon on the opposite side of the Earth 5. Supplementary Influences from the Sun) in winter, the same tide-raising force con- In succeeding chapters, the extension of the lunar and siderations indicated in the preceding paragraph hold but tidal days will be seen to be of importance in providing are now related to the full phase of the Moon. The full extra periods of time within which augmented tide-raising moon transits the local meridian about midnight, appar- forces such as those associated with perigee-syzygy can ent time, and its maximum gravitational effects in the act. This influence applies in particular to those cases Nor-them Hemisphere are felt only during these late night- in which the Moon is near its maximum possible declina- time hours. tions. As will be noted in this same connection, the tidal In spring and autumn, with the Earth's rotational axis flooding potential may, therefor@, also be increased by the inclined at right angles to the plane containing Earth and diurnal inequality. Moon, the tides produced at the two positions of lunar The influence of a combined, two-dimensional align- quadrature should be equally high as far as seasonal causes ment of the gravitational forces of the Moon and Sun in are concerned, but should occur in unequal periods of both right ascension and declination as the Moon crosses time. If the Moon is above the horizon at first-quarter one of its two nodes coincidentally with the attainment, phase, the floodtides should be smaller and of shorter of new moon or full moon, producing a solar or lunar duration than the ebbtides; if the Moon is below the eclipse, will be treated in chapter 5. horizon at this time, floodtides should be larger and last longer than ebbtides. At last-quarter phase, just the op- Seasonal Factors Influencing posite.is true. In spring, also, the conditions at the two the Production of Heightened Tides quadratures are the exact reverse of those encountered in the fall. Again, all of the above influences are astronomi- As a further extension of the previously outlined prin- cal, and are 'not inclusive of local effects produced by ciples relating the po .sitions and motions of the Moon to other causes. the amplitudes and durations of the tides, certain seasonal effects also are noteworthy. Effects of the Phase Inequality In summer, the rotational axis of the Earth is tilted and Diurnal Inequality toward the Sun. It is, therefore, also inclined toward the position of new moon, which must lie along the line of The origin of the phenomenon of phase inequality lies syzygies and between the Earth and the Sun. This fact in the synodic revolution of the Moon, which is responsible implies that, close to the time of the summer solstice, in the for the regular succession of lunar phases as seen from the Northern Hemisphere, tides experienced during the day Earth. This phenomenon is characterized by a variation should be higher, and those observed during the night of tidal forces associated with different geometric con- should be lower because of the rel 'ative gravitational force figurations and the resulting vector additions or subtrac- components involved. These effects are independent of tions of the gravitational forces of the Sun and Moon. 152 Strategic Role of Perigean Spring Tides, 1635-1976 Such tidal force variations are caused by the alternating The foregoing sections of part 11, chapters I and 2, reinforcement of tidal forces created by the alignment of together with the appendix, provide a reasonably com- Sun, Earth, and Moon at the position of syzygy, and the prehensive summary of the principal astronomical influ- opposition of these same forces at the times of lunar quad- ences affecting the tides. All of these effects must be con- rature. A wide range of relative force values exists for all sidered as acting upon, causing potential modifications positions in between. The basic concepts of lunar phase in, or adding their contributions to, the particular factors production are fully explained in the appendix (fig. 3) causing perigean spring tides. It must further be empha- and will not be repeated further here. sized, strongly and repeatedly throughout this monograph, The diurnal inequality is caused by the position of the that the forces producing the tides are of harmonic nature Moon (and/or Sun) over a latitude north or south of the and that none of these effects is totally independent of the Equator, and results in the two successive high waters other or may be so regarded. ,and/or low waters being of unequal heights--or in a Although the isolation of the astronomical elements single low water. This phenomenon is also discussed in the associated with the production of perigean spring tides of appendix. various degrees of intensity and the satisfactory confirma- Certain perturbations of the lunar orbit resulting from tion of the special case of proxigean spring tides are ca- the gravitational attraction of the Sun will be described pable of direct analytic and empirical treatment, the estab- in the next chapter. The special conditions resulting from lishment of the relative tidal flooding potential of such the combination of perigee with syzygy which constitute tides, when taken in conjunction with various meteoro- the main topic of this work will be reserved for substantive logical factors, is not a simple, straightforward task. The discussion in part 11, chapter 4. following chapters represent an effort in this direction. Chapter 3. The Action of Various Perturbing Functions in Estab- lishing, Altering, and Controlling the Amplitudes of Perigean Spring Tides In chapters 1-2 of part II, certain standard astro- long ostensibly to the classic problem of three bodies in nomical principles and nomenclatural definitions have celestial mechanics. However, the comparative proximity been introduced pro forma. These are valid without of the Moon to the Earth, the unsymmetrical geodetic modification for all conditions in which the gravitational configuration and mass distribution of the terrestrial body, forces present are assumed to act in accordance with and the fact that the orbit of the Moon is in no sense a Newton's law of gravitation, upon unit or point masses, re-entrant one and permits only the establishment of an and in a closed two-body dynamic system, without the instantaneous osculating orbit, result in many nonperiodic intervention of any disturbing functions exterior to the variables which cannot be described by standard three- system. Such would be the case if the Moon were re- body methods. In lunar theory, the analytic solution of volving in an unperturbed Keplerian ellipse. the Moon's orbit involves 36 differential equations, which However, the presence of the Sun in the system com- cannot be treated rigorously. plicates matters to a considerable extent by exerting its Nonetheless, an empirical knowledge of the orbital mo- own very major force influences. This action serves con- tion of the Moon is well established -by observations ex- tinuously to disturb the motions of both the Earth and the tending over many centuries, and most of the irregulax Moon in their respective orbits. The result is to produce motions of this body resulting from perturbative influences so-called perturbations in the orbits of both bodies. In are well known. Only those perturbations which relate to, the case of the Moon, the existence of these perturba- and have a perceptible effect on, the Earth's ocean tides tions-through their accompanying changes in (1) the will be discussed in this work. The astronomical origins of lunar longitudes, (2) the instantaneous distances (or these perturbations as they affect the instantaneous longi- parallaxes) of the Moon, (3) various of the lunar orbital tude and the differential motion of the Moon in this co- elements, and (4) the times. of occurrence of the phase ordinate, as well as the eccentricity, major axis, and in- aspects or configurations, in turn exercises an important stantaneous shape of the Moon's orbit, the geocentric influence on the tides. horizontal parallax, the variable motion of perigee, and the length of the lunar day all will be described in the The Effects of Perturbations Upon present chapter. The corresponding influences of these Lunar Distances and Orbital astronomical variations upon tidal parameters will be re- Motions served for chapters 5-6. The Lunar Evection Lunar perturbations consist of dynamic disturbances in the instantaneous positions and orbital motions of the The first and foremost, largest, and earliest discovered Moon, resulting principally from the individual gravita- influence among the lunax perturbations is the lunar evec- tional attractions of the Sun and Earth, as well as their tion. This is a perturbation producing a continuous altera- mutual interactions. The dynamic conditions present be- tion in the shape of the Moon's orbit, .and is a function of 153 154 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR EVECTION EFFECT TO SUN PERIGEE PERIGEE-SYZYGY' A. NM/ ORBITAL VELOCITY INCREASES BETWEEN FM AND NM LINE OF APSIDES NEAR- COINCIDENT WITH LINE OF SYZYGIES LO FO ORBITAL VELOCITY DECREASES BETWEEN NM AND FM Ul uJ ECCENTRICITY OF ORBIT cn >- 0. N INCREASES; PERIGEE < >- DISTANCE BECOMES LESS; u- (n LUNAR PARALLAX IS 0 U. AUGMENTED LU 0 ORBITAL ECCENTRICITY z uj IS EXAGGERATED FOR CLARITY FM APOGEE TO SUN PERIGEE-QUADRATURE B. ORBITAL ECCENTRICITY NM IS EXAGGERATED FOR CLARITY APOGEE LINE OF APS DES NEAR-COINC@DENT LINE OF APSIDES E LO WITH LINE OF S QUADRATURES FQ LINE OF QUADRATURE PERIGEE ECCENTRICITY OF ORBIT ORBITAL VELOCITY AT DECREASES; PERIGEE PERIGEE-QUADRATURE DISTANCE BECOMES GREATER; IS MUCH LESS, THAN LUNAR PARALLAX IS REDUCED F AT PERIGEE-SYZYGY. I E KLINEOF A@PSIDES RE NE OF @QUADRM S LI @T E @R ICED FM Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 155 the relative positions of the line of syzygies with respect to However, exactly at the configuration of perigee-syzygy, the line of apsides in the lunar orbit (see figs. 26A, B). the acceleration in lunar velocity due to this perturbation The effects of this disturbance upon the Moon's orbital is zero and, close to the position of perigee-syzygy, it is motion are twofold: When the line of apsides and line nearly so. As a result of the previously mentioned increase of syzygies coincide, the Moon moves faster in celestial in the eccentricity of the lunar orbit at perigee-syzygy, the longitude between the phases of full moon and new moon main contribution of the lunar evection to the phenome- and slower between new moon and full moon. In addition, non of perigean spring tides therefore comes about through when these same two axes come together, the eccentricity an accompanying marked increase in the geocentric hori- of the lunar orbit is increased, producing a redistribution zontal parallax of the Moon. This reduction in the lunar of the Moon's velocity in orbit. distance at perigee-syzygy, with its corresponding increase in gravitational tide-raising forces, will be treated exten- sively in a later section of this chapter. The influence of FIGUREs 26A, B.-Lunar evection consists of a periodic this perturbative function will also be discussed later in fluctuation in the eccentricity of the lunar orbit as a func- connection with the differences between mean and true tion of the phase angle and true anomaly of the Moon (its instantaneous angular differences in longitude from lunar parallax and mean and true lunar longitude. the positions of conjunction and perigee, respectively). Finally, if a coincidence occurs between the line of This phenomenon results in changes in the eccentricity of apsides and the lineof quadratures, the eccentricity of the the lunar orbit, produced by the combined interaction of lunar orbit decreases, and the Moon moves slower at this the tangential and normal components of the Sun's gravitational force. time. But this circumstance bears no direct relationship To illustrate the effects of evection. throughout a com- to the occurrence of perigee-syzygy responsible for peri- plete lunar revolution, a condition of perigee-syzygy gean spring tides. alignment will initially be assumed. At perigee-syzygy, the tangential component of the solar gravitational force, here applied at right angles to the lunar orbit, is ineffec- The Lunar Variation tive in altering the eccentricity of the orbit; however, the normal component of the Sun's force is negatively effec- The second important perturbative influence is the tive and tends to increase the orbital eccentricity. As the Moon moves from the position of perigee-syzygy, lunar variation. Lunar variation is a function completely the normal component decreases, while the now-negative dependent upon the particular longitudinal orientation of tangential component acts to decrease the eccentricity. the Sun with respect to the orbit of the Moon. This phe- The -superposition of these two forces results in an nomenon is responsible for a continuously changing shape eventual balance and a condition of zero change in eccentricity somewhere between perigee-syzygy and a of the lunar orbit. The change in orbital figure takes place point approximately 54'44' along the orbit. Thereafter, through a lengthening of the orbit along an axis at right the eccentricity decreases until the Moon reaches a posi- angles to a force vector extended from the Sun toward tion following apogee-syzygy. the lunar orbit. As the Moon passes through the vicinity of apogee- syzygy (a position never as well defined as perigee-syzygy), In its causal relationship, the Moon's variational effect the same process occurs in reverse as the eccentricity- is entirely independent of the angle between the line of after a brief interval similar to the preceding during which a balance is reached between the tangential and normal apsides and the line of syzygies. However, as the result components of force-now steadily increases while the of the variation, the respective sections of the Moon's orbit Moon approaches perigee-syzygy. on the same and opposite sides of the Earth from the Sun The net result is that, following upon any given align- become less sharply curved. The corresponding lunar dis- ment of perigee-syzygy, the effect of evection decreases the eccentricity of the lunar orbit during slightly more than tances from the Earth are reduced in these two sections by half of a synodical revolution. The eccentricity of the the Sun's perturbational influence. orbit then increases during the succeeding half -revolution, plus a little more. Significantly for the present discussion, if the Moon The associated variable gravitational force factors are happens to be simultaneously along this force-axis con- of greatest consequence in their contribution to tide- necting Sun and Earth (i.e., the line of syzygies), its dis- raising action in the period just prior to perigee-syzygy, when the influence of evection has collectively resulted in: tance from the Earth is slightly reduced, and its horizontal a maximum increment in orbital eccentricity; the greatest parallax is increased. This effect supplements the variable reduction in perigee distance of the Moon; a significant distances imposed by the revolution of the Moon in an augmentation in the lunar parallax; and a corresponding increase in orbital velocity to add to the Keplerian in- elliptical orbit (the elliptical variation) and resulting from crease in velocity at times of perigee (see the necessary the opposite orientations of perigee and apogee. However, velocity catch-up effects discussed in chapter 6). if the line of apsides and line of syzygies coincide, the 156 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR VARIATION EFFECT (ON VELOCITY) A. DECREASED ORBITAL VELOCITY F T Sx INCREASED FM NM INCREASED S - - - - - - - - - - - - - - - - - - - - - - - - S ORBITAL VELOCITY E ORBITAL VELOCITY G T Sx :M LQ DECREASED ORBITAL VELOCITY DISTANCES ARE NOT TO SCALE FIGURF_ 27A.-The phenomenon of lunar variation results from the considerable range of distances of the Earth and Moon from the Sun (and the corresponding difference between the Sun's gravitational force upon these two bodies) at various lunar phases. At the quadratures, the solar gravitational force acting upon the Moon and the Earth is the same; at the syzygies, the greatest difference in solar gravitational force upon. -these two bodies exists. On the side of the Earth nearest the Sun, the Sun attracts the Moon away from the Earth with constantly increasing force as the distance of the Moon from the Sun diminishes between LQ and NM. This force is exerted with its predominant compo- nent S. contributing a significant accelerative action parellel to one of the two rectangular components of velocity subject to which the Moon is moving. (The gravitational or centripetal component is directed along MG; the tangential or centrifugal component is exerted along MT.) A velocity accelerating influence is applied cumulatively (the angle of effective force action, < MSE, decreasing while the magnitude of the force itself increases) between LQ and NM. Since, between NM and FQ, the solar force is exerted with its principal component opposite to the corresponding veloc- ity component of the Moon's tangential motion, a negative acceleration (deceleration) results. Thus the Moon's velocity is accelerated between LQ and NM and retarded between NM and FQ. I On the opposite side of the Earth from the Sun, between FQ and LQ, the Moon is more distant from the Sun than the Earth is, and the latter body is pulled away from the Moon. The difference in the relative forces of the Sun on the Moon and the Earth increases steadily as the Moon approaches FM. In the gravitational action, the effect is exactly the same as would occur if an imaginary Sun were located at S', at the same distance as S from E, alon g the line of syzygies extended. For the same reasons above enumerated, between FQ and FM, the Moon's motion is accelerated, with a maximum veloc- ity attained at FM. Between FM and LQ, the Moon's motion is retarded, to a minimum at LQ. The lunar orbital velocity resulting from the effect of lunar variation is, therefore, greatest at the syzygies and least at the quadratures. As seen in figure 27B, correspondingly varying centrifugal forces result in a varying configuration of the lunar orbit. lunar evection. can measurably increase the value of the phase (fig. 27A) (except for the small angle subtended by parallax and reduce the lunar distance at the time of the radius of the lunar orbit at the distance of the Sun) perigee-syzygy. The increased tidal forces produced by the the tangent line from the Moon's orbit is oriented almost diminished distance of the Moon are related to a com- directly toward the Sun and the Sun's gravitational force posite of changes in several orbital parameters, as de- is fully effective in accelerating the orbital velocity of the scribed below. Moon. As the Moon moves toward conjunction, the angle 1. Alternating Acceleration and Deceleration'of between the force vector from the Sun to the Moon and the Moon's Orbital Motion the Moon's velocity vector increases from 0' to 90'. At The first factor contributing to ultimate variations in new moon, the Sun's gravitational force vector is directed the tide-raising forces involves the changing angle between exactly at right angles to the Moon's orbital motion and the direction of the Sun from any given point in the exerts a zero influence in producing any change in orbital Moon's orbit and a tangent line from this same point. The velocity. @ORBITAL V@ELOCITY@@ T Sx tangent line also represents the instantaneous vectorial di- Between new moon and first quarter, and again between rection of the Moon's motion in its orbit. At third-quarter full moon and third quarter, the situation is just reversed, Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 157 as the angle between the Sun and the Moon's velocity the Sun and Moon tend to reinforce each other in their vector decreases from 90' to 0', and the orbital decelera- actions on the Earth's tides. However, in considering the tion of the Moon varies from zero to a maximum. Like- reciprocal forces exerted on the Moon, the gravitational wise, the changing angular relationship that exists be- force of the Earth is respectively reduced or increased by tween third quarter and new moon prevails between first that of the Sun at the positions of new moon and full quarter and full moon, but with the Moon's velocity moon. The reasons for the latter circumstance will now be vector now oriented in the opposite direction in the sky. described. Between first quarter and full moon, the angle separating In moving from the position of new moon to a position the two vectors increases from 0' to 90'. very nearly that of first quarter, the Moon is at all times In recapitulation of the forces acting, at new moon and closer to the Sun than the Earth is, and hence is at all at full moon, since the gravitational attraction of the Sun times being attracted more by the Sun, and in a direction acts at right angles to the Moon's orbital motion, no in- slowing the Moon's orbital motion. As the Moon revolves crease in acceleration is produced. However, in moving from a path normal to the line connecting it and the Sun away from these two positions, the orbital acceleration of at new moon to a path nearly along this line at first- theMoon is altered by the Sun's gravitational force and quarter position, the attraction of the Sun upon the Moon attains maximum positive and negative values when the is exerted in a direction increasingly more opposed to the full force of the Sun is exerted directly along tangent lines Moon's orbital motion. In addition, as the Moon nears to the lunar orbit at the positions of third quarter and first first-quarter phase, a small sideward component of lunar quarter, respectively. deflection increases, directed toward the Earth, but caused by the Sun. This latter circumstance results from 2. Changing Lunar Orbital Velocity With Respect the fact that the Moon makes a small acute angle (as seen to the Earth from the Sun) with the line connecting the Sun and A second important influence of the lunar variation Earth. The Sun's gravitational attraction exerted along results from the combination of the previously described this line possesses a slight component impelling the Moon effects and the fact that the Moon,moves from a position inward toward the Earth. Both this inward deflection and inside the Earth's orbit around the Sun to a position out- the fact that the gravitational attraction of the Sun on the side this orbit during each monthly revolution. If only the Moon is exerted in a direction increasingly more opposed effect of the Sun's gravitational influence on the Moon to the Moon's orbital motion (thereby effectively reduc- durin these revolutions were considered, the resulting ing the latter) create the net result of diminishing the 19 lunar motion would be a relatively simple one. Consider, Moons orbital velocity with respect to the Earth. for example, the single effect of the Sun's gravitational in- In revolving through the first-quarter phase and pass- fluence as the Moon moves from its position of conjunc- ing on toward the far side of the Earth and the position of tion (between the Earth and the Sun) and revolves toward full moon, the Moon moves to a greater distance fro 'm its position of opposition, 180' from conjunction, on the the Sun than the Earth has. The attraction of the Sun side of the Earth farthest from the Sun. In this outgoing for the Earth-both because of the Earth's larger mass portion of the Moon's motion with respect to the Sun, it compared with that of the Moon and the Earth's closer would be moving against the Sun's gravitational attrac- distance to the Sun-becomes greater than the Sun's at- tion (and its motion would, accordingly, be subject to a traction for the Moon. retardation). Conversely, on the return portion of its orbit, Because a relative separation occurs between the Moon from opposition to conjunction, the Moon might be and the Earth, the effect of gravitational (centripetal) thought of as "falling" toward the Sun (and hence ac- force in restraining the Moon to the Earth is reduced, and celerating, in its velocity of motion). the satellite's own centrifugal force (associated with revo- Such a simplified assumption is not the true case, since lution in orbit and tending to cause an outward deflec- the gravitational force of the Sun is also exerted on the tion of the Moon) is augmented. The radius of curvature planet Earth. This results in the condition actually pres- of the Moon's orbit is increased, and along this straighter ent, in which a clear-cut distinction between the forces portion of the orbit, the motion of the Moon with respect acting must be observed: to the Earth is speeded up. The relative motion between When the Earth, Moon, and Sun are aligned at either the Moon and Earth is continuously accelerated until the new moon or full moon, the gravitational attractions of position of full moon is reached and the Moon's orbital 158 Strategic Role of Perigean Spring Tides, 1635-1976 motion is precisely at right angles to the gravitational the Earth, with the closest proximity thereto occurring at force vectors of the Earth and Sun. the time of extreme perigee-syzygy. Conversely, between full moon and third quarter, the At the position of perigee, which lies along the major Earth is subject to the Sun's gravitational attraction acting axis as well as along the line of apsides of the lunar orbit in the same direction as that of the Moon's motion. Be- (the former is but a portion of the latter), the curvature cause the Earth is closer to the Sun than the Moon is of the orbit, all factors considered, remains at maximum during this period, the Moon's velocity with respect to (i.e " the radius of curvature is the least). the Earth is effectively reduced. But as the Moon passes In accordance with dynamic principles, the centrifugal third-quarter phase, its distance from the Sun again be- force of the Moon at any point in its orbit varies directly comes less than that of the Earth's distance from the Sun. as the square of its velocity of revolution. It is this out- Responding to the consequent increase in gravitational wardly directed force which must be just balanced by the force, the Moon's motion with respect to the Earth is inwardly directed gravitational force of the Earth at any accelerated as it moves toward the position of new moon. point in order for the Moon to remain in a stable orbit. At new moon, this acceleration ceases, since the Moon's Since the centripetal or gravitational force of the Earth motion is here again completely at right angles to a line upon the Moon does not vary except with the Moon's joining Moon and Sun. changing distance from the Earth, any change in orbital In summary, at the syzygies, the Sun decreases the velocity and in the resulting centrifugal force must be gravitational attraction between the Earth and Moon by balanced by a corresponding change in the Moon's dis- separating the one which is closest to it from the other. At tance from the Earth. the quadratures, the full gravitational force of the Earth As the Moon changes its distance from the Earth, the on the Moon is effective, undiminished by that of the Sun, radius vector between the Moon and the Earth likewise which in these cases is exerted at right angles to the force changes in length. This radius vector also'corresponds with vector joining the Earth and Moon. The explanation of the radius of curvature at any point in the Moon's orbit. why the Moon, in consequence, travels faster in its orbit Therefore, according to the above relationships, when the at the syzygies and slower at the quadratures is contained Moon slows down, the Earth-Moon distance becomes less in the next section. and the curvature of the orbit becomes more pronounced. Whenever the Moon accelerates and the radius of curva- 3. Changes in Curvature of the Lunar Orbit ture and corr Iesponding circumference of the orbit become A subsidiary effect of the lunar variation is@ a flattening larger, the orbital curvature is reduced and the orbit it- of the orbital curvature (i.e., an increase in the radius of self becomes more nearly a straight line. A comparison curvature) at the lunar syzygies, coupled with the creation will now be made between the actual conditions existing of a more sharply curved orbit (smaller radius of curva- in the disturbed (three-body) -lunar orbit compared with ture) at the times of the lunar quadratures. Immediately, those that would theoretically exist if only the gravita- however, it must be emphasized that these dynamic ef- tional effects of the Earth on the Moon (two-body prob- fects are small, are superimposed upon, and act as modi- lem) were considered. fiers of, the larger and more meaningfully fluctuating At points 45', 1350, 225', and 3150 around the orbit orbital parameters of eccentricity, sernimajor axis, and from the position of new moon (dividing the orbit into mean parallax. The lunar variation involves a small in- octants), the curvature of the disturbed orbit corresponds dividual difference between the lunar distances from exactly witlithat of the undisturbed orbit. At these points, Earth at the times of the syzygies and the quadratures, which separate the regions of least and greatest orbital but only a secondary influence upon the lunar distances curvatures, the curvature is the same as that in the two- at perigee-syzygy. In this connection, the concept of a smaller radius of body orbit. curvature in terms of a more sharply curved orbit but Combining these relationships with the previously de- a slower orbital motion of the Moon should not be con- rived conditions of. acceleration and retardation of the fused with (1) a greater orbital eccentricity, which indi- Moon's motion at various points in its orbit, the following cates only a more elongated orbit, with the most sharply summary of conditions is obtained: between 315' and curved portions at the two apsides, or (2) a larger geo- 45', and between 1350 and 225', the orbital curvature centric parallax which, because of the inverse relationship is the least; between 45' and 135', and between 225' and in its definition, implies a closer distance of the Moon to 315', the orbital curvature is the greatest. Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 159 Since the'actual eccentricity of the lunar orbit is quite The satellite body revolves around the Earth in an small (0.054900489), its undisturbed configuration may, elliptical orbit which, subject to maximum perturbations, for purpose of graphic representation, be regarded as a can cause an overall variation of about 50,274 kra circle. The perturbed orbit resulting from the effect of (31,238 mi) in distance from the Earth. At the same lunar variation alone may then be comparatively repre- time, the Moon, along with the Earth, undergoes a larger sented by the elliptical orbit shown in figure 27B. variation in distance from the Sun caused by the Earth's annual motion in an elliptical orbit. The Sun-Earth dis- The Elliptic Variation tance can vary from about 147,100,000 km (91,408,000 The elliptic variation is, in actuality, not a true physical mi) to 15 2, 100,000 km (94,515,000 mi). The Sun-Moon perturbation, but a variation of periodic nature in the distance will fluctuate over a still greater range, depend- Moon's motion which occurs as a result of the Moon's ing on which side of the Earth the Moon is at the time monthly revolution around the Earth in an elliptical orbit. considered. As described in part If, chapter 2, this motion results in The maximum effect of this variation in terms of re- inforcing the already augmented gravitational and tidal the Moon's Alternating passage through the perigee and forces associated with perigean spring tides will, be evident apogee positions in its orbit where it is respectively at its around the time of solar perigee-the time of closest an- closest and farthest distances from the Earth in each nual approach of the Moon to the Sun-which must monthly cycle. occur within one-half of a lunar month of perihelion. The As in all of the other examples of physical perturba- particular consequence of the annual variation is discussed tions, this effect is accompanied by a corresponding in- later in this same chapter. crease in, and reduction of, the gravitational force ex- erted by the Moon upon the tidal waters of the Earth. The Lunar Reduction The 'amount of the distance variation, in the present case, can be represented completely by means of a simple quan- One further orbit-refining procedure it is necessary titative function, viz., the geocentric horizontal parallax to consider astronomically in the representation of the of the Moon. the actual increase in the value of this Moon's precise position is applicable as a positional trans- term at the times of perigee-syzygy-and the augmented formation known as the lunar reduction. The necessary gravitational force resulting-will be discussed in several corrective factor results from the difference between the ensuing sections. Moon's true longitude in orbit and its apparent longitude The minimum parallax of the Moon is 3,235", cor- in the ecliptic as conventionally tabulated. However, any responding to a maximum possible distance from the effect upon tide-raising forces resulting from this correc- Earth of approximately 406,154 kin or 252,364 mi; the tive term is so small as to be considered negligible in the maximum lunar parallax is 3,692" which corresponds present discussion. to a minimum Earth-Moon distance of about 355,880 km Differences Between the Mean and or 221,126 mi (fig. 41). From a tidal standpoint, the elliptic variation is equivalent to the lunar inequality. True Astronomical Positions of the The Annual Variation Moon and Sun This perturbation in the Moon's apparent position re- As a matter of ready verification (tables 10, 17, 20), sults from the Earth's annual revolution around the Sun because of the Moon's elliptical orbit and the respective in an elliptical orbit, carrying the. Moon with it. The perigee and apogee effects upon the orbital velocity as origin of the analogous tide-related phenomenon of solar predicted by Kepler's Law, the lunar velocity varies con- parallactic inequality has been discussed in part 11, chap- siderably throughout both the synodic and anomalistic ter 1. Its effect is that of bringing the Earth, revolving in months. The Moon slows down appreciably between peri- an elliptical orbit, to a position of closest annual approach gee and apogee, and speeds up in nearly the same pro- to the Sun (perihelion) around January 2-4 of each year, portion between apogee and perigee. and causing the Earth to withdraw to its greatest distance For convenience in the prediction of tides, during an from the Sun about July 3-6. Tied to the Earth by mutual early period in which hand-computations were necessary, gravitation, the Moon shares this same motion. any pen-nissible means of reducing the computational load 160 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR VARIATION EFFECT (ON ORBITAL CURVATURE) B. MAXIMUM ORBITAL CURVATURE FQ B A 0 ;4, MINIMUM MINIMUM ORBITAL TO ORBITAL FM E NM CURVATURE @N CURVATURE, THE LUNAR ORBIT IS ELONGATED ALONG AN AXIS AT RIGHT ANGLES TO THE FORCE VECTOR BETWEEN THE 0 SUN AND THE LUNAR ORBIT. C D THIS PHENOMENON IS INDEPENDENT OF THE ORIENTATION OF THE LINE LQ OF SYZYGIES WITH RESPECT TO THE LINE OF APSIDES. MAXIMUM ORBITAL CURVATURE (SHORTEST RADIUS OF CURVATURE). FIGURE 27B.-The phenomenon of lunar variation also results in changes in the shape of the lunar orbit. To demonstrate these changes more clearly, the Moon may initially be assumed to move in the circular orbit ABCD rather than in its true elliptical orbit of small eccentricity. As was seen in figure 27A, at FM, the Earth, being closer to the Sun than is the Moon, is pulled away from the Moon. The Earth's gravitational attraction on the Moon is thus decreased, and the centrifugal force generated by the Moon's revolution in orbit exceeds the centripetal force. The radius of curvature increases, the local curva- ture decreases, and this portion of the orbit becomes flattened. At NM, the Moon similarly is pulled from the Earth. Here also the Earth's gravitational attraction for the Moon is decreased, the centrifugal force exceeds the centripetal force, and the Moon's orbit is flattened. The greater is the orbital velocity of the Moon, the more the centrifugal force exceeds the centripetal, and the greater is the orbit-straightening action. As shown in figure 27A, the greatest velocity increase produced by the effect of lunar variation is at the syzygies and the greatest decrease is at the quadratures. Accordingly, the, lunar orbit will be flattened to the greatest extent at the syzygies and possess the greatest curvature at the quadratures. Approximately midway between these four positions, the orbital path must pass through points of inflection where the curvature remains unchanged. In the octants (at angles of 45', 135', 225', and 315' from NM), no alteration in the shape of the lunar orbit occurs from the effect of lunar variation. The unperturbed (cir- cular) and perturbed (elliptical) orbits here coincide. In the case of the Moon's actual elliptical orbit, the same extension of this ellipse along an axis perpendicular to the instaneous direction of the Sun takes place-together with a slight flattening in the orbital curvature close to the two posi- tions where a line from the Sun cuts the orbit. The orbit-distorting effects of lunar variation are simply superimposed upon the true elliptical configuration, adding to the total complexity in the shape of -the perturbed orbit. Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 161 resulting from the very numerous astronomical terms was tation. The coordinate system in which the celestial object is highly desirable. The necessary and sufficient calculating referenced still includes the coordinate-altering effects of procedure, involving minimum complexity, and capable astronomical precession and nutation. Here any further re- of re resenting the lunar orbital velocity as well as other semblance ends between the position-referencing system for p the Moon and Sun presently under discussion and an ap- related functions, was sought after and instituted. Aver- parently similarly designated system for indicating the posi- age values were freely resorted to wherever possible, and tions of the stars and other distant celestial objects. are still tacitly utilized in tidal computations. By contrast, when the precise positions of the stars are Using basic formulae derived by Simon Newcomb in considered, the origin of coordinates is the center-of-mass the late 19th century, the mean longitudes of the Moon of the solar system (barycenter) which is very close to the I center of the Sun (heliocenter). Because the distance of and Sun, and various of their orbital parameters, were the Earth from the Sun and the velocity of the Earth's originally adopted for epochs corresponding to the first revolution around -the Sun are now additionally involved, day of each year, and these values still appear in standard corrections for annual parallax and annual aberration, re- tidal reductions. In addition, mean values are employed spectively, must be applied to the apparent place to yield for the daily angular motions (real and fictitious, respec- stellar true place. As in the case of apparent place, true place is still given in a coordinate system which contains tively) of the Moon and Sun. The instantaneous mean the effects of, and is uncorrected for, precession and nuta- positions of these two bodies are computed for any date tion. The star position is referred to the true equator and subsequent to a standard epoch by adding their average equinox of the date of observation. (mean) daily motions to their positions at the time of the Finally, if a reduction for nutation is applied to stellar standard epoch. true place, the position of the star is represented in mean place. In all other respects except that the stellar position is now referred to the mean equator and equinox of the The Derivation of True and Mean date of observation, mean place is exactly similar to true Astronomical Positions place. Mean place also still contains the uncorrected effects The actual, observed position of the Moon or Sun at of precession. any time, reduced through the application of a correction for parallax to the Earth's center-and with other correc- The Assumption of Mean Positions tibns for atmospheric refraction and diurnal aberration However, for tidal prediction purposes, the average or duly applied-becomes the true (apparent) astronomical position of the object. mean position of the Moon or Sun, referenced to a con- venient zero-point in time by application of similarly aver- aged increments of mean daily motion, is used. 'ne con- cept of mean position as used in tidal computations has It is important to observe at this point that the distinc- tions between observed and apparent positions for the Moon been extended to include the mean longitudes of the and Sun are the same as those applied generally to the Moon, the Sun, the position of lunar perigee, the position positions of all celestial ob*ects. However, the meanings of of solar perigee the point of intersection between the celes- true and mean positions as used in the present connection tial equator and the Moon's orbit (reckoned in the orbit are not the same as those of the terms true place and mean place u'sed astronomically in relation to star positions. plane), as well as the lunar ascending node. The mean For all celestial objects, the observed place is that deter- positions and motions are referred to the origin of coordi- mined by direct instrumental means by an observer on the nates at an appropriate mean epoch, in each case. surface of the Earth (topocenter), corrected only for errors in the instrument and others dependent on the method of observation (instrument collimation, leveling errors, in- equality of the pivots and V's, index or circle errors, appar- The mean positions of these lunar and solar elements ent semidiameter of the Moon or Sun, dip of the horizon, together with their mean daily motions appropriate to the clock errors, etc.) . years A.D. 1800-2000 are available in table 4 of Manual of The apparent place is a geocentrically referred position Harmonic Analysis and Prediction of Tides' (1940). Certain (i.e., corrected by application of the geocentric horizontal values among the total list also are contained in tables of parallax where necessary). It also includes reductions for the Mean Orbital Elements of the Moon and the Inner astronomical refraction and diurnal aberration. Thus, in ap- Planets in annual volumes of The American Ephemeris and parent place, the observed position is not only referred to Nautical Almanac. the center of the Earth, but is free of atmospheric effects and The value of the mean motion of the Moon in its own the light-velocity altering influence of the Earth's diurnal ro- orbital plane is obtained from the relationship 202-509 0 - 78 - 13 162 Strategic Role of Perigean Spring Tides, 1635-1976 3600 3600 Conversely, at the times of perigee-syzygy, when the -LL - M., 27.3216616 tide-raising forces are considerably augmented, that part 13.176396T of the lunar evection. term which acts to produce an accelerated motion in longitude, and a corresponding dif- The mean apparent motion of the Sun is similarly ob- ference between true and mean longitude, completely tained from the mean angular velocity of the Earth in its disappears. However, in subsequent sections, it will be orbit during a sidereal year noted that other and equally important tide-producing 3600 3600 factors, whose magnitude could vary sensibly with the T@@_d 365.256360d difference between true and mean place, also occur at 0.985647'/d perigee-syzygy and are not self-compensating. However, because of the elliptical orbits of both the Moon Further comment on the previously accepted simplifi- and Earth, the two values determined above in no way cations and assumptions will, therefore, be reserved until express the real (lunar) or apparent (solar) angular veloci- certain lunar perturbations and resulting influences pe- ties of these two bodies on any one day during an entire culiar to the phenomenon of perigee-syzygy-and the revolution. The real daily orbital motion of the Moon at production of perigem spring tides-have been discussed. perigee will be appreciably larger than the mean value, and the apparent daily motion of the Sun will be measurably The Special Perturbative Influences of faster at perihelion than the respective mean motion. Lunar Evection and Lunar Variation As a secondary step in these computations, the mean Hugh Godfray in An Elementary Treatise on the Lunar value of the lunar longitude, obtained as indicated above, Theory" (1871) has provided an excellent exposition is converted to an approximate true value by the appli- from which it is possible to derive the effects of the most cation of arbitrary reduction coefficients representative of significant individual perturbations. These establish the the lunar perturbations previously discussed. In addition, differences between true and mean position in the lunar the value of the true parallax of the Moon expressed as a orbit. function of the mean parallax for each specified date The effects of these perturbational terms are regarded enters into the tidal computations. Higher powers in these as corrections to the mean longitude necessary to obtain reduction equations are neglected, and various other sim- the true longitude in orbit. By transforming the symbols plifying assumptions are made, under the rationalization in Godfray's equations to a compromise of those more ihat the difference between the true and mean longitude familiarly used in The American Ephemeris and Nautical of the Moon never exceeds 7.8' (0. 137 radian) and that Almanac and other modern sources, the individual anal- this latter value differs very little from the sine function ysis of the several terms can proceed as below: (0.136) by which it is subsequently replaced. Where: The justification for this procedure in evaluating the X(C= the true longitude of the Moon true position of the Moon from its mean position may n(c =the mean daily angular motion of the Moon easily be supported, based on the fact that, for tidal com- L'=nct= the mean longitude of the Moon at any putations of the order of accuracy heretofore required, the time t L'(,=the mean longitude of the Moon at t=O existing methods are adequate. The differences between e([@the eccentricity of the lunar orbit the true and mean positions of the Moon are indeed quite rl,=the mean longitude of the lunar perigee at small. For all ordinary predictions not subject to the com- time t=O putatiohal refinements made necessary by increased rl=(l-c) n([t+r'o= the mean longitude of the knowledge of perigean spring tides, potential tidal flood- lunar perigee at any time t, assuming a uni- ing attendant thereon, and burgeoning coastal popula- form rate of motion tions now vastly more dependent upon these predictions, c=an arbitrary factor introduced by Clairaut the approximation would suffice. Furthermore, the maxi- to indicate that the lunar perigee is itself mum differences between mean and true positions in some in motion b=a factor similar in purpose and usage to significant cases (but, as will shortly be seen, not all) that of c occur at times when the tide-raising forces are at their N= the position of the lunar node when the lowest possible values and, therefore, are not seriously lunar longitude is X([ affected by these differences. s=tan N Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 163 a =the longitude of th e mean ascending node of where the sine term represents the angu lar distance in the lunar orbit on the ecliptic longitude of the Moon from perigee. If this difference is the true longitude of the Sun positive, the Moon is ahead of perigee (i.e., has a greater n =the mean apparent daily angular motion of longitude); if the Moon has a smaller longitude, and the the Sun difference is negative, the Moon is behind the perigee P the ratio of the mean daily angular position. n( Owing to the fact that the correction to the mean longi- velocity of the Sun to that of the Moon tude is subtractive, the true place of the Moon is ahead of (=0.0748) L=the mean longitude of the Sun at time t=O the mean place if the Moon at either of the two syzygies L=n0t+L=n(pt+L= the mean longitude of is between apogee and perigee (i.e., L'-1`<90'>0'). the Sun at any time t The true lunar position is behind the mean position when e=the eccentricity of the Earth's orbit the Moon at syzygy is between perigee and apogee (i.e., =the mean longitude of the solar perigee at L'-< 180>90). time t=0 In the quadratures, the first equation above reduces to r the mean longitude of the solar perigee at any time t. X(r =8qLp + 15 pe(qC sin q[2(900)(L'-V)] The general equation which includes all of the 4 principal perturbational terms is: and, since sin [1800-(L'-r1)]=+ sin (L'-r),. X[ (true longitude of the Moon) 15 =L' (mean longitude of the Moon) X:=L'+Tpe([ sin (L'-rl). 5 +2e(r sin (c8qL'-rlo)+ ie Q:2 sin 2 (c8qL- rl 0q) Because the corrective term is now additive, the true (elliptic inequality) place of the Moon lies ahead of the mean place between + 15 pe(c sin [(2-2p-c)L'-2L(,+r'0] perigee and apogee and behind the mean place between (evection) apozee and perigee. If the line,of apsides coincides with either the line of + g_p2 sin [(2-2p)L'-2L,] syzygies or the line of quadratures (i.e., if one of the lunar (variation) apsides occurs simultaneously with the new, first quarter, 3peo sin (L- r,) full, or third quarter moon), the difference between the (annual . equation) true and mean longitudes of the Moon becomes zero. The 182 sin 2 (bL'- a) same zero correction applies also when the Sun is midway 4(reduct ion) between the Moon and either apse. The foregoing analysis relates to the perturbative effect In keeping with the purpose of this investigation, a de- of the lunar evection terrn alone. It is seen that, at the tailed analysis will be made only of those actual perturba- position of perigee-syzygy, this perturbation function by tional functions which are capable of producing a mean- itself plays no part in altering either the true longitude ingful change in some tide-related parameter at a time of of the Moon or the difference' between the true longitude perige-syzygy.'Somewhat simplifying the second additive and the mean longitude thereof. As will be noted later, term in the previous equation, the correction for lunar this is not true ' however, of either the eccentricity of the evection may be written as lunar orbit or the instantaneous parallax of the Moon. 15 In actuality, the influence of the lunar evection X(0qc24qL'32q+ pe(c sin [22q(L'-L)-(L'-r)] produces a significant change in the lunar orbit, as 4 discussed in a preceding section dealing with the astro- Because, at the syzygies, L=L', and since sin [-L' nomical cause of this perturbation. When the effect of -rl)]=-sin (LI-r'), this yields, at either con- the lunar evection is combined with that of the elliptic junction or opposition inequality, the quantitative result is to alter the eccentricity of the lunar orbit by an algebraic factor 15 15 X=L'- 4 pe( sin (L'-rl) equal to approximately -, pe(. 164 Strategic Role of Perigean Spring Tides, 1635-1976 The corrective term, whose complete value is Between conjunction and a mean elongation o f 45', given by the expression 15 peq: cos 2(r'-L) is addi- as the result of the lunar variation alone, the Moon's true longitude lies ahead of the mean longitude by an tive if the line of zipsides coincides with the line -of amount which varies from zero to a maximum. Between syzygies, and subtractive if the line of apsides coin- elongations of 45' and 90', the angular amount by which cides with the line of quadratures. Thus at a time of the true moon lies ahead of the mean moon decreases perigee-syzygy, considering the effect of lunar evec- from a maximum to zero. Between elongations of 90' tion alone, the increased eccentricity of the Moon's and 135', and between 135' and 180', the true position orbit e'(c is related to the former, unperturbed ec- of the Moon (in either longitude or right ascension) lies centricity e(C through the relationship behind its mean position. 1 1 +L5 The difference varies in the same manner from zero to e (1=e(I 8 p cos 2(r'-L)I. a maximum between elongations of 90' to 135' and- between 135' and 180'-ranges back to zero again. Be- Similarly, the perturbational effects of the lunar tween opposition and conjunction, the same cycle is're- variation may be analyzed as follows: peated. Thus, the difference between true longitude and In the previously given general expression for the mean longitude varies in repetitive cycles throughout suc- longitude of the Moon at any time t, the representa- cessive octants of the lunar orbit according to the basic tion of that part of the Moon's disturbed motion pattern shown in figure 34. The effects of these differ- caused by the lunar variation is given by ences upon the length of the tidal day later to be dis- cussed follow the same pattern. ,N(c=Ll+ P 2sin [(2-2p)L-2L0] Summary of the Effects of the Principal Lunar Perturbations in Differentiating where the various symbols are as previously defined. Between the Mean and True Orbital Posi- If the Sun's mean longitude at the time t is now tions of the Moon represented by L, such that L=nDt+L,), and since The following summation is given of four physically p@nc)/n([ or no=PnT, and L'=n(ct, the above equation perturbing influences whose individual effects can pro- reduces to duce a difference between the mean and true places of X(c=L'+ P 2 sin 2(L'-L). the Moon. 1. Effects of Elliptic Inequality From this equation, certain interpretations are From perigee to apogee, the true place of the Moon immediately obvious. When the difference between the is ahead of the mean place, considering this cause alone; mean longitudes of the Moon and Sun (the mean from apogee to perigee, the true place of the Moon is elongation) equals 45, 135*, 225', or 315', the addi- behind the mean place. At perigee and syzygy, true place tive term in this expression reaches a maximum with its will be the same as mean place. value equal numerically to P2 (plus other higher- 2. Effects of Evection (combined with the elliptic order terms for greater accuracy). The value 11 p2 is inequality) . 59 9- The true place of the lunar apse (perigee or. apogee) only a first coefficient. The next is T2 pl. An entire is behind its mean place when the apse I ies in either series can be developed, and at least five terms are the first or third quadrant ahead of the Sun, and the necessary for comprehensive accuracy. When the apse is ahead of its mean place when it lies in the mean lunar elongation is 0* or 180' (i.e., at either second or fourth quadrant ahead of the Sun. The dif- syzygy), the true longitude of the Moon is equal to ference in longitude between apse and Sun is given by its mean longitude and the effect of the lunar varia- 15 tion on change in longitude is zero. At the lunar Arl=_,_ k sin 2 (r I -L), quadratures, (mean elongation@90' or 270'), the lunar variation term also reduces to zero and the with the symbols as previously indicated. When the Moon's true longitude is again equal to its mean lunar apse isIcoincident with the direction of the Sun, longitude. the true and mean places of the lunar apse are the same. Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 165 3. Effects of Lunar Variation view of the comparative magnitudes of the solar forces Between syzygy and quadrature, the true place of the exerted at these times on the Moon revolving in its orbit, Moon is ahead of the mean place; between quadrature this statement might appear to some extent paradoxical. and syzygy, the Moon's true place is behind the mean Considering the effect of the annual equation place. The maximum difference between true and mean totally apart from the other perturbational effects, place occurs in the octant positions. The relative angular the solar gravitational attraction exerts a varying velocities of the Moon at various positions in orbit may influence consistent with the changing distance of the also be readily obtained. Earth from the Sun throughout the year. In accord- The expression for lunar variation given in the last ance with the inverse-distance relationship of New- equation of the preceding section is ton's law, this results in the Sun's greatest gravita- tional force being exerted upon the Earth (and Moon) 11 when the Earth is situated along the line of aspides X(E=L'+ @-p' sin 2(L'-L) of. the solar orbit and at its perihelio In position. The Since: L'=nv; L=not+Lo; and appropriate, equation connecting the two variables no=n(cp; then L=n([pt+Lo. P(C and a([ in an undisturbed orbit is: Substituting: P(C 21ra(Im k (MED + m (c) X(E =n(c t + P2 sin 2 [n(c t-(nCpt+L,,)j- where Pq:= the sidereal period of the Moon's revolution Differentiating this equation with respect to t to find around the Earth the variation in angular velocity of the Moon with position lr=in this case, the mathematical constant, in orbit as the result of this perturbation alone, and there- 3.14159, denoting the ratio @of the circum- after converting back to the original symbols, wherever ference of a circle to its diameter possible, for nomenclatural consistency: a([= the spinimajor axis of the lunar orbit Mq)=the mass of the Earth dx([=n([+ 11 n(lp'(1-p) cos 2(L'-L)- m(,= the mass of the Moon 7t k=the Gaussian constant of gravitation, or amount of attraction between two bodies Hence, at the syzygies, where L-L=O, or 1800, (in this case, the Earth and the Moon) per the lunar velocity in orbit reaches its maximum value. unit mass, and at unit distance. At the quadratures, the angular velocity becomes minimum. In the octants, the Moon's velocity is As the Moon revolves in its disturbed orbit, the equal to its mean value, nr. gravitational attraction of M. on mq: changes con- 4. Effects of the Annual Equation tinuously for many reasons. Among the various normal components of force affecting the Moon's orbit, there In terms of the influence of the annual equation upon are more of negative than of positive value. This fact lunar position, the principal result is that, between perigee results inevitably in an average reduction in the force and apogee, the true place of the Moon lies behind the of M., on mc which, in turn, implies a lessening in the mean place; between apogee and perigee, the true place assumed constant value of k. The ensuing increase in of the Moon lies ahead of the mean place. Pq: with decrease in the value of k according to the Additionally, however, with regard to a subsequent above equation results in a lengthening of the lunar analysis of lunar catch-up times as these contribute to the month. Such an extension of the lunar month.would production of increased perigean spring tides, another provide a consistent rule if the Sun's gravitational somewhat counterproductive relationship derives from the attraction on the Moon's orbit was itself constant. annual equation. This involves the difference in lunar However, this inverse variation of Pz with k is orbital velocities as affected by the Sun, and is most evi- valid only for motion which is accelerated from a dent at times of solar perigee and solar apogee. When the source of attraction at a constant (unit) distance. Sun is at its closest position to the Earth and Moon (solar The fact that the Earth revolves in an elliptical orbit perigee), the angular velocity of the Moon in its orbit is and varies constantly in distance from the Sun gen- the least; with the Sun at its greatest distance (solar erally invalidates the previous equation and its ac- apogee), the Moon's angular velocity is the greatest. In companying increase in period with decrease in k. 166 Strategic Role of Perigean Spring Tides, 1635-1976 Thus, as the Earth moves from perihelion to aphelion with the corresponding mean values. In tidal computa- and toward greater distances from the Sun, the tions, this fact results in the use of the following equa- previous influence of the equation in increasing the tions relating true and mean longitude and true and mean length of the lunar month is rendered correspondingly parallaxes. These approximations of the corresponding ineffectual. astronomical equations are employed in an endeavor to The net result is a.relative decrease in the length of the take into account the various lunar perturbations. lunar month. This, in turn, causes a progressive accelera- Where: tion in the Moon's daily motion in orbit as the Earth L'=the mean longitude of the Moon, measured revolves from perihelion to aphelion, and a decrease in in the ecliptic from the mean equinox of the Moon's motion as the Earth revolves from aphelion date to the mean ascending node of the to perihelion. Because of carry-over effects, the greatest lunar orbit, and then along the orbit and least lunar velocities (due to this cause alone) occur X(E=the true longitude of the Moon ' measured at the times of aphelion and perihelion, respectively, al- from the mean equinox of date in the same though the normal components of the Sun's gravitational fashion force on the Moon's orbit are actually zero then. The r, =the mean longitude of the lunar perigee induced effects of lunar velocity in orbit are, of course, L=the mean longitude of the Sun superimposed upon, and vectorially either added to, or eq:=the eccentricity of the Moon's orbit subtracted from, the lunar velocity effects produced by p=the ratio of the mean daily motion of the Sun to that of the Moon the Moon's passage through perigee and apogee, and by 7r(c=the true geocentric horizontal parallax of other f actors. the Moon The expression representing the effect of the annual f([=the mean geocentric horizontal parallax of equation as noted at the beginning of the preceding sec- the Moon, tion is X([=L'-3pe@ sin (L-r(,) the tidal equation relating the mean longitude and the true longitude in the lunar orbit is Because L'=Pt, and L_r@ is equal to the mean solar X(C (in radians) (true longitude of the Moon) anomaly g, or angular separation of the Sun from perihe- =L' (mean longitude of the Moon) lion, assuming a uniform motion of the solar line of 5 apsides, +2e(C sin (L'-rl)+ 4 eq:2 sin 2 (L'- r1) X(C=pt-3pe(D sin g 15 (elliptic inequality) Differentiating this equation with respect to the + 4 pe(c sin (L'-2(L'-2L+r1) time, to determine the Moon's velocity in orbit as a (evectional inequality) function of the Sun's mean anomaly: + 11P 2sin 2 (L'- L) . . . . T dX(C (variational inequality) _dt- =p[J_3p2eE) COS g] The corresponding equation relating the ratio of Since both P and e E) are decimal values, this equation the true and mean parallaxes of the Moon is yields the smallest lunar angular velocity from this per- 7r(C /JF([ turbational cause alone at the solar perigee (g = 0'), and a value equal to p at g = 90'. At the solar apogee + e C COS (L'- V) + e ([2 COS 2 (L'- F') (g == 180'), the Moon's velocity reaches its maximum (elliptic inequality) value. + peq:- COS (L'-2L+rl) Corrections for Lunar Perturbations as Used (evectional inequality) in the Tidal Equations +P 2 COS 2(L'-L) . . . . As the result of the previously enumerated deviations (variational inequality) in the positions and motions of the Moon produced by The astronomical terms involving the effects of annual perturbations, neither the instantaneous true longitudes equation and reduction (from longitude in the ecliptic to of the Moon in its orbit nor its true distance (parallax) longitude in the Moon's orbit) are not included in the with respect to the Earth in the perturbed orbit agree foregoing series-nor are higher-order ternis in various of Perturbing Functions Establishing and Controlling Amplitudes of Perigean Spring Tides 167 the individual perturbations. As will be noted in subse- nology have rendered possible vastly more complex com- quent chapters, the inclusion of these terms to a higher putational procedures. At the same time, new require- order of accuracy is necessary in order to ensure a mean- ments for even greater precision in certain local tidal pre- ingful representation of the lunar motions concerned. dictions have arisen. These have come about as the result Particularly is this true, for example, in the case of tk of the burgeoning development of coastal communities, alternating progression and regression of the position of the increasing establishment of vacation homesites, beach the lunar perigee. The present computations of this effect cottages, and condominiums ever closer to the high water- assume, at all points in the lunar orbit and at all force- line, and the expanded and proliferating recreational use angles with respect to the Sun, a mean daily motion for of the coastal zone. the lunar perigee of +0.111404'/'. It will be seen in Such growing demands make a review of the previous connection with figure 28B that, at the time of a proxigee- tide-computing methodology both necessaryand desirable. syzygy (close perigee-syzygy) situation, the true motion As a part of this evaluative process, new techniques and of perigee may exceed -1.60/'. refined computational methods are worthy of considera- Similarly, the mean longitude of lunar perigee tion. The direction of effort pursued should include an enters into the tidal equations for determining true additional emphasis on the tidal characteristics of low- longitude and true parallax as affected by the elliptic lying, flood-prone localities subject to potentially catas- inequality and the evectional inequality. The appro- trophic attack from the sea. priate corrections occur only through the term whose Numerous examples of extremely severe property dam- coefficient is 11 p'. This coefficient is, but one of an age and, upon occasion, attendant loss of life, are shown 8 among the previously tabulated instances of coastal flood- infinite series. Unless at least four more of these ing produced by perigean spring tides which have oc- higher-order terms are included, the resulting value curred in combination with winter storin conditions. This of the total angular difference between true and mean fact points realistically to the need for greater public longitude is far from accurate. awareness of the potential hazards existing in connection The aforementioned assumptions and approximations with this type of tide when accompanied by the appropri- used in this series of corrective expressions for transform- ate meteorological conditions. ing from mean to true longitude and mean to true parallax Salient investigations should include special attention were adequate for their time. They are still sufficiently to the delineation of factors useful in analyzing, predicting, accurate to define the more usual tidal circumstances and gauging the probable intensity of tidal flooding well which do not involve, for example, the special combina- in advance of such catastrophic events. The factors ex- tions of astronomical tide-raising forces and other factors plored would also involve the determination of those con- necessary to'the production of perigean spring tides. The ditions of air-sea coupling most vulnerable to the produc- effects of such amplified forces, the extended intervals of tion of tidal flooding, should the accompanying meteoro- their action, and the perturbative influences which con- logical conditions of low atmospheric pressure and strong, tribute to both, will form the principal subject of the next persistent, onshore winds prevail. two chapters. The development of a combined theoretical and em- The nearly phenomenal advances during.recent years pirical basis for effectuating this knowledge will be dis- in high-speed electronic data processing and related tech- cussed in the ensuing chapters. Chapter 4. Identification of the Specific Astronomical Forces and Influences Contributing to the Production of Perigean Spring Tides Proceeding progressively toward the problem at hand- Moon at syzygy, and the closer approach of the Moon to that of identifying the physical origins of perigean spring the Earth at perigee; (4) An increase in the eccentricity tides, together with the possibility of their subsequent of the Moon's orbit caused by the perturbative actions of amplification and development-it is now necessary to lunar evection and variation; (5) As the result of this consider the role played by the interrelationships between increase in the eccentricity of the lunar orbit, a further various dynamic influences in the production of such en- decrease in the perigee distance of the Moon toward a hanc'ed tides. The following three chapters therefore will possible proxigee relationship, and an increase in the gee deal with the consequences of the combination of the vari- centric horizontal parallax (generally related in amount, ous individual factors (positions, motions, forces, and to the closeness of the perigee-syzygy separation) ; (6) perturbations) enumerated in the preceding three chap- Through the reduced distance of the Moon, an increase ters, plus the Appendix. in the lunar gravitational forces exerted upon the waters of the Earth, thus augmenting the tide-raising forces; and The Principal Concurrent Tidal Forces (7) A corTesponding increase in the amplitude and range of the tides. Among the coactive, maximizing, tide-raising influ- ences, those resulting from the astronomical alignments Basic Force Equation Defining the described in the next two sections constitute the most Magnitude of Tidal Uplift important conjugate factors in the production of perigean In his monumental five-volume Manual of Tides spring tides. The concepts which succeed them in the same chapter are equally substantial, but secondary in (1898), Rollin A. Harris, formerly chief mathematician their influence to these. in the U.S. Coast and Geodetic Survey, presented a com- prehensive treatment of the tide-producing potential. In The Effects of a Near-Alignment of Perigee chapter IV of part 11, he included the development of and Syzygy in Producing Tides of In- the expression for the height of the tides above the un- creased Amplitude and Range disturbed sea level as a function of numerous related The production of increased high and low water's at factors. Carrying this development one step further, an times of perigee-syzygy takes place in consequence of a exhaustive analysis of perigean spring tides on the basis chain of interrelated events. These are: of Harris' original equations is included below. The sym- bols of this earlier treatise have been converted to those (1) The orbital motion of the Moon in an ellipse, sub- used in the present volume for consistency and continuity. ject to the parallax-enhancing effects of the elliptic in- equality; (2) ne occurrence of a near-coincidence Where: (minimum angular separation) between the positions of AS=height,of the tide above undisturbed sea level, perigee and syzygy because of commensurable relation- m(c=Moon's mass Me =Earth's mass ships between the synodic and anomalistic periods of the PED@Earth's mean radius Moon; (3) 'Augmented tide-raising forces produced by a(c=Moon's mean distance from the Earth (equal the combined gravitational attractions of the Sun and to the sernimajor axis of the Moon's orbit) 169 170 Strategic Role of Perigean Spring Tides, 1635-1976 =eccentricity of the lunar orbit For diurnal tides: 0 =geographic latitude of the place of observa- 105 tion Xz=_ pe(cu-v sin (,ar-2,,L'r-L'T+2,LT-r'T) P =(-)=ratio of the mean angular daily motion (4) n(C of the Sun to that of the Moon (=0.0748) For fortnightly tides: ,a,r difference in right ascension of the extremity 1(X-+Y---2Z2) of the x-axis of the coordinate reference systern used, measured along the celestial 1 (u1-4U2+V4) 45 pe: cos (,L',r-2,LT+,r1T) (5) 'equator from the northward-crossing point 3 of intersection between the lunar orbit and The equations representing the effects of lunar the celestial equator variation are L', =difference in the Moon's mean longitude, For semidiurnal tides: measured in the lunar orbit from its north- X2-y2= 23 P2U4 cos (2,a,-2,L',-2,L'T+2LT) (6) ward crossing point of intersection with the 8 celestial equator For diurnal tides: ,LT mean longitude of the Moon, measured in the ecliptic from the mean equinox of date XZ=O (7) to the mean ascending node of the lunar For fortnightly tides: orbit, and then along the orbit (X2+Y2-2Z2) ,L,r =mean longitude of the Sun, measured in the ecliptic) from the mean equinox of date (u'-4U2V2 +vl)3p' cos (2,L',r-2,LT) (8) VT =mean longitude of the Moon's perigee, measured in the ecliptic from the mean equinox of date A closc analysis, term by term, of the foregoing general I =angle of inclination between the lunar orbit equation (1) for tidal height will reveal the effect of a and the celestial equator perigee-syzygy alignment in producing augmented high tides, principally through the perturbations associated U =COS with lunar evection and lunar variation. The effects of the individual expressions involving these two perturbative in- V =sin fluences will be evaluated first, and the results will then be combined in the general equation. Terms in X Y, and Z will be defined below. 1. 'Lunar Evection Effects If the value of AS represents the theoretical height of (a.) The first analysis will begin with the term at the the tides produced, subject to a given combination of cir- extreme left of the parentheses in equation (2) and then cumstances and perturbations involving the Sun and proceed toward the right. Moon, the appropriate equation for this tidal height is The term a, involves a rectangular coordinate system -3 m(c p P COS2 O(Xl-y2) whose origin is at the center of the Earth and whose As= 2MED z-axis is coincident with the Earth's axis of rotation. The ,r2q) J_eT2)3 2 _ I +sin 20Xz+X-sin2)1(X2+Y2-2Z2)] (1) x- and y-axes are mutually perpendicular thereto and are 2 3 located in the plane of the Earth's Equator. The angle a, represents the position of the extremity of the x-axis, meas- where a typographical correction has been made in the ured as a difference in right ascension along the celestial first Y' (from Y' in Harris' report). equator from the point of intersection of the lunar orbit The equations which represent the effects of lunar evec- with the celestial equator. (The latter origin is assumed to tion are move only as the equinox moves, due to precession. This For semidiurnal tides: westward motion of the celestial equator along the ecliptic X2-yl= 105 pe(ul Cos (2,a,-2,L',-,L'T+2,LT-,r1,r) also shifts the lunar intersection point along the celestial 16 equator.) 15 (2) The continuous increase in the value of ear through 24" _T6Pe(1 u cos (2,a,-2,L',+,L'T-2,LT+,r1T) (or 360') of right ascension each day is an indication of (3) the eastward movement of the end-point of the x-axis Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 171 along the celestial equator. This rectangular coordinate value of 2oal is closing continuously on 2,LI, but at a system is tied to, and the motions of the x- and y-axes are slightly lessening rate. a function of, the rotating Earth. Since, to the accuracy required in tidal predictions, the The x-axis as selected will intersect the geographic angular velocity of the rotating Earth (affecting the value longitude of the place of observation on the Earth's sur- Of q4l) does not vary, any rate of change affecting the in- face. As this x-axis rotates with the Earth through 360' stantaneous difference between 2qal and 2oL/ can be a once in each 24', it passes through all possible values function only of the Moon's changing velocity in orbit. of right ascension or celestial longitude, whereas the As the Moon approaches pezigee-syzygy, its angular Moon's mean longitude increases by only 13.176396'/day veloci'ty increases as the result of Kepler's Law. The value due to its orbital motion. of 2,,Lr' will also increase at a slightly faster rate. The en- Because the effect of tidal forces in producing the excep- suing situation involves the subtraction of a larger posi- tionally high waters of'perigean spring tides is under con- tional angle (being swept through at a slightly increasing sideration, the concepts of the phase and parallax lags angular velocity) from a smaller positional angle (being must later be introduced in determining the exact dates swept through at a constant rate). Accordingly, as the of the maximum tides. However, on any one date, the Moon's velocity increases, the instantaneous value of the high tides will necessarily occur with the Moon close to difference (2qal- 2oL,') changes less rapidly. During this the position of the upper or lower meridian of the place period, the angular difference (2qa, -2,L,') will, there- (i.e., subject only to the lunitidal interval and@ at open fore, be reduced by a steadily increasing, but decimally seacoast locations, usually within an hour or so of meridian small amount (with a negative angle resulting from the transit of the Moon). subtraction). Thevalue of the cosine function of the total The existing mean longitude of the Moon will, there- expression in parentheses in equation (2) is increased in fore, be at a point near the local meridian, while the proportion (although its value is so near unity, the effect x-axis of the coordinate system under discussion passes acts more to extend the period close to perigee-syzygy and through the geographic location of the observer. to prolong this period of maximum tide-raising influence Although all symbolic values arc initially as defined in than to increase the tidal amplitude). the above legend, through the introduction of the trans- As the Moon, Su -n, and lunar perigee come into formation equations P = cos Y2I and q = sin Y21 in the alignment at pcrigee-syzygy, J-"r=J-T=rr'T. There- reductions necessary for equations (l)-(8), the value of fore, grouping the last three terms contained within qaz has been projected from the equatorial plane into that the parentheses, -,L',r-1r'T+2,LT=O, and the dif- of the Moon's orbit. Hence, the direct subtraction of L/ ference between 2,al and 2,,L'r remains the,only sig- from qM1 is possible as indicated in the various equations. nificant fa 'ctor left inside. Since this difference is a As, subject to the Earth's rotation, the longitude of the negative angle prior to perigee-syzygy, it lies in the observer's position approaches and transits the meridian, fourth trigonometric quadrant, where the cosine is the difference between 2qar and 2,,L/ will become succes- positive. sively smaller and, on the meridian, as qaz and Z/ be- Because, at perigee-syzygy, this difference amounts to come equal, will converge on 0'. Since cos 0* - 1, this only a small increment above the value of cos, 0' pro- circumstance contributes its maximum additive influence duced by the cancellation of the other terms, the cosine to the resulting height of the tides. of the total function in parentheses will be only very One further factor-although a somewhat academic slightly less than its maximum possible value, +1. This one because of the small angles involved-serves also to maximum possible value of, the cosine function ensures decrease the angular difference between 7q, and oL/ as a full application of the constant ternis and variable co- the Moon approaches pezigee-syzygy and thus increase efficiehts by which it must be multiplied to evaluate the the value of the cosine function to a near-maximum. This entire first expression for X-Y' in the case of semi- is the effect of the Moon's varying speed in orbit. diurnal tides. Attention will now be given to these various The actual longitude value of ar may be either smaller coefficients and constants. than L/ (before catch-up therewith at perigee-syzygy) It has been seen in'a previous section that, at or larger (following perigee-syzygy). The difference qar perigee-syzygy, and as the result of lunar evection, minus L/ at any time represents the faster angular mo- the eccentricity e(E of the lunar orbit always increases. tion of the rotating Earth in catching up on the Moon 105 -revolving in orbit. Prior to perigee-syzygy, the greater At the same time, j6 andp are constants, and the 172 Strategic Role of Perigean Spring Tides, 1635-1976 value of u is a decimal taken to the fourth power and as in the case of semidiurnal tides. The terms in is always very small. Therefore, subject to the condi- parentheses again cancel out at perigee-syzygy, and tions of perigee-syzygy, allfactors in thefirstpart of the cos 00 reaches its maximum value. The remaining fac- equation for X2_Y2, the semidiurnal portion of the total tors 1 45, 4, and p are constants, and eq:, u, and v evection term, contribute their maximum values toward raising pring tides. are sm the height of the resulting perigean s all positive variables. Since the sum of the val- I (b.) The second expression (3) in the semidiurnal ues u4 and v1 will always be larger than the term portion of the total equation for the effect of lunar -4U2V2, all terms in the expression for the effect of lunar evection is algebraically subtractive. However, being evection on the fortnight@y @ype of tide thus contribute toward 15 increasing this ype of tide at times of perigee-syzygy. preceded by the coefficient 16,which is only 1/7th However, the fortnightly constituents of the tide are not of part of the numerical coefficient 105 in the first ex- major consequence. 16 pression (2), it represents but a small decrease in the 2. Lunar Variation Effects value of this first expression. The analysis of the effects of lunar variation upon The last three terms in the parentheses of equation (3) the heights of semidiurnal, diurnal, and -fortnightly are identical (with reversed algebraic signs only) to those tides can proceed in exactly the same way from equa- in the first expression (2) and, at perigee-syzygy, the tions (6)-(8) above. algebraic sum of these terms is 0'. Likewise, in taking the (a.) Within the parentheses of equation (6), the difference between 2qai and 2Xr-the first two terms in values of the terms 2,al and 2,L/ are exactly the the parentheses-the difference is still negative, and de- same as in the case of semidiurnal tides which are creasing in numerical value with approach to perigee- subject to lunar evection. The difference between syzygy. In evaluating the cosine function, as well as the these terms is also negative as before, and increases effects of p, e and u, the same general results apply (al- numerically with approach to perigee-syzygy. In the though with only 1/7th the total value) as those deduced present calse,ithe terms -2,L', and +2,r'T exactly from the first expression. cancel out at perigee-syzygy, leaving the cosine of 0* Thus, at times of perigee-syzygy, the net result of the and whatever small negative difference is represented combined expressions (2) and (3) associated with lunar by 2,af-20L,'. Again,; the cosine of this small negative evection serves to increase the height of the semidiurnal angle (in the fourth quadrant) yields a result for the tides., cosine function which is very nearly the maximum (C.) In the expression (4) for the effect of the lunar possible value. evection upon the diurnal type of tides, a sine func- Both the fraction L3 and the symbol P' are constants, tion rather than a cosine function is involved. As in 8 the expressions for the evectional effect on the semi- and the coefficient u' is numerically very small. Accord- diurnal tides, the algebraic sum of the terms within ingly, at a time of perigee-syzygy, all terms in this equation the parentheses is very small. The second term contribute to an increased value of the semidiurnal term 2,L/ is, however, approximately twice the magnitude X2 -Y' corresponding- to the' effects of lunar variation. of the first, qar, resulting in a somewhat larger value (b.) As noted, the effect of lunar variation on the of their small individual difference. Although the diurnal tides, represented by the term XZ1 is zero. effect of the lunar evection on diurnal tides thus acts (c.) Finally, there remains the influence of the in an opposite direction-to decrease the height of lunar variation upon the fortnightly tides, given by these tides-the result of this sine function, when the expression I (X2+y2-2 Z2). In this equation it 105 3 multiplied bythe constants f6 and p, and the small is obvious that, at a time of perigee-syzygy, the terms variable quantities e,[, U3 , and v is still quite small. +2@LT' and -2,LT' cancel out, leaving cos 0' as the This subtractive quanti@y will, however, prove to be of some cosine fun .ction, and the maximum possible value of importance in connection with a subsequent discussion of the unity for this part of the expression. lesser effect of perigee-syzygy upon the diurnal ype of tides. the factors I (d.) Finally, the influence of lunar evection. upon Since 3, 4, 3, and p are all constants, the fortnightly type of tides in equation (5) is seen to and since U4 and 0 are always positive and their be positive, additive, and to contain a cosine function sum > -4u' V2, this part of the total expression also is Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 1,73 always positive, and increasing as the value of either levels with lower latitude, becoming maximum at u or v increases. the Equator. Thus, lunar variation also contributes toward increasing Finally, there remain common multipliers for all the fortnight4y component of the tides at a time of perigee- three expressions, involving the constants 3/2, m(c, M,,, syzygy. and p,, and the parameters ac and e(c, which are vari- 3. Summary Analysis able because of perturbational effects. Since all of the constants have positive values, providing additive It now becomes important to see how these various influences, only some major variability in a([ or ea: tidal components, as affected by lunar evection and lunar could conceivably produce a downward adjustment variation, provide a sensible increase in water level, to in tide heights, or subtract from the enhanced tides create perigean spring (and, upon certain occasions later produced by the other factors in the tidal equation. to be discussed, proxigean spring) tides. For this,. it is Both a([ and e([ increase at a time of perigee-syzygy. necessary to go back to the original, full-length equation The magnitude of a([ becomes dynamically greater (I) of which these three types of tides form a part. due to the perturbations introduced by changing (a.) In a procedure opposite to that used for the tangential forces as the Moon attains a greater veloc- separate components of each expression, analysis will ity in orbit (its maximum is at perigee-syzygy) and begin with the last expression in the series and move as the value of a,[ itself increases.' toward thefirst. Theexpressionin X'+Y'-2Z' rep- resenting the fortnightly components already has been Where: seen to be at its maximum value at perigee-syzygy as V([ =the velocity of the Moon in orbit the result of both the lunar evection and lunar varia- k2= the universal (Gaussian) constant of grav- itation tion. The constants 1 and 1 in this last expression will 2 3 MED= the Earth's mass not decrease its maximum value. The remaining func- m(c =the Moon's mass tion I - sin2 is a function of the latitude of the r(c=the radius vector, or instantaneous distance G -0) of the center of the Moon from the center of tide station. As the value of 0 increases, the value of the Earth the term in parentheses decreases, so that the effect aa:=the semidiameter of the Moon's orbit of the entire expression is to increase the tide heights at perigee-syzygy to a greater extent at low latitudes, Then: with a maximum value at the Equator. VC=k1(M(D+m(1) 2 _ 1 (b.) Returning to the second expression in the series Q[ a(C for AS-that indicating the contribution of diurnal tides- it was found earlier that, in the case of lunar evection,, and the expression.for rate of change caused by the the effect was to reduce the height of the diurnal com- tangential force T exerted, on the Moon's orbit is ponent of the tides very slightly at a time of perigee- cla aa c)V 2a(c"Vc V syzygy. The presence of the lunar variation exercises no VT@W bt @kI(ME)+mq:) Yt influence at all upon the height of the diurnal tides. ('c.) Contrastingly, and by no means last in importance, which bears out the above statement concerning the there is the contribution to the increased height of the direct variation of aq: with V([ and with its own tides at time of perigee-syzygy provided by the semidiumal changing value. component. As will be revealed in subsequent tide-curve Both ac: and e(c reach a maximum due to the effects analyses, this component is actually that most significant of lunar evection at the time of perigee-syzygy. The to the technical concepts of this work. Moon also reaches its distance of closest monthly approach, q(c, to the Earth at perigee. This fact is The function X'-Y' was seen, in connection with expressed in the relationship both the lunar evection and lunar variation effects, to exercise an influence in augmenting the height of the tides at times of perigee-syzygy. The immediately preceding factor, COS2 0, is a function of the geo- Although the eccentricity of an ellipse in theory might assume any value from 0 (a circle) to I (a graphic latitude and, as in a similar case for the straight line), in the case of the Moon its average fortnightly tides, implies an increasing effect on tide value is 0.05490. The value of the eccentricity of 174 Strategic Role of Perigean Spring Tides, 1635-1976 the lunar orbit does, however, increase at a time of an elliptical orbit (and from certain dynamically induced perigee-syzygy, as explained in the earlier descriptive changes in the major axis of this orbit) has been seen in section dealing with the evectional perturbation. It chapter 3 to be measured in astronomy by a quantity may be seen from any number of actual observations, known as the equatorial horizontal parallax (7r). In brief or from tabular data appearing in The American review, this is defined as the angle (fig. 41) subtended, Ephemeris and Nautical Almanac, that the value of qq: at the distance of the Moon, by the Earth's equatorial becomes less at perigee-syzygy. The only remaining radius. As in the case of any object viewed at a distance, uncertainty, therefore, is an order-of-magnitude de- the smaller is the angle subtended, the farther away is termination of the corresponding effect of perigee- the object; conversely, the larger is the parallax angle, syzygy on the value of a,[. the closer the Moon is to the Earth. The conditions Using the data in this ephemeris, a representative creating the maximum value of the Moon's geocentric value of q(C (in units of Earth-radii) at a time of horizontal parallax and its closest possible approach to the perigee-syzygy is given as 55.877. From the preceding Earth are shown in this same figure. equation, substituting a value of e(C slightly greater In the last three equations of chapter 3, the effects of than its mean value in order to allow for the accre- the three terms involving the elliptic, evectional, and vari- tional effect of perigee-syzygy, and giving qr its above ational corrections to the lunar orbit were all shown as representative value, it is apparent that, throughout adding their near-maximum increments to the mean value an allowable range of e,,, the corresponding value of of 7r. This occurs whenever the angular differences be- a(,[ will always come out in excess of q(C. tween the longitudes of the Sun, Moon, and lunar perigee Since the value of a([ is always very much larger are close to zero (i.e., at the position of perigee-syzygy). than that of e(c, the relative influence of the two At the time of perigee-syzygy, the values of L1, r', and terms in raising the level of the tides at perigee- L are all very nearly the same. Hence, the trigonometric syzygy will be obvious by returning to the general differences L'-r' and L'-L in these parallax equations equation (1) previously given. Here the factors con- are equal to zero and, since cosine terms are involved in taining a(C and eq: are of the form both cases, the resulting corrections for the elliptic in- equality and the variational inequality reach their aa: and ( ), maximum additive 'values. Similarly, the value of P (L'+rl) -2L is also equal to zero, and again the cosine (1-ep) function provides a maximum additive value, this time where both appear in the denominators of fractional for the evectional inequality. It will now pro e meaningful to analyze the quan- terms. The fraction containing the much larger value titative extent ofvthese various corrections, and the of a(C in the denominator, when cubed, will always be far less than the term 1 - e 2(C (containing the small actual amount of change in the value of 7r resulting decimal value of e(C) when this term in the denomina- from their use. Therefore, taking the value of the tor of the second fraction is cubed. Hence, the increase mean horizontal parallax (transformed into seconds in e(C at perigee-syzygy is far more effective in raising the of. arc) as a base, and converting the coefficients e(r, -15 tides than the increase in aq: is in reducing them. m(C, and 8 in the successive additive terms from their In summation, the combined, net effect of all factors indicated radian equivalents to seconds of arc, a new associated with both lunar evection and lunar variation at equation for the actual or true parallax is set up. the time of perigee-syzygy is to raise the level of the tides- The terms involving LI-r' reduce to a single term in particularly those of the semidiurnal and fortnightly @Ypes. mean anomaly, and the angular difference L'-L be- The only small exceptions occur, as seen above, in comes the Moon's elongation from the Sun. In ternis the effect of the lunar variation upon diurnal tides and, of the corresponding symbolic quantities to be defined to an unimportant degree, the effect of the second below, the equation (with higher-order terms omitted) subtractive expression in the case of semidii-irnal tides. which expresses, in seconds of arc, the angular value of The Effect of Perigee-Syzygy Alignment in the Moon's equatorial horizontal parallax7r as a measure Increasing the Value of the Lunar Parallax of its distance from the Earth at Any time is: 3 The varying monthly distance of the Moon from the 7r'(c=3,422.608'+187' cos M+10' cos 2M Earth which results from the revolution of the Moon in +34' cos, (2D-M) +28' cos D+ Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 175 In this equation: of a small negative angle in the fourth quadrant is still 7r(C @ the true parallax of the- Moon. M= n(Ct rep- very nearly + 1. resents the mean anomaly, or angular separation in It is the lunar evection terin that is the most complex celestial longitude between the mean moon and the in the interpretation of parallax additions, since this term position of mean perigee. D is the angular separation involves the simultaneous positions of the Sun, the Moon, (elongation) in celestial longitude between the mean and lunar perigee. For example, because cos 188'= - 1, moon and the mean sun (i.e., the angular difference the fourth term is subtractive and the Moon's distance between their respective mean longitudes). from Earth is increased only by the remaining terms at At the Moon's position of alignment with the Earth first or third quarters (D=90', E. or W.) when the and Sun at new moon or full moon, the elongation is 0' Moon is simultaneously at perigee (M=00). Either of or 180', respectively; at first or third quarter moon, it these positions is called perigee-quadrature. At positions is approximately 90'. between D = 0' and D = 45', E. or W., and D = 13 5', E. In the case of both M and D, increasing positive angles or W., and 180', with the Moon also at perigee, the lunar in celestial longitude are measured eastward al ong the parallax is either decreasing or increasing in accordance ecliptic (counterclockwise as viewed from the north pole with whether the Moon 'is receding from or approaching of the ecliptic). The mean longitude of the Moon is syzygy. Between D=45' and D=90', E. or W., and measured in the ecliptic from the mean equinox of date D = 90' and D = 135', E. or W., with the Moon at peri- to the mean ascending. node of the lunar orbit, and then gee, the same relationship holds as in the previous sen- along the orbit. tence, but with the. parallax increasing with lunar recession Except for the effect of certain higher-order tenns from syzygy, and decreasing with approach thereto. omitted in the above series, the distance of the Moon For completeness, it must also be noted that when either from the Earth is seen to decrease for all conditions in new moon (D = 0') or full moon (D = 180') occurs in- which the angles M and D become small. The several dependently of perigee, some increment is added -to the parallactic terms will now be individually considered. parallax provided that M is not 90'. However, the paral- lax increases to a maximuni'value as M decreases toward 1. Effect of the Elliptic Inequality 0' or increases toward 180'. In the above total expression for lunar parallax, the The effect of evection on the lunar orbit is temporarily second and third periodic terms ( 18 7" cos M and 10" cos to increase its eccentricity about 20 percent-whenever the 2M) are called the elliptic terms, since they are a func- Sun crosses the line of apsides of the Moon's orbit (or tion of the Moon's motion in an ellipse, as well as the approximately 40 percent at the times of near-coincidence angular distance of the Moon at any time from the posi- of perigee and syzygy). Both the lunar perigee diftance tion of mean perigee in this ellipse (without any regard decreases (parallax becomes larger) and the apogee dis- to the lunar phase angle). With the approach of the tance increases (parallax becomes smaller) under these Moon to perigee, the angle M decreases, and each of the conditions. In a geometric relationship similar to that two cosine terms increases accordingly. At M=O', these distirmuishing between the manner of production of spring two terms add their maximum possible numerical incre- tides and neap tides (although enhanced perigean forces ments (187" and 10", respectively) to the parallax. are also involved in the present case), at perigee-quadra- ture or apogee-quadrature the eccentricity of the lunar 2. Effect of the Lunar Evection. orbit and parallax of the Moon are correspondingly de- Similarly, in the above equation, the term 34" cos creased, (See figs. 26A and 26B.) (2D - M) is known as the lunar evection. Whenever the Moon is at perigee, M=O', and, providing the corre- 3. Effect of the Lunar Variation sponding value of D is not 45' or 135', E. or W., some The cosine term in D alone is known as the lunar varia- positive increment is then always added to the Moon's tion. it is a function entirely of the lunar elongation, or parallax by this term. If the Moon at either new or full angular separation in longitude of the Moon from the Sun. phase (D=00 or 180') is coincidentally passing through Its i),resence in the above expression for parallax is to the position of perigee (M=O'), the cosine of the evec- cause the Moon's parallax to increase by a maximum of tion term reaches its maximum value, increasing the par- 28" (and the Moon's distance from the Earth to become correspondingly less) at both new and full phase, with a allax.by 34". Even close to M=00, the parallax correc-, minimum addition to the parallax at first or third quarter. tion is nearly maximum (with D=O'), since the cosine The addition to the parallax from this cause therefore. 176 Strategic Role of Perigean Spring Tides, 1635--1976 varies directly from 28" at new moon to 0" at first quarter, values. The,practical consequence is that the differences to 28" again at full moon, to 0" at third quarter; and to between true parallax and mean parallax also reach their 28" once more at new moon. No further complexities are greatest values at times of perigee-syzygy. involved. Furthermore, a second circumstance provides rein- 4. Summary Analysis forcement to a basic precept which appears variously throughout this treatise. The longer the period of time It is seen that several different lunar parallactic factors during which the angular differences between these re- can contribute toward reducing the distance of the Moon spective orbital positions remain near zero, the greater from the Earth at the time of a near-simultaneous align- will be the length of time in which the angular additions ment of either the new moon or full moon with perigee in to the lunar parallax remain at their maximum values. the condition known as perigee-syzygy. In general, an in- The fact that the Moon, the perigee position in its orbit, creasingly larger increment must be added to the base and the Sun are all apparently moving in the same direc- value of the lunar parallax the smaller is the elongation tion acts to favor such an extension in time. angle between Moon and Sun and/or the closer is the The comparative rates of daily angular motion affect- alignment (i.e., the smaller is the difference in time) be- ing the positions of the Moon, Sun, and lunar perigee are tween perigee and syzygy. important in this regard. The mean daily motion of the All of the preceding maximum increases in parallax Moon in longitude (13.176396'/') is far greater than result from the near-alignment of, and the reinforcing that of the Sun (0.985647 I/d) , and the mean daily mo- gravitational forces exerted by, the Earth and Sun upon tion of the Moon is far greater than the mean daily mo- the Moon's orbit at these times of perigee-syzygy. Such tion of perigee (+0. 111404'/'). gravitational reinforcements are seen to be a function of Summarizing the preceding numbered subsections-at the smallness of ( 1 ) the lunar anomaly and (2) the lunar times of perigee-syzygy, two distinct contributions toward elongation; and, especially, a very small difference be- the amplification of the tides result from the particular tween the angles (1) and (2). Practically speaking, the influence of solar perturbations upon the lunar orbit. separation-angle between the line of force action joining These are: (1) an increase in the lunar parallax, and a the Sun, Earth, and Moon (line of syzygies) and the per- corresponding decrease in the lunar distance from the turbed major axis (line of apsides) of the Moon's orbit Earth, thus augmenting the gravitational forces acting on can attain a value as small as 6 minutes in time. This the tidal waters; and (2) a lengthening of the period of happened, for example, in the perigee-syzygy alignment time within which these augmented tidal forces can act. of 19@ 1 March 4 (G.c.t.) .4 The two concepts cited provide widespread practical The actual dynamic effect of the combined gravita- support to a basic theory of tidal reinforcement. In a tional forces produced by such a near-alignment between variety of forms, but always involving the combination of perigee and syzygy is to increase the eccentricity of the (1) increased magnitude and (2) increased duration of Moon's orbit around the Earth. Since the perigee distance gravitational forces, they will find repeated -mention q of a celestial object moving in an elliptical orbit is re- throughout this volume in connection with the amplifica- lated to the eccentricity e of the orbit through the rela- tion of perigean spring tides. tionship q@_a(l-e), as e increaEes, q always decreases, At this point in the discussion, while considering factors for the reasons enumerated in the immediately preceding relevant to item 2, it is important to note the greater section. When perigee and syzygy occur at very nearly the length of time within which the Moon will be close to same time, the eccentricity of the Moon's orbit increases, alignment with the position of perigee if the respective and the value of q decreases in proportion. The Moon's true motions of the Moon and perigee, rather than their perigee distance from the Earth diminishes accordingly. mean motions, are considered. This will later be seen to he the cause of the situation Several of the effects resulting from the substitution of described in this volume as proxigee-syzygy. mean motions for true motions in tidal calculations will Two corollary factors are significant in relation to a form the subject of the section immediately following. circumstance to be reviewed quantitatively in chapter 5. (Note carefully the distinction 'between mean motions At the time of perigee-syzygy, when the differences be- and mean positions-, since the latter may be more readily tween these various alignment-angles become zero, the determined and adjusted.) The values adopted for vari- corrective terms necessary toconvert from mean parallax ous mean daily angular motions are given in part 11, to, true parallax simultaneously attain their maximum chapter 2. Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 177 The Concepts of Mean Motion vs. True between those months which are respectively close to, and Motion in Relation to the Earth, Moon, removed from, perigee-syzygy. (See fig. 28A.) and Lunar Perigee I At the same time that the- intramonthly and inter- monthly positions of perigee are oscillating back and forth The differences between true motion and mean motion in right ascension, the average position of perigee as rep- as these affect various aspects of the gravitational inter- resented by the curve as a whole is moving progressively relationships between Earth, Moon, and Sun are clearly forward (toward increasing values of right ascension) shown in four of the ensuing diagrams. Each diagram throughout the course of the year. It is from this net illustrates a particular phase of positional inaccuracy forward movement averaged over a long period of time resulting from these assumed average motions. that the adopted mean daily motion of perigee (amount- 1. The True Motion of Lunar Perigee ing to + 0. 111404'/ d) has been derived. Figure 28A is a plot of the motion of the true position However, the instantaneous, true angular velocity of the lunar perigee is extremely variable and attention al- of lunar perigee in units of right ascension during a period ready ha been drawn to the relationship between its of slightly more than 1 Y2 calendar years. These positions s of perigee were obtained from the positions of the Moon changing velocity and the apparent position of the Sun. itself in The American Ephemeris and Nautical Almanac. This is a perturbational effect, and comes about as a result The lunar positions were chosen for the exact times of of the dynamic influence of the Sun upon the Moon's perigee as tabulated in this same ephemeris. Since, at the orbit. time of perigee, the Moon must necessarily occupy this 2. Short-Period and Long-Period (Averaged) exact position in orbit, the tabulated right ascension of Perturbational Motions of Perigee the Moon corresponding to the tabulatedtime of perigee Figures 28A, 30, 32, and 33-which are based on the must also be the position of perigee. average true motion of perigee during several successive When these successive positions of perigee, one anom- anomalistic months-point to the necessity for applying a. alistic month apart, are plotted against the dates of oc- rigorous analytic solution to define the direction. and currence of perigee, and a smooth trace is made through amount of this motion at any one instant of time. The the resulting data-points, the sinuous curve of figure 28A purpose is to isolate those perturbational effects of shorter period occurring during a single monthly revolution of is obtained. This illustrates clearly that the position of the Moon. During such smaller intervals of time, the mo- perigee oscillates back and forth, fulfilling one complete tion of perigee may be either retrograde or direct as it is cycle of curve undulation in each 6.25-7.5 month period.a S inten-nittently over longer intervals, but the predominant The curves thus traced consistently show a point of inflec- (and hence also the net) motion of perigee is direct over tion and an enhanced,. average forward motion of perigee any extended period. corresponding to each case of extremely small perigee- The above-mentioned diagrams are plotted using the syzygy separation-interval. At these times, the position times of perigee (and either the corresponding right of the juxtaposed event (representing the Sun, Moon,and ascensions or celestial longitudes of the Moon and Sun) perigee aligned in very nearly the same right ascension) interpolated from The American Ephemeris and Nautical occurs exactly halfway along that portion of the curve Almanac. Iri-,this process, the positions of the Moon and having the least curvature and whose values are increas- Sun expressed in either of these coordinates for the time of ing in right ascension with increase in time. The period perigee are obtained directly from t he tabulated time of from one perigee-syzygy to the next is approximately the perigee. By definition, the positions of the Moon and anomalistic month of 27.6 days, but is quite variable perigee at the time indicated for the Moon's passage ' The commensurability between the anomalistic and synodic through perigee must be one and the same. However, such, months is such that, once a very close alignment of perigee-syzygy a graphical delineation as here represented showing the has occurred, the next comparably close (nonco ,nsecutive) alignment ensuing motion of perigee based on successive monthly will be either 6.25-6.50 or 7.25-7.50 synodic months later. The returns of the Moon to this position involves only an inter- exact period depends upon the sequential arrangement and separa- tion-intervals of intervening cases of perigee-syzygy and the varying polation by monthly intervals. lengths of the interposed anomalistic and synodic months (see ch. 6, Although this procedure is sufficiently accurate to indi- table 17). If the first extremely close alignment of perigee-syzygy cate, as a composite icture, the alternating direct and occurs at full moon, the next will occur at new moon; thereafter, p the phase will alternate in each succeeding set of such close align- retrograde motions of perigee during several successive ments. months and throughout the course of the year, the number 202-509 0 - 78 - 14 178 Strategic Role of Perigean Spring Tides, 1635-1976 OSCILLATORY MOTION AND PROGRESSION OF MOON'S TRUE PERIGEE AS SHOWN BY RIGHT ASCENSION DATA 1961 1961-1963 JUL 28.38 ATp 28.W AUG 25.76 10.30h 28.41 SEP 23.17 PERIGEE-SYZYGY (-8h) Aug 25.96 28.12 OCT 21.29 26.92 NOV 17.21 24-79 DEC 12.00 1962 27-58 JAN 8.58 28-34 FEB 5.92 2850 0 23.10h MAR 6.42 28A6 PERIGEE-SYZYGY (-0.5h) cc ui APR 3,88 ATP Mar 0.43 2 d w 28.20 MAY 2-08 Lu 27.46 !R MAY 29L54 In uj 25.29 Lu a JUN 23.83 2659 JUL20A2 27.91 AUG 1 Z33 28-34 SEP 14.67 28A6 0 OCT13.13 13.20h 28A "".",,.,,,...YIERIGEE-SYZYGY(-10h) NOV 10.58 Oct 13.32 28-13 DEC 8.71 1963 26.62 JAN 4.33 24.96 JAN 29L - h S 2h .5 Ih .5 oh 5 23h .5 22h .5 21h .5 APPARENT RIGHT ASCENSION OF PERIGEE FiGuRE 28A.-(Discussed in. text.) I Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 179 of data poi 'nts available is not sufficiently large, nor closely 3. The Special Motion of Perigee Close to the enough spaced, to reveal the pattern of perigee movement Position of Perigee-Syzygy Alignment over a few days at a time. Several different short-period The Sun's apparent annual motion brings it recurrently and long-period motions of perigee must be separately to the same celestial longitude as the line of apsides of the distinguished: lunar orbit, and at varying phases of the Moon. The result a. Analytic computations made possible from the re- is an induce 'd perturbation and angular displacement of duction formulae given in table 16B indicate a variable- the position of perigee. Since this perturbation is some- speed, short-period retrograde motion of perigee on either times' in a direct sense of rotation and sometimes in a retro- side of, and including, the time of perigee-syzygy. This grade sense, but with the greatest percentage of motion particular retrograde motion is the result of the perigee- being in the forward direction, the net, long-term effect is syzygy alignment itself, and occurs only in those lunations the mean progression of perigee around the lunar orbit in containing such alignments. a period of 8.849 tropical years. The average motion of b. The much larger and longer lasting net retrograde perigee is thus +0.111404'/day or approximately motion of perigee accompanying certain lunations in the + 3.043 742'/month. This perturbational angular velocity aforementioned diagrams is caused by the perturbational is a mean value based on the composite forces produced action of the Sun when it is at or nearly at right angles to at all possible positions, configurations, and alignments of the line of apsides, with the only opportunity for the Moon the Moon and Sun. to pass through perigee being at quadrature. (See the However, the perturbations of perigee are distinctively further clarification under "'a" in the explanatory notes affected by the alignment of the Sun, Earth, and Moon at in connection with figs. 28B, C, below.) perigee-syzygy as the Moon moves to a position near the c. Finally, the year-by-year net forward motion of line of apsides at the same time the Sun is along this line. perigee-resulting from an excess of direct motion in the The orbital velocity of the Moon always exceeds the ap- alternating forward and retrograde movements of perigee parent velocity resulting from the annual motion of the in those'months containing situations of close perigee- Sun as well as that of perigee in any phase of its 6sciHa- syzygy or perigee-quadrature, respectively-is exemplified tory motion. It is, therefore, the motion of the Moon by the continuing progression of this lunar position toward bringing this body, upon occasion, nearly simultaneously greater right ascensions or celestial longitudes. to the position of perigee and into a syzygy configuration The situation cippicted by these four diagrams accords, with the Earth and Sun which permits relatively short- with the general concept of the motion of perigee during period recurrences of perigee-syzygy alignment. This successive orbital revolutions of the Moon. This concept coincidence of events is responsible both for the phenome- i-, renrese@ted in cla-ic reference sources ranging from non of perigee-syzygy and the associated special perturba- Sir Isaac Newton's Principia, 1686 (proposition LXVI, tions of the lunar orbit. theorem XXVI, corollary VII, and subsequent manu- The increases in the eccentricity and sernimajor axis of scripts in the Portsmouth Collection) through Roger the Moon's orbit due to perturbations by the Sun at the Long's Astronomy in five volumes, 1764 (book 4, chap. 4, time of perigee-syzygy have been discussed previously. pp. 624-625) down to Forest Ray Moulton's Celestial The value of e can then increase by a maximum of 0.023 Mechanics. 2d rev. ed., 1914 (pp. 352-356). to a value 40 percent above its mean value (0-05490). More recent and comprehensive mathematical devel- Conversely, if the. Moon reaches perigee bwhile in a posi- opments of lunar theory have been made by George W. tion of quadrature with the Sun, the value of e is mini- Hill and Ernest W. Brown (see Reference Sources and mized (i.e., if the Sun is at a position along the extended notes, pt. If, ch. 3), together with the publication of the Improved Lunar Ephemeris, 1952-59 (1954) by the b It is noteworthy that although there are two orthogonal con- U.S. Naval Observatory. These advances-plus the in- figurations involving perigee and either of the quarter phases of the Moon which are possible at the time of quadrature, only one of novation of the high-speed electronic computer-have these represents true perigee-quadrature. The first (and true situa- made possible modern analyses such as those represented tion) is the actual arrival of the Moon at perigee while in either of its quarter phases, the Sun then being at right angles to the line by the algorithmic expressions contained in the supple- of apsides. The alternate, spurious relationship is the arrival of the ment to table 16 (table 16B-Refined Reduction For- Sun at the longitude of the Moon's perigee position in orbit, with mulae, para. 3). The retrograde motion of perigee brack- the first- or third-quarter moon located at right angles to the eting the time of perigee zygy alignment is described in line of apsides. It is the astronomically defined case, with the Moon -sy physically occupying the position of perigee, which is considered the immediately following section. here and is depicted in the top portion of fig. 28B. 180 Strategic Role of Perigean Spring Tides, 1635-1976 minor axis of the Moon's orbit while the Moon is at peri- The net result of this retrograde motion of perigee in the gee, the smallest possible eccentricity of the lunar orbit vicinity of perigee-syzygy is to prolong slightly the period of results) time in which perigee and syzygy are close to each other. The motion of perigee is also affected in varying de- Thus, immediately prior to a perigee-syzygy alignment, grees by solar perturbations. These perturbations are a with the motion of the Mocn and perigee being in opposite function of the phase angle between Earth, Moon, and directions and their relative (head-on) velocities increased to a maximum, a tendency exists to hasten the time at which Sun, and the closeness of alignment between the line of the Moon reaches the position of perigee-syzygy. Subse- syzygies and the line of apsides in the lunar orbit. quent to the perigee-syzygy alignment, with the motion of The general expression for the angular rate of motion of perigee in the same retrograde direction as before, but perigee at any relative longitude with respect to the Sun diminishing in velocity, the effect is to keep the'position and at any elongation of the Moon from the Sun is, very of perigee in the vicinity of syzygy for a slightly longer approximately: period. 6=+0.1 1 0/d The greater duration of time in which perigee remains in - 3.05'/4 COS (t-2D) the vicinity of syzygy, together with the dual reinforcement +0.96 1/d COS (t + 2D) of gravitational forces resulting from this near-alignment, +0.820/d COS (29-4D) yields a correspondingly increased tide-raising potential. -0.66'/d ccs t. . . . This phenomenon will be discussed further in chapter 6 along with other factors producing an extension of the in- (many higher-order terms have been neglected; note that terval during which enhanced gravitational forces act at the this motion is projected along the ecliptic rather than in time of perigee-syzygy. the Moon's orbit plane) where Explanation of the Short-Period 6=the angular rate of motion of perigee, in longitude, in Motions of Perigee degrees per day (a minus sign indicates retrograde motion, and a plus sign, direct motion) In figure 28B, the positions of an hypothetically unper- t=the angular distance, in longitude, of the Moon from turbed lunar orbit and that of the actual perturbed orbit are perigee. (Note: This value is equivalent to the "average" shown. The latter orbit is a function (among other factors) mean anomaly L used in the computer printout of of the changing value of e produced by the gravitational table 16-see the introduction to table 16.) attraction of the Sun. As has been shown earlier in this chapter, the perigee dis- D=the lunar elongation, or angular separation of the tanc@ (q) of the Moon from the Earth is given by: Moon from the Sun, in longitude (1 e) With the Moon at perigee, E@0', and this equation reduces to: where a and e represent the semimajor axis and eccentricity 6=-0.55-/d-2.07-/ dcos 2D of the lunar orbit, respectively. a. It also has been noted previously that, at the time of +1.26'/d COS 4D-0.26 1/d COS 6D. . . . perigee-quadrature, both the eccentricity and sernimajor At perigee-syzygy, the corresponding value for the rate of axis of the lunar orbit decrease (the former relatively faster motion of perigee becomes approximately: than the latter), the value of the perigee distance increases, At either new moon (E=O', D=O'.) or full moon (t=0' the curvature of this part of thelunar orbit becomes less, and the perturbed orbit lies outside the unperturbed orbit. D=1800), 6=-1.601'. And (with C@00, D=90') for This situation is illustrated in the top portion of figure perigee at first or third quarter, 6 =' + 3.00/d. 28B. (For comparison, the phenomena of perigee-quadrature Hence, with the Sun at right angles to the line of apsides, and perigee-syzygy have been plotted simultaneously on the and the Moon at perigee and either first or third quarter same diagram, and the primed symbols corresponding to the (see fig. 28B), the motion of perigee is direct, with an position of perigee-syzYgy alignment should, for the moment, angular velocity of approximately +3.01/d. In a situation be completely disregarded. These two phenomena do not, possible only in a different lunation, as the Moon approaches of course 'occur together in any single lunation.) perigee-syzygy at either new or full phase, an induced small In the present analysis, the position M, corresponds to retrograde motion increases steadily in magnitude, reaching the position of the Moon at a time approximately 7 days a maximum velocity of - 1.60/d at the time of perigee- prior to the alignment of the Moon with the Sun at con- syzygy. (See also par. I under "Tidal Force Evaluat- Junction. The assumption is here made that no perturbing effects on the lunar orbit due to the Sun are present. The ing in ch. 5.) Thereafter, the direction of niction position P, similarly indicates the original position of perigee remains retrograde, but the negative angular velocity toward which the Moon is moving in this undisturbed orbit. diminishes toward zero and then turns positive. At apogee- However', subject to the action of solar perturbations, the syzygy, 6= +3.3'/d, approximately. value of q increases and the perturbed orbit results. To con- Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 181 MOTION OF LUNAR PERIGEE 7 B. 7 0 0 PERTURBED ORBIT (P PO MO P7 M7 UNPERTURBED ORBIT M3 q0 q7 M,0 LINE OF S,0- - - - - - - - - - - - - - - - - - - - P,0 q'o E APSIDES A'0 r \ts P3 SO FIGURE 28B.-The positions of perigee-syzygy (P'oM',,) and perigee-quadrature (P,,M@) are plotted on the same diagram to show the opposite motions of perigee-retrograde at perigee-syzygy and direct at perige@,-quadrature. The location of the perturbed orbit outside the unperturbed orbit at quadrature, inside it at conjunction also is indicated. See the text discussion under "Explanation of the Short-Period Motions of Perigee." form with this change in the distance of the Moon, beyond est during the perigee portion of its orbit, and it covers this the position M, the p ath of the Moon swings outward from portion of the orbit in the least number of days. Hence, the the Earth, producing the new orbital arc M7P11- Matching cumulative effect of the motion of perigee in that half of the Moon's motion in the same period of time, the position the orbit containing perigee is the least and is overshadowed of perigee moves outward to establish an increased perigee by the cumulative effect of perigee motion during the distance q(, at position Po, very close to Mo. It is readily Moon's passage through the opposite half of its orbit, com- apparent from the diagram that the arc distance M,Mo pleted over a greater number of days. is longer than the original span of the Moon's motion b. It has further been demonstrated previously that, at M7P1 necessary to reach perigee. the time of perigee-syzygy, the value of e increases in the The net effect is to displace the original perigee position lunar orbit due to the effect of solar perturbations, and at a P,,along the arc P,P(,, which possesses a continuously in- faster rate than a increases. A retrograde velocity of perigee creasing radius with respect to the Earth. This displace- becomes quantitatively significant at M,, some few days ment is evidenced as a direct motion of the lunar perigee. prior to lunar conjunction with the Sun, and reaches its The@'amount of the forward movement is a maximum in maximum value when the perigee-syzygy alignment (M.') this case neax perigee-quadrature. is reached. In this approach interval, the value of q continu- This motion represents a short-period displacement of ously decreases (i.e., the lunar parallax becomes steadily perigee during only a portion of one lunation. As such, it greater). provides only a partial contribution to the average perigee In figure 28C, the path of the Moon close to the time of motion over the entire lunation and throughout successive perigee-syzygy has been enlarged from figure 28B in order lunations. These short-period motions of perigee near peri- better to show the relationships between the perturbed and gee-quadrature and perigee-syzygy arc, as a seeming para- unperturbed orbits of the Moon. In this figure, the posi- dox, exactly opposite to the average perigee-to-perigee.mo- tion P, represents the original position of perigee toward tions shown in figures 30 and 32" It must be remembered, which the Moon is moving in its undisturbed orbit, from its however, that the angular velocity of the Moon is the great- initial position M,. The distance qo' represents the corre- 182 Strategic Role of Perigean Spring Tides, 1635-1976 lunar line of apsides corresponding to a very dose align- C. ment of perigee-syzygy (1962 Mar. 6.5), as well as the P3 S, positions of the Sun during the course of this same year, 0 S1. are indicated as the Sun apparently revolves around the /101 Earth in consequence of the Earth's actual annual revolu- tion around the Sun. The family of concentric ellipses*shown represents the q3 PO successive monthly cycles of revolution of the Moon. Dou- wo ble-shafted arrows indicate the corresponding monthly M 3 motions of perigee. Figures 29 and 31 portray the mean motions of perigee, as they are assumed, for convenience q10 in computation, in tidal theory. Figures 30 and 32 repre- sent the true motions of perigee. As noted earlier, succes- E sive lunar orbitings are in no sense re-entrant ones, but continuously fail to close on the same position as the result of perturbations encountered in any one revolution. Ac- cordingly-without loss in factual integrity--the Moon FIGURE 28C.-Enlargement of the left portion of figure may, for greater case in graphic presentation, be depicted 28B, defining the retrograde motion of perigee at the time as revolving, month by month, in the separate orbits in- of perigee-syzygy. dicated. These are drawn to successively smaller sizes to sponding perigee distance of the Moon from the Earth in prevent overlapping and confusing crossovers between the this undisturbed orbit. In a period of I day t .he Sun, in its adjoining elliptical paths. apparent annual motion eastward in the sky, has moved According to the assumption of a perturbationally in- from S,' to S,,'. duced, but constant, mean daily motion, the Moon's peri- As the Moon also moves ea'stward toward the position of gee is conceived to move in a counterclockwise direction perigee-syzygy alignment (M,'S,,' or Po'), the Sun's pertur- in the orbital plane, with the previously stated mean bational influence due to this alignment acts to increase the eccentricity of the lunar orbit, correspondingly reducing angular velocity of +0.1114041/d. The rather sizable the value of q. The path of the Moon beyond M@, in tu Irn differences between this value, adopted for computational swings nearer to the Earth to accommodate this reduction convenience, and the constantly changing lunar velocity in the perigee distance, thus producing the new orbital arc which actually prevails is revealed by a comparison of M,Mo'. It is obvious that the arc M,M,' necessary for the figures 29 and 31 with figures 30 and 32. Moon to reach the new position of minimum distance (q.') When the true motion of perigee is plotted, over suc- from the Earth is shorter than the original arc M3PI- The physical result is to displace the original perigee posi- cessive months, from the same data used to construct tion P@, along the arc P@Po' possessing a continuously short- figures 30 and 32, the considerable differences between ening radius with respect to the Earth. This displacement the true and mean motions is evident. The maximum true action is evidenced as a retrograde motion of the lunar motion in orbit may be determined by taking the total perigee. The amount of the retrograde displacement be- angular distance through which the Moon revolves in comes greater, the greater is the reduction of q (i.e., the closer the position of perigee is to alignment with syzygy). orbit during an anomalistic month (a time period which The maximum retrograde motion therefore occurs at the is itself subject to a considerable variation in length-see time of perigee-syzygy. After the Moon passes through this table 17), and dividing this angle by the exact period position (P,,'), the retrograde motion of perigee decreases between consecutive perigee-syzygies. By this means, the again. true average angular velocity of perigee in an anomalis- tic month containing a close perigee-syzygy alignment is 1. Comparison of True and Mean Motions found to be some 0.55'/', or approximately five times Another way of representing the difference between the that assumed for its mean motion during this same mean and true motions of perigee is by means of a graphic interval. comparison of the relative motions of the Sun and Moon, Selecting, as a starting point, and representative ex- plotted in the true and mean systems of reckoning. These ample, a date when the position of the Sun first comes comparative motions are illustrated in figures 29-30 and within less than 30' of alignment of the line of apsides 31-32. In these diagrams, the angular position of the of the lunar orbit (on 1962 Jan. 8.5, in figure 30), the Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 183 SUN. JUN 24.0 MAY 29.5 MAY 2.0 A-PERIGEE 0 (D 0 92" 67* 3T JUL 20.5 0 lie APR 4.0 0 IT cr AUG 175 0 145' 35@ _-A 34 MAR 6.5 24 41f 0 A ------ ------ -- 4.0. MAR 34f 344! ------ - - 6.5 FEB 1 339 6.0 ... JAN ----------------- --- - ----- - --- ------- 8,5 SEP 14.5 Q 173* FEB 6.0 0 316* CT 13.0 0 201 JAN 8S LONGITUDES GIVEN ARE 0 MEAN MOTION OF THE MEAN GEOMETRIC POSITIONS NOV 10.5 DEC 8.5 288r LUNAR LINE OF APSIDES REFERRED TO THE MEAN 0 0 1962 EQUINOX OF DATE 22T 257' JAN 8.5 - JUN 24.0 FIGURE 29.-(Discussed in text.) subsequent motion of lunar perigee can be closely ob- than three successive months (or, at the absolute maxi- served. As the Ion itude of the Sun comes increasingly mum, during four successive months) in any one peri ee- 9 ..g closer to that of the perigee position during the immedi- syzygy cycle. ately following months, it is obvious that a marked accel- Following upon these maxima in perigee motion, the eration occurs in the true motion of perigee. (The pengec separation-time between perigee and syzygy becomes attains an average angular velocity of some 16' in 28.5 larger, and the forward motion of perigee diminishes. days, or 0.56'/' between the perigee-syzygy alignments Some 4V2 to 5 months after the first considerable forward of Jan. 8.5 and Feb. 6.0 depicted in figure 30.) motion of perigee began, this motion reduces to 0', and This forward motion of the line of apsides (and with thereafter reverses in direction. it the Moon's perigee position) continues for several suc- Thereafter, the motion of perigee continues in a retro- cessive anornalistic months (at an average angular veloc- grade direction,and again this motion accelerates (in the ity of between 0.54'/' and 0.56' /d in the example period of regression illustrated in fig. 32, for example,-to shown). The largest forward angular motions of peri- an average angular velocity of 0.98'/'). The retrograde ,gee- are generally centered around that perigee-syzygy motion is maximum at the time the Sun lies approximately date (of several always occurring in a row) when the at a right angle to the line of apsides. The motion dimin- separation-time between perigee and syzygy is the least ishes rapidly as the longitude angle between the Sun and of the series. Such maximum values in the forward angu- perigee further increases. (The latter angle is nearly that lar motion of perigee usually do not occur during more which, in the plane of the lunar orbit, separates the Moon 184 Strategic Role of Perigean Spring Tides, 1635-1976 SUN C) MAY 29.5 MAY 20 APR 4.0 A=PERIGEE 4f JUN 24.0 (D MAR 6.5 IV (D 345* 'AY JUL 20.5 E) 117' 331 i@ela FES 6.0 0 31 317* AUG IZ5 (D 144@ JAN 8.5 288' 45 7 LONGITUDES GIVEN ARE TRUE MOTION OF THE APPARENT GEOCENTRIC OCT 13.0 NOV 10.5 DEC 8.5 LUNAR LINE OF APSIDES POSITIONS REFERRED TO (D (D 0 1962 THE TRUE EQUINOX OF DATE 199 228' 256 JAN 8.5-JUN 24.0 FIGURE 30- (Discussed in text.) from perigee and is known as the true anomaly.) By con- event of this type depicted in figure 30, and which was trast with the direct motion of the line of apsides, the associated with the great mid-Atlantic tidal flooding of retrograde motion usually lasts for only two or, at most, 1962 March 6.5. three months between the two forward-moving cycles of In this diagram, the mean motion of perigee is de- perigee which normally occur in any one calendar year. rivable from its successive positions in mean longitude Since the forward (counterclockwise) motion of perigee along the straight line a-z. The corresponding true motion takes place during approximately 4V2 months of each of perigee may be obtained by taking differences in true year, while the retrograde motion generally occupies only longitude from the curve b-y. Forward motion occurs 2-3 months, the net result is an average, cumulative for- from b to n, retrograde from n to q. ward motion of the axis connecting perigee and apogee 5. The Minor Sinusoidal Variation Between True which is known as the progression of the lunar apsides. and Mean Longitude Both the averaged, long-range, forward motion of peri- Finally, the effect of the previously discussed perturba- gee and the intermittent retrograde movement may be tions in causing a small but measurable difference be- furthergraphically illustrated by preparing, for the same tween the mean and true longitudinal positions of the dose perigee-syzygy situation in each case, a comparative Moon is shown in figure 34. The diagram represents a plot of the true and mean motions of perigee with respect period of approximately 2 lunar months. to the time, as shown in figure 33. This diagram repre- It is immediately apparent that, in terms of the small sents, in a somewhat different form, the same astronomical incremental function in longitude it is necessary to apply Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 185 SUN-C) JUN 24.0 MAY 29.5 A. PERIGEE JUL 20.5 0 0 0 92* 67' 1187 MAY 2D 0. 39 AUG 17.5 0 145" APR 4.0 0 12, '6 A s-6 3 -@Ep ------ ce 14.5 WUG 359r or SEP 14S .......... . ............... 17.5 jUC- 356' 0 20.5 N 354 . JU;I 173' 24.0 . ......... AY ............................. 29.5 .................. MAR 6.5 0 3447 OCT 13.0 0 201' FEB 6.0 0 316' LONGITUDES GIVEN ARE NOV 10.5 MEAN MOTION OF THE MEAN GEOMETRIC POSITIONS 0 DEC 8.5 JAN 8 *5 LUNAR LINE OF APSIDES REFERRED TO THE MEAN 229 0 (2) 1962-63 EOUINOX OF DATE 257* 286@ MAY 29.5 -JAN 4.5 FiGURE 3 1.- (Discussed in text.) in order to convert mean positions of the Moon to true Subordinate and Counterproductive positions, -the correction becomes 0'0' at times of both perigee and apogee. At these two positions in every luna- Effects on Perigean Spring Tides tion, the straight line representing mean longitudes of the Certain ancillary tidal influences are in no way as- Moon and the sinusoidal curve representing the deviation signable as direct causal factors in the production of of positions in true longitude from those in mean longi- perigean spring tides. However, because of their general tude come together. Hence, any variation in lunar gravitational force or dynamic influence upon all types of tides, they may play in tide-raising potential resulting from the difference in a significant role in either increasing or decreasing the position of the Moon in these individual coordinate sys- amplitude of perigean spring tides after these have been tems is of no consequence at either of these two lunar generated by their own causal factors. Other actions apse positions, or at times of perigee-syzygy. present among the broad range of gravitational forces mav be definitely counterproductive in connection with Paradoxically, the effect is exactly the opposite to that perigee springs, or any other tides. In this concept of encountered under the analogous requirement for.apply- providing a potential modification of existing forces and ing corrections to mean parallax to achieve true parallax. actions, these secondary influences will be included here. In this previously discussed case, the differences between Other important astronomical, oceanographic, and true and mean parallax were found to reach a maximum hydrographic factors contributing to the maximization of at times of perigee-syzygy. perigean spring tides will be discussed in the next chapter, 186 Strategie Role of Perigean Spring Tides, 1635-1976 SUN=O AUG 17.5 JUL 20.5 JUN 24.0 '#JA( 70 A= PERIGEE (D 0 0 (D - "S MAY 29.5 144@ 117 92' (D 68' MAY 2.0 0 41' SEP 14.5 0 171' A @sl @g 192'.18cf.lZ .6 APR 4.0 . ....................... ..................... IT ---- ---- - 14 . MAY 29.5 0 1 14- OCT 13.0 (FM) 0 199* '3S6' ----------- CIP 0, MAR 6.5 NOV 105 0 0 345' 228* LONGITUDES GIVEN ARE TRUE MOTION OF THE APPARENT GEOCENTRIC DEC 8 5 JAN 8.5 FEB 6.0 WNAR LINE OF APSIDES POSITIONS REFERRED TO Q Q 0 1962-63 THE TRUE EOUINOX OF DATEI 256' 28Er 317' MAY 29.S-JAN 4.5 FIGURE 32.-(Discussed in text.) and both the additive and partial amplitude-negating is given by a([, so that the geographic latitude of the effects of wind and atmospheric pressure will be covered observation station, o=0+6([. The distance of the in chapter 7. place of observation from the center of the Earth is designated by,p. In the plane of the paper (i.e., with the Moon on the Effects of Declination on the local meridian of the place), the total gravitational force Tide-Raising Forces of the Moon at S is indicated by the force vector F, which is resolvable into two components X, parallel to X, In figure 35, a tidal force reference system is defined and Y, parallel to y. The angle H represents the angular by the rectangular coordinate axes x, y, and z. In this altitude of the Moon above the horizon. D is the distance reference system, the xz plane represents that of the of the observing position from the center of the Moon, Moon's orbit and xy (the plane of the paper) a plane and R is the distance between the center of the Ear .th, 0, at right angles thereto, containing the zenith of the and the centerof the Moon, C. observing station S, located on the surface of the The respective tide-raising components of force in Earth. The angle o in the xy plane represents the terms of X, Y and Z are: angular distance of the zenith above the Moon's orbital plane, and therefore is also equal to the zenith X= 2x Y= -Y; Z@ - Z distance of the Moon. The declination of the Moon K3_ R3 Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 187 Since the gravitational force potential is related Since, for the present purpose, it may be assumed to each of these components by the relationships that p=p: X= ou Y= au Z= au U= g m C P`' P" (3 COS' 0- 1) VX; _Y; a-Z) W_) W _Y the value of this potential can be derived by integra- Further, in dealing with the height AS through tion as follows: which any unit mass m, of the equilibrium tidal waters au au ou will be raised by the potential energy against the U= YX + FY + -Z gravitational acceleration g, U=m,gAS or, since m, I 2x dx- f y dy-1 z dz equals unity, U R-3 f IF3 R3 f As_ 9 (2x'-y 2- Z2) COS2 M3 P' (3 [2X2+X2-(Xl+y2+Z2)]. Developing this solution further by means of a standard 2R3 astronomical triangle on the celestial sphere, the Moon is Or, since p2=X2+ yl+Z2, now represented as being at a point B, on the celestial U 1 (3X2_P2). equator, such that 8-0'. The astronomical triangle is Ora composed of the points P (the celestial pole), B (the posi- Since x = p COS 0, X1=P2 COS2 0; 3x'=3p' COS' 0; tion of the Moon), and Z (the zenith of the observer). W-p2=3 P2 COSI 8_P2=p1 (3 COS2 0-1) Employing the equation (pt. 11, ch. 1) for conversion P 2(3 cos'0-1) from the horizon system to the equatorial system of ..2p= 2R3 coordinates, and since 0 is equivalent to the zenith Introducing appropriate coefficients representing distance, r(c: the effects of the relative masses of the Moon and COS Ocos P(C=sin S(C sin O+cos 8(c COS h(c COS Earth on the gravitational force potential U respon- where ([the zenith distance of the Moon sible for the tides, where: 0, the angular distance of the zenith above g=the acceleration of gravity' the plane of the Moon's orbit m([=the mass of the Moon 5([the lunar declination M(D= the mass of the Earth h(c the hour angle of the Moon p=the radius of the Earth, assumed to be a .0=--the geographic latitude of the observing true sphere position P,=the mean radius of the Earth, regarded as Substituting the trigonometric portion of the tidal a standard spheroid of revolution, with force potential, (3 cos2 o- 1) from its previous deri- Then: mass M,9 vation, and letting U g (mc 3 2 20 3 cos2 0-1=3 [sin ba: sin 0 (P) (3 COS 1) Y 2p, + COS b(c COS h(c 0]2 According to the us Iual convention, the term gravity, here de- 3 [sin 2 ba: sin2 0 noted symbolically by g, implies a modification of the universal + 2 (sin b(c COS 6([ sin 0 COS 0 COS h(c) force of gravitation to include certain other dynamic effects which +COS2 b(C COS' h (E cos' 01 are active beneath, on, or above the Earth's surface. The central I force of gravitational attraction due to the mass of the Earth is Since sin b(I COS 8([=@ sin 26(C reduced both by centrifugal force associated with the rotating Earth and by varying distance from the source of attraction result- ing from a flattening in the Earth's figure toward the poles. The and sin 0 COS 0 sin 20, term gravitation is reserved for the general gravitational field in r outer space, exclusive of these terrestrial effects. The universal or AS=28qLs 3 sin' 2b(c sin' 0 Gaussian constant of gravitation, denoted by k, is used in some 2 me R) L equations involving the comparative ratios of the gravitational forces 3 of extraterrestrial bodies (e.g., the Moon and Sun). It may be noted + (sin 23: sin 20 COS h([) parenthetically that the symbol g also has been used on occasion 2 in the text to indicate mean anomaly, a standard, although less +3 COS2 b(C COS2 hj: COS' 1. frequent usage. 188 Strategic Role of Perigean Spring Tides, 1635-1976 ANNUAL PROGRESSION OF SYZYGIES AND APSIDES (IN TRUE LONGITUDE AND MEAN LONGITUDE) 206 -1962-, u i sof A 111 E I Jun 1.751 0 t 16 (Off 140P 1 11 95 126 1 10 101 80f JU 110.75 66 k 4 W Y FM @ct 13.52 W W h 11 n X z 0* @PERIGEE @j 0@ 360F P 0 Mar 6.42 r z ------- Oct 13.12 340f._2L ------0------ 'Ps @ NM Ma r 6.44 1 320P 300f 2F3Cf 266 t 2406f PS I PS 01 iMar 6.43 1 Oct 13.321-.5 1 IOD BETWEEN PERIGOE-SYZYGI if (21Z0.9 220f 0 daysl 200f JAN FEB MAR APR MAY I JUN JUL AUG SEP OCT NOV DEC FIGURE 33.-(Discussed in text.) For a location at the Equator, 0=0, and in this Similarly, when the Moon is on the meridian, h([=O* position: which has a significance in tide-raising action de- scribed particularly in chapter 6. For h(C=O: 3 XP' 3 as=L"@Mfz @_' [3 COS2 SC: COS2 hc-11. as@L-(Mmc- ky) [3 cos' 5,Z-11 2 VM@XR) R R Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 189 COMPARISON BETWEEN TRUE AND MEAN LONGITUDES OF THE MOON WITH POSITION IN ORBIT 60F PERIGEE Mar SA2 T L 345.10, 40' ML 345.31' 20' 300P 80' 1962 True Mean Mar Long. Long. 60' P 6.42 345.1 Op 345.3f P-S 6.43 345.25 345.45 N M 6.44 345.40 345.60 40' F 0 13.19 82.07 74.62 A 19.88 163.06 162.65 F M 21.33 180.22 181.82 20P L 0 2%17 277.94 285.18 200' 8 APOGEE Feb.20.88 APOGEE Z TL 166.09, Mar 19.88 q 66 ML 166.88' T L 163.03' ML 162.650 40f 20' 1962 True Mean Feb Long. Long. loop NM 5.00 315.609 317.71- P-S 5.46 322.54 323.75 P 5.92 329.49 329.79 8 F 0 11.65 52.37 45.39 of F M 19.55 150.37 149.48 A 20.88 166.09 166.49 L 0 27.66 248.59 256.28 40f 20' 6 FEB - MAR APR 1 8 10 12 14 16 18 20 22 24 26 28 1 2 4 6 8 10 12 14 16 18 20 22 24 26, 28 30 1 FiGURE 34.- (Discussed in text.) or the tidal height is a fixed function of the constants at which the orbit of the Moon crosses the'ecliptic.) The indicated, and varies directly only as cos' a([. slow, retrograde motion of the nodes is the result of perturbations induced in the lunar orbit by the Sun's Maximization of Declination in the 18.6- gravitational influence. Year Period of the Lunar Nodical Cycle Since the Moon's orbit is inclined to the ecliptic by some 5'9' (the actual value may range from 4'56' to Another tide-modifying factor which has a direct con- 5'20' due to other perturbations), the Sun continuously nection with the lunar declinational effects above de- strives to pull the plane of the Moon's orbit into its own scribed is the lunar nodical cycle. This involves a periodic plane, that of the ecliptic. However, in accordance with revolution of the Moon's line of nodes in a westerly or the laws of precessional motion in rotating bodies, in- retrograde direction around the lunar orbit. (The line stead of this action being completed, an alternate motion of nodes is the axis joining the two points, 180' apart, is introduced at right angles to the applied force. This 190 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR DECLINATIONAL EFFECT ON THE TIDE-RAISING FORCE y /Z P X S Y D P ............. .....C _-X R ------- - MOON EARTH z NOTE: FOR CLARITY IN GRAPHICAL REPRESENTATION, THE MOON IS SHOWN IN A POSITION CLOSER TO THE EARTH AND AT A GREATER DECLINATION THAN IT EVER ACTUALLY ATTAINS. FIGuRE 35. '(Discussed in text.) results in a revolution of the pole of. the Moon's orbit Thus, when the Moon's ascending node coincides with around the pole of the ecliptic. the vernal equinox, the maximum declination (either pos- At the same time, rather than any permanent change itive or negative) of the Moon is 23.50+5', or 28.5'. occurring in the inclination of the Moon's orbit, the nodes When the Moon's descending node coincides with the shift westward and complete one circuit of the lunar orbit vernal equinox-and the ascending node coincides with in 18.6 years. the autumnal equinox-the value of the maximum decli- This regression of the nodes along the ecliptic gradually nation is only 23.5'-5', or 18.5'. The first condition re- alters the maximum angle which the orbit of the Moon sults in a corresponding range of 57' in lunar meridian can make with the celestial equator. The average angle altitude; the second produces a range in meridian altitude of inclination of the Moon's orbit with the ecliptic is the of only about 37'. aforementioned 5'9', and the average angle between the The above-mentioned variations in lunar declination. celestial equator and the ecliptic (termed the obliquity involving a maximum semimonthly range of -28.5' to of the ecliptic) is 23'27'. Because of the geometric rela- + 2 8.5', and a minimum semimonthly range of - 18.5' tionships involved (see fig. 36), the separation between to +18.5' occur, under the appropriate circumstances the lunar orbit and the celestial equator may range, over at times which are one-half of a nodical cycle, or 9.3 years one-half the nodical cycle, from the direct sum of these apart. The effect of this variation in increasing or decreas- angles to the simple difference between them. ing the Moon's orbital velocity at certain epochs in the Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 191 nodical cycle is shown at the end of the present chapter The foregoing statement, it is emphasized, defines an (Case 2). This readily verifiable phenomenon leads quite event of lesser statistical probability, but does not imply naturally to another related aspect of the lunar declina- total exclusion. This assertion should in no way be inter- tional influence on the tides which is of direct importance preted to mean that tidal flooding will not ensue when a to the present discussion. situation of large lunar declination occurs at the same time as perigee-syzygy. An exception is particularly possible Aside From a Lack of Onshore Winds, Why where the Sun is in an exactly opposite (or similar) Does Coastal Flooding Not Occur With declination and therefore in the same plane as the Moon, Every Perigean Spring Tide? and the production of a large lunar parallax results from The principles of scientific method require the applica- this circumstance (see table 13). Furthermore, cohditions tion of a series of negative as well as positive tests for the may exist where the additional tidal range induced by adequacy of any scientific hypothesis. Specifically, this the phenomenon of diurnal inequality associated with a necessitates the fulfillment of both the negative and posi- large lunar declination is locally important to the pro- duction. of flooding. Finally, yet another exception to the tive premises in the classic set of syllogisms: "If p is true, previously stated example exists in the second case of q is true;' if P is false, q is false," described as equivalent the two which follow, illustrating the oppositely acting propositions in deductive logic. effects of an extreme lunar declination. As space permits, an effort will be made throughout It is necessary, at this point, to distinguish between this work to include such a positive-negative balance of these two different circumstances which arise from the supporting checks. (A meaningful example is the inclu- 18.6-year nodical cycle and, which involve, respectively, sion'in table 27, of a realistic sampling of cases of ex- the association of a perigee-syzygy situation with: tremely high astronomical flooding potential, yet total 1. A path of extreme lunar declination, resulting in a absence of any tidal flooding, despite the extremely close corresponding very large inclination between the lunar perigee-syzygy alignments. These situations are clearly ex- orbit and the celestial equator-with the Moon being on plainable, however, by means of the accompanying or near the celestial equator at the time of perigee-syzygy. weather maps as lacking the necessary- contribution of on- 2. A flattened peak of the declination curve, combined shore winds.) The first of two examples entails an equally accountable with an extreme maximum in lunar declination, thereby reduction in the flooding potential of perigean spring tides permitting a correspondingly large lunar motion in right under certain conditions. The accompanying analysis also ascension-the Moon being' at this high declination at helps to answer the very cogent question "Why does tidal the time of perigee-syzygy. flooding not occur at every dose alignment of perigee and These two cases will be discussed from their contrasting syzygy?" points of view, first in an analytic fashion, and then by the Each of the examples under discussion involves the ap- application of actual numerical data. parent daily motion of the Moon on the celestial sphere. The first example selected for investigation occurred on In both instances, actual daily changes in lunar right 1950 April. 2. In this case, the coincidence between the, ascension have been obtained from The American ascending node of the lunar orbit and the vernal equinox Ephemeris and Nautical Almanac for the dates concerned. just prior thereto produced (1) an extreme declination As an extension of the similar ' although more general of the Moon and, in consequence, (2) a maximum angle example in part 11 chap@er 2, it is now possible to evaluate of inclination between the Moon's orbit and the celestial these two separate situations in which the combined ef- equator. fects of the Earth's diurnal rotation and the Moon's orbital The situation presented is one in which, near the celes- motion are incorporated. tial equator, the component of declinational movement One definitely significant aspect shown by the results of of the Moon (see analogous curves of figs. 44, 152) is the subsequent computations is the strong likelihood that very large, while the movement in right ascen@ion as a a perigee-syzygy alignment occurring in the first of'the function of steep orbital inclination alone is small, As two circumstances under consideration will have a rela- noted earlier, unless this factor is offset by a large tively small tidal flooding potential. This is despite the parallax (e.g., at perigee-syzygy) it tends to reduce the simultaneous presence of other generally favorable tide- possibility for a protracted tidal day. The declinational building forces and conditions. motion of the Moon likewise remains large throughout 192 Strategic Role of Perigean Spring Tides, 1635-1976 most of the lunation, producing relatively sharp-pointed and a smaller maximum. These may occur for either peaks at the two declination maxima. This results in com- (+) or (-) values of B([ and without regard to the paratively short periods of time in which the corresponding sign of Ab([. The two distinct maxima having dif- motion of the Moon in right ascension remains at or near ferent amplitudes are a function of the Moon's its own largest values (i.e., at the top of the crest and at varying velocity in its elliptical orbit. .the bottom of the trough of the curve, where the slope is During the anornalistic month, the Moon moves zero, and where most of the Moon's motion is in right the fastest in its orbit (and therefore in either celestial ascension). longitude or right ascension)-from the effect of parallax alone--in a period extending from approxi- Combined Effect of Changing Parallax and mately 5 days before perigee to 5 days after perigee. Large Declination on the Moon's Hourly Conversely, the Moon's apparent motion from this cause alone is the slowest from about 5 days after Motion in Right Ascension perigee to 5 days before perigee (bracketing the apo- The major influence controlling the apparent hourly gean portion of the orbit). The relative angular veloc- motion of the Moon in celestial longitude, ANC, is the ity of the Moon is also a function of the comparatively Moon's instantaneous parallax, with but little contri- greater proximity (or the greater distance) of the bution from celestial latitude because of its small value, Moon from the Earth, subject to the dynamic condi- even at maximum. By contrast, the Moon's motion tions creating such extremes at times of proxigee- in right ascension, Aa([, is strongly affected by its corre- syzygy and exogee-syzygy-or establishing moderate sponding position and motion in declination. Although parallax distances at times in between. The Moon the Moon's movement in right ascension, as in celestial moves considerably faster than usual and the value longitude, is duly influenced by its variation in orbital of Aa([ increases when the parallax is large, and the velocity between perigee and apogee, this is by no Moon's motion is slower when the parallax is rela- means the sole contributing factor in its apparent tively small-even though the latter parallax value daily and hourly motions. may represent a maximum for that particular lunation. There is no consistent, one-to-one correlation between 3. The largest '@alue of Aaq: does not necessarily the hourly motion of the Moon in right ascension and occur coincidentally with the largest value of 3(@ any single astronomical circumstance-because of the during the year; neither must it occur simultaneously harmonic interrelationship between all parameters in- with the closest separation-time between perigee and volved. However, the following general principles may syzygy in the year. be deduced covering the various major factors of influ- 4. The maximum value of ASE, on the other hand, ence. All deal specifically with the Moon's relative motions usually occurs very close to, but not necessarily in right ascension and declination, as a cofunction of its simultaneously with, the two times each month when instantaneous position in declination: the Moon crosses the celestial equator. This cor- I . Exclusive of the effects of parallax, the two times at responds to the point of inflection in the curve of the which the maximum hourly motions of the Moon in Moon's motion in declination, when this is plotted right ascension occur in any one month are usually less against motion in right ascension. At such times, the than a day from, but rarely exactly coincide with, the maximum component of the Moon's total motion is two times of maximum declination during this same lu- in the coordinate of declination, and the least motion nation. (See also paragraph 3, below.) As the positions of is in right ascension. the respective semimonthly peak and trough of the curve The combination of a small lunar motion in right of 6(c plotted against ac: or time (fig. 44) are reached, and ascen the value of the slope ASE/Aa(c becomes equal to zero, sion and a limited period of maximum tidal force all of the Moon's motion occurs in a. Accordingly, application establishes a somewhat less favorable situation the maximum value of Aa([ also occurs very nearly for either enhancing or prolonging the tidal forces present. at the time that Aac reaches its zero value. The value Therefore, despite the fact that very large parallax values of Aa,[ is always positive, since the direction of the may occur at such times through the coincidence of a Moon's movement is continuously counterclockwise. close perigee-syzygy alignment, the situation remains an 2. The two maximum values of Acic which occur in essentially negative one for the maximum development each synodic month consist of a larger maximum of perigean spring tides, and offers an excellent oppor- Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 193 tunity for verification of the "If not p, then not q" aspect from a point on the surface of the Earth, its value is of,the hypothesis being tested. defined by: Xt-C Effects of Extreme Lunar Declination on tan (90'-J)=v@@- Motions in Right Ascension where A subsequent frequently'discussed aspect of the Moon's x'=(1/7r)'15 Cos apparent daily and hourly motions in right ascension re- Y,=(1/7r)'(A5(C)` lates to the catch-up motion of the rotating Earth upon p Cos 0' Cos h(c (dhldt) these lunar motions in a variable with different times and circumstances. When the Moon is observed in a 77' = P Cos .0, sin b(C sin h([(dhldt). position close to the celestial equator, the factor of chang- Assuming the Moon to be subject to its various actual ing angle of inclination of the Moon's orbit with respect and apparent motions on the celestial sphere, and to be to the celestial equator becomes of considerable signifi- referenced both in a rectangular coordinate system, x and cance. As a seeming paradox, both at the minimum as y, and in the equatorial coordinate system, a and 6, then: well as the maximum lunar declinations, the conditions which determine the amount of motion of the Moon in x' andy' are the rates of change of the rectangular right ascension are affected (but in an opposite manner) coordinates x and y (with origin at the center of by the ultimate magnitude of the greatest northern and the Earth). southern declinational excursions of the Moon. As will X= P Cos ac Cos 3(c; Y=p sin a([ C Ios b(C be shortly seen, the effect of observation of the Moon p= the radius vector from the center of the Earth from the Earth's surface rather than from its center, to through the point of observation on the which all geocentric parallaxes are referred, is also an Earth's surface to the Moon important factor in the present connection. and q' are the rates of change of the coordinates The increased steepening of the angle of inclination be- tween the lunar orbit and the celestial equator at times of of the observer on the surface of the Earth, along extreme lunar declination is demonstrated in the first of the radius vector from the Earth's center to the the following quantitative analyses. The especially notable Moon (the motion being caused by the rotation increase in the angle between the Moon's orbit and the of the Earth) celestial equator is revealed as one proceeds toward the 7r([=the geocentric horizontal parallax of the Earth's Equator. It is at this point that the angle of in-clin- Moon ation reaches a maximum and reduces the length of the 6([=the apparent declination of the Moon lunar day (the period of time between successive lunar AaE=the hourly change in geocentric right ascen- transits of the meridian) to its extreme minimum value. sion of the Moon This shortening of the available time during which the ASC=the hourly change in geocentric declination increased gravitational forces created by a perigee-syzygy of the Moon alignment can act partially offsets the greater amplitudes h([=the hour angle of the Moon, taken as posi- tive in a westerly direction from the local and flooding potential of perigean spring tides when they meridian are associated with such conditions. dhldt=rate of change of the Moon's hour angle As shown in figure 36, upon those occasions when the with time, taken as positive west of the vernal equinox and the ascending node of the lunar orbit meridian, and negative cast of the meridian coincide, the geocentric angle of inclination (J,,) between .0'=the geocentric latitude of the place of the Moon's orbit and the celestial equator can attain its observation maximum value slightly in excess of 28.5'. However, the As in the example of chapter 2, the Moon is as- Moon's sizable parallax angle can add appreciably to this sumed to be on the celestial equator, and to be transit- value as measured from the Earth's surface. ing the meridian of the U.S. Naval Observatory in Woolard and Clemence ' have given appropriate equa- Washington, D.C. tions which permit a quantitative analysis of the differ- 0'=38055'14.0" ences caused by the parallax effect. If I represents this same angle of inclination, but as measured topocentrically p Cos 0'=0.77906. 202-509 0 - 78 - 15 194 Strategic Role of Perigean Spring Tides, 1635-1976 EFFECT OF MOON'S 18.6-YEAR NODICAL CYCLE UPON THE MAXIMUM LUNAR DECLINATION EARTH VIEWED FROM THE VERNAL 'EQUINOX ALONG THE MOON'S LINE OF NODES A. MOON'S DESCENDING NODE 23.5 18.5' AT VERNAL EQUINOX ...... EARTH CEL. EOT. 0. -------------------------------- ----------------- N B. -18.5* 2 8. 5' .-23.5* 23 5' 00%%-**` S N CEL.E0T. ------------------------ ---- ------ -------------- 0 'EARTH MOON'S ASCENDING NODE -23. AT VERNAL EQUINOX -2 5 PLANE OF PAPER ISTHATOFTHE CELESTIAL MERIDIAN FIGUREs 36A, B.-(Discussed in text.) The Moon's parallax 7r(I is also assumed for con- in lunar declination persisted during every lunation venience to be 60'(=3,600"). throughout the year. In the year 1950, a very good example of the coin- cidence of the lunar ascending node and the position of the vernal equinox occurred.' (With a at rr, The probability that a simultaneous alignment between. X,=O'.) On September 19 at 0400 G.c.t., the Moon pengee and syzygy, as well as the lunar node, will occur at attained a maximum southerly declination of the exact time of either the vernal or autumnal equinox is, statistically, very remote. The period of revolution of the -28'43'47.3" for this year. Approximately 6 months vernal equinox caused by the precession of the equinoxes is earlier, near 1200 G.c.t. on March 26, as the ascending 25,800 years (one-half of this, or 12,900 years is, therefore, node coincided with the position of the autumnal equi- required for either of the two equinoxes to revolve to the nox (X = 900) tl ie Moon reached a maximum northerly position of the other). For all practical purposes in the declination of + 28'42'19. 1 " for the year. The values present tidal discussion, the vernal equinox may be re- of the astronomical latitude around these same tirnes garded as essentially stationary, and only the motion of the lunar node with respect to it in a mean revolutionary period were j3([=-50l6'55.9" on September 19.0, G.c.t., of 6,798.4 days (18.6 years) need be considered. and g(j=+5110'31.3" on March 26.0, G.c.t. A A period of time equal approximately to the average of relatively high value of each semimonthly maximum a synodic and an anomalistic month occurs between each Specific Astronomical Influences Contributing to the Production of Perigean Spring Tides 195 instance in the customary pairs of perigee-syzygy alignments TA13LE II.-Approximate Dates on Which Maximum Lunar possessing a separation-interval (P - S) of + 24 hours. (See Declinations Occurred, According to the 6,798.4-Day Nodical table 16.) Following the smallest P - S value of any one close Cycle perigee-syzygy alignment, the mean interval to the next (Based on Epoch 1932 January 12. 1) comparably close alignment will be either -191.95 days or 221.48 days, depending upon the controlling conditions enumerated in chapter 6, "Cycles of Alternation in Perigee- 1634 Mar. 19.7 1820 May 7_7 Syzygy Alignments." 1652 Oct. 29.1 1838 Dec. 18.1 The possibility of securing a coincidence between the 1671 June 10.5 1857 July 29.5 combined condition of perigee-syzygy and both the lunar 1690 Jan. 19.9 1876 Mar. 9.9 node and one of the equinoxes is made further remote by 1708 Sept. 1.3 1894 Oct. 20.3 the fact that, as perigee and syzygy come into alignment, 1727 Apr. 13.7 1913 June 1.7 1745 Nov. 23.1 1932 Jan. 12.1 the position of perigee moves rapidly forward, subject to, 1764 July 4.5 1950 Aug. 23.0 solar perturbations. The opportunity for arriving at even a 1783 Feb. 13.9 1969 Apr. 3.4 near-commensurability between these four elements is thus 1801 Sept. 26.3 (1987) Nov. 13.8 even further reduced. For the record only-recognizing that the periods covered by the tabulated data, and the data alone, do not cover all possible cases, with any rigorous interpretation thereof thus When the Moon crossed the celestial equator on April being rendered invalid-the following summation is made: 2, during that particular cycle which contains the extreme 1. Only two among the 1,318 cases of perigee-syzygy maximum lunar declination, the relatively large hourly w ith a separation-time of 24 hours or less occurring between motion\in declination necessary to accomplish this large 1600 and 1999 and listed in table 16, fall within even the excursion from the celestial equator was clearly evident. same year as one of the 19 cases of extreme lunar declination listed in table 11, covering the 342-year period of the present This position represented a point of inflection between study. the trough and peak of the curve, where the slope of the 2. Among the 100 representative examples of major .curve in the declination component reached a maximum. coastal flooding occurring at a time of perigee-syzygy, cata- % The hourly differences in right ascension and decli- loged in tabl 'e 1, only three cases occur even in the same nation of the Moon subject to this circumstance, year as that in which an extreme value of the lunar declina- occurring at approximately 0230 G.c.t. on April 2, tion occurs. The three flooding cases involved (which are were Ace(c=130.97" and As(c=-1,075.6". The latter mutually inclusive of the two indicated in the first para- graph) are those of 1894 January 22 (perigee-syzygy sepa- value indicates the greatest hourly change in declina- ration-time, -24h), 1932 November 2 (-13h), and 1969 tion for the year. The corresponding hourly differences December 10-14 (+38h). with the Moon on the celestial equator during the 3. For several years in a row 'both before and after an second cycle of maximum declination, at about 2130 extreme declination is attained, the lunar declination re- G.c.t. on September 12, were Aa([@125.408 and mains above-average in its monthly values throughout the Aa(C 1,030.8". (It should be pointed out that, for entire year. However, the three cases mentioned of flooding various reasons, the maximum value of Aa(C does not which occurred in the same year as that of an extreme lunar coincide precisely with the time at which the Moon declination were at least 8 months removed from the exact crosses the Equator. In the first case, Ab(c reaches a date of the extreme declination. It is tacitly obvious that no solar or lunar eclipses can greater value of - 1,078.6" at about 0930 G.c.t. on occur on these exact dates of highest possible lunar declina- April 2, in the second case, AF(C reaches a value of tion-but may occur on dates during the same year of high - 1,033.2" at about 0330 G.c.t. on 6eptember 13. lunar declinations when the lunar node and the position of The greatest value of Aar more nearly-but again not the Sun very nearly coincide. In the same manner, perigee- exactly-agrees with the time the Moon reaches its syzygy may *occur on some other date of node-perigee- extreme declination for the year.) syzygy alignment throughout the year when the Moon may also be in a position of crossing the celestial equator. On the other hand, previously mentioned factors may apparently 1. Decrease of Motion in Right Ascension, and somewhat paradoxically support an increase in tidal flood- Shortening of the Tidal Day at Times of High ing potential undercertain conditions of high lunar decli- Lunar Inclination to the Celestial Equator nation, as will be brought out in subsequent chapters. It is because of the various commensurate possibilities that an Selecting the April 2 example of the Moon's examination of the differences between the two cases in- crossing of the celestial equator as representative of cluded in the following discussion is important. such a high-inclination situation, and using the 196 Strategic Role of Perigean Spring Tides, 1635-1976 appropriate value of the lunar parallax (7rc ne latter figure may be compared with the only =60125.88") at this time: slightly smaller parallax of 61' 26.702" associated with x'@ 1/3626" X 15 cos 00 X 130.9711 the great mid-Atlantic tidal flooding of 1962 March 6.5, and, the somewhat larger value of 61' 30.0009" which 0.00028 X 15 X I X 130.97 =0.55007 accompanied the west coast tidal flooding of 1974 Janu- y'= 1/3626"-X 1075.6" ary 8.5-both discussed extensively in chapter 7. = 0.00028 X 1075.6 = 0.30117 However, the distinctive feature of the 1950 Decem- t'=0.77906Xcos O'XO.24956 radian ber 9 event was the extraordinarily large daily motion @0.19442 of the Moon in longitude on this date. As indicated, this 7)'=0.77906X sin O'X sin O'XO.24956 radian was 15'21' during the latter event compared with =0.77906XOXOXO.24956=0.00000 values of 15'15' on the 1974 date and 15'14' on the 1962 date. tan (9o'-,7)= 0.55007-0.19442 Since the Moon is never far from the ecliptic, the 0.30117-0.00000 rapid motion in celestial longitude is directly corre- 0.35565 _z 1.18089 latable with the rapid motion of 173.0111/-1111 in right 0.30117 ascension which occurred on 1950 December 9. This are tan 1.18089=49.740 was associated with the relatively large declination of J=90.0'-49.74'@40.26' -28'20'23.4", increasing, within some 7 hours, to an extreme declination of -28'25'41.9" for the month. Since the geocentric inclination of the lunar orbit to For comparison, the declination of the Moon on the celestial equator WO) reaches a maximum value of 1962 March 6.5 G.c.t. was -7'42'05.42", with a about 28.5', the topocentric inclination involves an angle corresponding value of Aa(C = 146.543". The maximum which is approximately 11.8' greater than the geocentric. declination for this lunation was -19'50'19.35", With this increased angle of inclination, and the maxi- having a corresponding Acq = 147.955". On 1974 Jan- mum component-motions in declination which result, the uary 8.5 G.c.t., the declination was +20'36'21.33", apparent movement of the Moon in right ascension is with a value of AaT.=159.999". The maximum decli- reduced proportionately. As noted in chapter 2, the tidal nation for this lunation. was +23*52104.4011, with day is thereby shortened, and the tide-amplifying effects Aa (c = 163.965s. are reduced. The effect of an increased daily motion in longitude produced by the Moon's extremely close distance to the 2. Increase of Motion in Right Ascension and Earth in 1950, 1962, and 1974 thus was added to in 1950 Lengthening of the Tidal Day at Times When by the effect of the relatively large declination at the time the Moon is at an Extreme Declination of perigee-syzygy, and a consequent increased motion in Contrastingly, in the perigee-syzygy situation which right ascension. The comparatively high declination at occurred with a mean epoch of 0500 G.c.t. on perigee-syzygy was, in turn, a function of the extreme dec- 1950 December 9, within 24 hours of an extreme lination of -28'25'41.9" during the same lunation, lunar declination of -28'25'41.911, the direct motion caused by the coincidence of the lunar ascending node of the Moon in celestial longitude reached one of its with the vernal equinox in this year. largest possible values (A X(C @ 15'20'49.4", or 15.347*, Ile greater speed of movement in right ascension re- between December 8.5 and 9.5). The hourly motion sults in an extension of the necessary catch-up time, an of the Moon in right ascension, Aa,[ @ 173.0 Is, likewise increase in the length of the tidal day, and an augmenta- reached a maximum value for the entire year between tion of the tides.' 2130 and 2330 G.c.t. on December 9. (The exact The synoptic weather map for this 1950 December 9 repetition of the same maximum difference over a date has been included among those grouped in chapter 7 3-hour period indicates a flattened peak on the'dec- to indicate a logical reason for the lack of attendant tidal lination curve, yielding a protracted maximum.) The flooding. Although the tides predicted for December 9-10. semimonthly maximum declination of -28'25'41.9" were appropriately high, in the complete absence of any occurred at about 0500 G.c.t. on December 10. The strong, persistent, onshore winds on either the east or west value of 7r(C on December 9.0 G.c.t. was 61'27.09". coasts of North America, no major tidal flooding occurred. Chapter 5. The Essential Conditions for Achieving Amplified Perigean Spring Tides As a direct follow-on to the theoretical discussions of In accordance with Kepler's third law, these same cir- the preceding chapter, it is noteworthy that certain other cumstances also cause a temporarily increased apparent astronomical influences may act to produce both regular daily motion of the Moon in both longitude and right and irregular, but measurably significant increments in ascension. An appropriate catch-up motion b@ the rotat- the positive and negative amplitudes of perigean spring ing Earth becomes necessary in order to bring any given tides-tending toward their ultimate maximization. In meridian on the Earth's surface into alignment with the the present chapter, a brief summary of each such con- axis of enhanced gravitational attraction of the Moon tributing influence will be followed by a quantitative anal- (and Sun). As will be seen, this required catch-up motion ysis of its individual effects. in turn increases the period of maximum tide-raising force application during the course of the tidal day. The General Concepts of Maximization The total tide-raising potential present is thus a func- of Peri ean Spring Tides tion of two separate categories of influence: (I) those 9 factors which, causing a very close alignment and a rein- One *immediate cause of the secondarv enhancement forcement of lunisolar gravitational attractions, coupled with an extreme proximity of the Moon (and Sun) to the of tide-raising potential is a purely statistical one estab- Earth, increase the tide-raising forces exerted,upon the lishing, in varying degrees-over both quasi-periodic Earth's waters; and (2) those factors which lengthen the and aperiodic intervals of time-more exactly commen- tidal day--the interval within which these or other aug- .surable relationships between the synodic and anomalistic mented tidal forces can act-and by this means likewise months. This close commensurability results, in turn, in cause an increase in both the positive and negative ampli- an accompanying more precise spatial orientation between tudes of the tides. the line of syzygies and the line of apsides in the lunar In dealing with the influences which act to generate orbit. increased high and low waters at time of perigee-syzygy, Increased dynamic factors acting upon the Moon's it is necessary to consider both of the above categories. orbit because of the near-coincidence in the lines of gravi- Those factors involving purely force influences will be tational force action connecting Earth, Moon, and Sun discussed in the present chapter; those associated with are responsible for an increased eccentricity and parallax, various astronomical influences producing changes in the and hence a considerably closer proximity of the Moon length of the tidal day, often accompanied by other time- to the Earth at perigee. This condition may also be ac- related effects, will be covered in chapter 6. companied, on occasion, by an independently originating, close alignment of the Moon and Sun in declination- Factors Increasing the Intensities of whose influence is most effective when the two bodies the Tidal Forces Acting are simultaneously at perigee-syzygy. Accordingly, for reasons involving both decreased lunar distance from (a) Unquestionably, one of the most important con- the Earth and a mutually reinforcing combination of ditions-next to the positions of the Moon and Sun at lunisolar forces, the tide-raising potential is augmented. perigee and perihelion, respectively-which serves 197 198 Strategic Role of Perigean Spring Tides, 1635-1976 strongly to increase the tidal forces acting is the pres- through uniformly high tides on both sides of the Earth. ence of either or both of these two bodies near to, or di- There is no diurnal inequality. (See fig. 5 in the appen- rectly in the local zenith (i.e., at an altitude of 90'). dix.) Since the effect of increased tidal range is influen- From a point of view related solely to the tide-raising tial at certain locations in adding to the heights of potential, a greater vertical gravitational force exists perigean spring tides, this lack of a higher high water under these conditions because the shortest distance be- in equatorial type tides can, in some cases, be partially tween either the Moon or the Sun and the Earth's surface counterproductive to the increased lunar gravitational in- is at all times along a perpendicular to the surface. For fluence present with the Moon on the Equator. reasons given in the preceding chapter, nowhere north (b) A second very important influence upon the avail- or south of a declination of --L28.5', respectively, can the able tide-raising force is the alignment of the Sun and Moon be perpendicular in altitude to the Earth's surface. Moon in the same (or exactly opposite) declination at the Similarly, the Sun cannot reach the.zenith if the latitude same time they are aligned in celestial longitude (at times oIf the location is greater than _L23.5'. Since tidal forces of syzygy). The coincidence of perigee-syzygy with a vary inversely as the cube of the distance of the attractincy common alignment of the Sun and Moon in declination body, this perpendicular distance to the Moon and its adds appreciably to the tide-reinforcing effect caused by position in the local zenith are very important elements lunar proximity to the Earth. The possibility of both the in establishing the greatest tide-raising potential a Moon (in its orbit) and the Sun (in the ecliptic) being In considering relative tidal heights at any station, the exactly aligned also in the plane of the celestial equator location of the Moon directly over the Equator ' is of fur- (8=0') at the same time they are aligned at perigee- syzygy is definitely less common. Such a situation is pos- ther importance in another connection-that of diurnal inequality. In the equilibrium theory of the tides de- -sible only when a lunar node coincides with one of the scribed in the appendix, it is seen that the tractive or equinoxes-this action taking place (when within the horizontal force of the Moon tends to draw the waters angular limits defined in the footnote (c) on page 7) at of the Earth to a point where the line of gravitational at- the same time as a total lunar or solar eclipse. traction between Moon and Earth is perpendicular to However, the likelihood of the Sun and Moon becom- the, surface of the Earth. The maximum peak of the ing aligned at some declinational angle other than 0', tidal bulge is produced in the vicinity of this sublunar either on the same side of the Earth (at new moon) or point (together with an almost identical tidal bulge on on the opposite side (full moon), is not uncommon, con- the diametrically opposite side of the Earth). Because of sidering that the Moon goes through its complete range several accelerating and retarding factors to be discussed of declination once in each tropical month of 27.321582 in chapters 6 and 8, the Earth's two tidal bulges do not mean solar days (from vernal equinox to vernal equinox usually lie directly beneath, or in a position exactly 18W again) around the Earth in longitude from, the Moon. However, (c) Seasonal factors also enter into the frequency of, when the Moon is directly over the Equator twice each occurrence of various reinforcin' combinations of gravi- lunar month, the two crests of the hypothetical tidal 9 force envelope (see fig. 5, appendix), do tend to be tational force. As will be seen in table 13, the most favor-, centered precisely in, the equatorial plane. able situation for increasing the forces acting at time of The Earth's diurnal rotation occurs in a manner to syzygy-thereby decreasing the distance of the Moon carry any point on its surface in a direction which is from the Earth-4xists during the winter months. This always parallel to the Equator. When the tidal bulges is because the Earth is then closest to perihelion, per- lie on the Equator, therefore, any point on the Earth's mitting the Sun's gravitational force to be exerted to its surface in high-middle to low latitude rotates (between fullest extent upon the tides. The Sun is, during the winter high and low water) into and out of the tidal bulges and season of the Northern Hemisphere, at its maximum ' It is important to note in this same respect, however, that the negative declinations. In order-for the Moon to achieve a maximum horizontal or tractive tide-raising force is exerted upon direct or opposite alignment in the Sun's declinational the Earth's surface by the Moon along a small circle everywhere plane, it is necessary for the new moon to reach the 45' from the current instantaneous position of the Moon. (See same comparatively large negative declination as the Sun, fig. 35 and the accompanying discussion.) or the full moon to attain an equal positive declination. ' As will be seen in chapter 6, the apparent westward (rising and setting) motion of the Moon caused by the Earth's rotation These declinational alignments will act to enhance the is the greatest when it is on the celestial equator, but the Moon's already greater tide-raising forces produced as the gravi- apparent eastward motion in right ascension due to its real mo- tational forces of Moon and Sun are combined at syzygy. tion in orbit is then the least-factors of importance in connection with relative catch-up times. Should the calendar year begin with the declinational Essential Conditions for Achieving Amplified Perigean Spring Tides 199 plane of the Moon close to that of the Sun, while the cisely or very nearly aligned in celestial longitude with Sun itself is near perigee with the Earth, (i.e., at peri- the Sun is that of a total solar or total lunar eclipse. The helion) an additional amount of tide-raising force is type of eclipse which occurs depends upon whether the produced. Moon lies between the Earth and the Sun, , (at new moon) or on the opposite side of the Earth from the Sun A Quantitative Evaluation of the Various (at full moon), respectively. Tide-Maximizing Factors The combination of the gravitational forces of the Earth and Sun, exerted along nearly the same axes in Table 12 illustrates the effect upon the proximity of A and P, creates an additional perturbing force upon the the Moon to the Earth resulting from the astronomical lunar orbit. However, as will be seen in table 14, the condition of perigee-syzygy when this geometrical align- effect upon an increase in the lunax parallax is not as ment is combined with the location of both the Moon and pronounced as in either of the two preceding examples. the Sun on or near the celestial equator. The Sun, in This is due in some degree to the Lct that, in the its apparent annual motion along the ecliptic, crosses the case of a total solar eclipse, the gra@vitational forces of celestial equator around March 21 and September 23 the very massive but vastly more distant Sun and the less of each year-at the vernal and autumnal equinoxes, massive but closer Earth-exerted in opposite directions respectively. on the Moon's orbit-are partially compensating. On the Since the Moon is never more than 5'9' from the other hand, the production of a maximum lunar parallax ecliptic, the time at which the Moon, while at perigee- is the result of undiminished, maximized solar forces and syzygy, can be simultaneously near the celestial equator perturbations. will always be close to one of these dates, a fact confinned Consider, for example, the large but not extreme lunar in table 12. This table lists 45 cases of perigee-syzygy in parallaxes at the times of the solar eclipses of 1967 No- which the separation between the two components is:!@ 24 vember 2 and 1985 November 12 in table 14; also the hours and the declination of the Moon is < + V (one comparatively large parallax values in the following cases case of 1.1' is included). The additional solar gravita- chosen from table 1, associated with coastal flooding. tional and perturbational forces acting on the Moon when the Sun is in, or very nearly in, the same plane Date and Time Maximum Sepa- as the Moon around the times of the equinoxes-as shown (G.c.t.) of Duration 7r ([ at 8([ at ration- Conjunction in of Eclipse syZygy Syzygy Interval by the relatively larger lunar parallaxes resulting under Longitude Totality P-S these conditions-are clearly revealed by these data. ,However, a comparison is also desirable between this 1901 April 18 2200h @6.5 ...... 61124. 3" +12.80 -37- table and table 13-which shows the effects of the addi- 1949 October 21 2100h (Partial).. 61'23. 4" -11.80 -6h tional gravitational force of the Sun on the lunar orbit caused by the occurrence of perigee-syzygy close to the h time of perihelion' Such a comparison reveals that the All four cases have a perigee-syzygy alignment within 6 latter situation is far more effective, in increasing the or less. The first two cases also are approaching the time lunar parallax, if the Sun and Moon are coplanar in of perihelion. However, the further coincidence of lunar declination. As examples of this, in table 13, note especially opposition and very close proximity in time to perihelion necessary to achieve either an extreme or a maximum the lar e value of the parallax for the date 1912 anuary 9 J proxigee-syzygy (table 13) is lacking. 4, despite the very high lunar declination of + 2 7.6', and again for 1930 January 14, with a lunar declination of Summary of Relative Gravitational + 26.0'. Both dates are, of course, very close to that of Force Influences perihelion, when the Sun's gravitational effect reaches its maximum. Assuming a common limiting condition in which the Finally, a comparison can be made between the data separation between perigee and syzygy is <24': of table 13 and those of table 14, which show the effect A situation in which the Moon (passing through one of upon the lunar parallax of a situation in which the Moon the two lunar nodes at times of solar or lunar eclipse) is at one of the two nodes of its orbit (i.e., crossing the. crosses the ecliptic at the same time the Earth is near ecliptic) at the time of both perihelion and perigee- perihelion (between November 2 and February 26 in syzygy. The circumstance under which the Moon is simul- table 14) is, in general, not as effective in increasing the taneously in the plane of the ecliptic, and either pre- lunar parallax as either- 200 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 12.-Selected Cases of Perigee-Syzygy, Showing the Relationship Between the Equinoctial (Near-Equatorial) Position of the Moon and the Lunar Parallax Over the 400-2ear Period 1600-1999 Primary Limiting Range for Perigee-Syzygy Separation: P-S < �24h Secondary Limiting Range for Proximity of Moon to Celestial Equator: 6([::5 �10 Resulting Bracketing Ranges for Proximity of Perigee-Syzygy to Vernal or Autumnal Equinoxes: Spring dates 3/8-4/2 Autumn dates 9/9-10/6 Date Time (G.c.t.) Lunar phase Horizontal parallax k Perigee - syzygy ofsyzygy atsyzygy at syzygy h 0 h 1617 Sept. 15 4 F 61 19.0 -0.6 +13 1621 Mar. 8 2 F 61 18.3 +0.3 - 16 1626 Mar. 27 19 N 61 20.3 +0.3 - 10 1635 Mar. 18 19 N 61 25.1 +0.6 + 1 1649 Mar. 28 11 F 61 8.1 +0.8 +19 1662 Mar. 20 2 N 61 10.8 -0.3 + 17 1675 Mar. 11 18 F 61 19.8 -o.7 +13 1679 Mar. 12 9 N 61 26.3 -0.4 - 2 1679 Sept. 20 2 F 61 20.0 +0.6 + 12 1684 Mar. 31 2 F 61 27.8 +0.1 + 4 1696 Sept. 11 9 F 61 25.4 -0.1 6 1701 Oct. 2 2 N 61 26.0 +0.3 1 1705 Oct. 2 17 F 61 14.8 +0.3 -16 1710 Mar. 15 9 F 61 27.8 +0.3 - 3 1718 Sept..24 9 N 61 5.3 +0.8 -20 1745 Sept.25 17 N 61 23.2 -1.0 - 5 1750 Mar. 8 8 N 61 23.0 -0.5 + 8 1759 Oct. 6 9 F 61 20.9 +0.5 +13 1780 Sept.28 7 N 61 4.2 +0.7 -20 1789 Mar. 11 14 F 61 6.8 -0.9 -22 1794 Mar. 31 7 N 61 12.3 +0.9 -16 1820 Sept.22 7 F 61 22.1 +0.2 - 9 1825 Sept.12 15 N 61 9.5 -0.4 +18 1830 Mar. 24 15 N 61 19.7 +0.2 +10 1834 Oct. 2 23 N 61 22.9 +0.7 + 9 1847 Mar. 16 21 N 61 23.1 +0.2 - 8 1860 Sept. 15 6 N 61 24.9 -0.7 + 3 1864 Sept. 15 21 F 61 18.8 +0.8 -12 1869 Mar. 27 22 F 61 7.0 +0.8 -21 1869 Oct. 5 14 N 61 23.5 -0.6 - 7 1874 Sept. 25 22 F 61 7.4 -1.0 +20 1883 Mar. 9 4 N 61 8.6 -0.8 +19 1892 Mar..28 13 N 61 21.2 +0.3 + 9 1895 Sept. 18 21 N 61 14.4 +0.6 -13 1900 Sept. 9 5 F 61 18.4 -1.0 + 14 1905 Sept. 28 22 N 61 7.6 +0.7 +19 1922 Sept.21 5 N 61 24.0 +0.8 + 1 1927 Apr. 2 4 N 61 24.5 0.0 - 6 1935 Sept. 12 20 F 61 27.1 -0.3 - 2 1939 Sept. 13 11 N 61 9.4 +1.0 -17 1944 Oct. 2 4 F 61 21.2 -0.9 -11 1953 Mar. 15 11 N 61 18.2 +1. 1 -13 1967 Mar. 26 3 F 61 26.7 +0.6 + 5 1993 Mar. 8 10 F 61 30.0 +0.2 - 2 1998 Mar. 28 3 N 61 24.7 +o. 7 + 4 Essential Conditions for Achieving Amplified Perigean Spring Tides 201 TABLE 13.-Compilation of All Cases of Extreme Proxigee-Syzygy Occurring Over the 400-rear Period 1600-1999, Showing the Combined Influence of Perihelion, Lunar Opposition, and Approximately Coplanar Lunisolar Declinations in Reducing the Perigee-Syzygy Separa- tion and Increasing the Lunar Parallax (see text explanation). Selected Lower Limit for Lunar Parallax: 7r > 6 V29. 0" Resulting Limiting Range for Perigee-Syzygy Separation: P-S< �5h Resulting Bracketing Range for Proximity of Perigee-Syzygy to Perihelion: 10/31-3/8 Date Phase Parallax at syzygy Declination Perigee minus Parallax at perigee Declination syzygy (G.c.t.) 0 h 0 1603 Jan. 27 FM 61 29.9 +14.1 +5 61 30.2 +13.3 1609 Nov. 11 FM 61 30.4 +13.3 -1 61 30.4 +13.2 1627 Nov. 22 FM 61 30.6 +15.9 +2 61 30.7 +16.2 1629 Jan. 9 FM 61 29.8 +22.8 - 1 61 29.8 +22.8 1630 Feb. 27 FM 61 29.7 +12.9 -3 61 29.9 +13.7 1645 Dec. 3 FM 61 30.3 +17.8 +4 61 30.6 +18.2 1647 Jan. 20 FM 61 29.6 +20.8 +1 61 29.6 +20.7 1671 Nov. 16 FM 61 30.3 +23.2 -2 61 30.4 +22.8 1673 Jan. 3 FM 61 29.9 +26.3 -5 61 30.2 +26.7 1689 Nov. 26 FM 61 30.9 +25.6 0 61 30.9 +25.6 1691 Jan. 14 FM 61 30.5 +24.7 -2 61 30.6 +25.1 1707 Dec. 9 FM 61 31.0 +27.1 +3 61 31.1 +27.3 1709 Jan. 25 FM 61 30.5 +22.3 0 61 30.5 +22.4 1725 Dec. 19 FM 61 30.4 +27.8 +4 61 30.7 +27.9 1727 Feb. 6 FM 61 30.0 +19.2 +2 61 30.0 +18.8 1751 Dec. 2 FM 61 29.4 +21.4 -2 61 29.5 +21.3 1733 Jan. 19 FM 61 30.8 +15.4 -4 61 31.0 +15.9 1769 Dec. 13 FM 61 29.7 +22.5 1 61 29.1 +22.5 1771 Jan. 30 FM 61 31.1 +12.8 -2 61 31.2 +13.1 1787 Dec. 24 FM 61 29.4 +22.8 +3 61 29.6 +22.6 1789 Feb. 10 FM 61 30.9 + 9.5 +1 61 30.9 + 9.5 1807 Feb. 22 FM 61 30.1 + 5.8 +2 61 30.2 + 5.2 1813 Dec. 7 FM 61 30.3 +18.9 -2 61 30.4 +18.6 1830 Oct. 31 FM 61 29.7 +10.0 +2 61 29.8 +10.3 1831 Dec. 19 FM 61 30.8 +19.6 0 61 30.8 +19.6 1849 Dec. 29 FM 61 30.8 +19.4 +2 61 30.8 +19.4 1868 Jan. 9 FM 61 30.1 +18.4 +3 61 30.3 +18.2 1875 Dec. 12 FM 61 30.5. +27.9 -4 61 30; 8 +27.6 1893 Dec. 23 FM 61 31.4 +28.2 -2 61 31.4 +28.2 1912 Jan. 4 FM 61 31.6 +27.6 +1 61 31.6 +27.6 1930 Jan. 14 FM 61 31.3 +26.0 +2 61 31.4 +25.8 1948 Jan. 26 FM 61 30.4 +23.6 +4 61 30.8 +23.0 1954 Nov. 10 FM 61 29.7 +20.8 - 1 61 29.7 +20.7 1972 Nov. 20 FM 61 30.1 +23.6 + 1 61 30.1 +23.8 1974 Jan. 8 FM 61 30.0 +20.5 -2 61 30.0 +20.7 1975 Feb. 26 FM 61 30.0 + 4.4 -3 61 30.2 + 5.2 1990 Dec. 2 FM 61 30.0 +25.7 +3 61 30.1 +25.9 1992 Jan. 19 FM 61 29.9 +18.6 +1 61 30.0 +18.5 1993 Mar. 8 FM 61 30.0 + o.2 -2 61 30.1 + 0.6 A situation of perigee-syzygy with the aMoon simulta- tional plane as the Moon (see table 13). The influence of neously in or nearthe plane of the celestial equator (3([:!@ I') such combined perigee-syzygy, lunar opposition, and and close to the position of one of the two equinoxes (be- lunisolar declinational alignments occurring in the period tween March 8 and April 2, or September 9 and October 6 near perihelion-producing the largest geocentric horizontal in table 12), or parallaxes of the Moon over the entire 400-year period A situation in which the alignment of perigee-syzygy between 1600 and 1999-will be discussed further in the occurs concurrently with the Earth at or near perihelion, the Moon at opposition, and the Sun in the same declina- following section. 202 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 14.-Selected Cases of Perigee-Syzygv Occurring Simultaneously at a Lunar Node (Total Solar Echfise) and Near Perihelion, Showing the Combined Elect of These Factors Upon the Lunar Parallax Over the 100-Year Period 1900-1999 Limiting Range for Perigee-Syzygy Separation: P- S:5 � 24h Limiting Range for Celestial Latitude of Moon at Conjunction (Total Solar Eclipse Certain): )3([ < � 1 '24'36" Consequent Limiting Dates for Proximity of Perig@e-Syzygy to Perihelion: 11/2-2/26 Date G.c.t. of conjunction Maximum duration Horizontal parallax Perigee - syzygy in longitude of total phase at syzygy, h m 0 h 1908 Jan. 3 2144 4.5 61 16.1 -22. 7 +15 1926 Jan. 14 -0635 4.4 61 12.4 -21.2 +17 1944 Jan. 25 1525 4.4 61 8.3 -18.9 +20 1961 Feb. 15 0811 2.9 61 5.5 -11.9 -21 1962 Feb. 5 0011 4.3 61 3.5 -15.9 +22 1967 Nov. 2 0548 61 25.3 -15.5 - 4 1979 Feb. 26 1647 3.0 61 9.4 - 7.9 -19 1985 Nov. 12 1420 61 26.5 -18.7 - 1 1994 Nov. 3 1336 C 6 61 21.0 -15.4 +10 Astronomical Influences Producing Un- (b) The Moon and the Sun are in the same decli- national plane-either on the' Earth's near side (with even Heights Among Perigean Spring similar algebraic signs) or on its far side (with opposite Tides; Lack of a Current Procedure algebraic signs). Both bodies are coplanar, in a as well as in & (or A), but not in fl-and neither is over the for Variable- Intensity Classification celestial equator. This condition can be either additive or, under certain circumstances (see the second following The preceding three examples and their accompany- section), counterproductive in terms of tide-raising forces. ing, tables offer a straightforward empirical confirmation (c) The Moon and-at perigee-syzygy-the Sun also, of various possible combinations and reinforcements of are in the zenith of the place. The result is a reinforce- the gravitational forces of the Moon and Sun. These ment of their respective tide-raising potentials at perigee gravitational reinforcements act, in turn, to produce cor- and along a common axis in longitude by an increased responding amplifications in the tide-raising forces pres- lunar gravitational force produced by the Moon's geo- ent. In a general expansion of the preceding principles, metrically least distance at the sublunar position on the it is interesting to consider all possible interrelationships surface of the Earth. The effect of lunar augmentation between these forces which act toward an ultimate maxi- (fig. 25A) may also be involved to a slight degree. mization of perigean spring tides. The statistical likeli- (d) The Moon is crossing the celestial equator at a time hood of such extreme tidal enhancements is necessarily close to either of the two equinoxes, putting it in the equa- spread over longer and less regular periods of time, due torial plane (8 = 0') very nearly at the same time at which to the decreasing chance for commensurability among the Sun is crossing this plane. Various degrees of proximity the greater number of factors involved. to the times of the equinoxes may be involved. The two Among the force-related aspects which may provide bodies are also very nearly aligned in a or X (at syzygy) - a multisource amplification of perigean spring tides are (e) The Moon is at one of its two nodes (occurring those itemized below. every 9.3 years), and crossing the ecliptic at a time coin- Assuming a condition of perigee-syzygy, with the Moon ciding with one of the two equinoxes. This puts the Moon and Sun aligned in longitude (X) or right ascension (a), in the same latitudinal and declinational planes (,3 = 0', but not initially in either declination ( a ) or celestial 8=0') as that of the Sun, simultaneously with these two latitude (fl), tidal forces are increased when: bodies being aligned in the same or -opposite longitude or (a) The Moon is at one of its two nodes, crossing right ascension (at syzygy) . the ecliptic and therefore (at syzygy) is simultaneously (f) In all except cases (d) and (e), the tide-raising in both the same latitudinal and longitudinal planes as force produced as the result of the conditions present may the Sun, but not in the plane of the celestial equator; be further augmented if the given circumstances occur Essential Conditions for Achieving Amplified Perigean Spring Tides 203 when the Earth is also near perihelion (i.e., the Moon is name ultimate maximum proxigean spring tides has been close,to solar perigee) and especially if the Moon is at full given to the absolute high tide experienced in A.D. 1340. phase. I (g) The full moon is at one of its two nodes (i.e., in Perigean Spring and Other Tidal Equivalents the plane of the ecliptic at the time of perigee-syzygy, in International Terminology putting it simultaneously in the same latitudinal and lon- gitudinal alignments with the Sun), as well as at its closest Although no official nomenclatural counterpart exists monthly approach to the Earth. If these various circum- in international hydrographic dictionaries d or multilin- stances occur coincidentally with the time at which the gual technical glossaries of the French, German, Dutch, Earth reaches perihelion, the Sun (at its closest annual Spanish, Russian, and other languages for the term "peri- position to the Earth) also exerts a greater attraction. The gean spring tides," the German literal translation is, for added solar tide-raising force directly reinforces that of example, die Springtiden die wdhrend des Perigaums ein- the Moon, which is nearly colinear with the Sun in both treten. While no direct descriptor term is provided in the longitude and latitude. Subject to this coincidence in ori- French language for "perigean spring tides," "equatorial entation between the line of nodes and line of apsides of tides" are distinguished as marjes iquatoriales, "equinoc- the Moon's orbit, together with the line of apsides of the tial tides" are designated as maries de iquinoxe , "solsti- Earth's orbit and the common line of syzygies---all form- tial tides" are know as marges de solstice, and "perigean ing nearly the same axis, and with the respective second- tides" as maries de perig& The German equivalents are ary bodies at their lower apse positions-the greatest pos- Aquatorialgezeiten, Gezeiten wiihrend der Tagundnacht- sible lunar parallaxes result.c gleiche, Gezeiten wlihrend des Sonnenhdchststandes, and Upon more frequent occasions, closely commensurate Gezeiten wdhrend des Periga-ums. . relationships between the synodic and anornalistic months The respective expressions in the above five languages exist as the result of which the separation-interval between for ordinary "spring tides" are maries de vive eau, perigee and syzygy becomes very small, perturbations and Spring-tiden, springtij, mareas vivas o de sicigias, and the lunar parallax correspondingly large, and the Moon's C113HMIHME HPHJIHBbl. The multilingual equiv- perigee distance from the Earth is significantly reduced. alents for the combining form "perigee-syzgy" are: For purpos 'es of detailed analysis, this situation involving pirig@e-syzygie, Perlgdum-Syzygium, perigeum-syzigien, both an extremely close perigee-syzygy alignment and perigeosicigia, and IIEPHrEff-CHKirAff. In addi- minimum lunar distance from the Eaxth is here given the tion, certain other nominiversal terms are available for designation proxigee-syzygy. The corresponding proxi- various of the tide-raising conditions listed in the preced- gean spring tides will be discussed in detail in chapter 8, ing section. along with a suggested classification terminology based on quantitative factors. Thus, the tides produced under the circumstances as- If the conditions specified in (g) above take place sociated with (d) in this list are termed, in English, equi- simultaneously, the resulting tides have somewhat indefi- noctial spring tides. The French, German, and Spanish nitely been described in the literature as maximum perigee equivalents are maries de vive eau d'jquinoxe, Spring- springs,', a very rare circumstance which is predicted tide zur Zeit der Tagundnachtgleiche, and mareas equi- to have occurred last and most recently near the peri- nociales de primavera. helion of A.D. 1340. This designation should not be confused with that of the extreme tides categorized in As n6ted in the same paragraph, the position of perigee- chapter 8 as maximum proxigean spring tides-a specific syzygy (implying in part' the alignment in longitude of astronomicaly quantified entity in the nomenclatural sys- both the Moon and Sun)-together with the lunar crossing tem proposed. According to these rigorous definitions, the of the celestial equator-may occasionally occur within c The perigee-syzygy of 1912 January 4, 1300 e.t. (with a separa- a short time of one of the equinoxes (see table 12). This tion-interval of only +6.5 minutes) is an app@oximate example, al- situation is described by the French as la grande marie though g(C was very nearly 5' at that time. The lunar parallax at the d'@quinoxe (high equinoctial spring tide), or marie extraor- mean epoch of perigee- (proxigee-) syzygy was 61'31.6", compared with the theoretically, highest possible value of 61'32". An atmospheric dinaire de vive eau d'iquinoxe. Typical examples are those of high pressure system prevailed on the west coast, and offshore winds south of a low prevented tidal flooding in New England. Although a Cf. International Hydrographic Organization, Hydrographic weak low lay over eastern Canada, the normal completely ice-free Dictionary, Special Publication No. 32 (2d ed., in five languages), season here extends only from May I to November 30. (See fig. 72.) Monaco, 1951; (3d ed., Part I-English-French), Monaco, 1974. 204 Strategic Role of Perigean Spring Tides, 1635-1976 1918 March 12, 2000 G.c.t. (e.t.)" (6(C=+1.2'), 1935 shows all cases of perigee-syzygy during the 400-year pe- September 12, 2000 G.c.t. , OT = -0.3'), 1967 March 26, riod 1600-1999 in which the accompanying lunar paral- 0300 G.c.t. (8(C @ +0.60), and 1976 March 16, 0300 G.c.t. lax is equal to, or greater than 61'29.0". In this table, (3q: = 7- 1.'7'). The last example also provides a documented column I indicate.- the year and date of the event to the case of tidal flooding, listed in table I and described in nearest day; column 2 indicates the phase of the Moon chapter 7. at the time of perigee-syzygy; column 3 shows the paral- Compensating and Counterproductive lax at the nearest hour to new or full moon; column 4 Tidal Force Influences tabulates the corresponding declination at the time of Finally, from a contrasting, tide-reducing point of view, new or full moon; column 5 shows the separation-interval there is one factor which may act to neutralize, or equal- between perigee and syzygy, in hours, in the sense perigee ize in @ compensating fashion, the effective forces of Sun minus syzygy; column 6 notes the parallax at the exact and Moon as a,consequence of the relative declinations instant of perigee; and column 7 gives the declination of of these two bodies. the Moon for this same time. Ephemeris time, which is The tide-raising force of the Moon, because of the very nearly equal to Greenwich civil time (see explana- satellite's much closer distance to the Earth than to the tory remarks on page 13), is used throughout. Table 13, Sun, and despite the Moon's much smaller mass compared together with figs. 37-38, will be used later in this chapter with that of the Sun, averages 2.2 times that of the Sun. to illustrate a very interesting phenomenon of phase dis- The tide-raising force of the Sun, accordingly, is 0.45 tinction in connection with the Moon's changing dis- that of the Moon. Thus, in a relative sense, in consid- tance from the Sun. ering the forces exerted by the Sun and Moon when they In dealing with the Earth-Moon system alone in terms are in longitudinal alignment at syzygy, a difference of of tides, the gravitational force of the Moon may ' be approximately I V in declination of the Moon corre- thought of as exerted along a force vector extended from sponds to a difference of approximately 23Y2' in declina- the center of the Moon to the center of the Earth. In tion of the Sun. this tidal model, the difference in magnitude between the At new moon, if the Moon has a declination of 23V2' tide-raising forces acting upon two positions located north and the Sun a declination of I V south-or the at the Equator on directly opposite sides of the Earth Moon has a declination of 1 V north and the Sun a is of very little consequence. Quantitatively, the tide- declination of 23Y20 south-the individual gravitational raising force producing the direct tide (fig. 2, appendix) forces counteract. Two opposite tidal bulges are created is only 0.000000005 greater than that producing the which are symmetrically disposed north and south of opposite tide, since two points in diametrically opposite the Equator, nullifying the effect of diurnal inequality. positions on the surface of the Earth are only 2 X 6,378.- Similarly, at full moon, if the Sun has a declination 388 km @ 13,757 krn (7,927 mi) apart. of 23Y2' north and the Moon likewise has a declination However, in dealing with the changing lunar distance of I I ' north-or the Sun has a declination of 23V2' south from the Sun when the Moon is in opposite extremes and the Moon a declination of 11 ' south-their forces (with respect to the Sun) of its orbit around the Earth, compensate and two tidal bulges, again symmetrically the difference is 2 X 384,404 km= 768,808 krn (477,714 disposed with respect to the Equator, are produced. mi). This is no longer insignificant, gravitationally speak- Although the diurnal inequality (see appendix) dis- ing, since the inverse cube of this distance is involved in appears at these times at any geographic latitude, the the resultant tide-raising force (different by one power important consideration in terms of the present discussion of the distance from the inverse square law of gravitation). is that the lunar and solar gravitational forces offset, In discussing the solar gravitational forces heretofore, rather than reinforce each other. consideration has been given to the Sun's gravitational influence on the tides only in terms of its modification Variation in Parallax and Orbital of the Moon's gravitational attraction on these tides, Curvature with Lunar Configuration without regard to any disturbances the Sun's gravita- tional attraction might impose on the positions or mo- Table 13 represents a sample section from a master tions of the Moon itself. The further assumption has computer printout later to be discussed (table 16), and been made that, in accordance with Newton's law of ' Because of the span of years involved between these dates, gravitation, the Moon is subject to a centrally acting in which the time-zone designations G.m.t., G.c.t., u.t., and e.t. force varying inversely as the square of the Moon's dis- have variously been used (see page 13), the times indicated have been converted consistently to the e.t. of table 16, which differs tance from the Earth. In the presence of the Sun's addi- but slightly from G.c.t. tional gravitational force, such is not actually the case, Essential Conditions for Achieving Amplified Perigean Spring Tides 205 and consideration must be given to the dynamic prob- for distance in these various tabulatio, 'ns are given in lems of three bodies. At this point, the issue involved is units of Earth-radii (one Earth-radius is equal to 6,378.- the gravitational force of the Earth and Sun on the Moon 160 kms at the Earth's Equator). rather than the tide-raising force of the Moon and Sun One immediate indication from these comparisons on the Earth. is, of course, the fact that the particular time of occur- Since the tide-raising forces vary inversely as the cube rence of perigee is of much greater importance in estab- of the distance between the Moon (or Sun) and the lishing the actual time of the least distance of the Moon Earth, these forces may increase enormously when the associated with perigee-syzygy than is the component of Moon's distance from the Earth is reduced. A similar syzygy. The tables also reveal an interesting relationship effect,. although not to such a prominent degree, occurs in comparing lunar distance data re 'sulting from this during the Earth's closest annual approach to the Sun near-coincidence of perigee and syzygy with like data at perihelion. However, because of the greater proximity from either the preceding or following apogee. The com- of the Moon to the Earth compared with that of the parison between the respective values at pengee-syzygy Sun, the tide-raising force of the Moon at any time is and apogec-syzygy yields a far greater range in 'the dis- 2.2 times that of the Sun. tances of the Moon from the Earth than does a similar comparison between the lunar distances at either perigee- Comparative Effects of Various Lunisolar syzygy or apogee-syzygy and those at perigee-quadrature. Configurations Upon Lunar Distance from Thus, the Eart-h-Moon distances range from 63.733 the Earth and the Curvature of the Lunar to 55.901 (or 7.832 Earth-radii) in comparing the apo- Orbit gee-syzygy of 1973 December 25.2 with the perigee- The dynamic effect of perigee-syzygy in increasing the syzygy of 1974 January 8.5, and from 55-901 to 63.728 or a nearly similar 7.827 Earth-radii) between the eccentricity of the lunar orbit, as well as the considerable perigee-syzygy of 1974 January 8.5 and the apogee- reduction in the distance of the Moon from the Earth yzygy of 1974 January 22.5. at a time of very close perigee-syzygy, can be seen in table Much smaller differences are obtained in comparing 15. On 1974 January 8.5, in an instance shown from the distances of the Moon at the time of the perigee- table 13 to have an unusually large parallax (61'30.0" quadrature of 1974 November 7.7 with those occurring at syzygy or 61'30.1" at maximum value)-and appro- at the full moon of 1974 October 31.1 or the new moon priately defined in table 22 as a case of "extreme proxi- of 1974 November 14.0. The latter syzygy dates occur gee-syzygy"-th 'e separation-interval between perigee nearly symmetrically on either side of perigee-quadrature, and syzygy (at full moon) was only -1'36m. The with syzygy then at its greatest possible separation-interval corresponding values of true geocentric distance of the (approximately 7 days from perigee). The geocentric Moon from the Earth for a week on either side of this distances of the Moon var@ from 60.521 to 58.021 Earth- perigee-syzygy date, as taken from The American Ephem- radii in the first case and from 58-021 to 59.756 Earth- eris and Nautical Almanac, are also indicated in table 15. radii in the second (providing individual ranges of only From the same table, the variation of the Earth-Moon 2.500 and 1.735 Earth-radii, respectively). distance before, during, and after this closely aligned In like manner, a comparison can be made of the var- perigee-syzygy situation may profitably be compared with ious geocentric distances (and their differences) around similar data for an instance of perigee-quadrature oc- such significant times as: (I) apogee-syzygy; (2 ) apogee- curring around 1974 November 7-8. In this case, the quadrature; (3) ordinary syzygy (separated to the great- separation between perigee and quadrature (at last quar- est extent possible from either perigee or apogee) ; (4) ter moon) was +25 hours. ordinary quadrature (subject to a similar maximum sepa- Finally, an interesting comparison also is possible be- ration from the line of apsides) ; (5) perigee-quadrature; tween the values of the Earth-Moon distance at and (6) perigee-syzygy. The general results obtainable perigee-syzygy and the respective distances at the apogee- from the analysis of examples of changing geocentric dis- syzygy alignments next preceding it on 1973 December tances of the Moon previously cited show that: (a) the 25.2 (at new moon) and consecutively following, on occupied portion of the orbit has a considerably smaller 1974 January 22.5 (also at new moon). The corre- curvature at syzygy than at ordinary quadrature, and sponding component separation-intervals in these latter (b) an even smaller orbital curvature exists at perigee- two cases are +31 hours and +37 hours. All values syzygy than at ordinary syzygy. As above defined, the 206 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 15.-True Geocentric Distance of the Moan Date Distance Date Distance Date Distance (Earth-radii) (Earth-radii) (Earth-radii) 1973 1974 1974 Dec. 9.0 56.690 165 Jan. 0.0 62.088 438 Oct. 24.0 63.390 466 9.5 56.444 821 0.5 61.729 311 24.5 63.412 087 P-S 10.0 56.268 904 1.0 61.336 876 25.0 63.384 060 Dec. 10. 5 10.5 56.166 337 FQ 1.5 60.914 330 25.5 63.308 309 FM, 10. 1 11.0 56.138 847 Jan. 1.8 2.0 60.465 972 26.0 63.187 606 11.5 56.185 898 2.5 59.997 253 26.5 63.025 490 12.0 56.304 752 3.0 59.514 777 27.0 62.826 173 12.5 56.490 670 3.5 59.026 261 27.5 62.594 426 13.0 56.737 208 4.0 58.540 433 28.0 62.335 460 13.5 57.036 598 4.5 58.066 867 28.5 62.054 791 14.0 57. 380 166 5.0 57.615 743 29.0 61.758 098 14.5 57.758 755 5.5 57.197 537 29.5 61.451 073 15.0 58.163 125 6.0 56.822 650 30.0 61.139 269 15.5 58.584 304 6.5 56.500 972 30.5 60.827 956 16.0 59.013 875 7.0 56.241 432 31.0 60.521 986 FM LQ 16.5 59.444 197 7.5 56.61 541 Oct. 3 1. 1 31.5 60.225 667 Dec. 16. 7 17.0 59.868 552 P-S 8.0 55.936 984 Nov. 1.0 59.942 676 17.5 60.281 232 Jan. 8.5 8.5 55.901 289 1.5 59.675 989 18.0 60.677 566 FM 8.5 9.0 55.945 614 2.0 59.427 850 18.5 61.053 896 9.5 56.068 676 2.5 59.199 786 19.0 61.407 518 10.0 56.266 830 3.0 58.992 645 19.5 61.736 588 10.5 56.534 278 3.5 58.806 686 20.0 62.040 010 11.0 56.863 408 4.0 58.641 689 20.5 62.317 303 11.5 37.245 202 4.5 58.497 092 21.0 62.568 467 12.0 57.669 689 5.0 58.372 146 21.5 62.793 845 12.5 58.126 401 5.5 58.266 063 22.0 62.993 981 13.0 58.604 803 6.0 58. 178 171 22.5 63.169 502 13.5 59.094 665 6.5 58.108 031 23.0 63.320 995 14.0 59.586 368 7.0 58.055 549 23.5 63.448 913 14.5 60.071 146 P-Q 7. 5 38.021 031 24.0 63.553 492 LQ 15.0 60.541 247 Nov. 7. 7 8.0 58.005 212 24.5 63.634 691 Jan. 15.3 15.5 60.990 037 LQ, 7. 1 8.5 58.009 231 A-S 25.0 63.692 157 16.0 61.412 040 9.0 58.034 571 Dec. 25.2 25.5 63.725 208 16.5 61.802 935 9.5 58.082 954 NM, 24.6 26.0 63.732 848 17.0 62.159 514 10.0 58.156 198 26.5 63.713 792 17. 5 62.479 601 10.5 58.256 059 27.0 63.666 530 18.0 62.761 965 11.0 58.384 050 27.5 63.589 391 18.5 63.006 198 11.5 58.541 266 28.0 63.480 646 19.0 63.212 594 12.0 58.728 214 28.5 63.338 606 19.5 63.382 019 12.5 58.944 672 29.0 63.161 745 20.0 63.515 778 13.0 59.189 579 29.5 62.948 824 20.5 63.615 481 NM 13.5 59.460 977 'P. 0 62.699 026 21.0 63.682 919 Nov. 14. 0 14.0 59.755 984 30.5 62.412 089 21.5 63.719 945 14.5 60.070 829 31.0 62.088 438 A-S 22.0 63.728 363 15.0 60.400 921 31.5 61.729 311 Jan. 22. 5 22.5 63.709 838 15.5 60.740 967 32.0 61.336 876 NM, 23.5 23.0 63.665 816 16.0 61.085 107 "ordinary" cases are separated by a maximum distance and Nautical Almanac since the 1972 edition. One im- in time from perigee. portant fact must be borne in mind in this transfer from However, a more sensitive measure of changes in figure the direct measurement of the Moon's geocentric distance of the lunar orbit is provided by use of hourly values of the in Earth-radii to the inverse measure of this distance .by lunar parallax, tabulated in The American Ephemeri5 use of parallax values indicated in minutes and seconds of Essential Conditions for Achieving Amplified Perigean Spring Tides 207 arc: namely, Ithat the two methods and their correspond- the theoretically assumed'and the actual times are given ing units also indicate a change in distance in exactly in the examples which follow, with the data given con- opposite ways. forming to the latter circumstance. Allowing for this small Secondly, in interpreting the figure of the lunar orbit exception from idealized lunar motion, the instantaneous in general, a change in the major axis of the orbit through curvatures of the lunar orbit at times agreeing quite induced perturbations is necessarily accompanied by a closely with the particular astronomical conditions enum- change in orbital size and shape, but the exact configura- erated above are discussed in each case. Although the tion assumed is also dependent upon resultant or simul- combinations of perigee-syzygy and perigee-quadrature taneous changes in the orbital eccentricity. The eccen- cannot occur within the same lunation, examples chosen tricity bears no one-to-one 'relationship with either the from successive lunations closely spaced in time have been local or instantaneous curvature of the orbit. Eccentricity used for purposes of comparison. The individual ex- (e) is a function of the relative lengths of the major (a) amples are arranged in order of increasing parallax so and minor (b) axes of the ellipse according to the re- that the numerical, progression in parallax values from lationship: e= (a'-V) @6/a. Curvature (related to in- apogee-syzygy to perigee-syzygy is clearly evident. stantaneous values of the geocentric distance) is a func- 1. Apogee-Syzygy tion of the changin / -values of the radius vector directed 9 In this case, because of the position of the Moon at toward the Moon fro'm 11 this same geocentric position (see apogee, the distance of the Moon from the Earth is great. fig. 24). Since the eccentricity of the lunar orbit is increased by In this same connection, it is also important to note the coincidence of syzygy with apogee, the lunar distance that the actual curvature of the orbit is expressed con- from the Earth is further increased and the parallax versely by the terni "radius of curvature." A large radius reaches a corresponding very low value. of curvature implies a relatively flat orbital curve, and a At this time also, the hourly differences in parallax are small radius of curvature indicates a more sharply curved decreasing very slowly from already small values toward section of the orbit. 0.00" at minimum parallax, and thereafter increasing by Finally, in the following comparisons, it will be noted the same small increments. The approximate hourly rate that neither the points of maximum change in the hourly of change around the time of apogee-syzygy in the two parallaxes, nor the times of convergence of those values examples is only about - 3"' per lunar day. on 0.0", necessarily agree with the exact times of occur- In terms of the changing value of the lunar distance rence of the above-designated orbital positions-or with with time which defines the instantaneous figure of the the mean times of their various combinations. Rather, by lunar orbit, this very small change over an extended nature, they must coincide with the exact times of the period results in a section of the orbit having a com- greatest or least distance of the Moon from the Earth, paratively small curvature and at maximum distances whereas the positions specified may or may not do so. Both from the Earth. Examples Date Phase Variation in A?r Approx. Value of Approx. Value of Of Mean A-S Of Zero A7r ir at A7r-O A7r Per Tidal Day 1973 Dec. 25.3 ............... Dec. 25.9 ......... NM to 0.0 to 53156.50" - 2.94" 1974 Jan. 22.7 ............... Jan. 21 .9 ......... NM to 0.0 to 53156.73" -3.3011 2. Apogee- Quadrature The extension of the lunar orbit along this latter axis Under this circumstance, the apogee position in orbit which occurred at apogee-syzygy is not present and, after is as far removed as is physically possible from any influ- passing through apogee-quadrature, the parallax is in- ence of syzygy. In consequence@ the resultant configura- creased slightly as the Moon, moving toward new or full tion represents a modified condition of apogee in which moon, is deflected toward the Earth by the normal com- the lunar orbit is perturbed by the Sun exerting its ponent of the Sun's gravitational force. gravitational force at right angles to the line of apsides. The hourly differences in the parallax values decrease 208 Strategic Role of Perigean Spring Tides, 1635-1976 numerically through very small negative values toward tricity than that associated with apogee-syzygy. The con- 0.0" near apogee-quadrature, and thereafter increase figuration produced is also one of very slightly increased positively. at the same slow rate. The result of this astro- local curvature at apogee-quadrature, in which position nomical alignment in terms of the instantaneous figuie the average change in lunar parallax has increased to of the lunar orbit is an ellipse of somewhat smaller eccen- approximately -5.6" per lunar day. Examples Date Phase Variation in Ar Approx. Value of Approx. Value of 7r at A7r= 0 A7r Per Tidal Day Of Mean A-Q Of Zero A7r 1974 Oct. 23.8 .............. Oct. 24.5 ......... FQ to 0.0 to 54'12.9011 -5.7011 1974 Nov. 21.6 .............. Nov. 21.3 ........ FQ to 0.0 to 54! 13.1211 -5.5711 3. Ordinary Syzygy hourly difference at the time of syzygy. Upon reaching This represents an orbital situation in which the po- this maximum, the hourly rate of change holds constant sition of syzygy is located as far as possible from either for some hours, and then declines as slowly as it increased. perigee or apogee-i.e., itinvolves. a syzygy that occurs in In consequence of the rather large values of the hourly the same lunation in which perigee coincides with differences in parallax, both the parallax and the curva- quadrature. ture of the orbit change considerably. The effect of the Under this condition, the lunar parallaxes are increas- small value of the second difference is to extend this steady ing rapidly as the result of relatively large values of the increase in parallax over a longer period of time. Through- hourly differences. The rate of change (second differ- out this period, the hourly increase in parallax is cumu- ence) is itself slowly increasing numerically (either posi- lative, building to a difference of slightly more than 0.5' tively or negatively) toward a maximum value of the per tidal day in the following typical cases. Examples Date Phase Max. A7r Approx. Value of Approx. Value of Of Mean S Of Max. A7r 7r at A7r = max. A7r Per Tidal Day 1974 Oct. 31.0 ............... Oct. 30.3......... FM + 1. 44" 56121. 03" +35.50" 1974 Nov. 14.0 .............. Nov. 15.5 ......... NM - 1. 60" 56139.1611 -39.2911 4. Ordinary Quadrature slowest rate, of growth or decline encountered among any This configuration is one in which the position of of the examples considered, thus maintaining a nearly quadrature is located at a maximum separation from constant, large increment or decrement. either perigee or apogee-i.e., the quadrature occurs in This implies that the parallax is continuously increasing the same lunation in which perigee coincides with either (and the lunar distances are decreasing-or vice versa) new moon or full moon. for a considerable period prior to quadrature, resulting When quadrature is, so positioned, the hourly dif- in a sizable cumulative change. Because of the large ferences in lunar parallax attain their maximum values hourly differences, the increase in parallax amounts to (increasing positively toward first quarter moon and nearly .1' per lunar day in the present examples. The negatively toward last quarter moon) and thereafter de- crease numerically, but carry the same algebraic sign. As accompanying orbital configuration will be one possessing they approach and pass their respective maxima, the both sharper curvature and greater instantaneous paral- hourly differences themselves are subject to change at the lax than are. present in the previous cases. Essential Conditions for Achieving Amplified Perigean Spring Tides 209 Examples Date Phase Max. Ar Approx. Value of Approx. Value of Of Mean Q Of Max. A7r 7r at A7r =max. A7r Per Tidal Day 1974 Jan. 1.8 ................ Jan. 3.8 .......... FQ +2.42" 58'33. 96" +59.76" 1974 Jan. 15.3 ............... Jan. 13.2 ......... LQ -2. 44" 56'38.62" -56.0711 5. Perigee-Quadrature effect of the greater parallax is felt is proportionately In this instance, the position of lunar quadrature is extended. subject to-the added influence of perigee. The existing In addition to the fact that the parallax values are small values of hourly difference in parallax decrease higher than at ordinary quadrature because of its coin- numerically only slowly--converging on 0.0" as the Moon cidence with perigee, the rate of decline (as well as en-. approaches this combined alignment-rather than in- suing growth) of these values proceeds at an average rate crease as in the case of ordinary quadrature. In conse- (in the examples represented) of -only about 3.01' per lunar day. This results in a prolongation of the relatively quence, the lunar parallax-itself at relatively high high values of the parallax, and a longer lasting, close-to- values-remains nearly constant at these values and minimum distance of the Moon from the Earth. The changes far less rapidly than in the case of ordinary curvature of the lunar orbit is, simultaneously, appre- quadrature. The resulting period of time over which the ciably flattened. Examples Date Phase Variation in Ar Approx. Value of Approx. Value of Of Mean P-Q Of Zero A7r r at Ar==o A7r Per Tidal Day 1974 Nov. 7.7 ............... Nov. 8.2 .......... LQ to 0. 0 to 59'16.20" +2.50" 1974 Apr. 28.5 .............. Apr. 27.7 ......... FQ to 0. 0 to 59'22. 24" +3.421/ 6. Perigee-Syzygy centricity as the Moon passes through apogee in the re- Subject to this combined effect, the gravitational forces maining half of the orbit; also (2) the normal com- on the lunar 'orbit caused by the Moon bei ng in direct ponent of the Sun's disturbing force (a) decreases the alignment with the Earth and Sun at syzygy are further lunar orbital eccentricity as the Moon revolves from reinforced by the Moon being simultaneously at peri Igee. apogee to perigee; and (b) increases the eccentricity dur- Other complex changes in the figure of the lunar orbit ing the Moon's motion from perigee to apogee; while which must be considered in this connection are: (1) (3) the tangential component of the Sun's disturbing the tangential component of the Sun's disturbing force force acts to increase the major axis of the lunar orbit at any position of the Moon. As seen from the equation on the Moon (a) increases the eccentricity of the lunar for tangential force in part II, chapter 4, this factor is orbit as the Moon moves from a point halfway between the most effective when the orbital velocity of the Moon apogee and perigee through perigee to a point halfway is the greatest, at the position of lunar perigee. between perigee and apogee'; and (b) decreases the ec- In addition,.the gravitational influences are reinforced by an extension of the period of time the Moon remains Supplementary Note: A summary table of the perturbational near an extreme minimum, gravitationally enhancing ap- effects of the normal, orthogonal, and tangential components of the disturbing force is given on page 332 of F. R. Moulton's An Intro- proach to the Earth at perigee-syzygy. The unusually duction to Celestial Mechanics (2d rev. ed., 1914). However, the small lunar distances from the Earth are created a con- influence of the tangential force on eccentricity during successive siderable time before perigee and last for an equal time intervals in the lunar orbit as tallied is just backward in comparison with the mathematical analysis on page 328 of this same work. afterward. These distances, as represented (inversely) 202-509 0 - 78 - 16 210 Strategic Role of Perigean Spring Tides, 1635-1976 by the lunar parallax, characteristically decrease quite proceed at very much slower rates than the change in slowly as the Moon approaches its perigee-syzygy position. parallax at either ordinary syzygy or ordinary quadrature. At perigee-syzygy, the very large values of the parallax The average changes in the lunar parallax in these three do, in fact, actually change at a very slightly faster rate separate cases are approximately 11", 37", and 58" per than the corresponding low values at -the opposite extrem- lunar day, respectively. And, of course, the value of the ity in orbit, lunar apogee. The maximum parallaxes (and parallax itself in the case of perigee-syzygy is greater than minimum lunar distances) at perigee-syzygy also last a that in all of the preceding examples. slightly shorter period of time at their extreme values Accordingly, the resulting instantaneous orbital con- than do the minimum parallaxes and maximum lunar distances at the previously discussed apogee-syzygy po- figuration is one.in which, while the Moon is at a position sition. (Cf., top and bottom solid curves in both figs. 37 of nearly closest possible approach to the Earth in its and 38.) orbit, the curvature of the orbit is also the smallest pos- However, approaching perigee-syzygy, both the in- sible. A corresponding increase in the duration of the crease to the maximum parallax and the amount of near-maximum tidal forces produced by the Moon's ex- change in these extreme maximum values of the parallax treme proximity to the Earth occurs. Examples Date Phase Variation in Ar Approx. Value of Approx. Value of Of Mean P-S Of Zero Air ir at A7r 0 A?r Per Tidal Day 1974 Jan. 8.5 ................ Jan. 8.5 .......... FM to 0. 0 to 61'30. 01" + 11. 64" 1973 Dec. 10.5 .............. Dec. 10.9 ......... FM to 0. 0 to 61'14.43" + 10. 96" The detailed representation of four contrastingly dif- through increasing longitude from 00 to 360' and then ferent curves of parallax, representative of cases 1, 2, 5, repeating. and 6, above, plotted for appropriate positions in the Near the top of each chart, along appropriate hori- lunar orbit, will now be analyzed. zontal axes, true elongations of the Moon from the Sun are indicated as angular values from 0' or 360' at new .A Quantitative Comparison of the Lunar moon (conjunction), through 90' at first quarter moon, Parallax at Times of Perigee and Apogee 180' at full moon, and 270' at third quarter moon. It If successive equatorial horizontal parallax values should be brought out in terms of an analytic discussion representing the Moon's changing distance from the in the next section that both of these scales represent Earth are plotted against the time (expressed in terms of true (apparent) rather than mean longitude. lunar longitude in orbit) and the true elongation of the The dashed horizontal line shows the relationship. of Moon with respect to the Sun, for a period on either side the mean or average horizontal parallax during one lunar of perigee-syzygy, the curve peaks represented in the year, for all dynamic conditions involving the Earth, upper left and central portions of figs. 37 and 38 result. Moon, and Sun. The cen ter-to-center distances of the In these graphs, the ordinate values represent the closer Moon from the Earth, in kilometers, corresponding to proximity of the Moon to the Earth as a function of in- various significant astronomical alignments and circum- creasing height (or positive amplitude)' of the curve. stances, are also included. Alongside each curve are numbers in circles which indi- In fig. 37, the solid curve depicts the decreasing dis- cate (from left to right) the passage of time in terms of tance of the Moon from the Earth between 1962 March successive dates of the month. The abscissa axis shows, 1 and the Moon's closest approach at the perigee of at the bottom (from left to right), movement of the Moon March 6.43, then through a distance increasing continu- FIGURE 37-This diagram illustrates typical values of the lunar parallax occurring at: (1) the close perigee-syzygy (proxigee-syzygy) alignment of 1962 March 6, greatly contributory to tidal flooding; (2) the immediately follow- ing instance of apogee-syzygy; (3) a representative perigee-quadrature; and (4) a case of apogee-quadrature. Figure 38 shows similar comparative examples. Essential Conditions for Achieving Amplified Perigean Spring Tides 211 -z:@-True Elongation- March -=>. 206' 29V 312' 326' 340' 354* Bo 22' 36, 50, 63' 75, 88. 9V 111' 122' 133o 144o 155o 165o 176o 187o 198o 2W 221o 23f 24C 356,8 k ,P-PERIGEE-SYZYGY 80 P Mar 6 1000 E.T. NM Mar 6 1031 E.T. 5 60 VARIATION OF LUNAR DISTANCE (PARALLAX) WITH PHASE AND APSE ALIGNMENTS-1962 40 4 9 20 12,546 km 360d' -3-True Elongation- June, July 179. 192- 20 210- 231- 244- 257- 210- 2 8V 29 309' 322' 335' 347' 360' 1.2. 23' 35' 47' 58' 69' 80' 90' 101* 11 V 124' 136' 80 10 60 @ri F - J(@@ - 25 369,394 km cc 40 4 U- 0 2 20 PADRATURE P Jun 23 2000 E.T. LLI LO Jun 24 2343 E.T. 0 35od 29 x 80 60 12 z 40, !Letj f [email protected]!LMo.n 3422.70" 0 20 ---------------- -------------------- ----- --------------------------------------------- (384,372 km) 13 3406 80 27 Uj 60 14 40 20 1 V ii 26 3300' APOG@E-OUADRATURE 25 A Jul 8 1200 E.T. 80 16 FQ Jul 9,2340 E.T.(: . 24 404,236 km 17 (@Oy 60 (D-, 23 APOGEE-SYZYGY ft% A Mar 19 2100 E.T. 18 2,04. l(m 22 32461 FM Mar 21 0756 E.T. 19 2a3-km- 260' 286 306 320' 340' 3611Y 26 46 60' W 100" 120Y9 140' 16 ' 186 200' 22a 240' 260P APPARENT LONGITUDE OF MOON 212 Strategic Role of Perigean Spring Tides, 1635-1976 ously to the position of apogee on March 19.88 and, there- abscissa and ordinate systems, but with different appro- after, diminishing again toward the next perigee on April priate dates to show the change in parallax values oc- 3.88. curring between successive conditions of perigee-quad- Certain comments are in order in connection with these rature and apogee-quadrature. The first set of curves graphs: (fig. 37) corresponds to times in June and July 1962 1. The mean epoch of perigee-syzygy in fig. 37 is 1962 when the Moon at last quarter and first quarter was in March 6 1015.5' or March 6.4274 (e.t.). On the scale a position very close to (although not precisely in agree- of these graphs, the values of r are plotted by half-day ment with) perigee and apogee, respectively. (In these intervals only. Rounding off to the nearest half-day, the various analyses, it is important to note a technical dis- ephemeris value for ?r on March 6.5 is 61'2.6702"= tinction: the date of perigee implies that the Moon ac- 3,686.702". Again, in figs. 37-38, one second of arc is tually occupies its closest monthly position to the Earth; the smallest unit plotted. In the interpretative discussion the position of perigee does not necessarily imply that the given here and immediately following, seven significant Moon is actually at this location in its orbit.) At times of figures will be retained and finally rounded back to six perigee-quadrature and apogee-quadrature, the gravita- only to demonstrate the, sensitivity of 0.001" in parallax. tional force of the Sun acting upon the Earth is directed Other practical considerations obviously preclude an ac- at right angles to the force of the Moon exerted on the curacy given to the nearest mile in the results. Earth, and the Moon's tide-raising action is considerably The formula for converting parallax angles to linear reduced. distance is In the January 1962 positions of perigee-quadrature R @ 206,264.8"r/s", where (fig. 38), the first quarter moon very nearly coincides R@ the center-to-center distance between the Earth with the position of perigee, while the third quarter moon and the Moon, in kilometers or miles is closely aligned with the position of apogee. Again, as r = the equatorial radius of the Earth in the same in the first example, a line drawn from the Moon to the Sun is at 90' to the line of apsides connecting perigee units (6,378.160 km=3,963.205 mi) and apogee. =the geocentric parallax of the Moon, equal to the In accordance with both the lunar evection and lunar arc, in seconds, subtended at the distance of variation effects on parallax outlined in chapter 4, when Moon by the Earth's equatorial radius the line of apsides coincides with quadratures, parallax is Thus, the lunar parallax at this approximate perigee- affected the least. The amplitudes of both the peak and syzygy position of 1962 March 6.5 corresponds to a dis- trough of the curve (fig. 37) are reduced (to parallaxes tance of 356,848 krn (221,735 mi) between the center corresponding to distances of 369,394 krn or 229,531 mi of the Moon and the center of the Earth. and 404 '236 krn or 251,181 mi, respectively). In this Lunar apogee (or exogee, in a later definition of the example, the greatest observed difference in the distance term) is attained at 2 100 e.t. on March 19. Calculated as of the Moon resulting from such syzygy-quadrature varia- before from the parallax (.7r=5358.102") for the nearest tions in parallax occurs between the mean perigee-syzygy half-day, 1962 March 20.0 (where the sign of A7r also is of March 6.43 and the mean perigee-quadrature of June changing appropriately), the Moon at this time recedes 24.41, and is 12,546 km or 7,796 mi. A much smaller to a distance of 406,283 km (252,453 mi) from the Earth. variation in distance (2,047 krn or 1,272 mi) occurs be- This is an increase in distance of 49,435 krn (30,717 mi) tween the mean apogee-syzygy of March 20.60 and the over the distance at perigee-syzygy. Since the tide-raising mean apogee-quadrature of July 9.24. force varies inversely as the cube of the distance, a siz- Similar'relationships are shown in figure 38 in the com- able additional force component is available at perigee- parison of the mean perigee-syzygy of October 13.32 with syzygy compared with apogee-syzygy. the mean perigee-quadrature of January 3.69, and the 2. A second pair of curves, consisting of alternate dots mean apogee-syzygy of October 27.86 with the mean and dashes, has been plotted with reference to the same apogee-quadrature of January 17.60. FiGURE 38.-The interpretation of these curves and those of figure 37 is contained in the text. The value of the mean lunar parallax indicated (3422.70") is that published in Explanatory Supplement to the Astronomical Ephemeris and The American Ephemeris and Nautical Almanac (1961) pp. 26s, 27s, just prior to the case examples indi- cated. This value was subsequently announced to be a misprint. The corrected value as it appears in Supplement to the A.E., 1968 (1966) pp. 20s, 26s, is 3422.608". The slight difference is, however, in this instance negligible. Essential Conditions for Achieving Amplified Perigean Spring Tides 213 -.*-True Elongation -October 11' No 1! 11.1' 1.1' 111' 117. 1W 1449 158- 173- 1117- 201- 215- 228- 241- 254- 256' 277- 289- 300- 311- 321- 332- 343, 356,934 krn PERIGEE-SYZYGY 13 80 P Oct 13 0300E.T. 4 FM Oct 13 1233E.T. 12 60 VARIATION OF LUNAR DISTANCE (PARALLAX) WITH PHASE AND APSE ALIGNMENTS - 1962- 63 40 20 8,088 km 16 3606 10 -,*-True Elongation -December, January (1963)-==> 313' 314' 325' 337o 3411o 360, 12* 25' 37' 50' 63, 76o 89 103o 116, 12 142' 155c 168o 180' 193' 205o 216o 228o 239o 250o 261o 272' 80 .91 60 ib 9 40 369,950 km LL 0 20 PERIGEE- OUADRATURE P Jan 4 0800 E.T. FO Jan 3 0102 E.T. LU 35Cd 0 X B 80 60 4 i.- z 40 0 7 N Mean Parallax of Moon 3422.7d' cc - - - - - - - - - - - - - 0 20 ------------------- -------------------------- ------------------------ 3: (384,372 km) 4 3406' 27 OR 6 20 80 w 26 60 40 21 V) 20 330d 22 APOGEE-QUADRATURE A Jan 17 0800 E.T. LO Jan 17 2035 E.T. 80 1& 23 404,3281tkm 60 2 APOGEE-SYZYGY 2 Oct 26 0400 E.T. *_@ A 1,9 km 3240 NM Oct 28 1305 E 5 20 230' 250' 27(Y 2W 310* 33a 350' 10' 34T 50' 71T W 110' 130' 150@ 176 90@ 21a APPARENT LONGITUDE OF MOON 214 Strategic Role of Perigean Spring Tides, 1635-1976 3. Most distinctive of the relationships between the tides as a result of the syzygy alignment. It will shortly be several curves, however, are the much steeper slopes and graphically demonstrated (figs. 153-163) that, because narrower and sharper crests shown for the perigee-syzygy of the Moon's closer approach to the Earth at perigee, dates compared with the corresponding perige@e,-quadra- considerably higher tides occur at perigee-syzygy than at ture, apogee-quadrature, or apogee-syzygy dates. apogee-syzygy. A cogent preliminary question is, why are Significantly, the period of time required to cover ap- some perigean spring tides higher than others? proximately 180' of celestial longitude centered around perigee in the first two cases is approximately the same, Effects of the Individual Syzygies 12 days. Yet, on each day of the 12-day period from 1962 In this respect, it is first necessary to note (figs. 39-40) March I to March 13, the Moon has moved a far greater the important distinction that the gravitational attraction distance toward the Earth (indicated by the steepness of of the Sun upon the Moon when it is at full moon is not the curve's slope) than in the 12-day period 1962 June the same as when it is at new moon. This difference in 18 to June 30. Because of this considerably greater "in- the force attraction of the Sun upon the Moon as exerted and-out" motion with respect to the Earth (substantiated at conjunction and at opposition can have a perceptible by the fact that radial components along the line-of-sigbt effect on: (1) the lunar evection term and the Moon's do no pro 'duce any apparent change in longitude), the resulting proximity to the Earth (i.e., the lunar parallax) ; Moon's orbital motion must also be far swifter at this (2) the corresponding tidal forces acting on the Earth; time to cover the same angular distance across the sky and (3) the orbital velocity of the Moon in crossing the in the same period of time. The sharper peak of the curve nearly common line of apsides and syzygies (here as- at the time of perigee-syzygy thus also graphically demon- sumed to be coincident, although such a precisely com- strates the dynamically imposed circumstance of greater mensurable relationship is practically impossible of attain- angular speed of the Moon at this time resulting from the ment in nature) parallactic inequality, and the need of an increased catch- The mass of the Sun is 333,432 times that of the Earth, up interval by the rotating Earth (see pt. II, ch. 6). and the Sun's gravitational force (disregarding its Conversely, the more rounded crest on the perigee- greater distance from the Earth) is proportionately larger quadrature curve indicates a smaller radial component than that of the Moon. However, because of the much of motion as well as a smaller orbital velocity. The effect closer distance of the Moon from the Earth compared is also very evident in comparing the rounded peak of with the Sun-Earth distance, the gravitational force of the curve depicting the Moon's approach to apogee- the Earth on the Moon will always be greater than, and syzygy and 'the much sharper peak associated with override that of the Sun. The basic eccentric configura- perigee-syzygy. tion of the Moon's orbit and the location of the perigee (It must be carefully noted that the daily differences and apogee positions are, nevertheless, subject to the alter- in parallax quoted in the discussion of local orbital curva- ing and perturbing influence of the Sun's gravitational ture in the preceding section represent corresponding attraction. changes in lunar distance over a very small portion at 1. Case One: Full Moon at Perigee the extreme peaks of the present curves. The curves of fig- ures 37, 38 represent the change in the parallax, while When full moon occurs nearly coincidentally with peri- their geometric slopes denote the rate of change of the gee (fig. 39), the Sun's evectional perturbing force is parallax, over periods of an entire week before and after exerted directly along the same axis representing the perigee. Different conditions of curvature of the lunar Earth's gravitational force on the Moon. The result of orbit obviously will result from the eight configurations these combined gravitational forces of Sun and Earth is represented.) to deflect the Moon earthward toward a position interior to that which would be the case subject to the Earth's Causes of Variation in the Shape of the gravitational force alone. In the case of a full moon occur- ring almost exactly at perigee, the forces of the Sun and Lunar Orbit and in the Consequent Earth act together in the same direction and the amount Tide-Raising Forces of inward deflection of the Moon, subject to the full re- sultant f6rce (EM+SM), reaches a maximum. Thus, In either of the two cases, full moon at perigee or new for increasingly closer perigee-syzygy alignments, the moon at perigee, the Sun's gravitational force reinforces Moon comes correspondingly closer to the Earth. The that of the Moon and acts to raise increased (spring) lunar parallax increases accordingly. Essential Conditions for Achieving Amplified Perigean Spring Tides 215 LUNAR SYZYGY EFFECT ON PARALLAX VECTOR DIAGRAM FORCE VECTORS AND VECTOR DIAGRAM DISTANCES ARE NOT TO SCALE S S E NM 11 TO SUN I/ @@_O_S_Q N N PERIGEE JE APOGEE I I APOGEE PERIGEE 1E FM F ki S S, E E VECTOR DIAGRAM VECTOR DIAGRAM FIGURE 39-The lunar orbital perturbing effect which FIGURE 40-The corresponding situation with all other exists when a perigee-syzygy alignment occurs at full factors unchanged, but with perigee-syzygy occurring at moon. The' reinforcing gravitational attractions of the new moon. The gravitational attraction of the Sun upon Sun and Earth together result in a greater parallax than the Moon is then subtracted from the pull of the Earth if their attractions on the Moon are opposing, as is the on the Moon. The resultant perturbational displacement case when perigee-syzygy coincides with new moon. of the Moon toward the Earth is not as great as in figure 39. As the Moon revolves from perigee-syzygy (FM) to the Moon, directly opposed to that of the Earth and reduced next succeeding apogee-syzygy (NM), it moves addition- thereby (SM-EM'), still acts to increase the apogee ally outward in orbit as the Earth's gravitational attrac- distance by a sensibly greater amount, and a maximum tion for the lunar body is reduced by that of the Sun ex- apogee distance is reached at the new moon immediately erted in the opposite direction. Because of the much preceding or following the full moon which occurs at smaller Earth-Moon distance compared with, the Sun- perigee. Oppositely stated, the net or resultant centripetal Moon distance, the Earth's gravitational force on the force vector obtained by subtracting the Sun's gravita-_ Moon is larger than that of the Sun and remains.in con- tional force from that of the Earth on the Moon is re- trol of the Moon's orbital revolution. The lunar apogee duced, and the Moon moves outward toward ai@ greater position is established solely by the Moon's elliptical mo- tion in the two-body Earth-Moon system. However, this distance from the Earth. configuration of new moon-apogee in which the Moon-is The lunar orbit acquires a larger eccentricity e (see farthest from the Earth also means that it is simultane- pt. 11, ch. 4), which has the same effect along the line of ously in a closer position to the Sun than at full moon, and apsides as if the entire orbit were shifted toward the Sun closer to the Sun than the Earth is. Ile Sun's force on the in fig. 39. S S E 216 Strategic Role of Perigean Spring Tides, 1635-1976 2. Case Two: New Moon at Perigee cident increase in the sernimajor axis a of the Moon's Now consider the situation where the new moon is at orbit, but to a lesser extent; (5) since the value of the perigee and the full moon at apogee (fig. 40). Ile Moon parenthetical term in the equation q-a(I-e) thus de- is closer to the Sun at this NM-perigee position than it creases at a faster rate than a increases, the value of q, the is at FM-apogee. The gravitational attraction of the Sun perigee distance, must also diminish at perigee-syzygy; upon the new moon, although greater than in the FM- (6) as q grows smaller, the orbital velocity V of the Moon perigee example, is now oppositely directed to the force must increase at this time in accordance with @Kepler's of the Earth on the Moon and must be subtracted there- third law. from. In terins of the net force EM-SM, because the The consequent catch-up effects responsible for length- Sun's force on the Moon is larger than in case 1, as well ening the lunar day and month will be desczibed in the as being opposed to that of the Earth, the resultant cen- following chapter. tripetal force is smaller, and perigee distance is not re- duced as much. Likewise, at the apogee position which is, in this second A numerical example showing the actual computed values (FM) case, more distant from the Sun than in the first of the eccentricity and semimajor axis of the lunar orbit (NM) case, the Sun's perturbing force is weaker than at a time of extremely close perigee-syzygy (proxigee-syzygy) before. The Earth is, however, now located closer to the as compared with the mean values of these same quantities will best serve to confirm the previous statements. The de- Sun than the Moon is, and is gravitationally displaced termination of these two elements of the lunar orbit would from the Moon toward the Sun, increasing the distance ordinarily pose all of the difficulties of a three-body problem between Earth and Moon. Thus, the apogee position is where the Moon, as here, is subject to the strong perturba- again moved to a relatively greater separation from the tional action of the Sun. However, where the Moon's Earth, but not as much so as in the NM-apogee case. In instantaneous position in orbit already has been computed from lunar theory, using the appropriate equations of dis- figs. 39-40, the Moon's orbit is effectively displaced to turbed motion, it is possible to reverse the computational the right with respect to the Earth in the first case, and process and determine the instantaneous values of these to the right (although not as much) in the second case. elements. For the foregoing reasons, the highest values of the The equations for a conic section given in a succeeding lunar parallax are all found in the combination of full paragraph apply, in general, only to a Keplerian ellipse moon and proxigee-syzygy in table 13. As described in completely free from external or interrial disturbing forces. Altemately, they are applicable in a so-called osculating the second following section, when the Moon is near solar orbit at the position (or instant) of osculation selected for perigee, these influences are further enhanced. computational purposes where the actual, or perturbed, In recapitulation, it is clear that, among the various f ac- and the theoretical, or unperturbed, orbits coincide. The tors contributing to a closer proximity of the Moon to the particular orientation of the Sun, Earth, and Moon along, Earth at perigee-syzygy, the initial cause is the change- in or very close to, the extended lunar line of apsides corre- sponding to a time of perigee-sy7ygy provides just such a eccentricity e of the lunar orbit resulting from evection. case lending itself to analysis using the special properties of The solar gravitational influence acts as an additive force, an osculating orbit. increasing the eccentricity of the lunar orbit as the Moon In methods of three-body or disturbed orbit computation, approaches the position of perigee. The sequence of events it is customary to choose as the initial osculating. position, is: ( I ) passage of the Sun across the lunar line of apsides in both the perturbed and unperturbed orbits, the position of perihelion-or, in the case of the Moon, the matching at either upper or lower apse--7a necessary accompaniment counterpart is perigee. Thus, the instant of t @ 0, the epoch of a perigee-syzygy alignment; (2) an increase in e with of osculation, becomes the position of perigee, and the orbi- the Moon at perigee-syzygy, produced by the solar tan- tal element T specifies the date and time when the Moon gential force (whose effect on e ranges from zero to a is at perigee. Subject to close perigee-syzygy conditions, this maximum influence to zero again between the two inter- time is also within less than an hour to a few hours of the sections of the force vector and the minor axis of the lunar instant of alignment of Earth, Moon, and Sun at syzygy. The circumstance of perigee-syzygy therefore provides a orbit) with a corresponding decrease in e as the Moon singular opportunity to study the effect of perturbations on nears apogee-syzygy; these effects are accompanied by a the lunar orbit in their least complicated form. The lunar decrease in e as the Moon moves between apogee and evection is the perturbation most effective in increasing perigee, produced by the normal force of the Sun's gravi- the values of both the eccentricity and semimajor axis of the lunar orbit at this time. Its effects will now be quantitatively tational attraction upon the lunar orbit; (3) a resulting. evaluated by the use of computed data in The American net increase in e at the time of perigee-syzygy; (4) a coin- Ephemeris and Nautical Almanac. Essential Conditions for Achieving Amplified Perigean Spring Tides 217 Where: of the Moon, at this position in orbit. This value corre- v=the true anomaly, or angular distance of the Moon sponds to the dimension of p. from perigee The value for q for the instant of perigee-syzygy also can p=the latus rectum of the Moon's elliptical orbit, be obtained from this same table. equivalent to the radius vector (p) for v=900 Then since: q=the perigee distance, or least monthly distance be- tween the Moon and the Earth e=E-1, and a= e=the eccentricit of the lunar orbit 9 p=the radius vector, or distance of the Moon from the substituting the appropriate values and following the pro- Earth at any instantaneous position in orbit cedure outlined above, a comparison can be made between Then: the results obtained for a condition of close perigee-syzygy and the adopted mean values for e and a which represent an p=q(l+e)=p(at v=900) average of all conditions encountered in the lunar orbit. q=a(l -e) =p(at v=00) For the close perigee- (proxigee-) syzygy alignment of 1974 Jan. 8.5 (G.c.t.): In 'a perturbed orbit, each of these equations is theo- (a) The value.of the apparent (true) longitude of the retically valid only for the moment of arbitrarily selected Moon interpolated from The American Ephemeris zero-disturbance in the osculating orbit-equivalent in this and Nautical Almanac for a time corresponding to case to the instant of perigee-syzygy as above described. that of perigee, and' therefor@ very nearly equiva- However, as noted several paragraphs earlier, the values of lent to the true longitude of perigee is: both the celestial longitude (A) and the -radius vector (p) 106.8287650 of the Moon tabulated in The American Ephemeris and Nautical Almanac contain the effects of perturbations and By comparison, a derivation of the approximate are, therefore, representative of the perturbed orbit. By mean longitudes of the Moon and perigee from definition, the value of p-the only quantity not evaluated tables 4-5 in Harmonic Analysis and Prediction of for the time of perigee-syzygy-is equal to the tabulated Tides gives: value of p for the position where v=90'. Hence, the time Mean longitude of the Moon corresponding to this position in the lunar orbit 90' from 106.950 perigee can be obtained by reverse interpolation in the tables for the instant where v = 90'. Mean longitude of perigee The true anomaly is the angular distance of the Moon, 106.230 expressed as a difference in longitude, from perigee. The true longitude of perigee is, in turn, equal to its instanta- (b) The apparent longitude of the Moon's position at neous angular distance from the vernal equinox. At a close point p is then: perigee-syzygy, the Moon itself must also be at very nearly 106.8287650+90.0000000= 196.828765- this same longitude. The true longitude of perigee may Whence, using inverse interpolation in the thus be obtained, to a close approximation, by extracting ephemeris to obtain the time at which the Moon the apparent longitude of the Moon from The American reaches p: Ephemeris and Nautical Almanac for the exact time of t,=Jan. 14.6866 perigee, also tabulated. An alternate proce Idure is to inter- polate the value of the mean longitude of perigee from (c) The value of p, and hence the corresponding various available tables. (At the time of perigee-syzygy, value of p at this time, obtained by the use of the mean longitude and true longitude of the Moon are polynomial coefficients in the table of true geo- theoretically the same.) However, because the instant of centric distances of the Moon is: the Moon's passing through perigee is being considered, the p=p=60.160203 Earth-radii accelerated motion of perigee at the time of perigee-syzygy (d) Similarly obtained, the value of q at the perigee of is not taken into account in the mean motion of the line 1974 Jan. 8.4583 is: of apsides, and hence in the mean longitude of,perigee. The 55.9010709 Earth-radii resulting differences are shown among the following com- P=q= putations. Then: If 90' is added to the derived true longitude of perigee, 6,@V-1=0.076005 the true longitude of the Moon at the position p is obtained. q This longitude of the Moon as it reaches the latus rectum (e) Comparing this with the mean value of the eccen- of the orbit (subject to the perturbed motion imposed in tricity of the lunar orbit: the interim since perigee) can then be used-again by a process of reverse interpolation in the ephemeris-to find e=0.05490 the time at which the Moon reaches this position. the value of the eccentricity at the time of a very Proceeding next to the table of true geocentric distance of close perigee-syzygy alignment thus represents an the Moon published in the ephemeris, this interpolated time increase of 38.4 percent above the mean value can be used to find the actual value of p, the radius vector of the eccentricity. (In the classic work, Astronomy- 218 Strategic Role of Perigean Spring Tides, 1635-1976 Vol. I, by Russell, Dugan, and Stewart, the authors The Effect of Coplanar specify that when the Sun crosses the line of apsides of the lunar orbit, the resulting increase in eccen- Lunisolar Declinations tricity is about 20 percent. This value, however, Another significant relationship evident from table 13 refers to the average of all cases, including both wide is the fact that, in each of these closest approaches of the separations between perigee and syzygy at the time of solar coincidence with the line of apsides, Moon to the Earth, the lunar declination has a positive and the special case of a close perigee-syzygy, as sign. Combined with the circumstance that all of these here exemplified. cases of maximum lunar parallax occur (near perihelion) (f) Also: in the winter months when the Sun is south of the Equator q and, therefore, always at a minus declination, the con- a= 1-e =60.509753 Earth-radii clusion is obvious. At these times of close proxigee-syzygy By comparison, at the Earth's mean distance and alignment and large values of parallax, not only are the eccentricity, the mean semidiameter of the lunar Sun, Earth, and Moon at full phase aligned nearly exactly orbit is: in celestial longitude (or right ascension) at a time near 239,000 m perihelion, but they also lie along a straight line passing d= 3,963.2 mi = 60.304804 Earth-radii from the negative declination of the Sun through the The lengthening of the semimajor axis of the center of mass of the Earth to the positive declination of Moon's orbit at the time of such a close perigee- the Moon. The combined gravitational force compo- syzygy alignment thus represents an increase of nents of the Sun and Earth, exerted in or very nearly in only 0. 3 percent with respect to its mean value. This the declinational plane, greatly enhance the total force, comparatively small increase in the sernimajor axis potential acting upon the Moon's orbit, serve to micrease over its mean value, when compared with the much the eccentricity of this orbit, and aid in augmenting the larger increase in the eccentricity of the orbit at this same time, accounts for the fact that the Moon's parallax at proxigee-syzygy to a near-maximum distance of the Moon from the Earth at perigee as value. For a further consideration of all elements con- given by the equation tributing to the above-cited winter phenomenon of the q=a(l -e) Northern Hemisphere, see also page 151, "Seasonal Fac- also consistently decreases at the time of a close tors Influencing the Production of Heightened Tides." perigee@-syzygy alignment. The three-dimensional alignment of Sun, Earth, and Moon in a common or near-common plane of declination as well as celestial longitude (or right ascension) during The Effect of Solar Perigee these winter months is thus an additional direct cause for in table 13, a very noticeable consistency appears in the preferential grouping of these tabulated maximum the fact that, over a 400-year period, the largest values of values of 7r. Significantly, the comparatively high fre- lunar parallax tabulated all occur in the winter months quency of severe coastal storms accompanied by strong, persistent, onshore winds in these winter months adds a of the year, between October 31 and March 8. This cir- further potential factor for tidal flooding at such times. cumstance immediately suggests the effect of the Sun's additional gravitational force (the solar inequality) on The Effect of Nodal Alignment the Moon at the closer distance of solar perigee, a phe- The alignment of Sun, Earth, and Moon in celestial nomenon which occurs near to the Earth's perihelion latitude is of further importance in the same connection. position. Because of the proximity of the Sun to the Moon A significant reinforcement in the magnitude of the lunar during this circumstance, the extra solar force acting adds parallax can occur when the Moon at perigee-syzygy is its effects to those noted above. By further increasing the simultaneously at one of .its two lunar nodes 0'), instantaneous eccentricity more than the sernimajor axis while the positions of perigee-syzygy and the lunar node are also in the same celestial longitude. of the lunar orbit in. accordance with the previously This condition can come about as the result of a com- described conditions, this supplemental force also in- mensurable relationship between the rotation period of creases the lunar parallax. At the same time, as will be the Moon's line of nodes and that of the lunar line of seen in chapter 6, it slightly diminishes the orbital velocity apsides. The former perturbed motion (taking place in of the Moon at perigee-syzygy by reducing the Earth's a direct, or counterclockwise sense as viewed from the pull on the Moon. north pole of the Moon's orbit) requires about 18-612 Essential Conditions for Achieving Amplified Perigean Spring Tides 219 years to complete one rotation; the latter, retrograding tween components is < 24 h, occurring over the 400-year in a clockwise sense, requires approximately 8.849 years. period between 1600 and 1999. From the special con- (The units specified are tropical years of 365.24219878 solidation of these data in table 13, it has been determined mean solar days.) that the closest approach 9 of the Moon to the Earth at a However, for the effect of nodal alignment to occur time of proxigee-syzygy during this 4-century period oc- simultaneously with both the Moon and the Sun being at curred on 1912 January 4, at 1300' G.c.t. (perigee-syzygy their closest distances from the Earth, as well as in mutual separation-interval +6.5 minutes). At this time, the full alignment in longitude-to yield the ultimate require- moon approached the Earth within a center-to-center ment for coincidence of node, apse, and perihelion-is a distance of 356,374 kin or 221,441 mi. However, this very rare astronomical circumstance. This is indicated distance can be considerably less for a point on the Earth's from the fact that, as previously specified, the last pre@ surface and directly beneath the Moon (i.e., with the vious occurrence was in A.D. 1340. Moon on the meridian of the place and directly in the zenith). For the purpose of determination of any local Summary Evaluation of Extreme tides, the effect of the lunar tide-raising action must be consider ed in terms of the Moon's distance from the Lunar Parallaxes Earth's surface at the latitude where the tides under The two principal astronomical perturbing effects re- evaluation occur. sponsible for significant changes in the values of the lunar In a similar connection, as a result of the lunar aug- parallax upon different occasions of perigee-syzygy are mentation effect (fig. 25A), the Moon is some 4,000 (a) lunar evection and (b) lunar variation. The phe- miles (a distance equal, to the Earth's semidiameter) nomenon of evection acts to increase the eccentricity of closer to the surface of the Earth when the satellite is in the zenith than when it is just rising or setting on the hori- the lunar orbit and thereby effectively to bring the Moon zon. The Moon's actual distance from the Earth's surface closer to the Earth at the position of perigee (see fig. is, accordingly, a function of the latitude of the place, the 26A). The lunar variation has a similar result, but in- vertical angular distance (altitude) of the Moon above volves a different cause in decreasing the Moon@s perigee the horizon, and the lunar declination (or vertical angular distance from the Earth at times of perigee-syzygy align- distance north or south of the celestial equator). Because ment (see fig. 27B). of the lunar nodical cycle, the latter value reaches a maxi- Because the Sun is closest to the Earth during the mum value every. 18.6 years. In the latitude of Atlantic Northern Hemisphere winter season, these two influences City, N.J., as an example, the theoretically closest possi- on the Moon's orbit occur most prominently in the winter ble approach of the Moon to the Earth's surface at this months. The closest possible approaches of the Moon to largest possible declination angle of the Moon ( -t 28'4 V) the Earth (with -resulting increased tidal forces) occur and with the Moon transiting the meridian, is 350,008 early in the month of January when the Earth is near its kin or 217,485 mi. perihelion position (closest annual approach to the Sun), 9 Note: The parallaxes listed in this table are expressed for the usually around January 2-4. times of perigee and syzygy, which may be uncertain by several The generally accepted absolute maximum value of the hours. Because of the difference between topocentric and equatorial lunar parallax (derived from Brown's lunar equations as geocentric horizontal parallax, on some occasions the lunar distance from a position on the surface of the Earth located at high the highest value theoretically possible) is w 6 V3 2" latitudes and with the Moon at a large meridian altitude may be (fig. 41) The corTesponding absolute minimum value is even less than at the precise time of perigee- or proxigee-5yzygy, as 5 3155". was the case for 1974 January 8.5 (G.c.t.). See footnote (c) in this same chapter for a further discussion of Table 16 represents a computer printout of all perigee- the 1912 January 4 instance of proxigee-syzygy in terms of the syzygy alignments in which the separation-interval be- lack of associated tidal,flooding. 220 Strategic Role of Perigean Spring Tides, 1635-1976 LUNAR PARALLACTIC INEOUALITY (MAXIMUM EFFECT) PRINCIPLE OF GEOCENTRIC HORIZONTAL ARALLAX M I N I III U M MAXIMUM EXOGEE- PARALLAX PARALLAX P R 0 X 10 E E - SYZYGY 3235 3692 SYZYGY Now or Full Now or Full Moon at More Earth ------- - ---------- Moon In Neer- Distant Apo- - Moon -------- --------- ------ *-*-( ----------------------- -,(D C nee@ iw oon W,:Inc Ide goo (Exogee) ------------------ IT Perigee, Which Next 406,154 35S,880 Reducing Its Fo ,ow@O It. k. Distance (Proxi - Proxigoo-Syzygy 252,364 2213.26 goo) from Earth Mi M. C E SEE TEXT MOON'S CHANGING DISTAN FROM EARTH FOR D 6 C L I N A T 10 H AND OTHER EFFECTS (D <24 HOURS OR <=15* (OR PRECEDES) I N LONGITUDE IS 0 10' R I. A A L 'FOR, :tle.5*to .6 44rn,e EQUATORIAL VL FiGuRE 41-A graphic representation showing that the geocentric equatorial horizontal parallax is equal to the angle subtended by the equatorial semidiameter of the Earth's figure as seen from the instantaneous distance of the Moon. The maximum value of the lunar parallax here indicated (61'32" 1") is that derived in a computerized evaluation of this term at the U.S. Naval Observatory in 1976. I TABLE 16 Cases of Perigee- (Proxigee-) Syzygy h P-S = <24 1600-1999 I . I Introduction to Table 16 The computer printout of table 16 was provided by Dr. A considerably more refined approach, more than Thomas C. Van Flandern, of the Nautical Almanac Office, doubling the number of terms defining the quantities most U.S. Naval Observatory. The mathematical expressions affected, was adopted in the preparation of the final used in deriving the quantities given in this table are listed printout. These more precise calculating expressions are below. It should be observed that several of these evaluating given in table 16B. All tables in the text (except No. 24- equations involve two different sets of series expansions. Certain of the original approximate solutions (whose see footnote in connection therewith) are now based on these constituent terms are indicated in table 16A) were found to more definitive values. show minor but unacceptable differences when compared The symbols and terminology used throughout tables with corresponding data appearing in The American Ephemeris 16A, B are given below. The corresponding symbols of and Nautical Almanac over the more than 120 years of its E. W. Brown's theory, employed' in the Improved Lunar publication. The small residuals (ephemeris value minus Ephemeris, as well as the notation used in the Explanatory computer printout value) appeared especially when the separation-interval between perigee and syzygy was 2 Supplement to the American Ephemeris and Nautical Almanac, hours or less (i.e., at a time of maximum perturbation of the adopted throughout most of the present work, are also lunar orbit in the parameters represented by the formulae). included:' Table 16 ILE ESAE L=the "average" mean anomaly of the Moon (the angular distance, in I=L-W M= (C - r I (not the longitude, of the Moon from its perigee) M of the first column) L'= the mean anomaly of the Sun (the angular distance,'in longitude, of the t'=L'-col g=L-r Sun from the solar perigee) F=the mean argument of latitude of the Moon (the angular distance, in F=L- a F= (C longitude, of the Moon from its ascending node) D =the mean elongation of the Moon from the Sun (the angular distance, in D=L-L' D= (E -L longitude, between the Moon and Sun) M= the mean longitude of the Moon=F+ Q L (I S=the mean longitude of the Sun Ll L T=the period of time, in centuries, from 1900 T T Other Equivalents the mean longitude of the Moon's node the mean longitude of the lunar perigee the mean longitude of the solar perigee r the mean anomaly of the Moon M the mean anomaly of the Sun 9 The values of the Julian Dates corresponding to syzygy The values may differ in tenths of a day from the values given in column I of table 16 are printed out from pro- given in hours in column 2. These Julian Dates form a grammed' magnetic tape compilations in the U.S. Naval direct part of an evaluative procedure only in table 24, Observatory, and are determined for the "mean instants" where an accuracy to a few tenths of a day is completely of syzygy. (See main Explanatory Comments for table 16.) adequate. Table 16A expression representing the difference in longitude between Approximate Reduction Procedure that of the Moon and Sun equal to zero: X([-XG)=D+22,640 sin L-4,586 sin (L-2D) 1. Column 2 gives the t ,line of syzygy rounded off to +2,370 sin 2D+769 sin 2L the nearest hour. Syzygy is defined as the instant the celestial -668 sin L' . . . longitudes (or, alternatively, the right ascensions) of the (All coefficients are in arc seconds.) Moon and Sun are the same, and hence the lunar elongation The results from this approximate formula were utilized is equal to zero. Initially, the following approximate finally only in table 24, where the least accuracy required equation was used for the determination of the times of is in tenths of a day. All other tables contain data derived syzygy. The desired values were obtained by setting this from the refined formulae (table 16B). 223 224 Strategic Role of Perigean Spring Tides, 1635-1976 2. The equation originally used for obtaining the geo- included in table 16B after the 17th term in the series. Data centric equatorial horizontal parallax of the Moon at the based upon the more fully expanded series of table 16B have instants of syzygy and perigee (cols. 4, 10) is given below. been recomputed for all tables included in the text. It represents a truncation of the more definitive expression 7r"(c=3,422.608+186.540 cos L +34.312 cos (L-2D)+28.233 cos 2D + 10. 166 cos 2L+ 3.086 cos (L+ 2D) + 1.918 cos W-2D) + 1.444 cos (L+L-2D) + 1. 153 cos (L- L') - 0.978 cos D -0.949 cos (L+L')-0.714 cos (L-2F) +0.622 cos 3L+0.601 cos (L-4D) -0.400 cos L'+0.372 cos (U-4D) -0.304 cos (2L-2D)-0.300 cos (L'+2D) . . . (All coefficients are in arc seconds.) 3. Perigee (or proxigee) is that position in the orbit of mate expression for rC was used in the initial computation the Moon where it reaches its closest approach to the Earth. for the time of perigee (and hence that of the separation- At this point, the parallax (which varies inversely as the interval P-S) in column 9 of table 16. The results cal- distance) attains its maximum value. Immediately prior to culated to this first degree of approximation have been the position of perigee, the values of the parallax which incorporated only in table 24, where less stringent accuracies have been increasing steadily (cf., figs. 37-38) begin to to the order of tenths of a day are involved. The corres- increase less rapidly, pass through a point of zero change at ponding series expansion given below represents a truncation perigee, and then begin a steady decrease. At the instant of of the more exact equation represented in table 16B perigee, the rate of change in parallax denoted by rC is, following the sixth term. therefore, zero. ir(c 42.54 sin L+ 6.78 sin (L - 2D) By differentiating the expression for 7r(r given in (2) and 12.01 sin 2D-4.64 sin 2L setting the resulting *: equal to zero at the maximum -2.02 sin (L+2D)+0.78 sin (L'-2D) value of 7r(j, the time of perigee is obtained. This approxi- (All coefficients are in arc seconds.) Table 16B for determining the difference in longitude between the Refined Reduction Formulae Moon and Sun. The instant at which this expression, equated to 0', shows that the lunar elongation is zero, 1. The time of syzygy to the nearest hour (col. 2) is corresponds to the time of syzygy. obtained by the use of the following improved equation X:-X0=D+l8,222 sin L-7,751 sin L' -471 sin 2F+470 sin 2L -321 sin (L+L')+190 sin (L-L') . . . (All coefficients are in arc seconds.) 2. A more exact expression used to derive the geocentric equatorial horizontal parallax (cols. 4, 10) of the Moon at times of syzygy and perigee (applicable also at any position in its orbit) is: 7r"(Cz--3,422.608+186.540 cos L +34.312 cos (L-2D)+28.233 cos 2D + 10. 166 cos 2L+ 3.086 cos (L+ 2D) + 1.918 cos (L'- 2D) + 1.444 cos (L+L- 2D) + 1. 153 cos, (L-L') - 0.978 cos D -0.949 cos (L+L')-0.714 cos (L-2F) +0.622 cos 3L+0.601 cos. (L-4D) -0.400 cos L'+0.372 cos (U-4D) -0.304 cos (2L-2D)-0.300 cos (L'+2D) +0.283 cos (2L+2D)+0.261 cos 4D +0.230 cos (L-L'+2D)-0.226 cos (L-L'-2D) +0.149 cos (L'+D)+0.125 cos (2L-L') -0. 119 cos (3L-2D)-0.109 cos (L+D) =0.105 cos (2F-2D)-0.103 cos (2L+L) +0.092 cos (2L'-2D)-0.083 cos (L+2F-2D) +0.067 cos (L+L'-4D)+0.048 cos (L+2L'-2D) -0.048 cos (L+L'+2D)-0.048 cos (L-2F+2D) +0.044 cos (L+4D)+0.040 cos 4L -0.038 cos (L-3D)+0.035 cos (L'-4D) . . . (All coefficients are in arc seconds.) Essential Conditions for Achieving Amplified Perigean Spring Tides 225 3. The reduction for the rate of orbital motion of the daily lunar velocity in the anomalistic month (360/ Moon with respect to the perigee is represented by the 27.554551') is added to this derivative of the true anomaly values given in degrees per day in cols. 5 and 11-These b([ (converted to '/), the result is equivalent to the Moon's values result from the fact that the angular distance along daily angular velocity with respect to perigee. the plane of the lunar orbit between the Moon and perigee The computer printout shows that even 169 terms are is equal to the true anomaly v(C. Accordingly, it is only insufficient to reduce the numerical coefficient to zero, in necessary to differentiate the appropriate algorithmic the fifth decimal place. Th e first 136 of these terms which expression for the true anomaly to obtain (in radians per were truncated after reaching a nearly integral digit 3 in day) the rate of motion of the Moon, in true anomaly. the fifth decimal place and employed in the computation When the constant term 13.064991/d expressing the mean of cols. 5 and I I are given below. b,r + 13.06499 I/d[+ 0.05715 cos (L-2D) +0.03578 cos L-0.01624 (L+2D) -0.01350 cos (2L-4D)+0.00943 cos 2D -0.00718 cos (3L-4D)+0.00558 cos 2L -0.00510 cos (2L-2D)+0.00333 cos U +0.00328 cos (4L-6D)+0.00313 cos (L+L'-2D) +0.00290 cos (3L-6D)-0.00232 cos (2L+2D) -0.00222 cos (3L-2D)-0.00154 cos (2L+L'-4D) -0.00112 cos (4L-2D)-0.00102 cos (5L-8D) +0.00093 cos (4L-4D)-0.00085 cos (L-L'+2D) +0.00081 cos (5L-6D)-0.00080 cos (3L+2D) +0.00077 cos (2L+4D)-0.00068 cos (4L+2D) +0.00065 cos (L'-2D)-0.00064 cos (L+4D) +0.00062 cos 4L-0.00060 cos (4L-8D) -0.00060 cos (3L+L'-4D)+0.00059 cos (6L-8D) -0.00054 cos (5L-2D)+0.00049 cos (3L+L'-6D) +0.00048 cos (4L+L'-6D)+0.00048 cos (5L-4D) +0.00048 cos (L-L')-0.00040 cos (L-L'-2D) -0.00035 cos (L-6D)-0.00034 cos (3L-L'+2D) +0.00029 cos (6L- I OD) - 0.00028 cos (2L+L'- 2D) +0.00024 cos (6L-4D)+0.00024 cos (7L-IOD) -0.00023 cos (5L+L-8D)-0.00022 cos (L'+2D) +0.00022 cos (2L+L')+0.00021 cos (L-4D) +0.00021 cos (2L-qL'-4D)+0.00019 cos (3L-2F-2D) +0.00019 cos (2L- 3D) - 0.000 19 cos L' +0.00018 cos 4D+0.00018 cos (L-L+4D) +0.00017 cos (2L-L')-0.00016 cos (6L-6D) +0.00015 cos (3L-L')-0.00015 cos (2L+L'+D) -0.00015 cos (3L+L'-2D)-0.00015 cos (2L-L'+2D) -0.00015 cos (4L+L'-8D)+0.00015 cos (3L+L) +0.00014 cos (2L+2F+2D)+0.00013 cos (L+L) +0.00013 cos (L+2L'-2D)+0.00013 cos (L+L'+2D) +0.00013 cos (5L-1OD)+0.00012 cos (L-2F) -0.00012 cos (2L+L'+2D)-0.00012 cos (2L+2L'-4D) +0.00012 cos (3L+4D)-0.00011 cos D + 0.000 11 cos 5L- 0.000 11 cos (4L+L'- 2D) +0.00011 cos (2L'+2D)-0.00010 cos (6L-2D) +0.00010 cos (3L+2F-2D)-0.00010 cos (6L+L'-8D) +0-00010 cos (2L-8D)+0.00010 cos (5L+L-6D) -0.00009 cos (2L+D)+0.00009 cos (4L+L-4D) -0.00009 cos (7L-6D)-0.00009 cos (7L-8D) -0.00008 cos (2L-2F-2D)-0.00008 cos (5L+2D) + 0.00008 cos (L- 2F+ 2D) + 0.00008 cos (8L- 1 OD) +0.00008 cos (7L-4D)-0.00008 cos (3L-5D) -0.00008 cos (2L-2L')+0.00008 cos (2L+2F-2D) +0.00007 cos (L-D)-0.00007 cos (4L-2F-4D) +0.00007 cos 6L-0.00007 cos (8L- 12D) -0.00007 cos (3L-L'-6D)-0.00007 cos (L+6D) + 0.00007 cos (6L+L'- I OD) - 0.00006 cos (3L-L'- 2D) 202-509 0 - 78 - 17 226 Strategic Role of Perigean Spring Tides, 1635-1976 (Continued) -0.00006 cos (3L-2F+2D)+0.00006 cos (2L-D) +0.00006 cos (L+L'+4D)+0.00006 cos (3L-L'-4D) +0.00006 cos (L-L'-4D)+0.00006 cos (4L-L') -0.00006 cos (4L-L'+2D)+0.0005 cos (4L+L') -0.00005 cos (4L-5D)+0.00005 cos (5L+L'-4D) +0.00005 cos (L'+D)+0.00005 cos (3L+2L-6D) +0.00005 cos (3L-8D)-0.00005 cos (4L-L'-6D) +0.00005 cos (7L+L-1OD)-0.00004 cos (L'-6D) +0.00004 cos (L'+4D)-0.00004 cos (5L-2F-4D) -0.00004 cos (2L+2F)+0.00004 cos (2F+2D) +0.00004 cos (5L-L')-0.00004 cos (2F-4D) -0.00004 cos (3L-3D)-0.00004 cos (2L-L'-3D) - 0.00004 cos (9L- 12D) - 0.00004 cos 6D +0.00004 cos (L-4D)-0.00004 cos (5L+L'-2D) +0.00004 cos (L+3D)-0.00003 cos (3L+2L'-4D) +0.00003 cos (4L+2L'-6D)+0.00003 cos (3L-D) +0.00003 cos (L+2F-2D)-0.00003 cos (4L-L'-2D) - 0.00003 cos (7L- 12D) - 0.00003 cos (L- 2L'+ 2D) -0.00003 cos (2L-2L+2D)+0.00003 cos (2L-2F+2D) -0.00003 cos (L+2F) . . . . ] radian/day. (All coefficients are in radians.) 4. The following expression is used in computing the cycle which causes-in addition to a 5' increase in the Moon's daily rate of angular motion in right ascension, range of the maximum declination of the Moon (fig. 36)- a([ (cols. 6, 12), determined for the instants of true syzygy a much smaller but gravitationally effective variation in and true perigee, respectively. This value represents lunar the extremes of lunar latitude. Such latitude excursions are motion as it is projected into the plane of the celestial responsible for periodic quantitative deviations in &([ from equator. As such, it more exactly represents the portion of the values to be expected from the existing parallax. These are diurnal motion of the Earth (occurring in a plane either approximately equal in magnitude to similar deviations coincident with, or parallel to the Equator)--through which it caused by the solar parallactic inequality. is necessary for any given meridian of the Earth to rotate in With these latter factors properly considered, a value order to catch up on the Moon. obtained from this equation is useful in determining the However, cyclically, over long periods, the calculated additional angular motion necessary for a given terrestrial motions in right ascension show deviations from values meridian to catch up with the Moon and occasion a lunar consistent with the existing parallax. These deviations are transit, subject to the Earth's rotation in, or parallel to, the the result of the effects of the 18.6-year nodical (draconitic) same equatorial plane. 13.17640'[+5,162 cos L-4,067 cos 2M - 1, 756 cos (F+ M) + 1,008 cos 2D +906 cos (L-2D)-668 cos (L+2M) +351 cos 2L-288 cos (L+M+F) + 227 cos (L- 2M) - 191 cos 2F + 176 cos; 4M+ 149 cos (3M+F) + 12 7 co's (L+ 2D) - 121 cos (L- 2M- 2D) - 107 cos (2M+ 2D) + 97 cos (L- M-F) - 80 cos (2L+ 2M) - 75 cos (3M- F) +68 cos (L'-2D)+53 cos (L+2M-2D) -53 cos (L-M-F-2D)+51 cos (2M+2F) +48 cos (L+4M)-46 cos (M+2D-F) -44 cos (M+F+2D)+41 cos (L+3M+F) +37 cos (L+L'-2D)-34 cos (2L+M+F) -33 cos (L+2F)+31 cos (L-L') -29 cos (L-4M)-27 cos (L+L') -27 cos D+26 cos 3L -25 cos (L-3M-F)-24 cos (L+2M+2D) +23 cos (L-4D)+23 cos (L+M+F-2D) + 15 cos (2L+ 2M- 2D) + 14 cos (2L+ 2D) + 14 cos (2L- 4D) + 14 cos (L'+ 2M) - 13 cos (L'- 2M) - 13 cos (L+ 3M- F) - 12 cos L'- I I cos W+ 2D) Essential Conditions for Achieving Amplified Perigean Spring Tides 227 (Continued) + 10 cos 4D+ 10 cos (L- L+ 2D) - 10 cos (L-2F)- 10 cos (L+M-F+2D) +8 cos (L+2M+2F)-7 cos (5M+F) +7 cos (M+3F)1/3,600 (All coefficients are in arc seconds.) 5. The expression used in obtaining the apparent declina- true perigee (col. 13), which is also applicable at any time tion of the Moon at the time of true syzygy (col. 7) and in the lunar orbit, is: 5'= [83,523 sin M+1 17,662 sin F +4,599 sin (L-M)+4,570 sin (L+M) +964 sin (L+F)+954 sin (L-F) - 952 sin (L+M-2D)-903 sin (L-M-2D) -594 sin (F-2D)-578 sin 3M +517 sin (M+2D)-434 sin (M-2D) +374 sin'(2M-F)-366 sin (2M+F) +274 sin (2L+M) - 183 sin (L-F- 2D) - 153 sin (L+F- 2D) - 133 sin (L'+M) - 133 sin (P-M) + 108 sin (F+ 2D) - 10 1 sin (2F- M) - 93 sin (2L+ M- 2D) -88 sin (L-3M)-87 sin (L+3M) +67 sin (L+M+2D)-65 sin (M+2F) +57 sin (2L+F)-54 sin (L-F-2M) - 54 sin (L+F+ 2M) - 47 T sin M -41 sin (L+L'+M-2D)-41 sin (L+L'-M-2D) -33 sin (L'+M-2D)-33 sin (L'-M-2D) +31 sin (L-F+2D)+30 sin (U-M) +29 sin (L-L'+M)+29 sin (L-L'-M) +29 sin (2L-F)-27 sin (L'+F-2D) -25 sin (M+D)+25 sin (M-D) -22 sin (L+L'+M)-22 sin (L+L-M) + 19 sin (L+ 3M- 2D) + 18 sin (L- 2M+F) + 18 sin (L + 2M-F) + 17 sin (L- 3M- 2D) + 14 sin (2M+ F- 2D) - 14 sin (2L+ F- 2D) + 14 sin (L+F+ 2D) + 13 sin (L- M- 2F) +13 sin (L+M+2F)]13,600". (All coefficients are in arc seconds.) 6. The corresponding declination of the Sun at the any other time in the apparent annual motion of the instant of true syzygy (col. 8) and true perigee (col. 14)-or Sun-is given by: 6' = [83,797 sin S+ 1,404 sin (L'-S) + 1,403 sin (L'+S) - 594 sin 3S - 46 T sin S- 30 sin (L'- 3S) -30 sin (L'+3S) +26 sin (2L'+S)]/3,600". (All coefficients are in arc seconds.) 7. The expression used to obtain the time of perigee and low. Because of the mathematical assumptions used, this ex- hence the separation-interval P-S (col. 9) by differentiating pression is the most accurate near the alignment of perigee expression (2) and setting ir(C (the rate of change in par- and syzygy. al 'lax) equal to zero at the maximum value of ir(C is given be- ir([=-42.54 sin L+6.78 sin (L-2D) - 12.01 sin 2D-4.64 sin 2L -2.02 sin (L+2D)+0.78 sin (L'-2D) +0.26 sin (L+L-2D)-0.24 sin (L-L') +0.23 sin (L+L')-0.17 sin (L-2F) +0.37 sin (L-4D)-0.43 sin (L+2L) -0.25 sin (2L+2D)-0.22 sin 4D 228 Strategic Role of Perigean Spring Tides, 1635-1976 (Continued) +0.2 1. sin D-0.15 sin (L-L'+2D) +0.15 sin (2L-4D)+0.13 sin (L+2D) -0.06 sin (2L-L) . . . (All coefficients are in arc seconds.) In considering the computer printout of table 16, two pair may have the smaller separation-interval between important characteristics common to such close perigee- perigee and syzygy. This results in the corresponding vari- syzygy alignments are readily discernible: able length of time (i.e., 6.5 or 7.5 periods of 29.5 days) 1. This table is based upon a maximum separation- between it and the component having the smallest separa- interval of �24' between perigee and syzygy. Accepting tion-interval in the preceding or following pair. this arbitrary 24-hour interval between the two astronomical 2. Since lunar months rather than calendar months are configurations as defining the upper limit of a typical close involved in the succession of perigee-syzygy events, one alignment of perigee-syzygy, it is obvious that such close or both components of any pair may also overlap 2 con- alignments almost invariably occur in pairs, averaging 29.5 secutive calendar years. The tropical or calendar year, days apart. These occurrences are followed and preceded, usually but not always) containing four ordinary perigee- in the average case, by another such pair, one component syzygy alignments with a separation-interval <24', of which is separated by approximately 6.5 or 7.5 periods of consists of 12.37 synodic months. Thus, the successive pairs 29.5 days from its matching component in the first pair baving the smallest interval between perigee and syzygy- belonging to a perigee-syzygy cycle of 6.5 or 7.5 periods of (Sometimes, however, as the result of the limiting 24-hour 29.5 days can easily lie in different calendar years, and due perigee-syzygy separation-interval, one component of either care must be exercised in relating these cycles over long pair may be eliminated.) Either of the components in each periods of time. Table 16 Designation of Columns Table 16 is reproduced by electronic composition directly ment in which the two components occur within the pre- from a computer printout of lunar and solar data provided scribed separation-interval of � 24 hours or less. by the Nautical Almanac Office, U.S. Naval Observatory. All dates, regardless of year, are given in the Gregorian This table contains data pertinent to all cases between the (New Style) Calendar. Prior to 1752, if Old Style dates are years 1600 and 1999 in which lunar perigee and syzygy occur desired for comparison purposes, the tabulated dates must within --L24 mean solar hours of each other. be corrected according to the procedure outlined at the close The arrangement of this table is as folloNVs: of part 1, chapter 1. Col. I gives the Julian Date to the nearest 0. 1 day, corre- In the data processing procedure, the necessary reductions sponding to the time of mean syzygy. This position is have been made, and all times given are in ephemeris time, based upon the mean apparent motions of the Moon which corresponds very closely with Greenwich ciyil time. (13.176396'/d) and Sun (0.985647'/d) and represents the Using data referred consistently to Greenwich civil time average time at which these two bodies reach syzygy align- throughout this and subsequent columns of the table, no ad- ment. The apparent discrepancy between the decimal por- justment is needed for the fact that, after January 1, 1925, tion of the Julian Day and the time (in hours) given for the beginning of the astronomical day changed from noon syzygy in column 2 is due to the fact that the latter time cor- (Greenwich mean time) to the preceding midnight (Green- responds to true rather than mean syzygy. For any date in wich civil time). To convert to eastern standard time, 5 history, the Julian Day also starts at noon (Greenwich mean hours should be subtracted; Pacific standard time similarly time), whereas all of the times given in column 2 are in is 8 hours earlier. Greenwich civil time (or more exactly, ephemeris time) Because of rounding-off and data-truncating procedures which begins at midnight. used in the computer processing, the times given in this col- umn will not, in all cases, agree exactly with those contained The inclusion of these Julian Dates makes more conven- in The American Ephemeris and Nautical Almanac and ient the subtraction of differences in time, and the estab- other ephemerides, or as reproduced in various governmental lishment of related periodicities between individual occur- tide tables. Where rounding-off errors combine in the same rences of perigee-syzygy. It is also possible by means of this direction, the differences may amount to as much as an hour. artifice to determine the day of the week for any instance of The more accurate ephemeris values have been used in all tidal flooding, making possible the cross checking of early cases throughout the text where times to the accuracy of documentary sources of such flooding. minutes are involved; however, the present tabular values For all practical purposes, one-half of the difference in will suffice for all instances in which values accurate to the hours (col. 9) between true perigee and true syzygy may be nearest hour are required. algebraically added (as a decimal part of a day) to the Column 3 indicates the phase of syzygy as either new Julian Date of mean syzygy to obtain the approximate mean moon (N) or full moon (F). date of perigee-syzygy. Proper allowance must also be made Column 4 lists the geocentric horizontal parallax in min- to convert from ephemeris time at Greenwich to local stand- utes, seconds@ and tenths of seconds of arc, corresponding to ard time at the location of the flooding by subtraction of the the time of true syzygy. appropriate number of hours which the station is west of Column 5 contains a series of angular values expressing Greenwich. For example, in establishing the corresponding the rate of orbital motion of the Moon with respect to the day of the week in eastern standard time, 5 hours (0.2d) is perturbed motion of perigee, determined, for the instant of subtracted from the Julian Date. The date and decimal syzygy, in I/d. The procedure by which this value is calcu- portion are then rounded off to the nearest unit. Any result- lated from the time rate of change of the Moon's true anom- ing decimal value of 0.5d is rounded off, in practice, to the nearest even unit, either higher or lower, as the case may be. aly is explained in the Introduction to table 16. The appropriate day of the week is obtained by dividing The method of using this angle, and that from column 6, the entire rounded-off Julian Date by 7. If the remainder is to obtain the special value designated in this monograph as 0, the day is Monday, if 1, Tuesday, etc., through a remain- the "A(o-syzygy coefficient" is described in chapter 8. This der of 6 for'Sunday. coefficient represents the astronomical portion of a total Column 2 contains the year, month, date, and 24-hour quantifier indicating the potential for tidal flooding associ- time of true syzygy (rounded off to the nearest hour) for ated with the simultaneous occurrence of perigean spring each case of syzygy associated with a perigee-syzygy align- tides and strong, persistent, onshore winds. 229 230 Strategic Role of Perigean Spring Tides, 1635-1976 Column 6 tabulates the'orbital motion of the Moon in and adding the result algebraically to the time of syzygy in right ascension (expressed likewise, for comparative pur- column 2. poses, in '/d) at the instant of true syzygy. Column 10, designates the geocentric horizontal parallax Column 7 is a tabulation of the apparent declination of of the Moon (in minutes and seconds of arc), in the same the Moon (to the nearest degree) at the time of true syzygy. manner as column 4, but now as it applies to the slightly Column 8 notes the apparent declination of the Sun (to different time and position of true perigee. the nearest degree) at the time of true syzygy. Column 11 repeats the instantaneous value of the rate of Column 9 indicates the increment or decrement (in the Moon's motion with respect to perigee (in I/d) de- hours) which, according to algebraic sign, it is necessary to scribed under column 5, but now referred to the time of add to, or subtract from, the time of true syzygy in column true perigee. 2 in order to find the corresponding time of true perigee. Column 12 gives the orbital motion of the Moon in right This difference in time is consistently taken in the sense ascension (expressed also in I/d) for the instant of true perigee minus syzygy, and represents the perigee-syzYgy "separation-interval" frequently referred to throughout the perigee. volume. With the exception of a few cases caused by the Column 13 reproduces column 7 but.gives the apparent combination of rounding-off errors, no value in column 9 declination of the Moon (in degrees) at the time of true exceeds :�--24 hours. perigee. The mean epoch of perigee syzygy (see column 8 of Column 14 provides the corresponding apparent declina- table 1) is obtained by dividing the figure in column 9 by 2 tion of the Sun (in degrees,) at the time of true perigee. 1 2 3 4 5 6 7 9 10 11 12 13 14 1 11 */DAY */DAY h WAY '/DAY 2305521.3 1600/ 3/15- 4 N 61 10.3 16.984 13.616 1.8 - 2.1 17 61 15.8 16.974 13.830 6.7 - 1.8 2305550.9 1600/ 4/13-12 N 61 25.1 16.974 14.580 13.9 9.2 - 4 61 25.3 16.971 14.465 12.9 9.1 2305742.8 1600/10/22- 5 F 61 25.6 @17.019 14.920 15.7 -11.1 10 61 27.0 17.017 15.236 17.6 -11.3 2305772.3 1606/11/20-15 F 61 21.7 17.091 16.404 23.3 -19.9 -12 61 24.5 17.073 16.076 21.8 -19.8 2305934.8 1601/ 5/ 2-13 N 61 9.0 16.895 15.511 19.2 15.4 u 61 14.0 16.916 16.058 21.7 15.6 2305964.3 1601/ 5/31-20 N 61 21.5 16.962 16.670 24.0 22.0 - 4 61 21.9 16.958 16.621 23.7 21.9 2306156.2 1601/12/ 9 -18 F 61 27.1 17.140 16.677. 23.4 -22.9 7 61 28.0 17.139 16.667 23.3 -22.9 2306185.8 1602/ 1/ 8 - .5 F 61 17.9 17.090 15.851 20.1 -22.2 -15 61 21.8 17.086 16.248 21.8 -22.3 2306348.2 16021 6/19 -20 N 61 7.9 16.892 16-316 22.2 23.4 18 61 12.9 16.889 16.086 21.0 23.4 1602/ 7/19 3 N 61 21.8 16.937 15.515 17.5 21.0 - 4 61 22.1 16.941 15.630 18.2 21.0 2306377.7 - 2306569.7 1603/ 1/27- 7 F 61 29.9 17.103 15.152 14.1 -18.5 5 61 30.2 17.099 15.051 13.3 -18.5 2306599.2 1603/ 2/25-17 F 61 15.0 16.979 14.245 4.4 - 9.0 -17 61 20.1 16.960 14.498 8.3 - 9.3 2306761.6 1603/ 8/ 7--3 N 61 10.5 16.872 14.817 11.9 16.6 17 61 15.3 16.850 14.540 8.6 16.4 2306791.2 1603/ 9/ 5-11 N 61 24.0 16.974 14.342 2.7 7.0 - 5 61 24.4 16.975 14.371 3.6 7.0 2306983.1 1604/ 3/15-19 @F 61 28.0 17.047 14.434 - 1.4 - 1.8 2 61 28.1 17.049 14.444 - 1.9 1.8 Z5, ;3 2307012.6 1604/ 4/14- 4 F 61 9.0 16.926 14.790 -10.6 9.4 -20 61 15.1 16.905 14.'548 - 6.9 9.2 2307175.0 1604/ 9/23-12 N 61 12.0 16.971 14.389 - 2.5 - 0.3 16- 61 16.4 16.962 14.542 - 5.8 0.5 2307204.6 1604/10/22-21 N 61 24.1 17.089 15.031 -11.3 -11.4 - 5 61 24.7 17.091 14.941 -10.4 -11.3 2307367.0 1605/ 4/ 3-20 F 60 58.8 16.917 14.457 - 5.9 5.5 24 61 8.3 16.920 14.838 -10.3 5.9 cl@ 2307396.5 1605/ 5/ 3- 5 F 61 25.5 16.982 15.351 -13.6 15.6 1 .61 25.6 16.982 15.382 -13.9. 15.7 @r w 2307426.1 1605/ 6/ 1-12 F 61 6.8 16.820 15.861 -18.0 22.1 -20 61 113 16.816 15.663 -16.5 22.0 2307588.5 1605/11/10-23 N 61 17.7 17.058 15.386 -14.3 -17.4 15 61 21.1 17.034 15.656 -15.9 -17.6 2307618.0 1605/12/10-10 N 61 26.0 17.084 16.074 @18.2 -22.9 - 8 61 27.1 17.083 16.023 -17.9 -22.9 2307780.4 1606/ 5/22- 5 F 61 0.5 16.803 15,486 -15.9 20.3 23 61 9.5 16,796 15.853 -17.7 20.5 230810.0 1606/ 6/20-12 F 61 26.0 16.893 16.109 -18.4 23.4 1 61 26.1 16.894 16.111 -18.4 23.4 2307839.5 1606/ 7/19-19 F 61 7.2 16.827 15.651 -16.6 20.8 -20 61 13.7 16.815 15.923 -17.9 21.0 2308001.9 1606/12@29-12 N 61 21.8 17.073 16.091 -18.5 -23.2 12 61 Z4.2 17.068 16.052 -18.2 -23.2 2308031.4 1607/ 1/27-22 N 61 23.0 17.096 15.584 -15.4 -18.3 -10 61 24.7 17.083 15.766, -16.5 -18.5 :2. 2308193.9 1607/ 7/ 9-12 F 60 59.4 16.777 15.879 -18.6 22.4 23 61 8.4 16.778 15.683 -17.1 22.3 2308223.4 1607/ 8/ 7-19 F 61 24.9 16.962 15.478 -14.8 16.5 2 61 25.0 16.962 15.446 -14.6 16.4 2308252.9 1607/ 9/ 6- 3 F 61 5.9 16.920 14.574 - 7.5 6.7 -20 61 12.7 16.929 14.923 -11.0 7.0 2308415.3 1608/ 2/16- 1 N 61 21.7 17.101 15.144 -12.8 -12.6 .9 61 23.3 17.100 14.979 -11.2 -12.5 2308444.9 1608/ 3/16-11 N 61 18.2 17.016 14.443 - 4.1 - 1.5 -13 61 20.8 17.012 14.581 - 6.6 - 1.7 2308607.3 1608/ 8/25-19 F 61 1.3 16.861 14.825 -12.0 10.5 24 61 10.0 16.830 14.500 7.6 10.2 2308636.8 1608/ 9/24- 4 F 61 27.9 17.016 14.413 - 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5.4 - 7.9 - 9 61 24.2 17.062 13.878 - 7.9 - 8.0 2366694.0 1767/ 9/ 8- 8 F 61 26.2 16.980 13.730 - 2.4 5.8 4 61 26.5 16.975 13.712 - 1.2 5.7 s 2366723.5 176711017-16 F 61 13.0 16.956 14.055 10.1 5.6 -17 61 18.2 16.954 13.791 5.5 - 5.3 2366885.9 1768/ 3/18-16 N 61 20.0 17.009 13.821 3.8 0.6 11 61 22.3 17.006 13.973 6.8 - 0.4 2366915.4 1768/ 4/17- 0 N 61 20.7 16.958 14.814 15.1 10.6 -10 61 22.5 16.944 14.526 12.8 10.4 2367107.4 1768/10/25-18 F 61 29.2 17.050 15.198 16.7 -12.5 3 61 29.4 17.052 15.299 17.3 -12.5 2367136.9 1768/11/24- 4 F 61 11.0 17.062 16.397 23.3 -20.7 -19 61 17.3 17.032 15,991 21.3 -20.5 2367299.3 1769/ 5/ 6- 1 N 61 17.5 16.948 15.758 19.6 16.5 11 61 19.5 16.963 16.058 21.0 16.7 2367328.9 1769/ 6/ 4- 8 N 61 16.7 16.947 16.578 23.4 22.5 -10 61 18.7 16.939 16.504 23.0 22.4 li2l 2367491.3 1769/11/13-20 F 61 2.2 16.978 15.829 20.2 -18.2 23 61 11.1 16.964 16.330 22.2 -18.5 2367520.8 1769/12/13- 6 F 61 29.7 17.154 16.587 22.5 -23.2 1 61 29.7 17.154 16.583 22.5 -232 2367550.3 1770/ 1/11-17 F 61 6.3 17.027 15.558 18.6 -21.7 -21 61 14.1 17.013 16.116 21.1 -21.8 2367712.8 1770/ 6/23- 9 N 61 16.8 16.930 16.241 21.1 23A 10 61 18,7 16.926 16.091 20.3 23.4 2367742.3 1770/ 7/22-16 N 61 17.3 16.900 15.334 16.1 20.2 -11 61 19.2 16.910 15.609 17.7 20.3 2367904.7 1771/ 1/ 1- 9 F 61 9.1 17,049 15.905 19.4 -23.0 21 61 16.3 17.011 15.548 17.0 -22.9 2367934.2 1771/ 1/30-20 F 61 31.1 17.093 15.077 12.8 -17.5 - 2 61 31.2 17.094 15.114 13.1 -17.5 2367963.8 1771/ 3/ 1- 6 F 61 2.2 16.924 14.187 3.3 - 7.6 -24 61 11.5 16.884 14.517 8.4 - 8.0 2368126.2 1771/ 8/10-16 N 61 18.9 16.909 14.838 10.8 15.5 10 61 20.8 16.900 14.672 8.8 15.4 2368155.7 17711 9/ 8-23 N 61 18.8 16.967 14353 1.7 5.5 -11 61 20.8 16.967 14.425 4.0 5.7 2368318.1 17721 2/18-21 F 61 12.0 17.015 14.571 7.4 -11.5 19 61 17.8 17.006 14.437 3.8 -11.3 2368347.7 17721 3/19- 7 F 61 27.6 17.055 14.498 - 2.1 - 0.3 - 3 61 27.8 17.052 14.488 - 1.3 - .0.4 2368539.6 17721. 9/27- 0 N 61 20.0 17.021 14.504 - 3.1 - 1.8 10 61 21.6 17.015 14.585 - 5.0 - 1.9 Ln IND 2 3 5 6 7 8 9 10 11 12 13 14 WAY '/DAY h */DAY WAY 2368569.1 1772/10/26-10 N 61 18.2 17.065 15.043 -11.5 -12.7 -12 61 20.8 17.069 14.870 - 9,5 -12.5 2368731.6 1773/ V 7- 9 F 61 11.7 16.980 14.600 - 6.3 7.0 17 61 16.7 16.978 14.851 - 9.4 7.3 2368761.1 1773/ 5/ 6-17 F 61 25.0 16.961 15.384 -13.8 16.7 - 5 61 25.4 16.962 15.306 -13.1 16.7 2368953.0 1773/11/14-12 N 61 25.1 17.073 15.480 -14.5 -18.4 8 61 26.2 17.063 15.627 -15.4 -18.5 2368982.6 1773/12/13-22 N 61 19.0 17.058 16.022 -18.2 -23.2 -14 61 22.3 17.046 15.936 -17.6 -23.2 ,2'369145.0 1774/ 5/25-17 F 61 12.8 16.855 15.623 -16.2 21.0 17 61,17.5 16.850 15.883 -17.6 21.2 2369174.5 1774/ 6/24- 0 F 61 25.0 16.894 16.117 -18.6 23.4 - 5 61 25.4 16.891 16.112 -18.5 23.4 2369366.5 1775/ 1/ 2- 0 N 61 27.3 17.102 16.162 -18.8 -22.9 6 61 27.9 17.103 16.140 -18.7 -22.9 2369396.0 1775/ 1/31-11 N 61 14.0 17.072 15.476 -15.4 -17.3 -17 61 18.7 17.047 15.790 -17.2 -17.5 2369558.4 1775/ 7/13- 0 F 61 11.2 16.854 16.001 -18.9 21.9 17 61 15.9 16.856 15.839 -17.9 21.8 2369587.9 1775/ 8/11- 7 F 61 23.7 16.966 15.417 -14.8 15.3 - 4 61 24.1 16.966 15.510 -15.4 15.4 2369779.9 1776/ 2119-13 N 61 26.2 17.110 15.091 -12.6 -11.3 4 61 26.4 17.109 15.029 -12.0 -111.2 co@ 2369809.4 1776/ 3/19-23 N 61 8.8 16.960 14.284 - 3.4 0.0 -19 61 14.7 16.947 14.513 - 7.3 - 0.3 2369971.8 1776/ 8/29- 8 F 61 13.6 16.921 14.807 -11.6 9.1 16 61 18.1 16.898 14.546 - 8.3 8.9 C% 2370001.4 1776/ 9/27-16 F 61 26.6 17.002 14.307 - 2.0 - 2.0 - 5 61 27.1 17.005 14.337 - 3.2 - 1.9 1112. 2370163.8 1777/ 3/ 9-15 N 60 58.6 16.949 14.277 - 8.0 - 4.2 24 61 8.2 16.925 14.099 - 2.6 - 3.8 2370193.3 1777/ Q 8- 0 N 61 25.9 16.991 14.216 2.6 7.2 2 61 26.0 16.992 14.226 3.0 7.3 2370222.9 1777/ 5/ 7--8 N 61 5.9 16.877 14.717 12.6 16.9 -20 61 12.5 16.841 14.361 8.4 16.7 2370385.3 1777/10/16-17 F 61 18.1 16.969 14.124 4.6 - 9.2 15 61 21.9 16.960 14.352 8.2 - 9.4 2370414.8 1777/11/15- 3 F 61 27.5 17.099 15.085 14.9 -18.6 - 7 61 28.3 17.091 14.916 13.6 -18.5 23705771 1778/ 4/27- 1 N 60 58.1 16.852 14.211 9.9 13.8 23 61 7.0 16.880 14.852 15.0 14.1 M 2370606.8 1778/ 5/26- 9 N 61 22.5 16.968 15.613 19.0 21.1 1 61 22.5 16.970 15.652 19*2 21.2 2370636.3 1778/ 6/24-16 N 61 2.4 16.861 16.462 23.7 23.4 -21 61 9.3 16.860 16.161 22.2 23.4 2370798.7 1778/12/ 4- 5 F 61 20.8 17.103 15.992 21.5 -22.3 13 61 23.7 17.099 16.374 23.1 -22.3 2370828.2 1779/ 1/ 2-16 F 61 25.5 17.130 16.842 24.8 -22.9 - 9 61 26.9 17.130 16.833 24.7 -22.9 2370990.7 1779/ 6/14- 9 N 60 57.3 16.833 16.367 24.3 23.3 23 61 6.1 16.838 16.762 25.5 23.3 FA: 2371020.2 1779/ 7/13-16 N 61 22.6 16.942 16.794 25.1 21.8 1 61 22.6 16.941 16.774 25.0 21.8 2371049.7 1779/ 8/11-23 N 61 3.9 16.838 15.367 19.6 15.1 -20 61 10.7 16.857 16.103 22.8 15.4 2371212.1 1780/ 1/21-19 F 61 25.3 17.098 16.466 24.1 -19.8 10 61 27.2 17.084 16.151 22.8 -19.7 Q@ 2371241.7 1.780/ 2/20- 5 F 61 23.9 17.032 14.748 15.7 -11.0 -12 61 26.1 17.024 15.175 18.2 -11.2 2371404.1 1780/ 7/31-16 N 60 59.6 16.809 15.827 22.8 18.0 23 61 8.2 16.781 15.003 18.4 17.8 2371433.6 1780/ 8/29-23 N 61 24.8 16.962 14.363 13.3 8.9 1 61 24.8 16.962 14.326 13.0 8.9 2371463.1 1780/ 9/28- 7 N 61 4.2 16.948 13.428 0.7 2.3 -20 61 11.4 16.942 13.660 6.6 - 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9 61 27.3 17.021 14.620 13.8 7.1 2378018.9 1798/ 9/10- 7 N 61 24.7 16.973 14.043 9.2 4.8 4 61 24.9 16.971 13.968 8.2 4.8 6.2 2378048.5' 1798/10/ 9-16 N 61 9.3 16.989 13.595 - 3.5 6.5 -18 61 14.9 16.981 13.594 1.6 2378210.9 1799/ 3/21-15 F 61 21.8 17.018 13.607 3.0 0.4 11 61 23.9 17.023 13.589 0.1 0.6 2378240.4 1799/ 4/20- 0 F 61 20.8 16.984 13.985 -10.1 11.4 -11 61 22.7 16.974 13.773 7.1 11.3 2378432.4 1799/10/28-17 N 61 25.9 17.093 14.267 -13.2 -13.3 3 61 26.0 17.092 14.346 -13.8 -13.3 2378461.9 1799/11/27- 4 N 61 6.9 17.043 15.957 -23.6 -21.1 -20 61 13.6 17.035 15.195 -19.8 -21.0 17.3 2378624.3 1800/ 5/ 9- 1 F 61 20.4 16.962 15.057 -19.0 17.2 10 61 22.2 16.961 15.490 -21.2 2378653.8 1800/ 6/ 7- 8 F 61 19.2 16.886 16.818 -26.6 22.7 -11 61 21.4 16.886 16.463 -25.3 22.7 2378816.3 1800/11/16-20 N 61 3.0 17.001 15.423 -21.8 -18.8 22 61 11.4 16.954 16.423 -25.6 -19.1 2378845.8 1800/12/16- 6 N 61 29.5 17.097 17.282 -27.9 -23.3 0 61 29.5 17-097 17.285 -27.9 -23.3 2378875.3 1801/ 1/14-17 N 61 4.5 17.005 16.505 -26.1 -21.3 -23 61 12.7 16.962 17.137 -28.0 -21.4 4 t'd 2379037.7 1801/ 6/26- 8 F 61 21.2 16.870 17.306 -28.3 23.4 10 61 22.9 16.867 17.204 -27.9 23.4 cn 0) 2379067.3 1801/ 7/25-15 F 61 19.7 16.889 16.055 -24.0 19.7 -12 61 21.9 16.882 16.520 -25.7 19.8 ;2 2379229.7 1802/ 1/ 4- 8 N 61 8.5 17.026 16.923 -27.4 -22.8 20 61 15.2 17.004 16.332 -25.1 -22.7 2379259.2 1802/ 2/ 2-19 N 61 28.0 17.109 15.214 -19.9 -16.8 - 3 61 28.1 17.107 15.317 -20.4 -16.9 2379451.2 1802/ 8/13-15 F 61 20.3 16.936 14.616 -16.7 14.8 10 61 22.0 16.934 14.264 -14.1 14.7 2379480.7 18021 9/11-23 F 61 19.0 16.987 13.463 - 4.0 4.6 -12 61 21.3 16.992 13.642 - 7.4 4.8 2379643.1 1803/ 2/21-21 N 61 10.1 17.055 13.837 -10.7 -106 18 61 15.5 17-048 13.527 - 5.6 -10.4 2379672.6 1803/ 3/23- 7 N 61 24.8 17.048 13.520 3.1 4 61 25.1 17.048 13.496 1.8 0.6 2379864.6 1803/10/ 1- 0 F 61 24.1 17.003 13.673 6.0 - 2.7 9 61 25.5 16-992 13.841 8.6 - 2.9 2379894.1 1803/10/30- 9 F 61 21.2 17.025 14.978 18.1 -13.5 -12 61 24.0 17.021 14.543. 15.2 -13.4 2380056.5 1804/ 4/10- 8 N 61 12.1 16.944 14.168 12.3 7.9 16 61 16.7 16-944 14.723 16.3 8.2 2380086.1 1804/ 5/ 9-16 N 61 23.5 16.944 15.906 22.1 17.4 - 5 61 23.9 16-938 15.709 21.2 17.3 2386278.0 1804/11/17-11 F 61 27.7 17.068 16.304 23.3 -19.0 7 61 28.6 17.069 16.537 24.2 -19.1 12380307.6 1804/12/16-21 F 61 19.0 17.105 16.940 26.0 -23.3 -14 61 22.7 17-084 16.967 26.0 -23.3 2380470.0 1805/ 5/28-16 N 61 9.9 16.885 16.612 24.7 21.4 16 61 14.3 16-905 16.819 25.4 21.6 2380499.5 1805/ 6/26-23 N 61 20.5 16.956 16.616 24.4 23.4 - 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5 61 28.9 17.134 16.307 21.5 2384190.8 1815/ 8/ 5- 7 N 61 21.0 16.951 15.896 20.3 17.2 7 61 21.8 16.942 15.710 19.3 17.1 2384220.4 1815/ 9/ 3-14 N 61 13.5 MAU 14.542 12.1 7.8 -14 61 17.2 16.928 14.963 15.2 8.0 2384382.8 1816/ 2/13-12 F 61-19.0 17.059 15.281 17.8 -13.6 15 61 22.8 17.038 14.858 14.9 -13.4 2384412.3 1816/ 3/13-22 F 61 27.3 17.017 14.110 7.2 - 2.7 - 7 61 28.1 17.014 14.245 9.1 - 2.8 2384604.3 1816/ 9/21-15 N 61 24.1 16.983 13.876 5.0 0.6 6 61 24.7 16.979 13.822 3.3 0.5 2384633.8 1816/10/21- 0 N 61 13.8 17.025 13.909 - 7.5 -10.6 -16 61 18.0 17.015 13.746 - 3.3 -10.3 2384796.2 1817/ V 1-23 F 61 18.3 16.985 13.642 - 1.3 4.7 13 61 21.4 16.991 13.764- - 4.9 4.9 2384825.7 1817/ 5/ 1- 8 F 61 22.6 16.978 14.454 -13.6 15.0 - 9 61 23.8 16.970 14.222 -11.4 14.9 2385017.7 1817/11/ 9- 2 N 61 25.7 17.104 14.807 -16.6 -16.7 5 61 26.0 17.102 14.982 -17.7 -16.8 2385047.2 1817/12/ 8-12 N 61 11.4 .17.066 16.488 -25.2 -22.7 -17 61 16.7 17.059 15.914 -22.7 -22.6 2385209.6 1818/ 5/20- 8 F 61 17.1 16.933 15.612 -21.6 19.9 13 61 19.9 16.931 16.142 -23.9 20.0 2385239.2 1818/ 6/18-15 F 61 21.7 16.894 17.093 -27.2 23.4 - 8 61 22.9 16.896 16.935 -26.7 23.4 2385431.1 1818/12/27-15 N .61 29.3 17.100 17.336 -27.9 -23.3 2 61 29.4 17.099 17.330 -27.9 -23.3 2 3 4 5 6 7 8 9 10 11 12 13 14 '/DAY -/DAY h '/DAY -/DAY 2385460.6 1819/ 1/26- 1 N 61. 8.9 17.013 15.951 -23.7 -18.9 -20 61 15.6 16.978 16.734 -26.4 -19.1 2385623.1 1819/ 71 7-15 F 61 18.3 16.856 17.068 -27.6 22.6 13 61 21.0 16.849 16.755 -26.4 22.6 2385652.6 1819/ 8/ 5-22 F 61 22.5 16.910 15.480 -21.3 17.0 - 8 61 23.8 16.906 15.857 -22.9 17.1 2385815.0 1820/ 1/15-17 N 61 3.8 17.009 16.421 -25.8 -21.2 22 61 12.0 16.982 15.581 -22.2 -21.0 2385844.5 1820/ 2/14- 4 N 61 27.8 17.099 14.605 -16.4 -13.4 - 1 61 27.8 17.099 14.616 -16.5 -13.4 2385874.1 1820/ 3/14-14 N 61 1.5 16.969 13.282 - 3.1 - 2.4 -23 61 9.9 16.935 13.693 - 9.8 - 2.8 2386036.5 1820/ 8/23-23 F 61 17.9 16.934 14.098 -13.2 11.2 12 61 20.5 16.931 13.765 - 9.6 11.1 2386066.0 18201 9/22- 7 F 61 22.1 17.019 13.392 0.2 0.3 - 9 61 23.5 17.022 13.430 - 2.5 0.5 2386228.4 1821/ 3/ 4- 6 N 61 5.3 17.021 13.465 - 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2 61 23.8 16.965 14.156 7.9 2387498.3 1824/ 8/24-14 N 61 23.6 16.961 14.111 7.2 .11.0 2387690.2 1825/ 3/ 4-21 F 61 28.7 17.052 14.039 1.8 - 6.3 5 61 29.1 17.049 14.030 0.6 - 6.2 2387719.7 1825/ P 3- 6 F 61 14.7 16.933 14.350 9.6 5.2 -16 61 19..5 16.910 14.115 5.5 4.9 2387882.1 1825/ 9/12-15 N 61 9.5 16.902 13.979 0.4 4.2 18 61 15.1 16.877 14.119 4.9 3.9 2387911.7 1825/10/11-23 N 61 25.8 17.036 14.664 -11.0 - 7.2 - 3 61 26.1 17.035 14.596 -10.3 -7.1 2388103.6 1826/ 4/22- 7 F 61 25.7 16.996 15.193- -14.6 12.0 4 61 25.9 16.999 15.280 -15.2 12.1 2388133.2 1826/ 5/21-15 F 61 9.7 16.891 16.060 -20.4 20.1 -18 61 15.1 16.877 15.755 -18.6 2388295.6 1826/10/31- 1 N 61 12.4 17.027 15.266 -15.3 -13.9 17 61 17.1 17.015 15.678 -17.6 -14.1 2388325.1 1826/11/29-11 N 61 25.8 17.124 16.256 -20.2 -2-1.4 - 5 61 26.3 17.125 16.198 -20.0 -21.4 2388517.1 1827/ 6/ 9-16 F 61 24.6 16.935 16.257 -20.0 22.9 3 61 24.8 16.934 16.260 -20.0 22.9 2388546.6 18271 718-23 F 61 9.8 16.819 15.748 -18.0 22.5 -18 61 15.2 16.822 16.046 -19.3 22.6 2388709.0 1827/12/18-14 N 61 18.6 17.077 16.141 -19.4 -23.4 14 61 22.1 17.054 16.080 -18.9 -23.4 2388738.5 1828/ 1117- 1 N 61 26.4 17.078 15.633 -16.0 -21.0 - 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4 61 28.7 17-071 14.889 -11.3 -15.4 2402101.1 1864/ 8/17-14 F 61 23.2 16.907 14.673 - 8.6 13.2 8 61 24.5 16-903 14.560 - 6.9 13.1 2402130.7 1864/ 9/15-21 F 61 18.8 16.968 14.338 0.8 2.7 -12 61 21.7 16.960 14.371 - 1.9 2.9 2402293.1 1865/ 2/25-20 N 61 13.2 17.020 14.451 - 5.0 - 8.8 16 61 17.8 17.022 14.391 - 1.7 - 8.6 24U322-6 1865/ 3/27- 5 N 61 24.0 17.048 14.543 4.5 2.6 - 5 61 24.6 17.041 14.506 3.4 2.5 2402514.6 1865/10/ 4-23 F 61 24.2 17.034 14.619 5.4 - 4.6 7 61 25.2 17-033 14.710 6.9 - 4.8 2402544.1 1865/11/ 3- 8 F 61 17.9 17.064 15.253 13.4 -15.1 -14 61 21.3 17,062 15-033 11.3 -14.9 2 3 4 5 6 7 8 9 10 11 12 13 14 WAY -/DAY WAY -/DAY 2402706.5 1866/ 4/15- 7 N 61 12.4 16.986 14.751 8.6 9.7 15 61 16.4 16.991 15.008 11.1 9.9 2402736.0 1866/ 5/14-15 N 61 21.5 16.957 15.565 15.3 18.7 - 7 61 22.2 16.956 15.458 14.5 18.6 2402928.0 1866/11/22-10 F 61 29.0 17.087 15.714 15.9 -20.1 6 61 29.6 17.082 15.811 16.5 -20.2 2402957.5 1866/12/21-21 F 61 17.8 17.056 16.047 18.4 -23.4 -16 61 22.2 17.037 16.022 18.1 -23A 2403119.9 1867/ 6/ 2-15 N 61 13.1 16.874 15.795 17.2 22.2 15 61 16.8 16.877 15.974 18.1 222 2403149.5 1867/ 7/ 1-22 N 61 21.3 16.911 16.072 18.4 23.1 - 7 61 22.1 16.907 16.095 18.5 23.1 2403341.4 1868/ It 9-23 F 61 30.1 17.126 16.103 18A -22.1 .3 61 30.3 17.127 16.072 18.2 -22.1 2403370.9 1868/ 2/ 8-10 F 61 12.0 17.049 15.232 .13.8 -15.1 -19 61 17.8 17.028 15.616 16.1 -15.4 2403533.4 1868/ 7/19-22 N 61 11.5 16.897 15.878 18.2 20.7 i5 61 15.2 16.899 15.679 16.9 20.6 2403562.9 1868/ 8/18- 5 N 61 20.3 16.981 15.167 13.0 13.0 - 6 61 21.0 16.986 15.299 14.0 13.1 2403725.3 1869/ 1/28- 1 F 61 0.8 17.031 15.599 17.5 -18.2 24 61 10.3 17.006 15.197 14.4 -17.9 2403754.8 1869/ 2/26-12 F 61 28.7' 17.106 14.883 10.4 - 8.6 1 61 28.7 17.105 14.863 10.1 - 13.6 2403784.4 1869/ 3/27-22 F 61 7.0 16.912 14.225 0.8 2.9 -21 61 14.1 16.902 14.397 5.3 2 .5 2403946.8 1869/ 9/ 6- 6 N 61 14.5 16.957 14.606 9.3 6.4 14 61 18.0 16.932 14.421 6.2 6.2 2403976.3 1869/10/ 5-14 N 61 23.5 17.004 14.270 - 0.6 - 4.9 - 7 61 24.4 17.010 14.281 1.0 - 4.8 2404138.7 1870/ 3/17-14 F 61 5.2 16.955 14.178 5.3 - 1.3 21 61 13-1 16.931 14.115 0.3 - 0.9 @u 2404168.3 1870/ 4/15-22 F 61 28.2 16.975 14.329 - 5.3 9.9 0 61 28.2 16.975 14.326 - 5.2 9.9 2404197.8 1870/ 5/15- 6 F 61 4.3 16.832 14.974 -14.7 18.8 -22 61 12.1 16.797 14.530 -10.4 18.6 2404360.2 1870/10/24-16 N 61 19.0 17.000 14.280 - 7.3 -11.8 13 61 21.8 16.990 14.535 -10.3 -12.0 2404389.7 1870/11/23- 1 N 61 23.8 17.097 15.382 -17.0 -20.3 - 8 61 25.2 17.089 15.149 -15.4 -20.2 ct 2404552.2 1871/ 5/ 4-23 F 61 4.2 16.860 14.514 -12.4 16.0 21 61 11.1 16.877 15.149 -16.7 16.3 -20.5 22.3 ;3 2404581.7 1871/ 6/ 3- 7 F 61 24.8 16.952 15.951 -20.6 22.3 - 1 61 24.8 16.952 15.934 2404611.2 1871/ 7/ 2-14 F 61 1.1 16.817 16.503 -23.9 23.0 -23 61 9.3 16.817 16.338 -22.9 23.1 -22.8 -210 11 61 23.6 17.109 16.579 -23.8 -23.1 2404773.6 1871/12/12- 4 N 61 21.6 17.115 16.323 2404803.2 1872/ 1/10-15 N 61 21.4 17.103 16.719 -24.4 -22.0 -11 61 23.6 17.101 16.814 -24.7 -22.1 2404965.6 1872/ 6/21- 7 F 61 3.8 16.836 16.616 -25.0 23.4 21 61 11.2 16.827 16.788 -25.4 23.4 2404995.1 1872/ 7/20-14 F 61 25.4 16.921 16.585 -24.2 20.5 - 1 61 25.4 16.921 16.597 -24.2 20.6 240024.7 1872/ 8/18-21 F 61 2.7 16.815 14.961 -17.4 12.8 -22 61 10.9 16.824 15.789 -21.4 13.1 2405187.1 1873/ 1/28-17 N 61 25.4 17.084 16.077 -22.5 -18.0 9 61 26.6 17.077 15.792 -21.2 -17.9 2405216.6 1873/ 2/27- 3 N 61 19.0 17.017 14.349 -12.9 - 8.3 -13 61 22.1 16.998 14.804 -16.1 - 8 .5 2405379.0 1873/ 8/ 8-14 F 61 6.0 16.811 15.446 -20.8 16.0 21 61 13.2 16.787 14.708 -16.4 15.8 2405408.6 1873/ 9/ 6-21 61 27.3 16.966 14.074 -10.4 6.2 0 61 27.3 16-966 14.089 -10.5 6.2 2405438.1 1873/10/ 6- 6 F 61 2.2 16.943 13.442 2.6 - 5.1 -23 61 10.9 16.925 13.540 - 3.9 - 4.8 2405600.5 1874/ 3/18- 5 N 61 23.8 17.047 13.582 - 4.0 - 1.0 6 61 24.5 17.053 13.543 - 2.1 - 0.9 2405630.0 1874/ 4/16-14 N 61 12.9 16.981 13.804 9.4 10.2 -15 61 16.9 16.961 13.558 5.0 10.0 2405792.5 1874/ 9/25-22 F 61 7.4 16.921 13.352 - 1.0 - 1.1 20 61 14.0 16.912 13.499 5.1 - 1.4 2405822.0 1874/10/25- 7 F 61 27.8 17.093 14.149 12.5 -12.1 - 1 61 27.9 17.093 14.098 12.0 -12.1 2405851.5 1874/11/23-18 F 60 59.4 16.997 15.781 23.4 -20.4 -25 61 9.2 16.980 14.835 18.3 -20.2 2406013.9 1875/ 5/ 5-15 N 61 21.9 16.990 14.953 18.6 16.2 5 61 22.4 16.991 15.188 19.8 16.3 2406043.5 1875/ 6/ 3-22 N 61 11.0 16.874 16.701 26.6 22.3 -16 61 15.3 16.870 16.151 24.4 22.3 2406205.9 1875/11/13-10 F 61 13.6 17.020 15.378 21.3 -17.9 18 61 19.1 16.993 16.203 24.6 -18.1 2406235.4 1875/12/12-20 F 61 30.5 17.102 17.254 27.9 -23.1 - 4 61 30.8 17.102 17.176 23 -23.1 2406427.4 1876/ 6/21-22 N 61 22.1 16.906 17.334 28.4 23.4 6 61 22.6 16.907 17.303 28.2 23.4 2406456.9 1876/ 7121- 5 N 61 11.0 16.879 16.093 24.4 20.4 -16 61 15.3 16.873 16.723 26.6 20.5 2406619.3 1876/12/30-22 F 61 18.1 17.061 17.061 27.5 -23.1 15 61 22.3 17.052 16.658 26.0 -23.0 2 3 4 5 6 7 8 9 10 11 12 T3 - 14 1 11 NDAY -/DAY h -/DAY WAY 2406648.8 1877/ 1/29- 9 F 61 28.1 17.123 15.351 20.5 -17.8 - 7 61 28.8 17.118 15.638 21.8 -17.9 2406840.8 1877/ 81 9- 5 N 61 21.0 16.970 14.744 17.2 15.8 6 61 21.5 16.968 14.539 15.8 15.8 2406870.3 1877/ 9/ 7-13 N 61 10.2 16.952 13.471 4.8 5.9 -16 61 14.6 16.969 13.787 9.5 6.2 2407032.7 1878/ 2/17-11 F 61 19.3 17.096 14.031 11.4 -11.9 13 61 22.5 17-086 13.750 7.7 -11.7 2407062.3 1878/ 3/18-21 F 61 24.7 17.031 13.555 2.1 - 0.7 - 9 61 25.9 17.033 13.546 0.4 - 0.9 2407254.2 1878/ 9/26-14 N 61 24.7 17.009 13.701 5.0 - 1.3 5 61 25.1 17.002 13.768 - 6.3 - 1.4 2407283.7 1878/10/25-23 N 61 12.3 16.987 14.797 -17.0 -12.3 -17 61 17.3 16.984 14.278 -129 -12.1 2407446.2 1879/ 4/ 6-22 F 61 21.0 16.973 14.196 -11.1 6.6 12 61 23.4 16.968 14.540 -14*.o 6.8 2407475.7 1879/ 5/ 6- 6 F 61 22.9 16.926 15.742 -21.0 16.4 - 9 61 24.4 16.915 15.401 -19.2 16.3 `11 2407667.6 1879/11/14- 1 N 61 27.6 1T073 16.123 -22.1 -18.1 3 61 27.8 17.074 16.226 -22.6 18.1 2407697.2 1879/12/13-11 N 61 9.4 17.072 16.770 -25.3 -23.1 -19 61 15.6 17.043 16.712 -24.9 -23.1 2407859.6 1880/ 5/24- 7 F 61 18.5 16.915 16.514 -23.6 20.8 11 61 20.8 16.925 16.698 -24.3 20.9 2407889.1 1880/ 6/22 -14 F 61 19.6 16.923 16.577 -23.9 23.4 -10 61 21.3 16.919 16.716 -24.4 23.4 2408051.5 1880/12/ 2- 3 N 61 0.4 17.014 16.430 -23.5 -22.0 24 61 9.4 16.987 16.520 -23.6 -22.1 2408081.1 1880/12/31-14 N 61 28.0 17,143 16.270 -21.8 -23.0 1 61 28.0 17.142 16.252 -21.8 -23.0 2408110.6 1881/ 1/30- 1 N 61 4.5 17,009 14.743 -14.2 -17.7 -22 61 12.2 16.989 15.423 -18.3 -17.9 2408273.0 1881/ 7/11-14 F 61 18.7 16.904 15.767 -19.3 22.0 12 61 20.9 16.893 15,476 -17.6 22.0 2408302.6 1881/ 8/ 9-21 F 61 21.1 16.900 14.647 -11.4 15.6 -10 61 22.8 16.906 14.889 -13.4 15.8 2408465.0 1882/ 1/19-16 N 61 7.1 17.040 15.248 -16.3 -20.2 21 61 14.3 17.001 14.798 -12;6 -20.1 2408494.5 1882/ 2/18- 3 N 61 28.6 17.064 14.438 - 7.0 -11.7 - 2 61 28.7 17.063 14.462 - 7.4 -11.7 i@: 2408524.0 1882/ 3/19-12 N 60 59.9 16.917 14-094 3.6 - 0.5 -24 61 9.2 16-867 14.117' - 1.9 - 0.9 2408686.4 1882/ 8/28-21 F 61 21.1 16.909 14.355 - 5.0 9.5 11 61 23.2 16.902 14.289 - 2.5 9.4 2408716.0 1882/ 9/27- 5 F 61 22.2 17.000 14.395 5.1 - 1.6 -10 61 24.1 16.993 14.331 2.9 - 1.4 2408878.4 1883/ 3/ 9- 4 N 61 8.6 16,987 14.249 - 0.8 - 4.6 19 61 14.6 16.992 14.338 3.2 - 4.3 2408907.9 1883/ V 7-14 N 61 24.4 17.036 14.735 8.8 6.8 - 4 61 24.6 17-031 14.687 8.1 6.8 2409099.9 1883/10/16- 7 F 61 22.6 17.042 14.837 9.6 - 8.8 10 61 24.3 17.040 15.023 11.4 - 8.9 2409129.4 1883/11/14-17 F 61 21.4 17.092 15.685 16.6 -18.3 -12 61 23.8 17.090 15.488 15.2 -18.1 2409291.8 1884/ 4/25-15 N 61 7.9 16.947 15.042 12.3 13.4 18 61 13.3 16-956 15.405 14.8 13.7 2409321.4 1884/ 5/24-23 N 61 22.4 16.953 15.911 17.6 21.0 - 4 61 22.7 16.953 15.862 17.3 20.9 2409513.3 1884/12/ 2-19 F 61 27.7 17.093 16.011 17.8 -22.1 8 61 28.8 17.085 16.089 18.2 -22.2 2409542.8 1885/ 1/ 1- 5 F 61 21.2 17.068 15.988 18.0 -23.0 -13 61 24.6 17.054 16.098 18.4 -23.0 2409705.3 1885/ 6/12-23 N 61 8.8 M846 15.941 18.2 23.2 17 61 13.9 16.846 16.006 18.4 23.2 2409734.8 1885/ 7112- 5 N 61 22.7 16,917 15.897 17.3 22.0 - 3 61 23.0 16.916 15.941 17.6 22.0 ORZI 2409926.7 1886/ 1/20- 8 F 61 28.9 17.117 15.793 16.4 -20.1 5 61 29.4 17.118 15.710 15.9 -20.1 2409956.3 1886/ 2/18-18 F 61 15.5 17.051 14.891 10.1 -11.4 -16 61 20.1 17.035 15.202 12.7 -11.7 2410118.7 1886/ 7/31- 5 N 61 7.6 16.882 15.498 15.8 18.3 18 61 12.8 16.880 15.220 13.5 18.1 2410148.2 1886/ 8/29-13 N 61 22.1 17.001 14.847 9.2 9.3 - 4 61 22.4 17-004 14.909 9.9 9.3 2410340.2 1887/ 3/ 9-20 F 61 27.6 17.089 14.630 6.1 - 4.4 4 61 27.9 17.087 14.597 5.4 - 4.3 2410369.7 1887/ 41 8- 6 F 61 11.1 16.916 14.368 - 3.4 7.1 -19 61 16.7 16.908 14.363 0.4 6.8 2410532.1 1887/ 9/17-14 N 61 11) 16.955 14.393 5.0 2.2 17 61 16.1 16.925 14.323 1.4 2.0 2410561.6 1887/10/16-23 N 61 25.6 17.027 14.460 - 4.7 - 9.0 - 5 61 26.0 17.031 14.427 - 3.7 - 9.0 2410724.1 1888/ 3127-22 F 60 59.4 16.908 14.107 1.0 3.0 24 61 9.2 16.886 14.259 - 4.4 3.4 2410753.6 1888/ 4/26- 6 F 61 27.4 16.956 14.648 - 8.9 13.7 3 61 27.5 16.957 14.687 '- 9.4 13.7 2410783.1 1888/ 5/25-14 F 61 9.0 16.846 15.437 -16.9 21.1 -19 61 15.1 16-817 15.037 -13.8 20.9 2410945.5 1888/11/ 4- 0 N 61 16.2 17.002 14.647 -10.9 -15.5 15 61 20.1 16.989 15.018 -13.9 -15.6 2 3 4 5 6 7 8 9 10 11 12 13 14 '/DAY */DAY h '/DAY '/DAY 2410975.1 1888/12/ 3-10 N 61 25.9 17.110 15.841 -18.9 -22.2 - 6 61 26.7 17.104 15.686 -18.0 -22.2 2411137.5 1889/ 5/15- 7 F 60 58.4 16.812 14.927 -15.2 18.9 24 61 7.8 16.832 15.640 -19.1 19.2 2411167.0 1889/ 6/13-14 F 61 24.4 16.942 16.259 -21.5 23.2 2 61 24.4 16.943 16.299 -21.7 23.2 2411196.5 1889/ 7/12-21 F 61 6.3 16.849 16.365 -22.6 21.9 -19 61 12.6 16.852 16.464 -22.8 22.0 2411359.0 1889/12/22-13 N 61 19.1 17.112 16.524 -23.2 -23.4 13 61 22.0 17.103 16.659 -23.7 -23.4 2411388.5 1890/ 1/21- 0 N 61 23.5 17.106 16.352 -22.3 -19.9 - 9 61 25.0 17.105 16.534 -23.1 -20.0 2411550.9 1890/ 7/ 2-14 F 60 58.2 16.801 16.561 -24.5 23.0 25 61 7.6 16.788 16.435 -23.7 22.9 2411580.4 1890/ 7/31-21 F 61 25.4 16.929 16.105 -21.7 18.1 3 61 25.5 16.927 16.042 -21.4 18.1 2411610.0 1890/ 8/30- 5 F 61 8.3 16.859 14.563 -13.6 9.0 -20 61 14.5 16.866 15.196 -17.6 9.3 2411772.4 1891/ 2/ 9- 2 N 61 22.9 17.069 15.466 -19.2 -14.8 10 61 24.8 17.060 15.127 -17.2 -14.7 2411801.9 1891/ 3/10-12 N 61 21.4 17.012 14.061 - 8.6 - 4.1 -12 61 23.6 16.998 14.333 -11.5 - 4.3 2411964.3- 1891/ 8/19-21 F 61 0.9 16.796 14.864 -17.4 12.7 24 61 10.0 16.765 14,188 -11.8 12.3 2411993.9 1891/ 9118- 5 F 61 27.7 16.981 13.865 - 6.2 2.0 2 61 27.7 16.981 13.840 - 5.7 2.0 2412023.4 1891/10/17-14 F 61 7.7 16.989 13.722 6.7 - 9.3 -20 61 14.6 16.969 13.589 1.1 - 9.0 2412185.8 1892/ 3/28-13 N 61 21.2 17.021 13.576 0.3 3.3 9 61 22.6 17.031 13.622 2.8 3.4 2412215.4 1892/ 4/26-22 N 61 15.8 16.981 14.258 13.1 13.9 -13 61 18.6 16.965 13.932 9.6 13.7 2412377.8 1892/10/ 6- 6 F 61 2.9 16.914 13.421 3.3 - 5.3 23 61 11.3 16.902 13.830 9.8 - 5.7 2412407.3 1892/11/ 4-16 F 61 28.5 17.109 14.678 16.1 -15.7 0 61 28.5 17.109 14.694 16.2 -15.7 2412436.8 1892/12/ 4- 2 F 61 4.8 17.028 16.367 25.2 -22.3 -22 61 12.9 17.014 15.588 21.7 -22.2 2412599.3 18931 5115-23 N 61 19.7 16.969 15.529 21.4 19.1 8 61 20.8 16.971 15.881 22.9 19.2 2412628.8 1893/ 6/14- 6 N 61 14.5 16.886 17.045 27.5 23.3 -13 61 17.5 16.886 16.742 26.3 23.2 2412791.2 1893/11/23-18 F 61 9.7 17.017 15.976 23.9 -20.5 20 61 16.6 16.984 16.780 26.7 -20.7 2412820.7 1893/12/23- 5 F 61 31.4 17.109 17.394 28.2 -23.4 - 2 61 31.4 17.109 17.389 28.2 -23.4 2412850.3 1/21-15 F 61 1.5 16.979 16.031 24.4 -19.8 -24 61 11.3 16.933 16.930 27.4 -20.0 2413012.7 1894/ 713- 6 N 61 20.3 16.896 17.166 27.9 23.0 8 61 21.4 16.896 16.993 27.3 22.9 2413042.2 1894/ 8/ 1-12 N 61 14.9 16.904 15.539 21..9 18.0 -13 61 17.8 16.901 16.129 24.3 18.1 2413204.6 1895/ 1/11- 7 F 61 14.3 17.048 16.622 26.3 -21.8 17 61 19.7 17.035 15.976 23.6 -21.7 2413234.2 1895/ 219-17 F 61 28.9 17.116 14.734 17.1 -14.6 - 4 61 29.3 17.113 14.916 18.2 -14.6 2413426.1 1895/ 8/20-13 N 61 19.7 16.972 14.214 13.8 12.4 8 61 20.8 16.969 13.971 11.6 12.3 2413455.6 1895/ 9/18-21 N 61 14.4 16.988 13.363 0.6 1.7 -13 61 17.6 17.002 13.478 4.7 1.9 2413618.1 1896/ 2/28-20 F 61 15.5 17.067 13.623 7.4 - 7.9 15 61 19.8 17.056 13.460 2.8 - 7.7 2413647.6 1896/ 3/29- 5 F 61 25.9 17.023 13.656 - 6.4 3.6 - 6 61 26.5 17.025 13.575 4.5 3.5 2413839.5 1896/10/ 6-22 N 61 23.9 17.021 13.875 - 9.2 - 5.6 7 61 24.8 17.010 14.055 -11.2 - .5.7 2413869.1 1896/11/ 5- 8 N 61 16.6 17.017 15.407 -20.6 -15.9 -15 61 20.3 17.013 14.859 -17.4 -15.7 2414031.5 1897/ 4117- 6 F 61 17.2 16.938 14.555 -15.1 10.6 14 61 20.8 16.933 15.094 -18.4 10.8 2414061.0 1847/ 5/16-14 F 61 24.6 16.920 16.321 -23.9 19.2 - 7 61 25.4 16.913 16.076 -22.9 19.2 2414253.0 1897/11/24- 9 N 61 27.1 17.080 16.652 -24.7 -20.6 6 61 27.5 17.080 16.784 -25.2 -20.7 2414282.5 1897/12/23-20 N 61 13.5 17.090 16.761 -25.6 -23.4 -17 61 18.4 17.064 16.966 -26.2 -23.4 2414444.9 1898/ 6/ 4-14 F 61 14.9 16.886 16.803 -25.3 22.5 14 61 18.4 16.896 16.856 -25.4 22.5 2414474.4 1898/ 7/ 3-21 F 61 21.8 16.933 16.360 -23.4 22.9 - 7 61 22.7 16.931 16.550 -24.2 22.9 2414666.4 1899/ 1/11-23 N 61 27.5 17.141 15.860 -20.5 -21.7 3 61 27.7 17.140 15.773 -20.1 -21.7 @414695.9 1899/ 2110- 9 N 61 8.6 17.014 14.298 -11.0 -14.3 -19 61 15.0 17.000 14.868 -15.4 -14.6 2414858.3 1899/ 7/22-22 F 61 15.6 16.893 15.309 -17.6 20.2 14 61 19.0 16.877 14.914 -14.9 20.1 2414887.9 1899/ 8/21- 5 F 61 23.7 16.926 14.268 - 8.1 12.2 - 7 61 24.6 16,931 14.408 - 9.8 12.3 2415050.3 1900/ 1/31- 1 N 61 2.1 17.015 14.730 -13.7 -17.5 23 61 10.9 16.972 14.292 - 8.7 -17.3 2 3 4 5 6 9 10 12 13 14 '/DAY '/DAY h '/DAY */DAY 2415079.8 1900/ 3/ 1-11 N 61 28.2 1 7.052 14.161 3.0 7.6 1 61 28.2 17.052 14.158 2.9 7.6 2415109.4 1900/ 3/30-21 N 61 4.5 16.923 14.250 8.0 3.8 -22 61 12.1 16.880 14-064 2.9 3.5 2415271.8 1900/ 9/ 9- 5 F 61 18.4 16.910 14.141 1.0 5.5 14 .61 21.6 16.899 14.182 2.2 5.3 2415301.3 1900/10/ 8-13 F 61 25.0 17.029 14.597 9.3 5.8 - 7 61 26.1 17.022 14.480 7.7 5.7 2415463.7 1901/ 3/20-13 N 61 3.4 16.948 14.184 3.5 0.3 21 61 11.0 16.957 14.472 8.0 0.0 2415493.2 1901/ 4/18-22 N 61 24.3 17.020 15.053 12.8 10.8 - 1 61 24.3 17.019 15.034 123 10.8 2415522.8 1901/ 5/18- 6 N 60 58.7 16.868 15.796 19.0 19.4 -23 61 7.3 16.849 15.404 16.4 19.2 2415685.2 1901/10/27-15 F 61 20.5 17.047 15.170 13.6 -12.7 13 61 23.1 17.044 15.451 15.4 -12.9 2415714.7 1901/11/26- 1 F 61 24.2 17.114 16.080 19.0 -20.8 - 9 61 25.9 17.113 15.954 18.3 -20.7 2415877.1 1902/ 5/ 7-23 N 61 2.8 16.905 15.388 --- 15.7 16.7 20 61 9.8 16.916 15.795 17.8 17.0 2415906.7 1902/ 6/ 6- 6 N 61 22.8 16.949 16.153 19.2 22.6 - 1 61 22.8 16.949 16.146 19.1 22.5 2415936.2 1902/ 7/ 5-13 N 60 58.6 16.787 15.743 18.1 22.8 -23 61 7.2 16.792 16.021 19.2 22.9 2416098.6 1902/12/15- 4 F 61 26.0 17.095 16.159 18.9 -23.2 10 61 27.7 17.084 16.164 18.8 -23.2, 2416128.2 1903/ 1/13-14 F 61 24.1 17.075 15.756 16.7 -21.6 -12 61 26.5 17.065 15.945 17.7 -21.) 2416290.6 1903/ 6/25- 6 N 61 3.9 16.817 15.925 18.5 23.4 21 61 10.8 16.812 15.819 17.6 23.4 2416320.1 1903/ 7/24-13 N 61 23.5 16.923 15.597 15.4 20.1 - 1 61,23.5 16.923 15.615 15.6 20.1 2416349.6 1903/ 8/22-20 N 60 58.7 16.853 14.664 8.9 12.0 -23 61 7.4 16.857 15.100 12.6 12.3 2416512.1 1904/ 2/ 1-17 F 61 27.1 17.104 15.396 13.7 -17.4 7 61 28.1 17.105 15272 12.7 -17.3 2416541.6 1904/ 3/ 2- 3 F 61 18.5 17.050 14'.639 6.0 - 7.4 -15 61 22.0 17.038 14.835 8.6 - 7.6 C@ 2416704.0 1900 8/11-13 N 61 3.2 16.867 15.085 12.8 15.3 20 61 10.1. 16.860 14.802 @!7 9.5 15.1 M 2416733.5 19041 91 9-21 N 61 23.3 17.019 14.629 5.1 5.2 - 2 fil 23.4 17.020 14.641 5.3 5. 3 2416763.1 1904/10/ 9- 6 N 60 57.6 16.933 14.374 - 3.9 - 6.1 -24 61 6.9 16.947 14.381 0.7 - 5.7 2416925.5 1905/ 3/21- 5 F 61 26.0 17.068 14.516 1 C) .8 0.0 5 61 26.6 17.065 14.508 0.6 0.1 2416955.0 1905/ 4/19-14 F 61 14.7 16.919 14.632 - 7.3 11.1 -16 61 19.0 16.914 14.506 - 4.2 10.8 2417117.4 1905/ 9/28-22 N 61 7.6 16.952 14.318 0.7 - 2.0 19 61 13.8 16.916 14.404 - 3.3 - 2.3 S; 2417147.0 1905/10/28- 7 N 61 27.1 17.047 14.764 - 8.6 -12.9 - 2 61 27.3 17.048 14.731 - 8.1 -12.9 2417338.9 1906/ 5/ 8-14 F 61 25.9 16.935 15.029 -12.1 16.9 5 61 26.4 16.937 15.128 -12.9 17.0 2411368.4 1906/ 6/ 6-21 F 61 13.2 16.858 15.811 -18.3 22.6 -16 61 17.7 16.836 15.527 -16.4 22.5 2417530.9 1906/11/16- 9 N 61 13.0 17.003 15.060 -13.9 -18.6 17 61 18.1 16.985 15.496 -16.6 -18.7 2417560.4 1906/12/15-19 N 61 27.4 17.118 16.160 -19.9 -23.2 - 5 61 27.8 17,114 16.088 -19.5 -23.2 2417752.3 1907/ 6/25-21 F 61 23.3 16.931 16.387 -21.6 23.4 5 61 23 '7 16.934 16.425 -21.7 23.4 2417781.9 1907/ 7/25- 5 F 61 11.0 16.881 16.075 -20.6 19.9 -17 61 15.6 16.885 16.328 -21.6 20 1 2417944.3 1908/ 1/ 3-22 N 61 16.1 17.104 16.493 -22.7 -22.9 15 61 19.9 17.092 16.453 -22.4 -22'8 2417973.8 1908/ 2/ 2- 9 N 61 25.2 17.105 15.879 -19.5 -17.2 - 8 61 26.0 17.105 16.064 -20.4 -17*2 2418165.8 1908/ 8/12- 5 F 61 24.9 16.938 15.591 -18.5 15.1 5 61 25.3 16.932 15.451 -17.7 15'0 2418195.3 1908/ 9/10-12 F 61 13.2 16.901 14.288 - 9.4 5.0 -16 61 17.9 16.906 14.703 -13.2 5.2 2418357.7 1909/ 2120-11 N 61 19.8 17.049 14.919 -15.4 -11.0 12 61 22.6 17.039 14.587 -12.7 -10.9 2418387.2 1909/ 3/21-20 N 61 23.2 17.006 13.939 - 4.3 0.2 - 9 61 24.6 16.995 14.060 - 6 7 0.1 2418579.2 1909/ 9/29-13 F 61 27.5 16.994 13.815 1.9 - 2.3 4 61 27.8 16,994 13.804 - 0,7 - 2.4 2418608.7 1909/10/28-22 F 61 12.5 17.029 14.136 10.5 -13.1 17 61 17.9 17.008 13.849 5.9 -12.9 2418771.1 1910/ 4/ 9-21 N 61 18.1 16.992 13.727 4.4 7.5 12 61 20.3 17.005 13.902 7.5 7.7 2418800.7 1910/ 5/ 9- 6 N 61 18.1 16.979 14.792 16.2 17.1 -11 61 19.9 16.968 14.463 13.7 17.0 2418992.6 1910/11/17- 0 F 61 28.7 17.122 15.272 19.1 -18.7 3 61 28.8 17.122 15.373 19.7 -18.8 2419022.2 1910/12/16-11 F 61 9.6 17.052 16.773 26.2 -23.3 20 61 16.2 17.041 16.263 24.1 -23.2 2419184.6 1911/ 5/28- 6 N 61 16.9 16.947 16.064 23.5 21.3 11 61 18.9 16.948 16.476 25.1 21.4 IND 2 3 4 5 6 7 8 9 10 1 12 13 14 C-n 00 '/DAY o/DAY h */DAY -IDAY 2419214.1 1911/ 6/26-13 N 61 17.5 16.898 17.162 27.5 23.4 -10 61 19.4 16.900 17.081 27.2 23.4 2419376.5 1911/12/ 6- 3 F 61 5.4 17.010 16.478 25.8 -22.3 22 61 13.7 16.970 17.096 27.7 -22.5 2419406.1 1912/ 1/ 4-13 F 61 31.6 17.112 17.249 27.6 -22.8 1 61 31.6 17.112 17.248 27.6 -22.8 2419435.6 1912/ 2/ @- 0 F 61 6.3 16.988 15.434 21.5 -17.0 -22 61 14.4 16.951 16.396 25.3 -17.2 2419598.0 1912/ 7/14-13 N 61 17.9 16.886 16.781 26.6 21.7 11 61 19.9 16.882 16.424 25.2 21.6 2419627.5 1912/ 8/12-20 N 61 18.2 16.928 14.973 18.9 14.9 -10 61 20.1 16.927 15.433 21.1 15.0 2419789.9 1913/ 1/22-16 F 61 10.0 17.030 16.008 24.1 -19.7 19 61 16.7 17.013 15.204 20.2 -19.5 2419819.5 1913/ 2/21- 2 F 61 29.2 17.105 14.204 13.4 -10.8 - 2 61 29.3 17.103 14.282 14.0 -10.8 2420011.4 1913/ 8/31-21 N 61 17.8 16.974 13.785 10.1 8.6 10 61 19.7 16.968 13.572 6.9 8.5 2420041.0 1913/ 9/30- 5 N 61 18.0 17.021 13.413 - 3.6 - 2.6 -11 61 20.1 17.031 13.379 - 0.3 - 2.4 2420203.4 1914/ 3112- 4 F 61 11.2 17.032 13.370 3.2 - 3.7 18 61 16.8 17.021 13.390 - 2.2 - 3.4 2420232.9 1914/ 4/10-13 F 61 26.6 17.013 13.922 -10.6 7.8 - 4 61 26.8 17.014 13.826 - 9.4 7.7 2420424.9 1914/10/19- 7 N 61 22.6 17.030 14.213 -13.3 - 9.7 9 61 24.1 17.015 14.548 -15.8 - 9.8 2420454.4 1914/11/17-16 N 61 20.2 17.042 16.068 -23.7 -18.9 -12 61 22.9 17.038 15.578 -21.5 -18.8 2420616.8 1915/ 4/29-14 F 61 12.9 16.900 15.033 -18.8 14.2 17 61 17.8 16.895 15.755 -22.2 14.5 2420646.3 1915/ 5/28-22 F 61 25.7 16.914 16.833 -26.1 21.4 - 5 61 26.0 16.910 16.709 -25.7 21.4 @u 2420838.3 1915112/ 6-18 N 61 25.9 17.083 17.049 -26.6 -22.4 8 61 26.9 17.083 17.136 -26.8 -22.5 2420867.8 1916/ 1/ 5- 5 N 61 17.0 17.101 16.500 -24.9 -22.7 -15 61 20.8 17.080 16.901 -26.3 -22.8 2421030.2 1916/ 6/15-22 F 61 10.8 16.855 16.903 -26.3 23.3 17 61 15.6 16.865 16.719 -25.5 23.3 2421059.8 1916/ 7/15- 5 F 61 23.3 16.942 15.967 -22.2 21.6 - 5 61 23.7 16.941 16.125 -22.9 21.6 2421251.7 1917/ 1/23- 8 N 61 26.5 17.135 15.321 -18.4 -19.5 4 61 26.9 17.133 15.1@8 -17.4 -19.5 2421281.2 1917/ 2/21-18 N 61 12.3 17.017 13.925 - 7.2 -10.6 -17 61 17.4 17.007 14.325 -11.7 -10.8 t@j rn 2421443.7 1917/ 8/ 3- 5 F 61 11.9 16.881 14.789 -15.2 17.7 17 61 16.6 16.860 14.356 -11.3 17.5 a) W1473.2 1917/ 9/ 1-12 F 61 25.7 16.950 13.972 - 4.3 8.4 - 4 61 26.1 16.954 14.025 - 5.5 8.5 2421665.1 1918/ 3/12-20 N 61 27.2 17.037 14.017 1.2 3.4 2 61 27.4 17.038 14.027 1.8 3.3 2421694.7 1918/ 4/11- 5 N 61 8.6 16.927 14.555 12.2 8.0 -19 61 14.7 16.891 14.207 7.8 7.7 1;: 2421857.1 1918/ 9/20-13 F 61 15.3 16.909 14.059 3.2 1.3 16 61 19.6 16.895 14.263 7.1 1.0 2421886.6 1918/10/19-22 F 61 27.1 17.051 14.942 13.5 9.9 - 6 61 27.7 17.047 14.817 12.4 9.8 2422049.0 1919/ 3/31-21 N 60 57.7 16.903 14.261 7.8 4.0 24 61 7.0 16.918 14.788 12.8 4.4 2422078.6 1919/ 4/30- 6 N 61 23.5 17.003 15.466 16.5 14.4 1 61 23.6 17.005 15.507 16.8 14.5 C-n 2422108.1 1919/ 5/29-13 N 61 3.6 16.885 16.173 21.2 21.5 -20 61 10.3 16.871 15.921 19.7 214 2422270.5 1919/11/ 8- 0 F 61 17.9 17.049 15.582 17.1 -16.2 14 61 21.5 17.046 15.916 18.8 -16 4 2422300.0 1919/12/ 7-10 F 61 26.5 17.131 16.356 20.8 -22.5 - 7 61 27.5 17.131 16.320 20.5 -22 5 2422462.5 1920/ 5/18- 6 N 60 57.0 16.858 15.730 18.5 19.5 24 61 6.1 16.872 16.073 19.9 197 2422492.0 1920/ 6/16-14 N 61 22.6 16.944 16.239 20.0 23.3 1 61 22.6 .16.944 16.232 20.0 23.3 2422521.5 1920/ 7/15-20 N 61 4.0 16.818 15.501 16.8 21.5 -20 61 10.7 16.827 15.902 18.8 21.6 2422683.9 1920/12/25-13 F 61 23.6 17.093 16.116 19.0 -23.4 12 61 26A 17.077 16.005 18.3 -23.4 2422713.5 1921/ 1/23-23 F 61 26.4 17.077 15.401 14.5 -19.4 -10 61 28.0 17.071 15.605 15.8 -19.5 2422875.9 1921/ 71 5-14 N 60 58.5 16.787 15.741 17.9 22.8 23 61 7.3 16.777 15.451 B.7 22.7 2422905.4 1921/ 8/ 3-20 N 61 23.7 16.929 15.226 12.9 17.5 2 61 23.7 16.928 15.197 12.7 17.5 2422935.0 1921/ 9/ 2- 4 N 61 4.4 16.898 14.444 5.1 8.1 -20 61 11.1 16.900 14.729 8.8 8.5 2423097.4 1922/ 2/12- 1 F 61 24.7 17.086 14.993 10.4 -14.0 10 61 26.4 17.086 14.860 8.8 -13.9 2423126.9 1922/ 3/13-11 F 61 21.1 17.046 14.510 1.8 - 3.1 -12 61 23.5 17.036 14.587 4.1 - 3.3 2423289.3 1922/ 8/22-21 N 60 58.3 16.851 14.702 9.3 11.8 23 61 7.0 16.838 14.497 5.1 11.5 2423318.9 1922/ 9/21- 5 N 61 24.0 17.034 14.535 0.8 1.0 1 61 24.0 17.033 14.533 0.6 1.0 2 3 4 5 6 7 8 9 10 11 12 t3- 14 ' 'I */DAY WAY h '/DAY WAY 2423348.4 1922/10/20-14 N .61 3.3 16.978 14.641 - 8.0 -10.2 -21 61 10.7 16.987 14.490 4.1 - 9.9 2423510.8 1923/ P 1-13 F 61 23.7 17.043 14.543 - 2.6 4.3 8 61 24.9 17.040 14.596 4.1 4.4 2423540.3 1923/ 4/30-22 F 61 17.9 16.920 14.985 -10.9 14.7 -14 61 20.9 16.917 14.802 8.6 14.5 2423702.8 1923/10/10- 6 N Bl 3.4 16.947 14.379 - 3.5 - 6.3 22 61 11.3 16-904 14.644 7.7 - 6.6 2423732.3 .1923/11/ 8-15 N 61 28.1 17.062 15.145 -12.0 -16.4 0 61 28.1 17.062 15.141 -11.9 -16.4 2423761.8 1923/12/ 8- 2 N 61 2.9 17.001 15.738 - 17.7 -22.6 -23 61 11.5 16.964 15.441 -15.4 -22.5 2423924.2 1924/ 5/18-22 F 61 23.9 16.913 15.414 -14.8 19.6 7 61 24.9 16.914 15.563 -15.7 19.7 2423953.8 1924/ 6/17- 5 F 61 16.8 16.870 16.044 -19.0 23.4 -14 61 20.0 16.854 15.905 -18.1 23.3 2424116.2 1924/11/2@-17 N 61 9.2 17.000 15.451 -16.3 -21.0 20 61 15.6 16.977 15.868 -18.4 -21.1 2424145.7 1924/12/26- 4 N 61 28.4 17.122 16.287 -io.o -23.4 - 3 61 28.5 17.120 16.273 -19.9 -23.4 2424337.7 1925/ 7/ 6- 5 F 61 21.6 16.921 16.323 -20.8 22.7 7 61 22.6 16.923 16.301 -20.7 22.7 2424367.2 1925/ 8/ 4-12 F 61 15.1 16,912 15.698 -17.9 17.3 -14 61 18.3 16.917 15.989 -19.3 17.5 2424529.6 1926/ 1/14- 7 N 61 12.4 17.091 16.247 -21.2 -21.4 17 61 17.5 17.076 16.031 -20.0 -21.3 2424559.1 1926/ 2/12-17 N 61 26.2 17.101 15.396 -16.1 -13.8 - 5 61 26.6 17.102 15.529 -16.9 -13.8 2424751.1 1926/ 8/23-13 F 61 23.8 16.945 15.115 -14.9 11.6 7 61 24.7 16.936 14.932 -13.5 11.5 2424780.6 1926/ 9/21-20 F 61 17.5 16.939 14.154 - 5.2 0.8 -13 61 20.9 16.943 14.375 - 8.4 1.0 2424943.0 1927/ 3/ 3-19 N 61 16.1 17.024 14.495 -11.3 - 7.0 15 61 20.0 17.012 14.234 - 7.9 - 6.7 2424972.6 1927/ P 2- 4 N 61 24.5 16.997 13.979 0.0 4.5 - 6 61 25.3 16.989 13.996 - 1.8 4.4 2425164.5 1927/10/10-21 F 61 26.7 17.004 13.920 2.3 - 6.5 7 61 27.4 17.005 13.972 4.0 - 6.6 2425194.0 1927/11/ 9- 7 F 61 M8 17.062 14.646 13.9 -16.6 -15 61 20.9 17.043 14.287 10.3 -16.4 > 2425356.5 1928/ 4/20- 5 N 61 14.4 16.959 14.011 8.3 11.4 14 61 17.7 16.976 14.345 11.8 11.6 w 2425396.0 1929/ 5/19-13 N 61 19.9 16.976 15.342 18.8 19.8 - 7 61 20.9 16.968 15.079 17.2 19.7 2425577.9 1928/11/27- 9 F 61 28.3 17.131 15.849 21.5 -21.1 5 61 28.6 17.131 16.021 22.3 -21.2 2425607.5 1928/12/26-20 F 61 13.8 17.070 16.933 26.3 -23.3 -18 61 19.1 17.062 16.727 25.4 -23.4 2425769.9 1929/ 6/ 7-14 N 61 13.5 16.922 16.480 25.0 22.7 13 61 16.7 16.922 16.851 26.2 22.8 2425799.4 1929/ 7/ 6-21 N 61 19.8 16.909 17.045 26.8 22.7 - 8 61 20.9 16.914 17.107 26.9 22.7 2425991.4 1930/ 1/14-22 F 61 31.3 17.109 16.855 26.0 -21.3 2 61-31.4 17.108 16.797 25.8 -21.3 10 2426020.9 1930/ 2/13- 9 F 61 10.6 16.993 14.857 18.0 -13.5 -20 61 17.3 16.963 15.721 22.2 - 13.8 2426183.3 1930/ 7/25-21 N 61 14.9 16.877 16.242 24.5 19.7 13 61 18.0 16.868' 15.717 22.2 19.6 2426212.9 1930/ 8/24- 4 N 61 20.9 16.950 14.468 15.3 11.4 - 8 61 22.0 16.951 14.764 17.2 11.5 2426375.3 1931/ 21 3- 0 F 61 5.1 17.005 15.322 21.2 -16.9 22 61 13.3 16.985 14.483 16.1 -16.6 2426404.8 1931/ 3/ 4-711 F 61 29.0 17.090 13.816 9.2 - 6.7 - 1 61 29.0 17.090 13.821 9.3 - 6.7 2426434.3 1931/ 4/ 2-20 F 61 3.5 16.926 13.362 - 4.6 4.8 -22 61 11.6 16.905 13.344 2.1 4.4 2426596.8 1931/ 9/12- 4 N 61 15.4 16.974 13.494 6.0 4.6 14 61 18.3 16.966 13.381 2.0 4.4 2426626.3 1931/10/11-13 N 61 21.0 17.049 13.629 - 7.8 - 6.8 - 8 61 22.3 17.056 13.503 - 5.3 - 6.6 2426788.7 1932/ 3/22-12 F 61 6.2 16.990 13.284 - 1.1 0.7 21 61 13.4 16.982 13.547 - 7.3 1.0 2426818.2 1932/ 4/20-21 F 61 26.7 17.000 14.338 -14.5 11.7 - 1 61 267 17.000 14.284 -14.1 11.6 2426847.8 1932/ 5/20- 5 F 61 0.8 16.796 16.011 -24.4 [email protected] -23 61 9*6 16.780 15.072 -19.8 19.7 2427010.2 1932/10/29-15 N 61 20.7 '17.037 14.698 -17.2 -13.5 12 61 23.0 17.018 15.200 -19.9 -13.7 2427039.7 1932/11/28- 1 N 61 23.2 17.062 16.683 -26.1 -21.2 -10 61 25.1 17-058 16.325 -24.7 -21.2 2427202.1 1933/ 5/ 9-22 F 61 7.9 16.858 15.580 -22.1 17.4 20 61 14.4 16.855 16.412 -25.3 17.6 2427231.7 1933/ 6/ 8- 5 F 61 26.2 16.906 17.195 -27.6 22.8 - 2 61 26.2 16.905 17.167 -27.5 22.8 2427261.2 1933/ 7/ 7 -12 F 60 59.9 16.790 16.540 -26.2 22.6 -24 61 8.9 16.770 .17.100 -27.8 22.7 2427423.6 1933/12/17- 3 N 61 24.3 17.083 17.223 -27.5 -23.3 9 61 25.8 17.081 17.177 -27.3 -23.3 IQ 2427453.1 1934/ 1/15-14 N 61 19.9 17.107 16.032 -23.3 -21.2 -13 61 22.7 17.091 16.521 -25.2 -21.3 91 aqavjL rla rl.1 P13 rl@ r%3 . . . . . . . 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CD w Cn Nl C-" - C" -9@ 00 = -4 9461-.901 'sgP!,L ffu?.14S uvd,@1-1,9d P 9109 9zff,91v.'yS z9z 2 3 4 5 6 7 8 9 10 11 12 13 14 11 -/DAY */DAY h WAY -/DAY 2440180.8 1968/11/20- 8 N 61 15.5 17.042 15-905 -23.5 -19.7 16 61 19.8 17.014 16.583 -26.0 -19.9 2440210.4 1968/12/19-18 N 61 27.6 17.086 17.372 -28.3 -23.4 - 6 61 28.2 17.085 17.324 -28.1 -23.4 2440402.3 1969/ 6/29-20 F 61 25.4 16.892 17.249 -28.0 23.2 4 61 25.6 16.893 17.189 -27.8 23.2 2440431.8 1969/ 7/29- 3 F 61 10.3 16.856 15.607 -22.4 18.8 -18 61 15.7 16.845 16.392 -25.4 19.0 2440594.2 1970/ 1/ 7-21 N 61 19.2 17.071 16.758 -26.5 -22.3 13 61 22.3 17.066 16.297 -24.7 -22.3 2440623.8 1970/ 2/ 6- 7 N 61 24.1 17.107 14.828 -17.8 -15.7 - 8 61 25.4 17,097 15.197 -19.8 -15.8 2440815.7 1970/ 8/17- 3 F 61 24.4 16.967 14.359 -14.4 13.6 4 61 24.6 16.966 14.241 -13.4 13.5 2440845.3 19701 9/15-11 F 61 9.5 16.936 13.373 - 1.5 3.1 -18 61 15.1 16.947 13.600 - 6.8 3.4 2441007.7 1971/ 2/25-10 N 61 19.8 17.091 13.761 - 8.2 - 9.3 11 61 22.1 17.086 13.599 - 5.0 - 9.1 -19 N 61 20.4 17.012 13.624 5.4 2.2 -10 61 22.3 17.008 13.538 2.3 2.0 2441037,2 1971/ 3/26 2441229.2 1971/10/ 4-12 F 61 28.1 17.011 13.894 8.1 4.2 3 61 28.2 17.008 13.953 8.9 - 4.2 2441258.7 1971/11/ 2-21 F 61 11.0 16.986 15.221 19.5 -14.8 -18 61 17.2 16.970 14.577 15.3 -14.5 2441421.1 1972/ 4/13-21 N 61 20.7 16.970 14.513 13.9 9.3 9 61 22.4 16.974 14.844 16.2 9.5 2441450.6 1972/ 5/13- 4 N 61 18.2 16.930 16.109 22.8 18.4 -11 61 20.5 16.912 15.718 21.0 18.3 2441613.1 1972/10/22-13 F 61 3.0 16.900 14.710 15.8 -11.2 24 61 11.8 16.873 15.578 20.4 -11.5 2441642.6 1972/11/20-23 F 61 30.1 17.098 16.495 23.6 -19.9 1 61 30.1 17-099 16.527 23.8 -19.9 2441672.1 1972/12/20-10 F 61 7.0 17.062 16.666 25.1 -23.4 -21 61 14.6 17.029 16.807 25.3 -23.4 2441834.5 1973/ 6/ 1- 5 N 61 17.8 16.939 16.691 24.4 22.0 9 61 19.3 16.950 16.768 24.6 22.1 2441864.1 19731 6/30-12 N 61 15.0 16.930 16.330 23.1 23.2 -12 61 17.4 16.929 16.585 24.0 23.2 2442026.5 1973/12/10- 2 F 61 7.1 17.040 16.557 23.9 -22.9 21 61 14.5 17.024 16.462 23.2 -23.0 2442056.0 1974/ 1/ 8 - 13 F 61 30.0 17.152 15.984 20.5 -22.2 - 2 61 30.0 17.153 16.022 20.7 2442085.5 1974/ 2/ 6-23 F 61 1.7 16.970 14.423 11.7 -15.5 -24 -61 11.0 16.952 15.132 16.6 - 15 8 2442248.0 1974/ 7/19-12 N 61 18.3 16.930 15.471 17.8 20.9 10 61 M9 16.920 15.216 16.1 208 2442277.5 1974/ 8/17-19 N 61 16.9 M906 14.387 9.0 13.4 -12 61 19.2 16.918 14.644 11.5 13*5 2442439.9 1975/ 1/27-15 F 61 13.3 17.053 14.999 14.3 -18.5 18 61 19.0 17.021 14.626 10.7 -18.3 2442469,4 1975/ 2/26- 1 F 61 30.0 17.059 14.310 4.4 - 9.0 - 3 61 30.2 17.059 14.348 5.2 - 9 *I 2442661.4 1975/ 9/ 5-19 N 61 20.7 16.943 14.270 2.4 6.8 10 61 22.2 16.937 14.256 0.3 6.7 2442690.9 1975/10/ 5- 41 N 61 17.7 17.009 14.499 - 7.6 - 4.5 -13 61 20.3 17.006 14.374 - 5.0 - 4.3 2442853.3 1976/ 3/16- 3 F 61 14.0 16.999 14.299 - 1.7 - 1.7 16 61 18.7 17.001 14.443 - 5.2 - 1.5 2442882.9 1976/ 4114-12 F 61 25.5 17.019 14.938 -11.0 9.6 - 5 61 26.0 17.015 14.848 -10.1 9.5 2443074.8 1976/10/23- 5 N 61 22.6 17.066 15.042 -11.8 -11.4 8 61 23.7 17.061 15.204 -13.1 -11.6 2443104.3 1976/11/21-15 N 61 16.8 17.075 15.851 -17.8 -20.0 -13 61 20.2 17.076 15.648 -16.4 -19.9 2443266,8 1977/ 5/ 3-13 F 61 13.4 16.944 15.298 -14.1 15.7 16 61 17.7 16.942 15.609 -16.0 15.9 F 2443296.3 19771 6/ 1-21 61 24.1 16.920 16.047 -18.3 22.1 - 6 61 24.6 16.921 15.996 -18.0 22.1 2443488.2 1977112110-18 N 61 27.5 17.089 16.108 -18.4 -22.9 5 61 28.1 17.083 16.138 -18.5 -23.0 2443517.8 1978/ 1/ 9- 4 N 61 16.0 17.050 15.816 -17.2 -22.2 -16 61 20.4 17.027 16.013 _18.2 -22.2 2443680.2 1978/ 6/20-21 F 61 14.3 16.839 16.012 -18.4 23.4 15 61 18.3 16.834 15.998 -18.2 23.4 2443709.7 1978/ 7/20- 3 F 61 24.3 16.902 15.748 -16.4 20.7 - 5 61 24.8 16.900 15.832 -16.8 20.8 2443901.7 1979/ 1/28- 6 N 61 27.7 17.111 15.583 -15.1 -18.3 4 61 27.9 17.113 15.526 -14.7 -18.3 2443931.2 1979/ 2/26-17 N 61 9.4 17.032 14.674 - 7.9 - 8.8 -19 61 15.3 17.007 14.996 -11.1 - 9.0 2444093.6 1979/ 8/ 8- 3 F 61 13.2 16.888 15.331 -14.3 16.3 16 61 17.3 16.885 15.080 -12.0 16.2 2444123.2 1979/ 9/ 6-11 F 61 23.7 16-995 14.702 - 7.0 6.6 - 6 61 24.4 16.997 14.778 - 8.0 6.7 2444285.6 1980/ 2/16- 9 N 60 58.2 17.014 14.933 -12.4 -12.6 24 61 7.8 16.993 14.612 - 8.2 -12.2 2444315.1 1980/ 3/16-19 N 61 25.9 17.072 14.517 - 3.7 - 1.4 1 61 26.0 17.072 14.509 - 3.4 - 1.4 2444344.6 1980/ 4/15- 4 N 61 5.0 16.901 14.421 5.8 9.8 -21 61 12.0 16.882 14.338 1.6 9.5 2 3 4 5 6 7 8 9 10 11 12 13 14 */DAY WAY h */DAY VDAY 2444507.1 1980/ 9/24-12 F 61 17.1 16-958 14.354 2.5 - 0.6 15 61 20.7 16.937 14.352 0.6 - 0.9 2444536.6 1980/10/23-21 F 61 26.9 17.033 14.598 7.2 -11.7 - 7 61 27.7 17.033 14.526 5.8 -11.6 2444699.0 1981/ P 4-20 N 61 1.5 16.912 14.137 1.6 5.9 23 61 9.8 16.907 14.372 6.5 6.3 2444728.5 1981/ 5/ 4- 4 N 61 25.0 16.959 14.847 11.2 15.9 1 61 25.0 16.959 14.853 11.3 15.9 2444758.1 1981/ 6/ 2-12 N 61 2.6 16.847 15.637 18.3 22.2 -22 61 10.1 16.815 15.212 15.3 22.1 2444920.5 1981/11/11-23 F 61 21.3 17.023 14.944 13.2 -17.6 13 61 24.2 17.021 15.284 15.5 -17.7 2444950.0 1981112/11- 9 F 61 26.1 17.126 16.094 20.1 -23.0 - 9 61 27.5 17.116 15.920 19.2 -23.0 2445112.4 1982/ 5/23- 5 N 60 59.8 16.839 15.243 17.1 20.5 22 61 7.8 16.868 15.872 20.2 20.7 2445142.0 1982/ 6/21-12 N 61 21.9 16.962 16,419 22.2 23.4 0 61 21.9 16.962 16.422 22.2 23.4 2445171.5 1982/ 7/201-19 N 61 0.1 16.844 16.164 21.9 20.6 -22 61 7.8 16.860 16.426 22.7 20.8 2445333.9 1982/12/30-12 F 61 23.7 17.135 16.657 23.5 -23.2 10 61 25.7 17.128 16.679 23.5 -23.1 2445363.4 1983/ 1/28-22 F 61 23.3 17.093 16.056 21.0 -18.2 -11 61 25.5 17.094 16.344 22.2 -18.3 2445525.9 19831 7/10-12 N 60 59.9 16.842 16.533 24.3 22.3 22 61 7.9 16.829 16.245 22.8 22.2 2445556.4 1983/ 8/ 8-19 N 61 23.4 16.945 15.747 20.0 16.1 1 61 23.4 16.945 15.737 19.9 16.1 2445584.9 1983/ 9/ 7- 3 N 61 2.3 16.858 14.235 10.9 6.3 -22 61 10.0 16.873 14.875 15.7 6.7 2445747.3 1984/ 2117- 1 F 61 26.9 17.075 15.093 16.9 -12.3 8 61 28.1 IT067 14.838 15.1 =12.2 2445776.9 1984/ 3/17-10 F 61 20.7 16.990 13.876 5.6 - 1.2 -13 61 23.7 16.975 14.120 9.1 - 1.4 2445939.3 1984/ 8/26-19 N 61 2.7 16.845 14.507 14.8 10.1 22 61 10.4 16.816 13.979 9.4 9.8 2445968.8 1984/ 9/25- 3 N 61 25.6 17.004 13.735 3.0 - 0.9 0 61 25.6 17.004 13.736 3.1 - 0.9 2445998.3 1984/10/24-12 N 61 1.3 16.982 13.898 - 9.8 -11.9 -22 61 9.7 16.967 11609 - 3.6 -11.6 2446160.8 1985/ V 5-12 F 61 24.7 17.023 13.660 - 3.6 6.2 6 61 25.6 17.027 13.740 - 5.5 6.3 2446190.3 1985/ 5/ 4-20 F 61 15.2 16.943 14.620 -15.8 16.1 -15 61 18.9 16.931 14.172 -12.1 16.0 2446352.7 1985/10/14- 5 N 61 5.2 16.966 13.574 - 6.5 - 8.1 20 61 12.1 16.949 14.079 -12.3 - 8.4 2446382.2 1985111/12-14 N 61 26.5 17.109 15.111 -18.7 -17.8 - 1 61 26.6 17.110 15.046 -18.4 -17.8 2446411.8 1985/12/12- 1 N 60 58.2 17.004 16.659 -26.4 -23.1 -24 61 8.0 16.982 15.926 -23.3 -23.0 2446574.2 1986/ 5/23-21 F 61 23.5 16.950 16.025 -23.4 20.6 6 61 24.2 16.948 16.277 -24.4 20.7 2446603.7 1986/ 6/22- 4 F 61 14.5 16.846 17.175 -27.9 23.4 -15 61 18.4 16.844 16.984 -27.1 23.4 2446766.1 1986/12/ 1-17 N 61 12.1 17.041 16.456 -25.6 -21.8 18 61 17.6 17.006 17.042 -27.5 -21.9 2446795.7 1986/12/31- 3 N 61 28.8 17.092 17.312 -28.0 -23.1 - 4 61 29.1 17.091 17.352 -28.1 -23.1 2446987.6 1987/ 7111- 4 F 61 24.1 16.885 16.926 -27.0 22.2 6 61 -24.8 16.885 16.736 -26.3 22.2 2447017.2 1987/ 8/ 9-10 F 61 14.7 16.888 15.048 -19.6 15.9 -15 61 18.6 16.880 15.732 -22.7 16.1 2447179.6 1988/ 1/19- 5 N 61 15.8 17.059 16.190 -24.6 -20.5 16 61 20.0 17.051 15.556 -21.8 -20.4 2447209.1 1988/ 2/17-16 N 61 25.4 17.101 14.277 -14.2 -12.1 - 7 61 26.1 17.094 14.516 -15.9 -12.2 2447401.1 1988/ 8/27-11 F 61 23.6 16.974 13.908 -10.8 9.9 6 61 24.2 16-972 13.761 - 9.0 9.8 2447430.6 1988/ 9/25-19 F 61 14.1 16.978 13.383 2.7 - 1.2 -15 61 18.2 16.986 13.401 - 1.9 - 0.9 2447593.0 1989/ 3/ 7-18 N 61 16.4 17.065 13.468 - 4.0 - 5.1 14 61 19.6 17.061 13.425 0.0 - 4.8 2447622.5 1989/ P 6- 4 N 61 22.1 17.006 13.849 9.6 6.4 - 9 61 23.2 17.004 13.684 7.3 6.3 2447814.5 1989/10/14-21 F 61 27.8 17.026 14.190 12.3 - 8.4 5 61 28.2 17.021 14.351 13.7 - 8.4 2447844.0 1989/11/13- 6 F 61 15.6 17.020 15.871 22.8 -18.0 -16 61 20.4 17.004 15.239 19.6 -17.8 2448006.4 1990/ 4/25- 4 N 61 17.4 16.941 14.964 17.8 13.1 13 61 20.0 16.946 15.460 20.4 13.3 2448036.0 1990/ 5/24-12 N 61 20.3 16.928 16.647 25.3 20.8 - 9 61 21.7 16.916 16.383 24.2 20.7 2448227.9 1990/12/ 2- 8 F 61 30.0 17.106 16.937 25.7 -21.9 3 61 30.1 17.108 16.988 25.9 -22.0 2448257.4 1,990/12/31-19 F 61 11.4 17.081 16.489 24.7 -23.1 @-19 61 17.6 17.054 16.903 26.0 -23.1 2448419.9 1991/ 6/12-12 N 61 14.7 16.915 16.854 25.6 23.1 12 61 17.3 16.927 25.2 23.2 2448449.4 1991/ 7/11-19 N 61 17.7 16.944 16.002 22.1 22.1 - 9 61 19.1 16.945 16.293 23.3 22.1 1 2- 3 5 6 7 8 9 10 11 12 13 14 */DAY -/DAY h VDAY, VDAY 2448611.8 1991/12/21-10 F 61 2.5 17.029 16.533 24.4 -23.4 24 61 11.4 17.007 16.120 22.4 -23.4 2448641.3 1992/ 1/19-21 E_@ 61 29.9 17.150 15.498 18.6 -20.3 1 61 30.0 17.15b 15.477 18.5 -20.3 244800.9 1992/ 2/18- 8 F 61 6.4 16.975 14.039 8.1 -11.8 -22 61 14.1 16.964 14.586 13.3 -12.2 2448833.3 1992/ 7/29-20 N 61 15.7 16.924 14.983' 15.6 18.6 12 61 18.3 16,909 14.659 13.0 18.4 2448862.8 1992/ 8/28- 3 N 61 20.0 16.934 14.075 5.4 9.7 - 9 61 21.4 16.944 14.213 7.6 9.8 2449025.2 1993/ 2/ 7- 0 F 61 8.7 17.028 14.497 11.3 -15.4 20 61 15.9 16.912 14.178 6.6 -15.1 C) 2449054.8 1993/ 3/ 8-10 F 61 30.0 17.046 14.130 0.2 - 4.8 - 2 61 30.1 17.046 14.131 0.6 - 4.8 2449084.3 1993/ 4/ 6-19 F 61 2.0 14.437 -10.6 6.7 -24 61 11.1 16.836 14.128 5.2 6.3 2449246.7 1993/ 9/16- 3 N 61 18.7 16.946 14.150 - 1.7 2.7 12 61 21.0 16.936 14.241 4.5 2.5 2449276.2 f993/10/15-12 N 61 21.01 17.037 14.796 -11.8 8.6 -10 61 22.7 17,034 14.614 9.8 - 8.5 2449438.7 1994/ 3/27-11 F 61 9.2 16.960 14.332 - 6.1 2.6 19 61 15.4 16.965 14.661 -10.0 2.9 2449468.2 1994/ 4/25-20 F 61 25.9 17.005 15.320 -14.9 13.3 - 3 61 26.0 17.003 15.258 -14.4 13.3 2449660.1 1994/11/ 3-14 N 61 21.0 17.072 15.428 -15.4 -15.1 10 61 22.8 17.066 15.659 -16.8 -15.2 2449689.7 1994/12/ 3- 0 N 61 20.1 17.095 16.178 -19.8 -22.0 -12 61 22.5 17.096 16.079 -19.2 -22.0 2449852.1 1995/ 5/14-21 F 61 8.8 16.904 15.649 -17.1 18.7 18 61 14.6 16.902 15.960 -18.6 18.9 to t, m 2449881.6 1995/ 6/13- 4 F 61 25.0 16.919 16.201 -19.4 23.2 - 3 61 25.2 16.920 16.201 -19.4 23.2 2450073.6 1995/12/22- 2 N 61 26.2 17.091 16.149 -18.8 -23.4 8 61 27.3 17.082 16.112 -18.6 23.4 2450103.1 1996/ 1/20-13 N 61 19.2 17.056 15.513 -15.4 -20.2 -14 61 22.6 17.038 15.775 -16.9 -20.3 2450265.5 1996/ 7/ 1- 4 F 61 9.9 16.814 15.900 -18.1 23.1 18 61 15.5 16.804 15.732 -16.9 23.0 2450295.0 1996/ 7/30-11 F 61 25.6 16.913 15.407 -14.0 18.4 - 3 61 25.7 16.912 15.460 -14.4 18.4 2450487.0 1997/ 2/ 7-15 N 61 26.3 17.099 15.178 -12.0 -15.2 6 61 26.8 17.102 15.091 -11.1 -15.1 2450516.5 199f/ 31 9- 1 N 61 12.9 17.034 14.501 - 3.7 - 4.5 -16 61 17.5 17.013 14.678 - 6.8 - 4.8 -2450678.9 1997/ 8/18-11 F 61 9.2 16.877 14.932 -11.0 13.0 18 61 14.8 16.870 14.707 - 7.8 12.8 Q 2450708.5 1997/ 9/16-19 F 61 25.4 17.018 14.564 - 2.7 2.4 - 3 61 25.6 17.019 14.583 - 3.4 2.5 2450900.4 1998/ 3/28- 3 N 61 24.7 17.055 14.498 0.7 2.9 4 61 24.9 17.055 14.506 1.4 2.9 2450930.0 1998/ 4/26-12 N 61 9.1 16.907 14.754 9.5 13.5 -.18 61 14.5 16.993 14.559 6.1 13.3 2451092.4 1998/10/ 5-20 F 61 13.8 16.959 14.374 1.7 - 4.9 17 61 18.7 16.933 14.515 5.3 - 5.2 2451121.9 1998/11/ 4- 5 F 61 28.8 17.056 14.969 10.7 -15.3 - 4 61 29.2 17.056 14.896 9.9 -15.3 2451313.9 1999/ 5/15-12 N 61 24.1 16.943 15.254 14.0 18.8 3 61 24.2 16.945 15.316 14.5 18.9 2451343.4 1999/ 6/13-19 N 61 7.2 16.864 15.938 19.2 23.2 -18 61 13.0 16.840 15.676 17.5 23.2 2451505.8 1999/11/23- 7 F 61 18.5 17.025 15.370' 15.7 -20.3 15 61 22.4 17.019 15.738 17.8 -20.4 2451535.3 1999/12/22-18 F 61 28.0 1 17.136 1 16.306 1_ 20.5 -23.4 1 7 61 28.8 17.129 16.237 20.2 -23.4 Tidal Force Evaluating Significance of the Daia Contained in Table 16 1. Lunar Motion in True Anomaly , which combine with lunar gravitational forces at times It has been seen in part If, chapter 4, that solar pertur- of perigee-syzygy to produce amplified, tides on Earth. bations produce a retrograde motion of the lunar perigee Thus, any variance in the solar force upon the lunar orbit at times of close perigee-syzygy alignment. This motion caused by the changing distance of the Earth from the of perigee is in a directly opposite sense to that of the Sun in consequence of the Earth's own elliptical orbit will of the Moon will add vectorially to the daily motion of be reflected in the rate of motion of the lunar perigee. As the Moon in true anomaly tabulated in columns 5 and I I noted in the introductory section above, any such motion of table 16 is measured with respect to perigee, any mo- of .perigee will, in turn, affect the velocity of the Moon tion of this orbital position in an opposite direction to that with respect to this selected reference point. of the Moon will add vectorially to the daily motion of A distinct advantage derives from the later use of this the Moon relative to perigee. particular velocity component as one astronomical con- The result will be a value of the daily rate of lunar stituent of a coefficient of tidal flooding potential. This motion which is in excess of the motion in celestial long* is because any diminished distance between Moon and tude obtained by taking daily differences in The Ameri- Sun appears directly as a small additive function to the can Ephemeris and Nautical Almanac. This accounts for rate of lunar motion in true anomaly. The circumstance angular velocities in columns 5 and 11 which are consist- may be confirmed by calculating the interval (in days) ently 1. 3 0 to 1. 7 0 greater than even the maximum daily separating each of the tabulated instances of perigee-syz- velocity of the Moon (15.4') at perigee-syzygy, measured ygy from the nearest date of perihelion (solar perigee). in celestial longitude and Iwith respect to the vernal equi- This will involve a maximum of 182.5 days' separation nox. The difference is du *e to the relative angular motion from perihelion to the next succeeding or following aphc- of perigee. (See ch. 4-"The Special Motion of Perigee lion, beyond which the time interval to perihelion again Close to the Position of Perigee-Syzygy Alignment.") decreases. A further advantage of these two columns of the table It is obvious from such an analysis that those values of is that they indicate the velocity of the Moon in its orbit the lunar motion in true anomaly which are seemingly too rather than as geometrically projected along either the large in comparison with the corresponding parallax are celestial equator (in right ascension) or the ecliptic (in the result of a particular closeness in time to solar perigee. celestial longitude). Similarly, velocity values which are apparently too low to Summarily presented, the use in columns 5 and 11 of accord with the indicated parallax contain the effects of the Moon's rate of angular motion in true anomaly at the a relatively. large separation from solar perigee. The instants of syzygy and perigee serves as an excellent single- principal factor establishing the value of the lunar paral- parameter indicator of the combined tide-raising . forces lax is the separation-interval between perigee and syzygy of the Moon and Sun at these, times for the following as described bclow-added to whose effects the variation reasons: of the Moon's distance from the Sun acts as a modulating influence. a. REPRESENTATION OF THE SOLAR INFLUENCE b. REPRESENTATION OF THE SEPARATION- It has been shown previously that variable solar forces INTERVAL determined by the Moon's changing distance from the A second practical advantage in the use of velocity in Sun and relative angle of alignment therewith are re- true anomaly is that it possesses a definite relationship to sponsible for perturbations in the lunar orbit and an oscil- the separation in time between perigee and syzygy. In this latory motion of perigee. It is these same solar forces respect it takes into account increasing values of the paral- 266 Essential Conditions for Achieving Amplified Perigean Spring Tides 267 lax (and a corresponding lessening of the perigee tational force described in paragraph 1. Thus, for "am- distance) as a function of closer proximity in the peri- ple, where a very high value of lunar parallax exists and gee-syzygy alignment. Exceptions from a nearly one-to- is not matched by a correspondingly high value of lunar one correspondence between the velocity in true anomaly velocity in true anomaly,- this lunar velocity has almost and the lunar parallax are imposed by any circumstance of inevitably been reduced by the occurrence of the perigee- a particularly . close approach of perigee-syzygy to solar syzygy alignment at a time considerably removed from perigee as previously noted. However, these and other solar perigee-perhaps even at solar apogee. In consider- modifying factors are applied in strictly incremental or ing the enhanced tide-raising action produced by the com- decremental fashion. The highest values of the rate of bined gravitational forces of the Moon and Sun at lunar motion in true anomaly are most commonly found at perigee-syzygy, it is necessary to have the effects of both close perigee-syzygy alignments (1-2 hours' separation) of these forces represented in any index-quantifier pro- occurring within at least a few months of perihelion. posed for potential tidal flooding. c. INDICATION OF INCREASED LUNAR VE- 2. Representation of Increased Lunisolar Tidal LOCITY IN ORBIT IN ACCORDANCE WITH Forces in Those Cases Where the Sun Is Simul- KEPLER'S THIRD LAW taneously in the Moon's Orbital Plane That part of the Moon s indicated angular velocity in It is further possible by means of table 16 to include an true anomaly which remains after the retrograde velocity evaluation of the additional small component of lunar of perigee is subtracted, constitutes by far the greater por- motion in true anomaly provided by the presence of the tion of the resultant of the vectorially combined velocities Sun in the Moon's orbital plane, should the Moon be tabulated in columns 5 and 11. Since the velocity repre- crossing the ecliptic at the same time it reaches perigee- sented is the true one occurring in the plane of the lunar syzygy. orbit, it is not affected 'by the Moon's excursions in decli- This situation can be at least approximately assessed nation as are the values in columns 6 and 12. by taking the algebraic difference between the declina- However, the velocity in true anomaly is directly influ- tions of the Moon and Sun at the time of syzygy as tabu- enced by the relative proximity of p erigee to the Earth in lated in columns 7 and 8. Should this difference be less any one lunation as the Moon revolves in its elliptical than 0.2', a solar or lunar eclipse is very apt to have orbit. Any diminished distance of the Moon from the accompanied this syzygy alignment, although-as pre- Earth becomes a direct function of (1) the increase in cisely determined-the exact position of the Moon's nodes orbital eccentricity at the time of perigee-syzygy align- along the ecliptic must be considered. (See footnote on ment, as determined by (2) the increased magnitude of p. 7.) At the same time, the gravitational force on the the perturbational forces acting at this time, which are, in Earth is enhanced by the combination of the solar and turn, dependent upon (3) the closeness of the perigee- lunar forces along two nearly superimposed axes. syzygy alignment and the commensurability of the lunar It is obvious from an analysis of columns 7-8 and 13-14 periodic relationships making possible these alignments. that, in those cases in which the differences between the The greater orbital velocities of the Moon at such times declinations of the Moon and Sun are very small (with of decreased distance from the Earth, as demanded by due consideration to algebraic sign) the lunar velocities Kepler's Third Law-with the accounted-for exceptions given in columns 5 and 11 are at least slightly above the previously noted-are quite logically found among the average value which would be indicated by the corre- values given in columns 5 and 11. sponding parallax. This increment in velocity represents The value of the lunar parallax, on the other hand, is the Combined gravitational influence of the Moon and implicitly related (through the chain of events above Sun exerted simultaneously in dual, orthogonally inter- enumerated) to the perigee-syzygy separation-interval of secting planes. column 9, and possesses a close degree of correlation there- In addition to the increased solar force on the Moon at with. It is important to note that, although a one-to-one perigee-syzygy associated with solar perigee as described relationship between increased parallax and increased in paragraph I a, therefore, an additional component of velocity in true anomaly does not exist, the variations caus- solar force is provided by the Sun being in or near the ing this lack of direct correlation have, for the most part, Moon's orbital plane. Such a coplanar alignment in been introduced by the changing conditions of solar gravi- celestial latitude (or declination) is evidenced by a, slight 268 Strategic Role of Perigean Spring Tides, 1635-1976 increase in lunar velocity with respect to a proportionately The apparent motion of the Moon in right ascension, accelerated, but oppositely directed.motion of perigee at as earlier explained, bears. a direct relationship to its this time. declination at the moment. It is obvious from a com- parison of columns 6 and 12 with columns 7 and 13 that 3. Representation of Increased Lunar Motion in such increased velocities in right ascension occur when Right Ascension at High Values of Lunar the Moon is near its highest declination angles. Declination In summary, it is seen that all of the principal factors which make for an increased gravitational attraction of Columns 6 and 12 represent the orbital motion of the the Moon and Sun on the Earth's tidal waters at times Moon as projected from the plane of its orbit on to the of perigee-syzygy are represented by the corresponding celestial equator. Since the latter plane is that in which pairs of values tabulated in columns 4, 10; 5, 11 ; 6, 12; or parallel to which the apparent diurnal motions of the 7, 13; 8, 14; and in column 9. The single terms con- celestial bodies occur as the result of the Earth's rota- tained in columns 5 and 11 likewise very effectively con- tion, these columns are especially advantageous in de- solidate the conditions expressed by seven of the remain- ing terms and incorporate the Sun's gravitational in- termining the relative catch-up motion required for the fluence as well. rotating Earth to bring the Moon to transit of the meridian. A separate a%vantage exists in the use of the data In chapter 8, this joint indication of necessary catch- given in columns 6 and 12 as a measure of the daily angular velocity of the Moon in a plane parallel to the up times and lengthening of the tidal day at times of celestial equator. The role of this term in establishing perigee-syzygy will be incorporated as a secondary astroi- the catch-up motion necessary for the rotating Earth to nomical term in establishing a coefficient of potential bring the Moon to the local meridian of a place will be tidal flooding. extensively discussed in chapter 6. Chapter 6. Conditions Extending the Duration of Augmented Tide- Raising, Forces at the Times of Perigee-Syz-ygy As had been seen in the preceding chapters, by far the the time at which the apparent motion of either of these greatest portion of the increase in amplitude (or range) two bodies will be predominantly in the coordinate of of the tides accompanying situations of perigee-syzygy is right ascension, and hence within a plane parallel to the the result of a vector combination of the augmented celestial'equator. Their apparent motions in the direction gravitational forces of the Moon and Sun-together with of the Earth's rotation will then be the greatest, and the a reduction in the distance of the Moon from the Earth necessary catch-up motion by the rotating Earth to at such times. These gravitational reinforcements and achieve a meridian transit of these bodies will reach a enhancements are responsible for a corresponding am- maximum. plification of the tide-raising potential, and-when a co- existing strong onshore wind prevails-add proportion- Factors Increasing the Length ately to the possibility for tidal flooding. of the Tidal Day Yet there is another category of dynamic influences Each of the above-mentioned influences acts to in- contributing to the increased rise of the tides associated crease the length of the tidal day (and, in similar fashion, with the near-coincidence of perigee and syzygy. On such that of the lunar day). These two slightly different occasions, the effectiveness of the tide-raising forces dis- chronological concepts are distinguished, in terms of their cussed in chapter 5 is further enhanced by an increase in immediate application, later in this sa Ime chapter: The the total period of time during which such forces act at circumstances yielding a contribution to tidal amplifica- magnitudes close to their maximum values. One of the tion as the result of such catch-up motions at perigee- factors conducive to such force-protracting influences is syzygy are outlined below and are amplified in subse- an extra "catch-up" motion required of any position on quent sections. the Earth's surface in accomplishing a meridian transit 1. Lunar Parallactic Inequality of the Moon (and a very nearly coincident transit of the Sun) at the time of perigee-syzygy. The force-prolonging influence associated with this phenomenon originates from the necessity for the rotating Earth to catch up with a temporarily induced, more rapid The General Principles of "Stern Chase" motion of the' Moon, revolving in its orbit around the Motion Earth in the same relative direction as the Earth rotates on its axis. This catch-up motion is imposed at perigee- The most important dynamic element involved in this syzygy by an increase in the Moon's orbital velocity necessity for catch-up motion is a temporary acceleration produced, in response to Kepler's third law, by a closer in the orbital angular velocity of the Moon at perigee, proximity to the Earth. The greater proximity of the which the rotating Earth must overcome for any surface Moon to the Earth is in conseque .nce of: (a) the elliptical point to achieve a lunar transit. Secondly, the declinations shape of the lunar orbit; (b) the location of the Moon at of both the Moon and the Sun just prior to, and while the lower apse ofthe orbit at time of perigee-syzygy; and passing through the position of perigee-syzygy, play a (c) a further incremental increase in parallax at this time contributing role in the amount of catch-up motion re- resulting from a corresponding increase in eccentricity of quired. The position of maximum declination determines the lunar orbit. 269 270 Strategic Role of Perigean Spring Tides, 1635-1976 It must be clearly emphasized that this catch-up these same two positions, the Moon's apparent angular motion, taken by itself, is of a magnitude having only a velocity in right ascension also acquires its maximum comparatively small influence upon the production of value. extreme perigean spring tides. Its principal significance In matching to this increased velocity, the requirement lies in providing support to other tide-raising and exists for a longer period of catch-up motion in order for tide-prolonging factors. Ile maximum catch-up effect the rotating Earth to achieve nearly coincident meridian extending the length of the tidal day because of the con- transits of the Moon and Sun at perigee-syzygy. The siderably greater lunar velocity in orbit at perigee-syzygy Earth must complete an additional portion of a full axial compared with apogee-syzygy (see table 10) is some rotation to accomplish each such meridian passage. Be- 10-13 minutes, depending upon declinational circum- cause of the increased motion in right ascension evidenced stances. as the Moon approaches either position of maximum dec- The effect of this extended duration of the tidal day lination, the greatest influence of this particular modi- is added to by another influence resulting from dynamic fication of the catch-up interval in extending the tidal conditions at the time of perigee-syzygy. As mentioned day occurs at these two times. on page 179, section 3, a perturbed rotation of the posi- (b) Twice each tropical year, at the summer and tion of perigee itself occurs in a retrograde sense as the winter solstices, respectively, the Sun similarly moves to Moon's apparent motion brings it simultaneously to syzygy declinations farthest north and south of the celestial equa- and perigee. Again, only when combined with other tide- tor. At these- times, the apparent solar motion in right raising influences does this small perigee motion achieve ascension also reaches its greatest values ( although a quantitatively significant meaning. However, for the variable within the draconitic or nodical cycle). sake of documentary completeness', the particular con- Since syzygy involves the common alignment of the tribution of this perturbed motion of perigee in the im- Moon with the Earth and Sun, the attainment of this mediate vicinity of perigee-syzygy will be described later syZygy position is dependent upon the Moon catching in this chapter. up with any such accelerated motion of the Sun over an appropriate interval of time., Likewise, to feel the addi- 2. Declination Effects tional tidal effect of the alignment of those two bodies at It has been shown that, in direct contrast to the re- perigee-syzygy, the Earth must rotate a little farther to flected (diurnal) motion caused by the Earth's rotation, catch up with the nearly common Sun-Moon axis and the greatest actual positional change of the Moon or the achieve a meridian transit thereof. The tidal day is Sun in right ascension (resulting from their respective engthened proportionately. monthly and apparent annual motions) occurs when 3. The Counterproductive Influences of Solar either of the two bodies is at its maximum declination. Perigee (Perihelion) Under the same conditions, the angular velocities of these celestial objects also attain their maximum components The effect of a combination of a large (coplanar) dec- in right ascension (a), with little or no constituent veloc- lination and proximity to perihelion in increasing the ity in declination (8). value of the lunar parallax and hence the tidal forces act- Both the Moon and the Sun in their corresponding ing, has been clearly demonstrated in the discussion real and apparent revolutions on the celestial sphere move accompanying table 13 of chapter 5. The influences of the eastward toward increasing values of a. The Earth also comparatively close agreement in time between the occur- rotates in this same direction. Accordingly, any increase rence of perihelion and the winter solstice as these phe- in the motion of the Sun or Moon will necessitate an nomena individually augment (a) the tide-raising forces additional catch-up motion by the rotating Earth to se- and (b) the length of the tidal day also have been de- cure the meridian transit of these two bodies. The result- scribed. Finally, as will be noted in a subsequent section, ing possibilities for the occurrence of such prolonged the proximity of the Sun to the Earth and Moon at time catch-up motions are: of perihelion adds to the solar gravitational force which, (a) Twice each tropical month, the Moon reaches at peri.gee-syzygy, swings the line of apsides; through a positions of maximum declination, alternatively north retrograde angle and, in so doing, slightly extends the and south of the celestial equator. In each of these two duration of the tidal maximum attained. positions, the Moon's orbital path reaches a minimum of By contrast, arising out of an astronomical ' quantity declination change, and then recurves; equatorward. In known as the annual equation,'.a counterproductive fac- Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 271 tor exists which causes a decrease in the orbital velocity of incidence between perigee and syzygy, as will be shown in the Moon at times of perihelion and hence acts as a direct. succeeding sections of the present chapter. The incremen- modifying influence upon the catch-up motion described tal amplification of the tides which results when these in (1) above. The apparent motion of the Moon in either particular catch-up induced extensions of the tidal day (as celestial longitude or right ascension is correspondingly opposed to extensions which occur also at each quadra- reduced. Should perigee and perihelion occur together, ture, for example) coincide with periods of increased tidal this factor subtracts from the tendency for an increase in force action will bediscussed both in this chapter and in the length of the tidal day at perigee-syzygy. chapter 8. It should be observed that a similarbracketing The motions of the Sun or the Moon in declination are of the times of low water by such a prolongation of the not strongly affected, either by the Sun's passage through period of increased gravitational force application does perihelion, or by the Moon's passage through perigee, not in any way interfere with, nor compensate for, the respectively. However, if perigee-syzygy and perihelion increased rise in water level at high tides. nearly coincide in time, together with a coplanar align- ment of the Sun and Moon in declination (see table 13), Reintroduction of the Concepts of the the influence of the combined action both in increased tide-raising force and extension of the duration of this Lunar and Tidal Day force by necessary catch-up motions usually is quite no- Various introductory concepts relative to the lunar ticeable in terms of the heightened tides produced. and tidal davs, citing the precise differences between As an additional relevant circumstance, the dates of them, have been discussed in part II, chapter 2, and it perihelion (usually about January 2-4) and the winter will not be necessary to repeat these. At this juncture, it solstice (averaging about December 23) occur quite close is important to point out certain practical variations in to, each other. This circumstance, which unites two influ- the length of the lunar day which result from changing ences (the one due to perihelion, yielding an increased catch-up motions of the rotating Earth. These are mspon- gravitational force, the other a maximum .solar declina- sible for similax variations in the length of the tidal day, tion, resulting in an increased apparent motion of the Sun and in this respect introduce new complications in the and a lengthened tidal day) acts to offset 3 (the slowing immediate problem at hand. action in the Moon's orbital motion produced near peri- The following brief review will, therefore, cover appro- helion). The net influence of such a combination thus priate aspects of the lunar day which relate to: (1) its still serves to reinforce the augmented tide induced by a origin in the respective revolutionary and rotational mo- perigee-syzygy alignment at this time. tions of the Moon and Earth; (2) fluctuations in the 4. Summary length of this day resulting from the necessity for the Significantly, in each of the cases described above, the Earth's rotational catch-up motion; and (3) the produc- lengthened periods of lunisolar tidal force action occur at tion of corresponding variations in the length of the tidal times during which the magnitudes of these forces also day. have been increased-partially by the reduced distances Specific astronomical factors which alter the length of of the Moon and Sun from the Earth, and partially by the lunar day, such as changes in the daily lunar retarda- their combined, reinforcing, gravitational attractions. tion time, also will come under consiAeration. In the asso- Each extended tidal day in which enhanced tide-rais- ciated quantitative analysis, an alternate method for ing forces are active contains (with some few exceptions) determining the length of the mean lunar day, using a dif- the occurrence of a higher high water. The resulting ferent approach but realizing the same results as those in quantitative effects thereon are illustrated by graphs for chapter 2, provides an independent confirmation thereof. various tide stations in figs. 153-163 of chapter 8. It is Fluctuations in the Lunar and Tidal Days noteworthy that, compared with the tide-heightening The lunar day is longer than the conventional mean effects produced by force amplification, this extended solar day of 24'Om because the Moon revolves around the period of force action can provide only a supplementary Earth in'the same direction as the Earth rotates on its and considerably less sizable role in the production of axis. If the period of time between two successive meri- augmented high waters. dian transits of the Moon is defined as the lunar day in However, such a small but observationally detectable the same way that the solar day represents the period lengthening of the tidal day accompanies each near-co- between two successive meridian transits of the Sun, a 272 Strategic Role of Perigean Spring Tides, 1635-1976 very obvious connection exists between these two periods may range from approximately 38' to [email protected] The figure of time as a function of the relative motions of the two 50.472m, representing the average difference between the bodies. lengths of the lunar and solar day, may also be thought of 1. Derivation of the Length of the Mean Lunar as representing the increment in time which, added to Day 24 mean solar hours, gives the period of elapsed time between two successive transits of the mean moon across The Moon orbits once around the Earth from position the meridian of the place. It is thus equivalent to the delay of new moon to new moon again (i.e., from one conjunc- in transit times caused by the eastward orbital motion of tion of the Moon and Sun to the next) in a synodic month the Moon, and is known as the mean daily lunar retarda- of 29.530589 mean solar days. As seen from the Earth, tion. Because of the dependence of this factor upon the during this period the Moon describes an average 389' actual observed transit times of the Moon, and the, pos- circuit of the celestial sphere (i.e., its sidereal revolution, sible large variations in the rate of motion of the Moon plus a catch-up motion on the apparent motion of the in right ascension, the instantaneous value thereof ranges mean sun in the same interval). The Earth rotates widely between the limits noted. through approximately 361' on its axis (allowing for the The differences between the instantaneous and mean Sun's own apparent mean daily motion) in 24 mean values of the daily lunar retardation are due largely to solar hours, to complete two successive meridian transits the elliptical shape of the Moon's orbit (including its of the mean sun and accomplish the mean solar day. Both changing' eccentricity, caused by long-terin perturba- of these cases involve catch-up intervals caused by the tions-as well as the effects of variation and evection orbital and rotational motions of the Earth in the same described at length in chapter 4). To these dynamic direction. effects are added the changing inclination of the Moon's Similarly, the Moon revolves in its orbit in the same orbit with respect to the celestial equator at different direction that the Earth rotates on its axis. The rotating latitudes on the Earth (which, as seen on pp. 193-196, Earth must, therefore, in a like fashion catch up with the further modifies the continuously changing declination position of the Moon in order for the Moon to transit the angle of the Moon associated with its motion in orbit). local meridian of a place and complete a lunar day. In In addition to these astronomically produced, worldwide so doing, the Earth must fulfill an additional portion of influences, the local meridian transit of the Moon is af- its rotation equal to the angular distance through which fected both by the latitude of the observer and the the Moon has moved ahead of the meridian' of the difference in longitude of the place of observation from place during that same day (i.e., a distance equal to Greenwich, England-for the transit of whose prime 1/29.530589th part of the Moon's mo n@'thly revolution). meridian the various astronomical data appearing in The In a period of 29.530589 days, the Earth falls back, in American Ephemeris and Nautical Almanac are equivalence of time, one full rotation with respect to the published. Sun. The corresponding period of time for the,Moon to A combination of these astronomical and geographic complete one synodic revolution, expressed in lunar days, influences results in a- continuously changing daily lunar is a full day less, and 29.530589 mean solar days exactly retardation which, if plotted against the time, follows equals 28.530589 lunar days. The mean lunar day is, ac- a pattern closely analogous to that of the Sun's annual cordingly, established in relation to the mean solar day equation of time. However, other factors resulting from by the proportion: the geographic location of the observer on the surface of the Earth-including the local azimuth and altitude I lunar day= 29.5.10589/28.530589 (or zenith distance) of the Moon, its topocentric distance = 1.035050 mean solar days from the surface of the Earth (affected both by geo- Or, expressed in terms of hours and minutes graphic latitude and, to a limited extent, by the elevation 1 mean lunar day= 24 hom X 1.035050 of the observer above mean sea level) -additionally in- 24-841200h @24150.472- fluence the lunar retardation and the times of moonrise and moonset on the local horizon. 2. Variations in the Lunar Day ' Most of this maximum increase in the length of the lunar day Therciore "It'he lunar day is, on the average, 50.472' is due to the increased velocity of the Moon at perigee-syzygy and the required catch-up motion by the rotating Earth. Thus longer than the mean solar day, but-of special signifi- dX 1 15.4'1'-- 360"'=0.0428 1,440-1d=61.6m.. The remaining dif- cance in relation to tides-the actual instantaneous value ference is principally due to declinational effects. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 273 3. Variations in the Tidal Day very narrow limits. It is obvious, therefore, that any purely It is now desirable to consider the effects of these vari- physical variations in the length of the tidal day-and ations in the length of the lunar day and in the amount of hence in the values of the daily tidal retardations-derived the daily lunar retardation as they influence the length of from tide tables must be due, in one way or another, to the tidal day and the maximum daily height of the tides. factors relating.to the changing positions, motions, and The tides are implicitly related to the changing positions velocities of the Moon, together with its phase relation- of the Moon-especially its distance, meridian altitude, ships with respect to the Sun. and time of meridian transit.'Additional and often larger However, other causes for such observed variations exist which are individually attributable to astronomical, variations are introduced in the corresponding daily re- geographical, and computational factors. tardation of high and low waters by hydrographic, hy- a. Astronomical causes for changes in the Moon's orbi- drological, climatological, meteorological, and other fac- tors. The hydrographic influences pertain principally to tal velocity are associated with: ( 1 ) the elliptical shape of the depth of the water and the local lunitidal interval at the lunar orbit which results in continually changing dis- the place; further local variations in the times of arrival of tances of the Moon from the Earth, and correspondingly the tides are introduced by the lunar phase age and altered lunar orbital velocities; and (2) both periodic parallax age for that locality. (See the correspondingly and irregular disturbing influences (perturbati 'ons) of an titled section at the end the present chapter.) external nature, which likewise act to alter the instanta- Thus, all factors considered, the length of the mean neous positions and velocities of the Moon. These various lunar day (the period between two consecutive upper astronomically induced tide-raising effects are felt world- transits of the mean moon across the local meridian of a wide over the Earth's surface. place) and the mean tidal day (the average period of time b. At any one position on the Earth, further sensible between two successive higher high waters or other tides changes in the times of local meridian transits, and in the of the same phase at the same location) are not synony- lengths of the tidal day and the daily lunar retardation, mous, although closely related. are introduced by 'the particular geographic longitude The deviation of the instantaneous value of the tidal and latitude of the place, the Greenwich hour angle of the day from the average value of 24 h50.47'@-which is gen- Moon, and its azimuth and altitude (or zenith distance) erally accepted for the length of the mean lunar day-has at the time of upper transit. a particular significance in terms of any near-coincidence The use of arbitrary corrections for the times of high between perigee and syzygy. In this regard, a very useful and low water at -a subordinate tide station, based upon quantitative indicator for tidal flooding potential results values determined empirically for certain standard sta- if the time intervals between successive higher high waters tions, is another approximation which may be responsi- are systematically tabulated. The special importance and ble for computational inexactness in the length of the tidal manner of application of such a series of daily tidal re- day. tardation times, computed from the tide tables, become c. Finally, other less marked variations are introduced appropriate topics for discussion in chapter 8. However, as a function of averaged, or approximate rather than with due consideration to the complex nature of the vari- actual, lunar positions. In the computational assumption ous forces involved, before the distinctive patterns revealed thereof, these can affect both the calculated length of the by these differences at times of perigee-syzygy are analyzed in terms of their possible value for prediction in connec- tidal day and the value determined for the daily tidal re- tion with tidal flooding, the respective astronomical causes tardation. Significantly, in this regard, the corrections for for the consistency of these patterns will be examined. certain velocity-related parameters are the result of ad- justments to the average (mean) , rather than real motions Causes of Systematic Variations in the of the Moon. Length of the Tidal Day Such approximations are subjective ones generally Two principal dynamic causes have previously been utilized as a matter of calculating convenience which, in given for the difference between the lengths of the tidal this arbitrary computational procedure: (1) incorrectly day and the mean solar day. These are (1) the Moon's represent the true positions and velocities of the Moon varying velocity of revolution in orbit, and (2) the rota- (such as by the customary representation of the lunar tional velocity of the Earth upon its axis. The Earth's motion in celestial longitude in lieu of its own orbital rotational velocity is'constant over centuries of time within plane or, in dealing with catch-up effects, in the plane 202-509 0 - 78 - 20 274 Strategic Role of Perigean Spring Tides, 1635-1976 of the Earth's Equator) ; (2) make use of averaged Effect of Increased Lunar Orbital Velocity (mean) lunar positions and motions rather than instan7 Upon the Length of the Tidal Day taneous, actual (true) positions. This results in a need Several cogent points of distinction are now necessary. for a successively adjusted series of computational cor- rections to accommodate the approximations involved. At the time of perigee-syzygy, because of the increased gravitational force caused by the Moon's closer proximity The Role of the Increased Tidal Day Viewed to the Earth, the lunar velocity in orbit is increased. The -in Perspective Sun's alignment with the Moon at either position of According to the thesis advanced in this study, the syzygy of itself also has a slight velocity-increasing effect potential for tidal flooding is dependent variously upon: on the Moon, induced by the lunar variation. By contrast, ( I ) the presence of increased gravitational forces; (2) a a small, net counterproductive influence in slowing the greater length of time for these increased gravitational Moon's orbital velocity is provided when the Earth forces to act; (3) a very rapidly accelerating growth rate reaches its annual perihelion position, about January 2-4. as represented by the curves indicating the rate of tide The Sun's retardation of the Moon's orbital velocity is, rise; and (4) a more readily achievable velocity coupling in fact, quantitatively dwarfed by the far greater average between the comparatively more rapidly moving surface value of the Moon's angular velocity in orbit, and es- current produced by perigean spring tides and any accom- pecially by the increase in velocity produced at perigee- panying wind movement over the sea. The first premise syzygy. Thus the occurrence of perigee-syzygy results at was adequately demonstrated in chapter 5; the second all times in a very considerable net gain in lunar velocity. will receive special attention in the present chapter; However, the above synopsis points amply to the fact and the third and fourth will be illustrated by examples that any catch-up requirements applied to the Moon's in chapters 7-8. The ensuing sections of this present orbital motions must be separately evaluated in terms of chapter will be devoted to an explanation of the condi- their relationship to ordinary syzygy, or to perigee- tions under which the total duration of the tidal day syzygy-the influences which lengthen the tidal day work- varies, and the nature of the factors which act to modify ing generally in the same direction, but in different de- its length, together with a quantitative interpretation of grees, at these two times. (Cf., tables 21-22.) these variations. The greatest increase in the Moon's orbital motion is At the outset, it should be duly emphasized that various from about 11.8'/day at apogee- ('exogee-) syzygy to astronomical factors may interact to alter the length of about 15.4'/day at perigee- (proxigee-) syzygy, a dif- the lunar day. Thus, apparently contradicting what has ference of 3.6'/day. This stated maximum value also been said concerning the special significance of the syzy- indicates an angular velocity at proxigee-syzygy which is gies, it must be clearly recognized that both the lunar 2.2'/day greater than the mean lunar orbital velocity and tidal days may, in fact, attain a maximum length (sidereal) of 13.20/day. It is the total gain in velocity around either of the quadrature phases of the Moon, due of 3.6'/day, acquired steadily between exogee-syzygy primarily to declination effects (see figs. 44-45). and proxigee-syzygy, with which the rotating Earth must However, with due regard to accompanying gravita- catch up during the 24-hour period bracketing proxigee- tional reinforcements, the lengthened tidal day is most syzygy. It should be reiterated that the effect of the daily effective in producing unusually high waters when the catch-up motion by the rotating Earth resulting from the Moon is in a position of closest monthly approach to the more rapid orbital motion of the Moon at perigee-syzygy Earth and the tide-raising forces have been increased compared with that at apogee-syzygy is small in units of both by this diminished distance and by the simultaneous time. The maximum lengthening of the tidal day due to longitudinal alignment between the gravitational forces of this cause alone amounts to 3.60 /d X ld=0.01 X 24' /d= the Moon and Sun at new moon or full moon. It is the in- . 360- /d variable increase in the lengths of both the lunar arid 0.24', or about 14.4 minutes. However, this effect is tidal days (not necessarily to a maximum) coincidentally additive to., and in support of, other influences. Further, or nearly so with the augmented gravitational forces re- and of greater importance to the present discussion, the sulting from the concurrence of perigee and syzygy that force-protracting influence of a perigee-syxygy alignment adds its influence to the production of tides of increased upon the tides is greater than that which exists at ordi- daily amplitude and range. nary spring tides, as described in chapte r 7. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-SyZygy 275 Quantitative Evaluation of Changing approximately therefrom, its exact value for any one revo- lution depends upon a presumably fixed and unperturbed Periods in the Moon's Monthly Revo- length of the semimajor axis a. (More precisely, P2 varies directly as a3. ) Any time in a lunar revolution that a varies, lution P varies accordingly. Therefore, as the instantaneous value of n increases at perigee (-syzygy) and decreases at apogee A quantitative evaluation of the influence of perigee- (-syzygy) the period is not directly affected thereby. syzygy alignments on the lengths of successive synodic Rather, its value is changed by corresponding alterations in and anonialistic, months during a 209 synodic-month the shape of the lunar orbit at these times. period from January 1959 through December 1975 is In the case of those months which contain a close align- provided in table 17. The discussion to follow will reveal ment of perigee-syzygy, both the NM-NM and FM-FM synodic months become longer when computed between the a maximum lengthening of the synodic month above its times of successive apogee-syzygies (see table 17), and the mean value amounting to +0.2992 day, and a maximum apparent daily motion of the Moon becomes faster in that leng-thening of the anomalistic month above its own mean portion of the orbit bracketing the time of perigee-syzygy. by 1.02 days, both at a time of perigee-syzygy. A corre- In the apogee-syzygy portion of the orbit, however, a much sponding lengthening of the individual lunar and tidal slower apparent motion of the Moon occurs, and the lengths of the synodic months calculated from perigee-syzygy to days contained within these months readily can be shown perigee-syzygy and containing the time of apogee-syzygy to be associated with perigee-syzygy. centrally located are considerably shorter than those com- puted from apogee-syzygy to apogee-syzygy, having the time of perigee-syzygy midway in the period. As the result of a frequent contiguous usage of these words It might thus be readily assumed that the relatively high in the text, several apparently related, but actually quite lunar velocity at perigee-syzygy would be compensated for different concepts involving the length of the lunar day and by the comparatively low angular velocity at apogee-syzygy, the length of the synodic month should be clarified at this and that the length of the month would average out un- point. The lunar day is measured by the time between con- changed. According to the specific time-referenced positions secutive transits of the Moon across the local meridian of a in orbit from which the data of table 17 are compiled, such place. Since, at perigee-syzygy, the Moon is moving faster in is not the case. the same direction that the Earth is rotating, an additional Finally, and worthy of special note in the light of ulti- catch-up time is required for transit of the Moon, and the mately more refined tidal predictions at these times of maxi- length of the lunar day is increased. mized amplitudes, it will be observed by reference to table 20 The length of the synodic month, on the other hand, is that the actual daily angular velocity of the Moon in celestial determined by the number of mean solar days between two longitude at proxigee-syzygy (15.2585'/d) is considerably in successive conjunctions of the Moon and Sun, as seen from excess of the assumed mean value (13.1764'/d) presently the Earth. Since the Earth's period of rotation, for the pur- used in tidal calculations; again, at apogee following even pose of the present discussion, may be assumed to be con- the ordinary syzygy alignment (with perigee at quadrature) stant, the synodic month varies only with the relative orbital given in table 21, the actual daily motion of the Moon motion of the Earth (hence also the apparent motion of the (11.84911/d) is much less than this assumed mean value. Sun) and that of the Moon as A function of its changing Such an average value is far from representative at times of orbital configuration, subject to perturbations. proxigee-syzygy and exogee-syzygy. As the orbital velocities of the Earth and/or the Moon are in creased, the necessary catch-up time to achieve the align- ment of Earth, Moon, and Sun at syzygy is likewise increased and, coincidentally, the length of the synodic month is in- Conditions Lengthening the Synodic and creased-as shown in column 8 of table 17. Thus, the Anornalistic Months - synodic month is composed of mean solar days, and may To illustrate these relationships clearly, the pertinent be. related also to a given number of tidal days, but the two concepts are not directly connected. lunar data have been tabulated (for double-verification A further distinction for the purpose of clarity should purposes) over a period of time equal to two complete here be made between the concepts of,period of revolution, rotations of the line of apsides in the anomalistic. cycle of in days, and both angular velocity in orbit and mean daily motion-each of the last usually expressed in '/day. In the 8.849 tropical years (table 17). In this table, columns 1-2 common physical case of uniform circular motion with con- contain the exact dates of full moons, and columns 5-6 stant angular velocity, as the period of rotation P increases, the exact dates of new moons, throughout this period. The the value of the unit angular velocity n decreases, and vice changing lengths of the "synodic months" (see the second versa. In an elliptical astronomical orbit, although P still 1 following paragraph), determined alternatively by the varies inversely as the mean angular velocity i! throughout the entire revolution of the orbit, and may be computed differences between, the times of two consecutive full 276. Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 17-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments Intervals between successive syzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P 1959 Jan. 24.8139 Jan. 9.2319 1959 Jan. 5. 833 1959 29.5569 29.5750 25.42 Feb. 23.3708 Feb. 7.8069 Jan. 31.250 29.4639 29.6451 26.17 Mar. 24.8347 Mar. 9.4521 Feb. 26.417 29.3827 29.6931 27.96- Apr. 23. 2174 Apr. 8.1451 Mar. 26. 3 75 ) 29.3215 29.6958 28.38 P-S May U.5389 May 7.8410 Apr. 23. 750 29.2944 29.6542 28.4641 June 20.8333 June 6.4951 May 22.208 P-S 29.3146 29.5882 28.33 July 20.1479 July 6.0833 June 19. 542 29.3868 29.5236 28. 04J Aug. 18.5347 Aug. 4.6069 July 17.583 29.5007 29.4729 27.08 Sept. 17.0354 Sept. 3.0799 Aug. 13. 667 29.6299 29.4417 25.04 Oct. 16.6653 Oct. 2.5215 1' Sept. 7.708 29.7389 29.4236 27.17 Nov. 15.4042 Oct. 31.9451 Oct. 4.875. 29.7965 29.4201 28. 17- Dec. 15.2007 Nov. 30.3653 P-S Nov. 2.042 29.7931 29.4326 28.46 1960 Jan. 13.9938 Dec. 29.7979 Nov. 30. 500 P-S 29.7312 29.4632 28. 54 40 Feb. 12.7250 Jan. 28.2611 1960 Dec. 29. 042 29.6264 29.5056 28.38 Mar. 13.3514 Feb. 26.7667 Jan. 26.417 1960 29.5014 29.5514 27. 71 j Apr. 11.8528 Mar. 27.3181 Feb. 23.125 29.3854 29.5882 25.17 May 11.2382 Apr. 25.9063 Mar. 19. 292 29.3049 29.6095 26.50 June 9.5431 May 25.5188 Apr. 14.792 29.2743 29.6230 27.96 P-S July 8.8174 29.2944 29.6277 June 24 11438 28.33 May 12.750 Aug. 7. 1118 July 23.7715 1114ne 10.083 29.3597 29.6146 28.38 Sept. 5.4715 29. 1 4570 29.5813 Aug. 22.3861 28.38 July 8. 458 P-S Oct. 4.9285 Sept.20.9674 Aug. 5.833 29.5701 29.5347 28.04 Nov. 3.4986 Oct. 20.5021 Sept. 2.815 29.6854 29.4889 27.04 Dec. 3.1840 Nov. 18.9910 Sept. 29. 917 1961 Jan. 1.9625 29.7785 29.4583 Dec. 18.4493 24.92 Oct. 24.833 29.8201 29.4465 27.33 Jan. 31.7826 Jan. 16.8958 P-S Nov. 21.167 Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 277 TABLE 17-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments-Continued Intervals between successive qyzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P 29.7834 29.4452 28.29- Mar. 2. 5660 Feb. 15.3410 1961 Dec. 19. 458 29.6756 29.4440 28.50 Apr. 1. 2417 Mar. 16. 7854 11 Jan. 16.958 P-S 29.5368 29.4493 28.50 Apr. 30. 7785 Apr. 15. 2347 Feb. 14.458 1961 29.4146 29.4702 28.29 May 30.1931 May 14. 7049 Mar. 14.750 29.3333 29.5152 27. 58J June 28. 5264 June 13. 2201 Apr. 11.333 29.3007 29-5799 25.17 July 27. 8271 July 12. 8000 May 6.500 29.3076 29.6417 26.62 P-S Aug. 26. 1347 29.3472 29.6764 Aug. 11.4417 27.92 June 12.125 Sept.24.4819 Sept. 10.1181 June 30.042 29.4146 29.6687 28.33 Oct. 23. 8965 Oct. 9. 7868 July 28.375 29.5091 29.6292 28.426 Nov. 22. 4056 Nov. 8.4160 Aug. 23.792 P-S 29.6236 29.5784 28.38 Dec. 22. 0292 Dec. 7.9944 Sept. 23.167 29.7326 29.5306 28.121 1962 Jan. 20.7618 Jan. 6.5250 1962 Oct. 21.292 29.7924 29.4819 26.92 Feb. 19.5542 Feb. 5.0069 Nov. 17.208 29.7764 29.4312 24.79 Mar. 21. 3306 Mar. 6.4382 P-S Dec. 12.000 Apr. 20. 0236 29.6930 29.3847 Apr.1 4.8229 27.58] Jan. 8.583 1962 29.5820 29.3611 28.33 May 19. 6056 May 4.1840 Feb. 5.917 29.4798 29.3764 28.50a June 18.0854 June 2.5604 Mar. 6.417 P-S 29.4014 29.4347 28.46 July 17.4868 July 1.9951 Apr. 3.875 29.3535 29.5215 Aug. 15.8403 July 31.5167 May 2.083 29.3347 29.6146 27.46 Sept. 14.1750 Aug. 30.1312 May 29. 542 29.3479 29.6882 25.29 P-S Oct. 13.5229 Sept.28.8194 June 23. 833 29.3965 29.7257 26.58 Nov. 11.9194 Oct. 28. 5451 July 20.417 29.4750 29.7257 27.92- Dec. 11.3944 Nov. 27.2708 Aug. 17.333 29.5702 29.6868 28.33 1963 Jan. 9.9646 Dec. 26. 9576 Sept. 14.667 29.6548 29.6132 28.46 Feb. 8.6194 Jan. 25.5708 1963 41 Oct. 13.125 P-S 29.7063 29.5167 28.46 Mar. 10. 3257 Feb. 24.0875 Nov. 10.583 29.7139 29.4194 28.12 278 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 17.-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-gyzygy Alignments-Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P Apr. 9.0396 Mar. 25. 5069 Dec. 8. 708 29.6854 29.3465 26.62 May 8.7250 Apr. 23.8535 P-S Jan. 4.333 29.6299 29.3132 24.96 June 7.3549 May 23. 1667 Jan. 29. 292 1963 29.5590 29.3236 27. 71 July 6.9139 June 21.4903 Feb. 26.000 29.4826 29.3729 28.33 Aug. 5.3965 July 20.8632 1 Mar. 26.333 29.4188 29.4528 28.460 Sept. 3.8153 Aug. 19.3160 Apr. 23. 792 P-S 29-3819 29,5528 28.38 Oct. 3. 1972 29.3834 29.6611 Sept. 17.8688 28.171 May 22. 167 Nov. 1.5806 Oct. 17.5299 June 19.333 29.4139 29. 7556 27.42 P-S Nov. 30.9965 Nov. 16.2854 July 16. 750 29.4646 29.8028 25.25 Dec. 30.4611 Dec. 16.0882 Aug. 11.000 29.5132 29.7757 26.67 Jan. 28.9743 Jan. 14.8639 1964 Sept. 6.667 Feb. 1 27.5278 29.5535 29,6792 Feb. 13.5431 27. 96] Oct. 4.625 29.5896 29.5500 28.38 Mar. 28.1174 Mar. 14.0931 Nov. 2.000 29.6237 29.4333 28.54 0 Apr. 26. 7431 Apr. 12.5264 Nov. 30.542 P-S 29.6520 29.3500 28.46 May 26.3951 29.6528 29.3062 May 11.8764 28.041 Dec. 29.000 June 25.0479 June 10.1826 P-S Jan. 26.042 1964 29.6174 29.2973 26.29 July 24.6653' July 9. 4799 Feb. 21.333 29.5611 29.3236 25.33 Aug. 23.2264 Aug. 7.8035 Mar. 17.667 Sept. 21.7299 29.5035- 29.3875 Sept. 6. 1910 27. 75- Apr. 14.417 29.4687 29.4896 28.25 Oct. 21.1986 Oct. 5.6806 May 12.667 29.4563 29.6229 28.42io Nov. 19-6549 Nov. 4.3035 June 10.083 P-S 29.4576 29.7514 28.38 P-S Dec. 19.1125 29.4536 29.8250 Dec. 4.0549 28.171 July 8.458 1965 Jan. 17.5681 Jan. 2.8799 1965 Aug. 5.625 29.4507 29.8118 27.46 Feb. 16.0188 Feb. 1.6917 Sept. 2.083 29.4562 29.7222 25.12 Mar. 17.4750 Mar. 3.4139 Sept. 27. 208 29.4854 29.6007 26.71 Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 279 TABLE 17.-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments-Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P Apr. 13.9604 Apr. 2. 0146 Oct. 23.917 May 15.4951 29.5347 29.4826 May 1.4972 28.08] Nov. 21.000 29.5882 29.3868 28.46 June 14.0833 May 30.8840 Dec. 19.458 P-S 29.6264 29.3195 28.5841 July 13. 7097 June 29.2035 Jan. 17.042 1965 29.6477 29.2861 28.42 Aug. 12.3556 July 28.4896 P-S Feb. 14.458 29.6250 29.2958 27.92_ Sept. 10.9806 Aug. 26.7854 Mar. 14.375 29.6125 29.3521 26.08 Oct. 10.5931 Sept. 25. 137,@ Apr. 9. 458 29.5847 29.4542 25.58 Nov. 9.1778 Oct. 24. 5917 May 5.042 29.5458 29.5819 27.71 Dec. 8.7236 Nov. 23.1736 June 1.750 29.4965 29.7035 28.25 1966 Jan. 7.2201 Dec. 22. 8771 June 30.000 29.4452 29.7805 28.38 P-S Feb. 5.6653 29.4083 29.793 18 Jan. 21.6576 28.42 July 28.375 P-S Mar. 7.0736 Feb. 20.4514 1966 Aug. 25.792 29.3945 29.7479 28. 171 Apr. 5.4681 Mar. 22.1993 Sept.22.958 29.4076 29.6590 27.50 May 4.8757 Apr. 20. 8583 Oct. 20. 458 29.4444 29.5466 24.88 June 3.3201 May 20. 4049 Nov. 14.333 29.4973 29.4347 26.92 July 2.8174 June 18. 8396 Dec. 11. 250 29.5618 29.3486 28.17- Aug. 1.3792 July 18.1882 Jan. 8.417 1966 29.6305 29.3035 28.50 Aug. 31.0097 Aug. 16.4917 Feb. 5.917 P-S 29.6903 29.3097 28.546 Sept.29.7000 Sept.14.8014 P-S Mar. 6.458 29.7174 29.3597 28.33 Oct. 29. 4174 Oct. 14.1611 Apr. 3. 792 29.6944 29.4410 27.79 1 Nov. 28.1118 Nov, 12. 6021 May 1.583 29.6271 29.5326 26.00 Dec. 27. 7389 Dec. 12. 1347 May 27.583 29.5396 29.6195 25.75 IS67 Jan. 26.2785 Jan. 10.7542 1967 June 22.333 29.4604 29.6930 27.71- Feb. 24.7389 Feb. 9.4472 July 20.042 29.4007 29.7403 28.25 F-S Mar. 26. 1396 Mar. 11. 1875 Aug. 17.292 29.3632 29.7438 28.42 Apr. 24. 5028 Apr. 9. 9313 Sept. 14.708 P-S 29.3465 29.6909 28.42 May 23. 8493 29.3570 29.5959 May 9.6222 28. 25@ Oct. 13.125 280 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 17.-Increasejn the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments-Continued Intervals between successive syzygies intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P June 22. 2063 June 8.2181 Nov. 10. 3 75 29.4048 29.4909 27. 38 July 21. 6111 July 7.7090 Dec. 7.750 29.4910 29.4084 24.67 Aug. 20. 1021 Aug. 6.1174 Jan. 1.417 1967 29.6062 29.3673 27.21 Sept. 18.7083 Sept. 4.4847 Jan. 28.625 Oct. 18.4243 29.7160 29.3653 Oct. 3.8500 28.25] Feb. 25.875 29.7792 29.3924 28.46 Nov. 17.2035 Nov. 2.2424 P-S 0 Mar. 26. 333 P-S 29.7701 29.4312 28.46 Dec. 16.9736 29.7014 29.4785 Dec. 1.6736 28_29 Apr. 23.792 1968 Jan. 15.6750 Dec. 31.1521 May 22.083 29.6049 29.5354 27.75_ Feb. 14.2799 Jan. 29.6875 June 18.833 29.5069 29.6014 26.00 Mar. 14.7868 Feb. 28.2889 1968 July 14.833 29.4160 29.6618 25.79 Apr. 13.2028 Mar. 28. 9507 Aug. 9.625 29.3423 29.6896 27.71- P-S May 12.5451 Apr. 27.6403 Sept. 6.333 29.2980 29.6722 28.25 June 10.8431 May 27.3125 Oct. 4.583 29.2944 29.6215 28.50 July 10.1375 June 25. 9340 Nov. 2.083 P-S 29.3438 29.5591 28.50 Aug. 8.4813 29.4409 29.5048 July 25.4931 28.2 J Nov. 30.583 Sept. 6.9222 Aug. 23.9979 Dec. 28.792 29.5688 29.4667 27.21 Oct. 6.4910 Sept.22.4646 Jan. 25.000 1968 29.6930 29.4417 24.67 Nov. 5.1840 Oct. 21. 9063 Feb. 18.667 29.7799 29.4284 27.40 Dec. 4.9639 Nov. 20. 3347 Mar. 17.063 29.8055 29.4285 28.23- 1969 Jan. 3.7694 Dec. 19. 7632 P-S Apr. 14.292 29.7695 29.4444 28.42 Feb. 2.5389 Jan. 18.2076 1969 41 May 12.708 P-S 29.6819 29.4771 28.42 Mar. 4.2208 Feb. 16.6847 June 10.125 29.56H 29.5181 28.25 Apr. 2.7819 Mar. 18. 2028 July 8. 375 29.4362 29.5583 27.75J May 2.2181 Apr. 16.7611 Aug. 5.125 29.3368 29.5910 25.96 May 31.5549 May 16. 3521 Aug. 31.083 29,2812 29.6125 25.75 Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 281 TABLE 17-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments--Continued Intervals between successive syzygies Intervals between successive perigees; Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P P-S June 29.8361 June 14. 9646 Sept. 25. 833 29.2792 29.6271 27.79- July 29. 1153 July 14.3917 Oct. 23. 625 29.3243 29.6294 28.38 Aug. 27. 4396 Aug. 13. 2201 Nov. 21. 000 29.4090 29-6103 28.50 Sept.25.8486 Sept. 11. 8306 Dec. 19. 500 P-S 29.3160 29.5722 28.30 Oct. 25. 3646 Oct. 11. 4028 Jan. 17.000 1969 29.6312 29.5222 28.17_ Nov. 23. 9958 Nov. 9.9250 Feb. 14. 167 29.7373 29.4799 26.92 Dec. 23. 7333 Dec. 9.4049 Mar. 13. 083 29.8056 29.4534 24.92 1970 Jan. 22.5389 Jan, 7.8583 1970 Apr. 7.000 29.8076 29.4431 27.46 Feb. 21.3465 Feb. 6.3014 P-S f ay 4.458 29.7320 29-4368 28.17- Mar. 23. 0785 Mar. 7.7382 June 1.625 29-6034 29.4354 28.38 Apr. 21. 6819 Apr. 6.1736 40 June 30.000 P-S 29.4695 29.4458 28.38 May 21. 1514 May 5.6194 July 28.375 29-3680 29.4792 28.25 June i9.5194 June 4.0986 Aug. 25.625 29-3132 29.5389 27.83_ July 18.8326 July 3.6375 Sept.22.458 29.3035 29-6118 25.71 P-S Aug. 17.1361 Aug. 2.2493 Oct. 18.167 29.3292 29-6688 25.92 Sept. 15.4653 Aug. 31.9181 Nov. 13. 083 29.3833 29.6875 27.92- Oct. 14.8486 Sept.30.6056 Dec. 11. 000 29.4632 29-6645 28.42 Nov. 13.3118 Oct. 30.2701 Jan. 8. 417 1970 29.5660 29-6153 28.5411 Dec. 12.8778 Nov. 28.8854 Feb. 5.958 P-S 29.6785 29.5611 28.46 1971 Jan. 11.5563 Dec. 28.4465 Mar. 6. 417 29.7645 29-5091 28.04_ Feb. 10.3208 Jan. 26.9556 1971 Apr. 3. 458 29.7861 29.4534 26.71 Mar. 12.1069 Feb. 25.4090 P-S Apr. 30.167 29.7341 29.3993 25.17 Apr. 10.8410 Mar. 26. 8083 May 25.333 29-6340 29.3598 27.42 May 10.4750 Apr. 25. 1681 June 21. 750 June 9.0028 29.5278 29.3541 May 24. 5222 28.17] July 19. 917 29.4396 29.3931 28.38 July 8. 4424 June 22. 9153 Aug. 17. 292 P-S 29.3791 29.4708 28.42 0 Aug. 6.8215 July 22. 3861 Sept.14.708 29.3473 29.5681 28.33 Sept. 5.1688 Aug. 20. 9542 Oct. 13. 042 29.3451 29.6590 27.79_ 282 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE, 17.-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments-Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P P-S Oct. 4. 5139 Sept. 19. 6132 Nov. 9.833 29.3750 29. 7201 25.42 Nov. 2.8889 Oct. 19.3333 Dec. 5.250 29.4368 29.7403 26. 17 Dec. 2.3257 Nov. 18.0736 Dec. 31.417 Dec. 31.8472 29.5215 29. 7202 Dec. 17. 7938 28.00] Jan. 28.417 1971 29.6097 29.6590 28.46 1972 Jan. 30.4569 Jan. 16.4528 1972 Feb. 25.875 P-S 29.6764 29.5673 28.50 Feb. 29.1333 Feb. 15.0201 Mar. 26. 373 29.7035 29.4625 28.38 Mar. 29.8368 Mar. 15.4826 Apr. 23. 750 29.6938 29.3723 27.96_ Apr. 28. 5306 Apr. 13.8549 P-S May 21. 708 29.6555 29.3173 26.71 May 28.1861 May 13.1722 June 17. 417 29.5958 29.3070 25.21 June 26. 7819 June 1,1.4792 July 12. 625 29.5264 29.3396 11 27.42 July 26. 3083 July 10.8188 Aug. 9.042 29.4570 2.9.4076 28.17- Aug. 24. 7653 Aug. 9.2264 Sept. 6.208 29.4062 29.5014 28.42 Sept.23.1715 Sept. 7.7278 Oct. 4. 625 P-S 29.3875 29.6111 28.46oo Oct. 22. 5590 Oct. 7.3389 Nov. 2.083 29.4042 29.7174 28.25 P-S Nov. 20. 9632 Nov. 6.0563 Nov. 30.458 29.4431 29.7937 27.87J Dec. 20. 4063 Dec. 5.8500 Dec. 28.208 29.4881 29.8042 25.00 1973 Jan. 18.8944 Jan. 4.6542 1973 Jan. 22.208 1972 29.5271 29.7368 26.58 Feb. 17.4215 Feb. 3.3910 Feb. 17.792 29.5598 29.6139 28.08- Mar. 18. 9813 Mar. 5.0049 Mar. 16.875 29.5958 29.4847 28.38 Apr. 17. 5771 Apr. 3.4896 Apr. 14.250 P-S 29.6298 29.3820 28.46 May 17. 2069 May 2.8715 May 12.708 29.6507 29.3188 28.29 June 15. 8576 June 1.1903 P-S June 10. 000 29.6396 29.2951 27.96_ July 15. 4972 June 30.4854 July 7.958 29.5979 29.3056 26.67 Aug. 14.0951 July 29.7910 Aug. 3. 625 29.5410 29.3514 25.21 Sept.12.6361 Aug. 28.1424 Aug. 28. 833 29.4952 29.4368 27.46 Conditions Extending Duration of Augmented Tide-Raising 'Forces at Perigee-Syzygy 283 TABLE 17.-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments-Continued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P Oct. 12. 1313 Sept.26.5792 Sept.25.262 Nov. . 10.6021 29.4708 29.5576 Oct. 26. 1368 28.21] Oct. 23.500 29.4632 29.6930 28.50 Dec. 10.0653 Nov. 24. 8299 Nov. 21.000 P-S 29.4597 29.8000 28.,540 P-S Jan. 8.5230 Dec. 24. 6299 Dec. 19.542 29.4500 29.8298 28.33 1974 Feb. 6.9750 Jan. 23.4597 1974 Jan. 16.875 1973 29.4438 29.7722 27.58-- Mar. 8.4188 Feb. 22. 2319, Feb. 13.458 Apr. 6.8750 29.4562 29.6597 Mar. 23. 8917 24.88 Mar. 10.333 29.4965 29.5368 26.83 May 6.3715 --- Apr. 22.4285 Apr. 6. 167 June 4.9236 29.5521 29.4285 May 21.8569 28. 08] May 4.250 29.6042 29.3486 28.33 July 4.5278 June 20.2056 June 1.583 P-S 29.6368 29.2993 28.42 0 Aug. 3.1646 July 19.5W P-S June 30.000 29.6444 29.2882 28.29 Sept. 1.8090 Aug. 17.7931 July 28.292 29.6341 29.3215 28.00_ Oct. 1.4431 Sept. 16.1146 Aug. 25.292 29.6118 29.4028 26.62 Oct. 31.0549 Oct. 15.5174 Sept. 20.917 29.5770 29.5194 25.12 Nov. 29.6319 Nov. 14.0369 Oct. 16.042 29.5285 29.6472 27.58 Dec. 29.1604 Dec. 13.6840 Nov. 12.625 29.4709 29.7466 28.29 1975 Jan. 27.6313 Jan. 12.4306 Dec. 10.917 29.4208 29.7895 28.54 P-S Feb. 26.0521 Feb. 11.2201 1975 Jan. 8.458 P-S 28.54 Mar. 27.4417 29.3896 29.77 .09 Mar. 12.9910 5j Feb. 6.000 1974 29.3882 29.7028 28.2 Apr. 25.8299 Apr. 11.6938 Mar. 6.250' 29.4139 29.6013 27.42 May 25.2438 May 11.2951 Apr. 2.667 29.4604 29.4889 25.00 June 23.7042 June 9.7840 Apr. 27.667 29.5236 29.3896 26.88 July 23.2278 July 9.1736 May 24.542 29.3972 29.3243 28.04- ,Aug. 21.8250 Aug. 7.4979 June 21.583 29.6681 29.3070 28r33 Sept.20.4931 Sept. 5.8049 P-S July 19.917 P-S 29.7194 29.3361 28.38 Oct. 20. 2125 Oct. 5. 1410 41 Aug. 17.292 29.7236 29.4041 28.38 Nov. 18. 9361 Nov. 3.5451 Sept. 14.667 29.6750 29.4896 28.00 284 Strategic Role of Perigean Spring Tides, 1635-1976 TABLB 17-Increase in the Lengths of the Synodic and Anomalistic Months With Proximity to Those Months Containing Perigee-Syzygy Alignments-Contiiiued Intervals between successive syzygies Intervals between successive perigees Synodic Synodic Anomalistic Year Date FM month month Date NM Year month Date P Year FM-FM NM-NM P-P Dec. 18. 6111 Dec. 3. 0347 Oct. 12. 667 26.50 Nov. 8.167 25. 12 Dec. 3.292 27.71- Dec. 31.000 28.38 Jan. 28.375 1975 28.544o Feb. 25.917 P-S 28.46 Mar. 26. 375 28.17J Apr. 23.542 27.29 May 20.833 25.08 June 14.917 26.92 July 11.833 28. 06- Aug. 8.833 28.33 Sept. 6.167 P-S 28.46 o Oct. 4.625 28.42 Nov. 2.042 28. 00j Nov. 30.042 26.12 Dec. 26.167 moons and two consecutive new moons, are given in col- A synodic month is, by convention,' defined as the pe- umns 3 and 4. riod of time between new moon and new moon. Because Because it is desired to determine the length of that of the shift in dates and in the position of the Moon in its synodic month which most nearly brackets each case of elliptical orbit, different values for the length of the syn- perigee-syzygy, it becomes necessary to consider the period odic period will be obtained if the month is reckoned of time between two succeeding occurrences of the oppo- from full moon to full moon. Ile possibility of mutual site phase of syzygy. That is, to determine -the length of the commensurability varies as either the synodic or anomal- synodic month which contains, midway in the month, a istic periods vary. The lengths of the synodic months will perigee-syzygy alignment at full moon, it is necessary to show either a maximum or minimum value according as calculate the period of elapsed time between the most the period chosen contains the date of perigee or apogee, closely bracketing new moons. To deten-nine the length of respectively. For analytic purposes, this nonconventional the synodic month in which the date of a perigee-syzygy procedure of computing both periods is used here. at new moon is centrally located, the procedure involves taking the difference in time between successive full See Explanatory Supplement to the Astronomical Ephemeris and moons. The American Ephemeris and Nautical Almanac, London, 1961, p. 107. Conditions Extending Duration of Aug7nented Tide-Raising Forces at Perigee-Syzygy 285 Maximized Lengths of Those Months An alternate choice of cyclical relationship therefore ex- Bracketing Perigee-Syzygy ists between these two sets of semiannually occurring, noncontiguous cases of perigee-syzygy. One element of The lengths of synodic months listed in table 17 reveal each pair will, however, invariably have a smaller sepa- the considerably different values which pertain for those ration-interval between perigee and syzygy than the other. dates which bracket a date of perigee-syzygy compared According to the procedure here adopted for establishing with those which bracket an apogee-syzygy situation. For the most meaningful perigee-syzygy cycle, the semiannual every condition Of full moon occurring nearly coinciden- period is defined as the difference in time between those tally with perigee, the next following (or preceding) new cases of perigee-syzygy alignment in each of the two pairs moon will occur re@sonably close to the time of apogee having the smallest separation, in hours, between their one-half of an anomalistic month later (or earlier). The individual components., interval represented is V2 of 27.55455-13.77728, while The riear-coincidence of perigee with syzygy (either the exact alternation of syzygy phases occurs in V2 of the new moon or full moon) will, because of recurring, ap- synodic month of 29.53059 days=14.76530 days. This proximately commensurable relationships between the gives a difference of only 0.98802 day between new moon synodic and anomalistic months, result in approximate and apogee in the new position. In terms of the limit of agreement again within definite cycles. Short-period repe- :i--l day between components established for a standard titions will occur (at the same lunar phase) an average perigee-syzygy situation (table 16), the latter case can, between one anomalistic and one synodic month earlier with consistency, be classified as a typical apogee-syzygy or later; also (at opposite lunar phases) separated from alignment. the first case by an interval established by the average From immediately adjacent values in columns 3 and 4 between either 6.25 (to 6-5) or 7.25 (to 7.5) anomalistic of table 17, it will be noted that each condition of perigee- syZygy at full moon (marked by a maximum len th of the and synodic months. The average must be taken between 9 the actual (not mean) lengths of the synodic and anom- synodic month) is very nearly matched, in the next suc- alistic months, such as are given in table 17. (Cf., fur- ceeding or preceding half month, by a near-coincidence ther page 25, last paragraph of Explanatory Commen'ts of aPogee-syzygy at new moon, (having a minimum to table 1, and the bracketed repetitions of tidal flooding length of the month) and vice versa. In this 2-week inter- in table 1; also table 4a.) In the terms of reference used, val, the Moon rev 'olves in its orbit through 1800 from the first set of two values involving an approximate 6- alignment with the Earth and Sun at perigee-s zygy to an 'Y approximate alignment with Earth and Sun again at month period applies to the situation in which two cases apogce-syzygy. Since the Sun has moved: only about 14' of perigee-syzygy-each possessing the smaller separation- of arc from the line of apsides in this same period, its per- interval within its own pair-are located consecutively turbative influence is still active thereon. within approximately one-half year of each- other in the Of most relevant importance to the present discussion, comprehensive perigee-syzygy series of table 16. The sec- however, is the fact that, because the Moon's velocity in ond, 7.25- to 7.5-month period applies to those cases orbit at apogee-syzygy is considerably slower than at peri- separated by one or more intervening perigee-syzygy oc- gee-syzygy, the necessary catch-up motion by the rotating currences. The 7.5-month pair possesses the smallest, Earth is less at the apogee position. The duration of each the intervening cases the largest separation-intervals in lunar day near the time of apogee-syzygy is less, and the their respective groups. lengths of both.the anomalistic and synodic months brack- The range from 0.25 to 0.5 month in each case con- eting apogee-syzygy are shorter than those bracketing notes an approximate averag'e rather than a specific perigee-syzygy@ value. It is due to the varying periodicities (resulting from altered orbital eccentricities) which may span two cases Cycles of Alternation in Perigee-Syzygy of close perigee-spring alignment. For convenience, only Alignments the 0.5-month values in each set hereafter will be referred to, as more indicative of the accompanying change from As noted later in this same section, an almost universal new moon to full moon or the reverse. It will be implic- tendency exists for cases of close perigee-syzygy alignment itly understood that, wherever this one value is cited to to occur in pairs, two in contiguous anomalistic months, the exclusion of the other, a several-day variation around followed by two more within about a half-year of the. first. either 6.25 to 6.5 or 7.25 to 7.5 months as defined above 286 Strategic Role of Perigean Spring Tides, 1635-1976 may actually be represented in the exact interval between The dates of the closest alignments of perigee-syzygy successive cases of perigee-syzygy. are indicated in column 9 by the letters P-S. It will be As seen in table 16, a perigee-syzygy situation at new noted that, very nearly opposite each of these P-S sym- moon becomes a perigee-syzygy situation at full moon bols, the figure in column 7 representing the length of 6.5 or 7.5 months later (or earlier), with the two remain- the anomalistic month also reaches a corresponding ing combinations of perigee-quadrature occurring ap- maximum-usually one of two possible maximum values proximately halfway inbetween. A more detailed anal- in the calendar year. (There are necessarily two such ysis of the exact cycles and relationships involved, which maxima within each 15 anomalistic months.) The cir- are dependent upon variations in the lengths of the syn- cumstance that the lengths of these particular anomalistic odic and anomalistic months and certain other astronom- months within each approximate 15-month period are ically varying influences, is presented in the following increased to a maximum value confirms the fact that the pages. rotational catch-up motions of the Earth are the greatest The Meaning and Relationships of High and at these times. Low Maxima in the Lengths of the Lunar For each successive approach to, and recession from, a Months case of close perigee-syzygy alignment, a set of square With each repetition of a close perigee-syzygy align- brackets encloses all values of the anomalistic month in ment, the Moon's orbital velocity accelerates to one of its column 7 which are in excess of the standard mean value maxima, and the Earth's required rotational catch-up (27.554551') used in astronomy. In the long-period, net times reach corresponding maximum values. Simultane- motion of perigee depicted in figures 28, 30, and 32 (as ously, the lengths of the synodic months centered around opposed to its short-period motion occurring immediately these perigee-syzygy positions increase toward their own in the vicinity of perigee-syzygy) another fact is note- maxima. worthy in this table: During each of. the anomalistic This increase in the lengths of the synodic months (and months contained within the square brackets, the net their constituent tidal days) to recurrent maxima cor- motion of perigee is forward; during the remaining responding to the times of perigee-syzygy gives support anomalistic months (whose lengths are all less than the to the premise variously enunciated throughout this established mean value) the net motion of perigee is monograph: (I) that the augmentation in height of peri- retrograde. The anomalistic month (or average of two gean spring tides is produced by the various reinforcing equal anomalistic months) of longest duration in each forces enumerated in chapters 3-4; and (2) these forces bracketed series is indicated by a bold dot (bullet) placed are contributed to through a prolongation of their period directly to the right of its value in column 7. of maximum action, caused by a coincident increase in It is, of course, possible to obtain the separation- various astronomical catch-up motions and (as will be interval representing the actual near-coincidence in time seen later in this same chapter) sometimes also by in- between the occurrences of perigee and syzygy at each creased individual motions in right ascension. The lengths of successive anomalistic months listed in such alignment by simply taking the difference between table 17 contain the effects of perturbations of the Moon's columns 2 and 8 of. this table for the appropriate P-S line of apsides at both perigee and apogee as the appar- date. The values should be subtracted in the sense perigee ent solar motion brings the Sun into coincidence with date minus syzygy date to maintain consistency in alge- this line; also the retrograde motion of the line of apsides braic sign. Because of the two-component -relationship re- induced at both longitudinal positions of the Sun which quired to establish the condition of perigee-syzygy, a close make an angle of 90' with respect to the lunar line of (if.not exact) correlation also will be observed between apsides.' any synodic month of maximum length and the anoma- Columns 7, 8, and 9 in this table show the influence of listic month of maximum length occurring in the same the changing speed of the Moon in orbit as it affects close proximity to perigee-syzygy. The maximum lengths the length of the anomalistic month. When the Moon's of the synodic months determined between successive oc- motion is accelerated at time of perigee-syzygy, the currences of both new moon and full moon are set in Earth's rotation must necessarily catch up. The length of boldface in columns 3 and 4. By noting the number of the anomalistic month which contains the coincidence of days separating each succeeding boldface value, the ap- perigee-syzygy is proportionately increased. proximate 6.5 or .7.5-month time span between consecu.- Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 287 tive alignments of perigee-syzygy is immediately evident. forward. motion of perigee during those anomalistic The typical alternation from perigee-syzygy at new moon months bracketing close pengee-syzygy alignments. The to perigee-syzygy at full moon can be seen by comparing relative lengthening of the anornalistic month will be columns 7, 8, and 9 with columns 3 and 4 and 2 or 5, more, the larger is the net forward motion of perigee with respectively. respect to its assumed mean motion. Supporting a previous statement regarding the closely related sequence of perigee-syzygy and apogee-syzygy, the 2. Variation in Length of the Synodic Month maximum length of a synodic month is inevitably accom- On the other hand, the synodic month is ordinarily panied in the adjoining column-and within a period not measured from new moon, which implies an alignment to exceed 2 weeks earlier or later-by a corresponding of the Moon with the Sun. The synodic month by defini- minimum. Inherent within the effects of solar perturba- tion already contains the effect of the Moon's catch-up tions are those altering the lunar period of revolution. motion with the Sun, viewed from the rotating Earth. Consistent with such dynamic influences, the varying Its period is measured in terms of the extra number of lengths of the synodic months considered as a whole are, rotations of the Earth required to achieve the simultane- of course, a function of their separation in time from ous meridian transit of the two bodies. The resulting perigee-syzygy. Likewise, individual variations in the mean value is based upon an assumed mean daily synodic, maximum lengths of the synodic months are a function motion of the Moon amounting to 13.176396 0/d_ of the smallness of the separation-interval between 0.985647- /d= 12.190749- /d. perigee and syzygy, the synodic (and anomalistic) In this evaluation of the synodic month, the Sun is months becoming longer as this separation-interval assumed to move with a mean apparent angular velocity becomes shorter. of +0.985647'/day. In the Sun's apparent motion, the variations from its mean value are much smaller than 1. Variation in Length of the Anornalistic Month those of the Moon from its mean angular orbital velocity. The mean value of the anornalistic month is based This'is due both to the smaller magnitude of the Sun's upon an assumed mean motion of the Moon with respect. mean motion and the smaller daily variations therefrom to perigee amounting to l3.l76396'/'-0.lll404'/'= which are cumulatively totaled. (In addition, the varia- 13.064992'/'. However, because of the increased angu- tions in the lunar orbital velocity between perihelion and lar velocity of the Moon at perigee-syzygy, while the aphelion are of too small a magnitude to have any influ- Moon is close to. this position the Earth requires a small ence in this connection.) extra portion of each day's rotation to catch up with the Consequently, the maximum variations in the length of Moon and enable it to transit the meridian to complete the synodic month are considerably less than those in the a lunar day. The maximum absolute angular velocities anomalistic month. The greatest individual values for the of the Moon (occurring at proxigee-syzygy) can be as length of the synodic month will bracket a perigee-syzygy high as 15.4'/day. alignment near the time of perihelion (in accordance It is obvious that the necessary catch-up motion of the with the Sun's greater apparent motion then). The small- rotating Earth resulting from such accelerated motions est values will occur bracketing an apogee-syzygy situa- of the Moon can account for the consistent lengths in tion near aphelion. As a direct corollary, the maximum excess of that of the mean anornalistic month found in difference of 0.5555 day in the lengths of the synodic the case of those months which contain a very close months appearing in this table exists between the months perigee-syzygy alignment. June-July 1960 and Jan.-Feb. 1964 corresponding to At the same time, a small additional modification is periods near aphelion and perihelion, respectively introduced by the net, long-term progression of perigee. The Correlation Between Smaller Perigee- The anomalistic month is measured from perigee to Syzygy Separation- Intervals and Longer perigee. It therefore contains the extra catch-up motion Months due to the net forward motion of perigee, but calculated From a detailed analysis of table 17, various pertinent for an assumed mean rate of only +0. 11 1404'/day. Ac- cordingly, the true anomalistic month also will be length- relationships may be summarized. ened to a slight extent because of the extra motion re- 1. Over any reasonably short span of time, it is appar- quired for the Moon to catch up with the greater net ent that: (a) the total number of lunar days in corre- 288 Strategic Role of Perigean Spring Tides, 1635-1976 sponding synodic and anomalistic months (a factor ANALYSIS OF THE RELATIVE GAINS IN THE determined by the relative orbital motion of the Moon LENGTHS OF THE ANOMALISTIC AND SYN- and the necessity for the rotating Earth to catch up on ODIC MONTHS CONTAINING A CLOSE this motion) ; and (b) the individual lengths of the lunar PERIGEE-SYZYGY ALIGNMENT days contained in each month (again determined by the 1. 'Anomalistic Month Moon's changing orbital velocity, as well as relative mo- tion in right ascension) must vary together. (a) The anomalistic month is defined as the period of The anomalistic months bracketed in table 17 are time between two successive passages of the Moon through perigee. grouped around those dates on which perigee and syzygy (b) During the period of one revolution of the Moon are in close alignment (the separation-intervals. for all around the Earth from alignment in longitude with a given examples labeled "P-S" are < 1 P). These months are star to aligm-nent with that same star again (i.e., the sidereal therefore, not only lengthened, but their constituent days month), the position of perigee has itself moved forward an are made longer at perigee-syzygy. average distance of 27.32166ldX 0.111404'/d or 3.043742'. (c) The Moon must revolve through this extra angular 2. The lengths of both the synodic and anomalistic distance to catch up with the position of perigee and com- months vary in inverse proportion to the separation- plete the anomalistic month. interval between perigee and syzygy. (d) In addition, in order to achieve a meridian transit of 3. The chance for coincidence between perigee and the Moon (and Sun) at perigee-syzygy, an observing posi- tion on the Earth must rotate through an additional angle syzygy exists twice a month in terms of either new moon to catch up with this extra forward motion of the Moon in or full moon in synodic months but (except for one calen- that part of the orbit where it is revolving the fastest. dar month in each year with perigee located both at the (e) An increased period of time is required for the rotat- beginning and end) occurs only once each month in con- ing Earth to achieve such a catch-up motion, and the lengths of the lunar (and tidal) days are extended. nection with anomalistic months. The two types of months (f) Significantly, the Moon must pass over this extra seg- regain a close commensurability, once it has been estab- ment of its orbit where it is moving the fastest (i.e., immedi- lished, after periods of approximately 28.5, 190, and 219 ately following perigee) a second time in order to catch up days.' with perigee. The extra period of catch-up motion by the rotating Earth while the Moon is traveling at its fastest 4. The solar parallactic inequality previously has been velocity contributes to the number of days or decimal parts described as a condition in which, by virtue of closer dis- thereof in all anomalistic months. This is especially true tance, the gravitational attraction of the Sun is exerted to where the perigee distance is greatly reduced by a very a greater extent upon the Moon as it reaches its position of near-coincidence between perigee and syzygy and the Moon's solar perigee once each year about January 2-4. The velocity at this time is increased considerably in proportion. Moon is then slowed down in its orbit around the Earth as 2. Synodic Month the result- of a partial reduction of the Earth's gravita- (a) The synodic month ordinarily is defined as the period tional attraction. This influence is not, however, of a between two consecutive alignments of the Moon and Sun magnitude which is critical in the changing lengths of the in celestial longitude at the instants of lunar conjunction (i.e., the period from new moon to new moon). However, synodic months where these are car-iried to 'only four in establishing certain relevant facts as part of the quanti- decimal places, in days. The decrease in the Sun's daily tative analysis of this section, both the. foregoing and an apparent motion between the position of perihelion (close alternate definition involving the period between full moons to that of solar,perigee) and aphelion (close to solar have been used. apogee) is only some 3-4' in celestial longitude.' A salient factor exists in this dual method of interpreta- tion: Under either of the two alternate definitions chosen (new moon to new moon, or full moon to full moon) the c More exact cycles of commensurability, for predicting a return starting and ending positions in each synodic month also to similar tide-raising conditions, based upon a number of astronomical variables, including' that of perigee-syzygy, are: have been selected as opposite in the lunar orbit from the 28.981403-, 162.502866d, 191.484268d , 205.892318'% 355.022184 d. position of perigee-syzygy and, accordingly, at the apogee and 384.003587d. end of the orbit. The effect of any one perigee-syzygy align- 'The coordinate of celestial longitude is carefully selected since ment is thus most accurately bracketed. the apparent daily motion of the Sun in right ascension is affected (b) While the Moon revolves through one sidereal month not only by the Earth's position with respect to perihelion and aphe- with respect to the stars, the Sun -advances in its apparent lion (i.e., the solar parallactic inequality) but by the declination of the Sun. The resultant daily motion in a varies throughout the annual motion through approximately 26.929513', assum- year according to the same pattern as the equation of time. ing a mean rate of 0.985647'/'. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 289 (c) In contrast to the example for the anomalistic tinuous) for-ward motion of perigee through successive month, the necessary catch-up motion by the rotating Earth lunar years----as well as a prolonging of the conditions to complete a transit of the Moon and Sun together at either responsible . for perigean spring tides by a retrograde conjunotion or opposition occurs while the Moon is moving I at its slowest velocity near apogee. I motion of perigee around the immediate time of each (d) Furthermore, the segment of the Moon's orbit over perigee-syzygy alignment. which it must pass a second time in catching up with the These separate motions are both due to the perturba- changing apparent position of the Sun to complete the syn- tional actions of the Sun as, in its apparent motion around odic month is that portion immediately following apogee in the ecliptic consequent upon the actual motion of the which the Moon is traveling at its slowest velocity. Earth, the solar body approaches an alignment in longi- (e) Accordingly, the necessary catch-up time by a posi- tion on the rotating Earth to complete the synodic month is tude with the lunar line of apsides. not as great as that required under the concept of the anom- As described in part 11, chapter 4, in the immediate alistic month, and the latter shows a greater gain in length vicinity of the position of perigee-syzygy alignment these than the former. The increase in the length of the synodic solar perturbations produce a retrograde rotation of the month containing a close perigee-syzygy alignment, although line of apsides of the Moon's orbit (clockwise as viewed significant (about 0.6 day), is less than one-sixth the in- from the north pole of the ecliptic). This retrograde crease in an anornalistic month (as much as 3.9 days) under the same circumstances. motion of perigee begins about 3 days prior to the perigee- syzygy alignment and reaches a maximum angular ve- This explanation accoun Its both for the indicated var- locity of approximately - 1.620 / dat this position, there- iations in the length of the synodic month and the fact after diminishing again to zero in the following 3 days. that, with the positioning of perihelion and aphelion in The physical effect of this retrograde motion of peri- the present astronomical epoch, the winter months are gee (in a direction opposite to that in which the Moon invariably a significant portion of an hour longer than the is revolving around the Earth) is to cause the passage of summer months, even without the combined influence the Moon through perigee-syzygy alignment to occur of perigee-syzygy noted above. This circumstance is of sooner, since the relative velocity between Moon and peri- related but mainly academic interest in chapters 7 and 8 gee is maximized at this position. Following perigee- in terms of the greatest frequency of tidal flooding ac- syzygy, as both the retrograde velocity of perigee and the companying winter storms. relative velocity betweery it and the Moon are diminished, a tendency exists for prolongation of the reinforcing grav- Prolongation of a Small Separation-Interval itational conditions associated with perigee-syzygy which at Close Perigee-Syzygy Alignments are responsible for perigean spring tides. This effect con- In the book Waves and Tides by R. C. H. Russell and tributes to the extension of the number of days of perigean Commander D. H. Macmillan (1953), the authors state spring tides compared with ordinary spring tides. (page 206): Although, over the long term5 the net motion of peri- "Another feature of interest in these variations depends gee is forward (the mean progression of perigee), as was upon the curious astronomical fact that perigee does not seen in figures 28, 30, and 32, during any one lunar year, fall back evenly around the synodic or lunar month, but the net motion of perigee is direct only in certain lunar 'hangs' or remains close to new moon for three or four months. The net forward motion of perigee begins I or 2 ters again anomalistic months prior to the time at which the Sun months. It then shifts rapidly through the quar 4steadying up' and 'hanging' as'it were at the full moon crosses the line of apsides, reaches a maximum angular before going on past the next quarter. value before the two longitudes agree, and decreases slowly to zero for 1 or 2 anomalistic months thereafter. "The resulting 'perigee springs' giving maximum lunar The length of each tidal day, and the average number of effects at syzygies (conjunction or opposition of sun and days between two successive returns of the Moon to peri- moon) consequently recur for about three months in gee, are both increased proportionately. succession during the year before they fall off in height." This is shown by- the considerably higher value con- In terms of the astronomical intricacies of perigean sistently attained in the length of any anomalistic month spring tides, the causal factors for this interesting circum- which brackets a date of close perigee-syzygy (see table stance are deserving of further consideration. The phe- 17). The anornalistic month is increased (as much as nomenon in question is a function of the distribution of 1.03' above its average value) by an amount considerably perturbations which is responsible for a net (not con- more than the synodic month as a result of this effect. 202-509 0 - 78 - 21 1 290 Strategic Role of Perigean Spring Tides, 1635-1976 The anomalistic period thus is not allowed to fall off The relative increase in gravitational force resulting during the months immediately preceding and following from a close perigee-syzygy alignment is a direct function perigee-syzygy by the full 1.9760' between the average of the smaller separation-interval between perigee and lengths of the synodic and anornalistic months. (It is this syzygy which is, in turn, associated with a condition of greater average difference as it accumulates that destroys more exact commensurability between the periods of the the commensurability between the two months, once at- anomalistic and synodic months. It is important to note tained.) In contrast, subject to these very small, localized in this connection that the relationship which permits differences, the lengths of the anomalistic months often the near-coincidence of perigee and syzygy to occur is a remain very nearly the same at maximum value (varying precise intermatching of the previously noted widely vary- only by a few digits in the second decimal place) for ing values for the lengths of these respective months. The several successive months around the time of a close extreme range in length of the anomalistic months as perigee-syzygy alignment. determined from table 17 is 28.58-24.67 or 3.91 days, With a near-commensurability between the synodic and and the corresponding extreme range of the synodic anomalistic months established at such times, and par- months is 29.8298-29.2743 or 0.5555 day. Because of tially maintaine d through the above circumstances, the these unequal differences, the positions of perigee and phenomenon of perigee-syzygy alignment tends to per- syzygy only rarely attain a separation-interval of less than sist. This is clearly seen among the curves of rate-of-tide- 6 to 6.5 minutes (e.g., 1912 January 4;'1931 March 4). growth depicted in figs. 153-163 of chapter 8. However, once a close approximation to the necessary An additional contribution to this influence is pro- commensurate relationship is attained and the two po- vided by the comparatively slow apparent motion of the sitions roughly coincide, they will not separate rapidly. Sun along the ecliptic with respect to the position of As noted earlier, succeeding anomalistic months vary by perigee-syzygy. The Sun's apparent velocity along the only a few hundredths of a day around the time of closest ecliptic is only about 10'11 (even less at the time of aphe- separation between perigee and syzygy, and the variation lion). The circumstances of a small separation-interval in the corresponding maximum values of the synodic between perigee and syzygy, once achieved, tends to be months is equally small. Thus, the existing nearly com- approximately retained and extended over successive mensurable relationship is not destroyed and the separa- perigee-syzygy alignments. tion-interval between perigee and syzygy often remains The lengths of the anomalistic months which either equal to, or less than � 24 hours for 3 or 4 (and occa-, contain, or closely adjoin other such months which con- sionally even 5) successive months (see table 16). tain instances of ordinary perigee-syzygy (as defined in chapter 8) are universally in excess of 28 days. Less Declinational Influences on the Length frequently, in the case of proxigee-syzygy, their periods of the Tidal Day are very close to 28.5 days-equivalent to *the simple av- In the discussion of this concept of induced changes erage between the synodic (29.530589-day) and anoma- in the length of the tidal day, four different aspects of listic (27.554551-day) months. These 28-day or larger apparent lunar and solar motions as seen from the Earth values occur, accompanying all such close perigee-syzygy are involved, all of which must be considered. These alignments, at least 1 month (and usually 2) on either aspects are: side of that containing the smallest separation-interval. 1. The direct reflection of the Earth's diurnal axial This. fact is confirmed in the representation of the rotation as an apparent oppositely directed motion to the varying lengths of both synodic and anornalistic months Moon and Sun on the celestial sphere. during a 17-year double lunar apsides cycle in table 2. A decrease in this apparent angular velocity of 17. The relationship between the greater lengths of the movement on the celestial sphere as the declination of tidal days these months contain and the "windows" either body increases. within which actual cases of tidal flooding often occur is 3. A variation in both of the above apparent motions also shown by the consistent pattern of 2-4 contiguous as the result of individual components of velocity (cre- curves of extreme amplitude, each having a peak indi- ated by the Moon's orbital motion and the Earth's catingan above-average rate of tide growth, among the orbital motion, respectively) which the Moon and Sun graphs of tidal flooding potential in figs. 153-163, chap- possess in right ascension (i.e., directed along the celestial ter 8. equator). Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 291 4. Further variations in apparent velocity introduced day is diminished the least from the foregoing cause at by (a) the inclination of the paths of individual motion such times of perigee-syzygy. of the Moon and Sun to the celestial equator, and (b) the (b) As either' the Sun or Moon moves northerly or declinations of these bodies at any given time. southerly in declination subject to its own apparent orbital The particular effects produced may be described as motion, its apparent'westward (diurnal) velocity de- follows: creases and hence the velocity component to be subtracted (a) The presence of the Moon and/or Sun on the from its eastward motion is less. The net value of the celestial equator may, because of the Earth's fastest linear eastward motion accordingly remains larger. The tidal rotation in the equatorial plane, slightly decrease the time day is lengthened in proportion. during which their forces can act. A celestial object (@) Furthermore, as described earlier, at the summer located over the Equator and lacking any motion of and winter solstices where the instantaneous change in its own would exhibit its greatest possible appaxent the declinational motion of the Sun becomes zero, the angular velocity across the sky. This is because the Sun's entire annual motion is eastward in right ascension, apparent motion of any body in this position reflects and the tidal day is lengthened the most from the Sun's the total velocity component of the rotating Earth trans- influence. The same holds true for the Moon, twice each ferred to an opposite direction. The period of time be- tropical month, as the influence of its eastward motion tween the rising and setting of such objects is, therefore, in lengthening the tidal day becomes the greatest near the the least, their apparent movement in a westward direc- crests and troughs of the curves representing the Moon's tion across the sky is the most rapid' ' and the angular dis- monthly motion in declination. (See figs. 44-45.) tance covered in right ascension at the end of the day (d) The conditions of maximum lunar declination is the smallest. necessary to achieve certain favorable declinational align- The apparent westward movement of the Moon due ments between Sun and Moon and consequent enhanced to the Earth's diurnal rotation is directly opposite to the tide-raising forces, as noted on page 196, are also favorable actual eastward movement pursued by that body in its in terms of lengthening the tidal day. Accordingly, as own orbital motion. Similarly, in the case of the Sun, its the result of these combined factors, it is often found that, apparent diurnal motion is opposite to the apparent east- where anomalistic. and semidiurnal tides are prominent, ward motion produced as a result of the revolutionary as on the east coast of Canada and the northeast coast motion of the Earth in its orbit. The westwardly directed of the United States, the coincidence of perigean spring diurnal motion of either of these two bodies must, there-@, tides with these high-dechnation circumstances for both fore, be subtracted from their respective eastward motions, the Moon and Sun-plus strong onshore winds-is often a fact which, by decreasing the eastward motion, tends to sufficient to produce extensive tidal flooding. The number decrease the length of the tidal day. of instances of this type in table I is statistically large, When the apparent diurnal motion of the object is the indicating. that the position of the Moon on the Equator greatest, as it is when located on the celestial equator, is not an overriding determinant for the production of the magnitude of the component to be subtracted from extraordinarily high tides and tidal flooding (cf., p. 112, the eastward angular motion-a motion which, by it- col. 2, final par.). self, lengthens the tidal day-is the greatest, and the tidal (e) In this same regard, one other phenomenon may day is consequently lengthened by the least amount. provide a significant contribution to the lengthening of This principle is also applicable to the Moon's own the tidal day at the points of greatest declination in the apparent orbital motion which-after subtracting the motions of the Moon. This is the nodical cycle (page Earth's full rotational velocity-also is the least in right 193) which, once in each 18.&year period, brings the ascension when the Moon is on or near the celestial Moon to its maximum possible declination (--h 28.5 0) with equator. However, the maximum velocity of the Moon's respect to the celestial equator. real motion in orbit at times of perigee-syzygy varies be- It has been seen (pp. 132-135) that the greater is the tween successive anomalistic months, being greatest at value of the declination at the peaks, and troughs of the times of close perigee-syzygy alignments. With this larger declination curve, the larger is the motion in right ascen- velocity vector of direct motion, the length of the tidal sion at that time. Thus, the 18.6-year nodical cycle pro- 292 Strategic Role of Perigean Spring Tides, 1635-1976 vides another circumstance wherein, with the lunar Modification of the Lunar Period declination at its maximum possible value, and with the by the Lunar Apsides Cycle motion in right ascension correspondingly augmented, In considering the relevant factors which act to alter the tidal day is also lengthened in proportional amount. (f) As derived mathematically on pages 186-189 and the period of revolution of the Moon, reference can be illustrated in figs. 165a, b, the rate of tidal growth, which made to the equation cited in the foregoing section, ex- is a direct measure of the strength of the tidal forces act- pressing the effect of perturbations on the lunar orbital ing, must also..be corrected by a term cos' 6 to, include motion, namely: 2raC 3/2 the effects of the Moon's variation in declination. PC= k (Ma) + m C) 172 Althouvh P C in this equation represents the sidereal The Effect of the Lunar Apsides Cycle period of the Moon, it may easily be converted to the By abstracting, as has been done in table 18, a series of synodic period of revolution without introducing further values representing the changing individual lengths of the significant variables, as later shown. It is obvious from synodic months, an interesting relationship is revealed in- the above equation that, since all other factors are con- volving: (1) the perturbational effect of the Sun upon stants, the period varies only as a', the semimaj or axis of the major axis of the lunar orbit at the.times of perigee- the lunar orbit. It is also apparent from the auxiliary syzygy; (2) the increased gravitational attraction of the equation on page 173 that, since. the rate of change of a Sun on the Moon's orbit at perihelion; (3) the synodic varies directly with its own value and with V([ , the period of the Moon's revolution; and (4) the lunar ap- Moon's orbital velocity, the effect of the Sun's tangential sides cycle of 8.849 tropical years (3,232 mean solar force in altering a is increased the most at perigee-syzygy, days).c The latter cycle is the period of time required for whdn the Moon's angular velocity is the greatest. Also, one complete rotation of the lunar line of apsides through when a becomes larger, its rate of increase grows larger. 360' of longitude at its mean rate of 0.111404'/day, TABLE 18.-Variation in Length of the Synodic Month, Within subject to the perturbational action of the Sun. the 8.8491.Year Lunar Apsides qycle The relationship in question is basically one deriving from the previously mentioned annual equation (see p. Maximum length of 165), further augmented by the coincidence of perigee- Dates synodic month syzygy. When various maximum lengths of the synodic (days) months created by the alignment of perigee and syzygy are taken from table 17 and are retabulated over an ex- 1959 November-December ............................ 29.7965 tended interval of time, a definite periodicity in these .1960-61 December-January ........................... 29. 7785 1961 January-January ............................... 129.8201 values is-noted. The synodic months vary through succes- 1962 January-February .............................. 29.7924 sive maxima and minima approximately 4.4 years apart, 1963 March-April ................................... 29.7139 1964 May-June ..................................... 29.6528 returning to the same phase again in just less than 9 years. 1965 July-August ................................... ?, 29. 6477 1966 September-October ............................. 29.7174 This is the value adopted by the International Astronomical 1967 October-November ............................. 29. 7792 Union as part of the IAU System of Astronomical Constants. The 1969 December-January - - . . @@ ............... --_- 29.8055 mean motion of apogee and perigee (although not its irregularities) 1969-70 December-January. ........................ 29.8056 in a forward direction at approximately 3o/anomalistic month was 1970 January-February .............................. 129.8076 known to Hipparchus as early as the second century, B.C. Sir 1971 February-March ............................... 29.7861 Isaac Newton discusses the theory of the progression of the line of 1972 February-March ............................... 29. 7035 1973 May-June .. ................................ 29.6507 apsides in Book 1, Proposition 66, Theorem 26, Corollary VII of ... 229.6444 his Principia, but gives neither the mean motion nor period. In his 1974 August-September .............................. 1975 October-November ............................. 29.7236 monumental work, Manual 'of Tides, 1894-1907 (part 1, page 491), Rollin A. Harris tabulates the value of 3,232.591040 days. Other modern sources agree with the value of 8.849 tropical (in place of I Largest maximum. either Julian or Gregorian) years. The figure 9V2 years quoted 2 Smallest maximum. on page 356 of Forest Ray Moulton's classic work Celestial Me- chanics is obviously a misprint. More exactly, Poca'. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 293 The variable magnitude, of T, the tangential force of shown in fig. 42. This period also very closely matches the, Sun on the, lunar orbit, depends upon the distance the interval between the largest and smallest maxima of the Moon from the Sun, which is a function of its in the table. position in orbit, and the relative orientations of the ellip- Positioning the perigee-syzygy situation of 1961 Jan- tical orbits of the Earth and Moon with respect to the uary 16 (occurring within the longest synodic month in Sun. (All cases represented in this list involve the Moon this 17-year series) at (1) as shown in figure 42, the at a position of perigee-syzygy. Hence, no case of an perigee-syzygy of 1965 July 29 (occurring within the absolute solar perigee can be included, since the latter shortest synodic month) almost exactly occupies position situation requires the coincidence of apogee-syzygy with (2). As shown in this figure, the Moon in position (1) the Earth at perihelion.) is approximately 3 million miles nearer to the Sun than is It will be observed that the difference, in years, between position (2). This positioning alignment can be repeated the two largest maxima in table 18 agrees very closely for the extreme maximum value of the synodic month with the period of rotation of the line of apsides through accompanying the perigee-syzygy situation of 1970 Jan- 360' in 8.849 tropical years-the only full lunar cycle uary 8, and the smallest maximum value related to the of this magnitude. The rotation of the lunar apsides perigee-syzygy of 1974 August 17. through one-half of this cycle in 4.424 years pro- Both the positions ( 1 ) and (2) will experience a length- duces the two different alignments of the lunar orbit ening of the major axis (and hence the semimajor axis) MAXIMUM VARIATION OF LUNAR DISTANCE FROM THE SUN WITH EACH HALF - ROTATION OF THE LUNAR LINE OF APSIDES IN 4.424 YEARS (1) (2) P-S ALIGNMENT P-S ALIGNMENT OF 1961 JAN. 16 PERIHELION DISTANCE APHELION DISTANCE OF 1965 JULY 28 91.5 MILLION MILES 94.5 MILLION MILES E M - - - - - - - - - -*-4 - - - - - - - - - - - - - - - - - - - - - - -ME S PERIHELION HALF-ROTATION OF THE LUNAR LINE OF APSIDES APHELION RESULTS IN THE GREATEST POSSIBLE DIAGRAM IS NOT TO SCALE. RANGE BETWEEN THE LENGTHS THE ECCENTRICITIES OF THE SOLAR AND OF THE SYNODIC MONTHS. LUNAR ORBITS ALSO ARE EXAGGERATED. FIGURE 42.-(Discussed in text.) 294 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE OF USUAL HARMONIC w9w ff Iff ANGULAR BPERD ARGUIENT TU KM OF MW PER MEAN SOLAR HOUR ORIGIN NAME V. +u E- E- z M, P-P-1 121+2h-28 2&-2v 255 (555) [X. + 0,) 28+2,1-2. 2(,(-.) 28e. 984 104 2 N, larger elliptio 29 +2h -31 +P 2E -21 245 1665) 26+27)-S0+- 2(T -0) -(- ---) 28o, 439 729 5 Li ...Der . 29+2h- s-p + 180* 2&-N-(R) 266 (455) (M4-Nj 20+2il- a-@; 2(y-a)+(o-r.) @V. 528 478 8 2N 2@ order o W +2A -U +2p 2E - 2v 235 (765) 20+21-4.+2Z; 2(T - 2(- -r) 27*. 995 N4 8 z @r larger evectional 2t +4h -31 -p 2& - 2v 247 (455) 20+4,j-3a-Z; 2(y-0)--(a-2n)-ZZ 28*. 512 588 1 ;4 ).. -11 29 - .+V + 180* 2E - 2v 203 (655) 20 - a+.- 2(y-.)-(*-2vj)-Z 29*. 465 625 3 9 k variational 2C+4A-41 2t-N 237 (555) 20+4,)-4. 2(y-a)-2(.--j) 27. 96B 208 4 S. 0 pri.-ili-I [Sj x 2 Z6ro 273 (W) IS.] x 2 Ti larger .1liptir, 29- A +P 272 (656) 20- 1 +a. 2(y-j)-ii 29o. 968 933 a Ri ernii&r . 29+ A -P, +'w 274 (554) 28+ ) -Zj. 2(y-,I)+,, No. 041 066 7 K, deeliriational 21+2A -2v" 275 (555) 29+21q 2y 301. 082 137 a 0, prrampal declinational I + h -2, + 90* 2@ 145 (855) [M2- Xj e+ yl-2. Y-2a IV. 943 035 6 00 2" order 9 + h +2. - W -2k-v 186 (565) 6+,1+2a Y +2- 16'. 139 101 7 Q, larger ellipti. 9+ A-38+p + W 2E -v 135 (655) [N2-X,] 0+ 7)-4q+Z; y-2o-jo-Z) W. 898 No 9 M, -.1ler I+ A- :+Pl- 90* 14 -"Q-) IN ((SN) [N.-Ol 0+ Zj y-(.-a) le. 496 093 9 + h - v +(Q) 555) z J, ani.1ler ellipti. t + A + .-P - W -v 175 (465) 0+ 7)+ a- Z Y+@- 10. ON 443 3 ;4 2Q, 2@ order s t + A - 48 +2p + No 2E-v 125 (765) 0+ q--4.+2&i y-2-2(-Z) 12'. 854 286 2 A P, law evectional 9+3h-3#-p + 90P 2E-v 137 (465) 0+3,2-3.- F. y-2a-(C-2@)-& iso. 471 514 5 rij variational 1127 (555)] 0+3,)-4. y+2,1-4. P, pruiripal declinational 9 - A + 90P 163 (555) [S,-Kj 6-) Y-2@n W. WS 931 4 1E0 dwlinatiorW 14.- h 90P -v' 165 (555) IMI-011 0 +-19 Y 15*. 041 068 6 IMet-logical Oand and - bre-) t zfiro 1" Y-71 15*. 1[ (from 46 Power of parallax) '355 (555) RAQ x 3 (43o.476 156 3@ w M4 41 q--di-xial [IMJX4 57'. 968 208 4) oixth-dirimsd X6 86'. 952 212 7) -ghth-diarad xg (115P. 936 415 9) 04 8, 0 ter-di-I [8j X3 45*@ 84 quarb-drurnal X4 60P. 81 urth-drumid X6 8, ighth-diural X8 MS ou (MS)4 quarter-di-mi IMAJ 5e. 984 104 2) 2MS on Ih .--drjW 287 (555) [M4- Sj 27-. 968 2D8 4) 3MB [Ml- So 13P. 476 156 3) pa 2 MS6 sixth-diurnal IMI+80 87-. 968 208 4) MN - (MN)4 qu.+-Z-ruil [M.+Nj 67'. 423 833 7) 2MN, sixth-di-nid [Afl+Nj 73o. 887 SW 7) z (MK), ter-diurnal 365 (455) [M.+Kj [M,-Ol 02r 172 9) 346 (655) (M,-Kl CM, + 0.] 42.927 130 8) '(2ME), ter-diricial offff). berri-diumal IS4- MJ 31o. 015 896 8) 38M diurnal [S-MA 16.. 015 896 8) so, diurnal iss (6w) IS2-011 le. 066 964 4) ter-diumal IIY.+Ej 45@ 041 088 6) .94 All fortnightly 28 -2E 075 (5N) -0] 2a, Io. 098 033 1 0 ([(D fortnightly synodio variational 073 (Na) [8,-Mj 016 Sm 8) M- q --thly -P Zbro 065 (455) [Af.- NJ 0*. 5" 374 7 Sw 0 semni,annual 057 (6W) [S.] x 2 OP. 082 137 3) so 0 meteorological annual (monarion Zfir. 056 11 OP. 041 068 6 ASTRONOMIC ELEMENTS FOR THE ARGUMENT SPEED OF CHANGE PER MEAN HOUR PER MEAN DAY Yangular P"d of Earth's wtadan. 13* 041 068 6, i hour angle of in,= (D (ineara tinii@ Y-n- 15* ,-e+A-.-L. . . ............................................ ....... ................. 360P - 10 190 749 39 hmean longitude of mov.-t of 0* 041 068 6 0* 985 647 34 &reetra longitude of J@. arasawa movement of OD 549 016 5 is* 176 396 73 P do do of Perigee i; do do of perigee it. - 0' 004 641 8 0* 111 404 08 P@ do do ' of petigee do do of parigai 0. 0* 000 002 0 0* 000 047 07 -N' = N do do of aeorading node 1I. ............................... .......................... ......................... 0* 062 953 02 E do do of intersection (reckoned on the orbit). vright aw-ensior, ofuitereertion. I inolination. of 41 orbit an Equator. L 1-1 longitude West of Gzeana@ih. FIGURE 43.-This table is reduced from a much larger chart appearing as a foldout in Tide Predicting Machines, Special reference source on the development of analytic constituents pertaining to the harmonic analysis of the tides. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 295 COMPONENTS OF, THE TIDE COMPONENTS AS GIVEN BY THE MACHINES MRA VALUE OF C(EFFICIENT 0 T@ OM. pa U. & Md. U@@ 1@ M.M. Ti M"hi. Xhi- P.di@ Pndtto, Pd J..h Xb6 P@Udw TWg AM-tk. Jp- P-twd 1.dtu N. I 0.4543 M, 12h42M M@ M2 M2 M@ M. M, M. N2 M2 M2 M2 Af2 M2 M. 0.0871 X, 12 65835 N2 N2 N, AV2 2 N, N, N@ N@ N. N@ N, N2 N2 N, 0.0128 L2 12 19162 L2 L, 4 4 4 4 44 4 L, L2 L2 4 0.0117 2N 12 8783 2N 2N 2N 2N@ 0.012310.0171 12 62601 V2 1, V2 V2 V. V2 V, V2 0.003310.DD74 )q 12 22177 )2 (-@pp-) )62 712 0.0074&0.0109 1A, 12 87186 9@ 92 Ih IL, 11@ Ih 11, IL2 IL2 @L2 0.2120 S@ 12 ho- S' S@ 8@ S@ @2 S2 82 S2 $1 82 S@ 82 8@ 0.0124 T@ 12 01"S T. 71 T, T2 0.0018 R, 11 98359 '% 0.05751 0-0393 K, 11 94724 K2 El K2 K. K@ K@ K@ KI K@ A, K@ K. K2 K, K, 010182 U, Us 0.1886 012ZA81935 0, 01 0, 0, 0'. 01 01 0. 0 0, 0 01 0, 0, 0.0081 00 2230 00 0.0365 Q, 26 8W6 Q. Q, Q. Q. Q, Q. Q, Q, Q. Q Q, Q Q. Q@ Q, 0.0149 M, 24 84120 M, M, 0.0149 J, 23 09947 J, J, J, 0.0049 20 28 006 2Q 0.0051 A 0.0071 p20 723 P, 0.0878 P, 24 OW89 P, P, P, P. p P, P" P, P'. P, P, P, P, P, 0.26541 0.1812 K, 23 93447 K, K, X. K, K, K, K, K, K, H, K, K, K, K, K, 0.0842 ..................... S. 24 h- S. S. S. 8, S, S, S. S, 0.0086 M, M, M. 02103 M. M. M4 Af4 M4 M4 M41 M4 -W4 M4 M4 H. M@ M4 M. 4 1402 M, M, M, M6 M, M, M. M. M, 3 1052 M. M. S, 8 h.- 8.1 6 h@ S. 84 S. S. 86 4 ho= 86 pait. I-& Ms. 6hI038 M84 MS. M 84 ms, MS4 MS4 ms, MS. ms, MS4 Ms. Ms. M84 M84 2MS 12 8718 ams 2MS, 2M8, AIN 6 2693 MN MN MN MN4 MN4 2NN. 2MN, MK, 8 1772 MK MR MK ME, 2MR, 8 SW 2MK 2ME 2MR 2AfK, 2SM@ 11 6070 2SM 2SM 2SM 2SM 2SN 2SM. 38M 38M so, 22 4w 80, 0.01713 MI1 17 Mt Aft Sj I:j.7 0.( 765 MS/ mst 0.0414: M7 M. M. .: @12 0.0361 sw S8a S_ Sw S. S. .................... Sa 365 242 Sa So S. S. Sa SO S. TOTAL NUMBER 10 20 21 15 16 1. 1'33'@i.'. 37, @2 26 OF COMPONENTS 7 + 3 dp- DATE OF 11872-1873 1 1879 1 -'1' 1"1 1 0.1 - 18- 1-.-111101 INO 1914 11915-191011'918_.l 1924 1924 1924-25 CONSTRUCTION 1991 920 1@ 7 .1 A- 1@b-d W @ Ar, * 8 Zd@ p- F@ AC& V@ I. SERVICE K@W_F. I 5- Sl@@ki A@ @M ,t;= - . = '. @q "-- _p@ P= .1 P-L ISM 19M & p @_ 4 =4't = xat p@@ B@ 191 'U C@ :@y Fa "ISO% N- X..@ W@ B=A-- dka-*w Ai. d. J. C@ @ dw 8-* U.&C- AL= I I j._ @jt 8"A A., = X. @ G.,-W ;:. - -9' @ SITUATION RK Al Publication No. 13, Inteynational Hydrographic Bureau, July 1926. It is of considerable significance as an historical 296 Strategic Role of Perigean String Tides, 1635-1976 of the lunar orbit as the Moon reaches perigee-syzygy. produce a delay in the response of the ocean waters However, because of the smaller distance and greater to the augmented force factors created respectively by: gravitational attraction of the Sun at ( 1 ), the increase (1) the direct alignment of Moon and Sun at conjunc- in a will be greater at (1) than at (2). This increase in a tion and opposition; and (2) the larger parallax and produces a corresponding increase in the value of P1, or closer distance of the Moon to the Earth at the time of M.Jd, the length of the sidereal month, from which the perigee. length of the synodic month may be obtained usingy the Because both of these effects are of dynamic origin, equation: they may be described most expediently by resorting to an analytic procedure employing the appropriate har- Mod Moyn Yold monic constants of the tides. The rigorous methods of where application of these constants are fully explained in Man- M,=the length of the'synodic month ual of Harmonic Analysis and Prediction of Tides (Wash- M,i,= the length of the sidereal month ingLon, D.C., U.S. Government Printing Office, rev. Y,,@,=the length of the sidereal year ( 1940) ed. ( 194 1 ) and the British Admiralty Manual of Tides (His Majesty's Stationery Office, London, 1941) ptl- and Other Time-Related Factors Susce * will not be repeated here, except for a brief r6sum6 ble to Analysis by the Methods of of the basic tidal constituents involved. (See fig. 43.) Harmonic Analysis Evaluation of the Principal Harmonic Constituents As an addendum to the main topic of this chapter, According to the methodology of harmonic analysis, and a necessary forerunner to certain discussions in chap- the composite of lunar and solar forces interacting to ter 8, several additional factors relating to the variable produce the tides and the resulting rise and fall of the of time as it affects the tides must be mentioned. These factors-rather than prolong the overall period of maxi- tidal waters are dealt with as a system of interrelated .mum force application as in the preceding examples- harmonic constituents, susceptible to integrated mathe- most commonly delay the exact time of occurrence of matical solution. The actual tides are treated as if they the observed effects of the tide-raising forces. (Although were made up of a series of idealized, mathematically possible worldwide, only a few cases of marked accelera- expressible component tides. The end products of this tion of tide arrival times occur in North American wa- analysis are tide height and arrival time. ters.) The result is that both the high and low waters In the computational process, the tidal amplitudes and may occur at a time considerably after those- at which arrival times are represented by a series of cyclical expres- the Moon crosses the local meridian, or reaches either sions containing both variable terms and constant coeffi- its perigee or syzygy positions. cients which allow for a discrete application of the solu- One cause of delay in the arriv 'al of high water following tions to individual tidal stations. It must be pointed out the meridian passage of the Moon is the inertial response' that these so-called constants also vary over the years, as of the vast mass of tidal waters set in motion. This response the result of both astronomical and hydrographic factors. is, in turn, locally affected by the combined hydrodynamic, In the latter case, repeated series of observations at local hydraulic, and hydrographic characteristics (including the stations, obtained and evaluated over successive 19-year free period of oscillation and dynamic resonance) of the Metonic cycles, make it possible to apply empirical ad- particular ocean basin or portions thereof in which the justments and corrections. waters are situated. Other modifications in the arrival The two most important of these constants are those times of the tidal maxima and minima are a function which represent the tidal forces reaching a maximum twice of physical, oceanographic, geographic, and astronorni- in each lunar and solar day. They are a direct function of cal parameters. the rotation of the Earth and the changing motions, Two such influences exist which are directly related gravitational attractions, and phase interrelationships of to the astronomical configurations responsible for the pro- the Moon and Sun during the different periods in which duction of perigean spring tides and, therefore, are caus- these two bodies pass successively through upper and ally connected with the exact time of their occurrence. lower meridian transit. The corresponding lunar and solar These are the phase age and parallax age. Singly, they components contributing their effects to tidal amplitudes Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 297 are designated (in units of feet or meters) byM2andS2, inequality later to be discussed) designated symboli- and are known as the principal semidiurnal lunar and cally as M;-when divided by two and converted from principal semidiurnal solar constituents, respectively. degrees of arc to hours of time-roughly approximates this A very interesting relationship exists between these two lunitidal delay factor. numerical constants and the phase interrelationships of However,, empirical data based upon repeated tide the Moon and Sun at syzygy and at quadrature, from observations provide far more accurate results. Many years which, with a knowledge of the established tidal range at of measurements at a given tide station serve to establish any station, both constants can be approximately evalu- the so-called mean high-water lunitidal interval, which is ated. If the mean spring range and mean neap, range are the average value of the difference in time between the determined at any tide station over a minimum 19-year meridian transit of the true Moon (all phases) and the Metonic cycle, these constants are directly calculable. next succeeding high tide. An actual example will illustrate For example, such continuous series of measurements the primary tide-raising influence of the Moon. reveal that at Sandy Hook (New York Harbor), N.J., the Since the period of P of M ;is 12.42060', and the mean mean range of high water springs (the average of many high-water lunitidal interval (HWI) at Sandy Hook, N.J., years of observation of spring tide levels) is R = 5.6 feet. as computed from many years of observations is 7'38-, Similarly, the value for the mean range of high water converting these two values into arc measurement, the neap tides (those produced successively at lunar quadra- value of M, may be computed approximately from the tures) is RN = 3.7 feet. relationship: Mo 360OXHWIO -360OX0.5090= Since the first value is the result of the vector sum of 2- PO 0.8280@ 2210 the forces of the Moon and Sun aligned at either new or A more accurate empirically derived value of M, for full moon and the second resul 'ts from the gravitational this location is 2220. force of the Sun counteracting (at right angles) that of By direct analogy, the principal semidiurnal solar con- the Moon, their combined forces (neglecting all other tide-altering functions) may be expressed algebraically as stituent of the tide is expressed by the termsS2, referring to its amplitude, and S,, its epoch. 2 (M2+S2)=Rs whence 2 (M@ - S@,) = j?,., The Phase Age and Parallax Age 2 M,+2S,=.k, The production of ordinary spring tides is dependent, 2 M,-2S2= 1?, upon the combined gravitational attraction of the Moon' 4M2=Rs+RN and Sun as both bodies are aligned at either new moon from which, inserting the values for 7?,, and kN, the value or full moon. Hence, with the occurrence of syzygy, the Of M2 can be determined and, by substitution of this value delay in time between meridian passage of the Moon and in either of the original equations, S2also may be obtained. arrival of the correspondingly amplified high tide is Since these values are here, computed independently of known as the age of the phase inequality. It is represented any other harmonic constituents, they are Only approxi-, at any location approximately by the difference between mate, but sufficiently representative to reveal much con- the respective epochs of the principal semidiurnal solar cerning the nature of the local tides. and lunar constants for that location. More exactly, ex- Despite the frequent previous references to high tides pressing the age of the phase inequality by 0: associated with a meridian transit of the Moon, one very (in hours) = 0.984 (S,- M;) (in degrees) important tidal characteristic easily observed at any sta- tion is the almost universal difference between the time That is, the greater is the influence of the Sun on the local a meridian transit of the Moon occurs and the actual tidal waters, tending to detract from the principal effect arrival of high water. of the Moon, the greater is the value of 0. Since the Moon is the predominant tide-raising body, it is important to mention at this point that this par- two additional constants can be used to indicate the theo- ticular syzygy influence of the Sun should not be con- retical interval in time or angle following the meridian fused with another solar gravitational influence occurring transit of the Moon at which the next followinff hivh water at any position in the lunar orbit in connection with the occurs. The tidal constituent known as the epoch or phase phenomena of tidal priming and lagging. Both of these lag of M (not to be confused with the age of the phase phenomena are discussed in chapter 8. 298 Strategic Role of Perigean Spring 'tides, 1635-1976 In the same manner, the augmentation in'the range of The ordinary spring tide, produced at time of new the tides produced by the passage of the Moon through moon or full moon (i.e., syzygy) alone, can add approxi- perigee does not occur exactly at the time of lunar transit mately 20% to the range of the tides above the mean across the local meridian of a place. A similar lag known spring range. as the age of parallax inequality is involved. This delay The passage of the Moorf-through perigee (creating factor may likewise be computed from the harmonic con- perigean tides) can also, by itself, increase the range of stants for any location. the tides by approximately 20% above the mean spring Two appropriate lunar constants dependent upon the range. anomalistic period in which the Moon revolves from peri- In the combination of these two phenomena at times of gee to perigee are indicated by N, and N2', and are perigee-syzygy, the daily range of the tides is increased termed the larger lunar-elliptic semidiurnal constituents. nearly as the sum of the two, or 40% above the mean Because the parallax effect resulting from the Moon's pas- spring range. However, a considerable number of other sage through perigee (represented in phase relation by factors, to be discussed in chapters 7 and 8, can alter this N,O) is superimposed upon the principal semidiurnal value, and it should be regarded only as a representative lunar effect (represented correspondingly by M2' ), their figure. approximate resultant may be obtained by subtracting Before entering into the discussions of chapter 8 it the one from the other. Representing by x the parallax is logical in the present connection to indicate that two age, or interval between meridian passage of perigee and other constants, diurnal in nature, are used to define the production of an augmented high tide near the time the declinational effects of the Moon on the tides (includ- of perigee: ing the diurnal inequality) - These are designated as K, x (in hours) = 1.83 7 (M 2' - N 2' ) (in degrees) and O:L (representing the lunisolar declinational and prin- Since it is possible for N2' to exceed M' (e.g., in parts cipal declinational constituents, respectively),. The pro- of the Gulf of Mexico), occasionally the 2result is nega- duction of the maximum range in the tides resulting from tive, and the perigean tides precede the meridian passage the effects of diurnal inequality undergoes a similar delay of the Moon. following the local transit of the Moon whirch is known As examples of the preceding two phenomena, the as the age of. the diurnal inequality and, if symbolized by phase age at Sandy Hook, N.J., is 0.984 (S20 -MO) is expressed in the relationship: 2 0.984 (244'-222- - +22', and the parallax age is 1.837 A (in hours) = 0.911 (K 01- 0',) (in degrees) (M2'.- N-2 ) @ 1.837 (2220-2040) = +33'. In the Significantly, in conjunction with the harmonic constant case of a meridian passage of (1) a new or full moon, M representing the principal lunar semidiumal constit- or (2) the position of perigee, these are the theoretical uent of the tides, these two constants also may be used intervals of time after which one would expect to find to isolate and identify the particular type of tide common the,arrival of augmented high tides associated with syzygy to any one oceanographic province. or perigee, respectively. As shown in figure 6 of the appendix, tides in which When the two phenomena, syzygy and perigee, occur the diurnal components (represented principally by the together, the delay in the resulting tides of increased range tide-raising influence of the Sun) predominate are de- following the time of lunar transit is noncumulative but scribed as diurnal tides. Those in which the influence of agrees approximately with the average of these two effects. the semidiumal constituent due to the Sun (S2) and semi- diurnal constituent due to the Moon (M,) are approxi- Variation in Tidal Range, and in mately equally felt are described as mixed tides. Finally, the Types of Tides those in which the semidiumal constituent of the Moon (M2) predominates are termed semidiurnal tides. An indication of the relative heights of the waterlevels A quantitative method of classifying local tides into produced at times of perigee-syzygy is given by the fol- one of these three t es available from the relationships . yp is ]owing rule-of-thumb analysis: given in table 19. Conditions Extending Duration of Augmented Tide-Raising Forces at Perigee-Syzygy 299 TABLE 19.-Types of Tides (With Index and Range) at Various Locations Along the Atlantic, Pacific, and Gu@f Coasts of North America Semidiurnal Tides: K'+O'>0.0<0.25 M2+S2 @ Value of harmonic constants Index: Spring Location of station H (ft) K ran - 1+01 (ftle K, 0, M2 S2 Argentia, Newfoundland 0.289 0.324 2.281 0.675 0.207 6.3 Quebec, Quebec, 0.740 0.690 5.850 1.380 0. 198 15.5 Halifax, Nova Scotia 0.340 0. 153 2.046 0.454 0. 197 5.3 St. John, New Brunswick 0.504 0.374 9.943 1.629 0.076 23.7 Eastport, Me. 0.476 0.376 8.468 1.413 0.086 20.7 Portland, Me. 0.459 0.367 4.356 0.702 0. 163 10.4 Boston, Mass. 0.465 0.380 4.422 0.717 0. 164 li.0 Newport, R.I. (Narragansett Bay) 0.212 0.164 1.690 0.396 0. 180 4.4 Bridgeport, Conn. 0.295 0.212 3. 185 0.538 0. 136 7.7 Willets Point, N.Y. 0.319 0.237 3.619 0.616 0. 131 8.3 New York (The Battery), N.Y. 0.328 0. 177 2. 138 0.431 0. 197 5.4 Sandy Hook, N.J. 0.318 0. 164 2. 154 0.447 0. 185 5.6 Philadelphia, Pa. 0.333 0.244 2.602 0.298 0. 199 6.2 Wilmington, N.C. 0.250 0.202 1.978 0.250 0.203 4.5 Charleston, S.C. 0.335 0.252 2.445 0.411 0.206 6.1 Savannah, Ga. 0.364 0.278 3.497 0.542 0. 159 8.6 Mayport, Fla. 0.269 0. 193 2.143 0.359 0. 185 5.3 Miami Beach, Fla. 0.136 0.105 1.203 0.237 0. 167 3.0 Diurnal range Anchorage, Cook Inlet, Alaska 2.240 1.251 11.471 3.250 0.237 29.0 300 Strategic Role of Perigean Spring Tides, 1635-1976 ' TABLE 19.-Types of Tides (With Index and R ange) at Various Locations Along the Atlantic, Pacific, and Gulf Coasts of North A merica- Continued Mixed Tides K,+O, >0.25<1.5 Mainly Semidiurnal: M2+S2 - Value of harmonic constants Index: Spring Location of station H (ft) K1+01 ran K, 0, M2 S2 M2+S2 (ft@e St. john's, Newfoundland 0.262 0.213 1.178 0.486 0.285 3.5 Harrington Harbour, Quebec 0.478 0.474 1. 742 0.576 0.411 4.9 Pictou, Nova Scotia 0.667 0.648 1.373 0.354 0.761 3.9 New London Conn. 0.238 0. 166 1.166 0.228 0.290 3.1 Breakwater Harbor, Del. 0.342 0.282 1.916 0.344 0.276 4.9 Baltimore, Md. 0.207 0.204 0.486 0.082 0.724 1.3 Key West, Fla. 0.290 0.290 0.565 0. 172 0.787 1.6 Diurnal range San Diego, Calif. 1.096 0.693 1.788 0.724 0.712 5.7 Los Angeles, Calif. (Outer Harbor) 1.112 0.704 1.695 0.665 0.769 5.4 San Francisco, Calif. (Golden Gate) 1. 195 0.748 1.796 0.406 0.882 5.7 Astoria, Oreg. (Tongue Point) 1.257 0.739 3.012 0.676 0.541 8.2 Aberdeen, Wash. 1.364 0.800 3.425 0.873 0.503 10.1 Seattle, Wash. 2.734 1.503 3.530 0.839 0.970 11.3 Valdez, Prince William Sound, Alaska 1.601 0.986 4.521 1.533 0.427 12.0 Nome, Alaska 0.317 0.208 0.366 0.038 1.300 1.6 Mixed Tides Ki+01 >1.5<3.0 Main@y Diarnal: ff2+S2 Value of harmonic constants Index: Spring Location of station H (ft) K1+01 range (ft) K, 0, M2 S2 M2+S2 South Boca Grande, Fla. 0.410 0.370 0.371 0.126 1.369 1. 7 St. Petersburg, Fla. 0.513 0.477 0.497 0. 159 1.509 2.3 Galveston, Texas (Galveston Channel) 0.384 0.364 0.309 0.098 1.838 1.4 Victoria, British Columbia 2.056 1.214 1.223 0.336 2.097 6.1 Dutch Harbor, Amaknak Island, Alaska 1.088 0.729 0.852 0.091 1.927 3. 7 Diurnal Tides: K@+01 > 3.3 to - M2+S2 Value of harmonic constants Index: Diurnal Location of station H (ft) ran K1+01 ft K, 01 - M2 S2 M2+S2 Pensacola, Fla. 0.401 0.384 0.062 0.021 9.458 1.3 Mobile, Ala. (Mobile River) 0.466 0.458 0.034 0.036 10.267 1.5 Biloxi, Miss. (Biloxi Bay) 0.568 0.514 0.112 0.091 5.330 1.8 St. Michael, Alaska 1.378 0.758 0.586 0.111 3.065 3.9 Sweeper Cove, Adak Island, Alaska 1.342 0.941 0.623 0.074 3.275 3. 7 Chapter 7 The Classification,, Designation, and. Periodicity of Peri- gean Spring lides, With Outstanding Examples of Accompanying Tidal Flooding From Recent History It has,been emphasized frequently in preceding chap- cases of tidal flooding; (5) the development of a basic ters that the coincidence of perigee-syzygy with certain intensity scale for rating the probable magnitude of the lunisolar positional relationships produces the high- tidal flooding event likely to accompany a given combi- est known astronomical tides. The resulting, proxigean nation of astronomical and meteorological circumstances; and perigean spring tides-when associated with strong, (6) the derivation of a suitable numerical coefficient as persistent, onshore winds-have been responsible for a a quantitative indicator to assist in evaluating the astro- large number of instances of major tidal flooding expe- nomical potential for tidal flooding subject to a given rienced over long periods of history (see table 1). At the set of perigee-syzygy conditions; (7) a survey of the sig- same time, among the examples of table 3, there is empir- nificance of rate of tide growth i -n producing especially ical evidence to show that the ordinary spring tide, when intense coastal flooding situations, and of variable wind- accompanied by sufficiently strong onshore winds, is also coupling conditions in driving the astronomically raised capable of causing coastal flooding conditions-although perigean spring tides onshore; (8) the determination of a these are, for the most part, of far smaller magnitude. schedule of combined astronornical-meteorological condi- It is imperative, therefore, that an evaluation be made tions which make the coastline particularly vulnerable of the particular characteristics which set each close to tidal attack; (9) an analysis of the relationships be- perigee-syzygy alignment apart from other tide-augment- tween perigean spring tides and other oceanographic phe- ing circumstances as one especially susceptible to the nomena-such as the high water lunitidal interval, in- production of major tidal flooding, when supported by ternal waves, turbidity currents, and.the marked increase the appropriate meteorological conditions. This analysis in the velocity of tidal currents; and (10) a consideration mustalso include other force-modifying factors involving of possible correlations between the astronomical occur- the combination of the gravitational forces of the Moon rence of perigee-syzygy and various other geophysical, and Sun-the most important of which are the respective selenophysical, and biological phenomena. phenomena of priming and lagging. These factors will be discussed, in the above order, in From an initial comparison of spring and perigean this and the following chapter. A suitable system of classi- spring tides, involving the differences imposed by these fication for the various types of tides mentioned in (1) latter two factors, a logical follow-on entails: (I ) the above must first be developed. establishment of a uniform system of classification for Comparison of Ordinary Spring Tides and ordinary spring tides, pseudo-perigean spring tides, peri- Perigean Spring Tides gean spring tides, proxigean spring tides, and extreme Reduced to the simplest terms, spring tides are caused proxigean spring tides, based upon the purely astronom- by the reinforcing action of the gravitational force of the ical parameters which go into their production; (2) an Sun with that of the Moon caused by the alignment of investigation of various periodicities which govern the these two bodies in celestial longitude (or, alternatively, recurrence of exceptionally close perigee-syzygy align- right ascension) at times of new moon (conjunction) or" ments; (3) the representation of a considerable number full moon (opposition). Accordingly, such tides occur of specific examples of tidal flooding associated with the without fail on the two occasions of syzygy in each synodic foregoing different classifications of tides; (4) the pro- month. At these times, the daily range of the tides is in- vision of significant comparative data of astronomical, creased by approximately 20 percent above the average. oceanographic, and meteorological nature relative to these The effect of lunar variation (see p. 175) is to add 28" 301 302 Strategic Role of Perigean Spring Tides, 1635-1976 to the lunar parallax at either new moon or full moon, is one separated in time as far as possible from perigee regardless of the angular distance from perigee; how- and thus lacking in the increased orbital velocity and ever, some additional component is also added to the necessary catch-up effects imposed thereby. From this parallax by the lunar evection term, depending upon the cause alone, therefore, the ordinary spring tide is not ac- Moon's anornalistic angle. companied by an increased tidal day. On the other hand, Certain other astronomically related factors may oc- the astronomical alignment producing spring tides is cur to cause considerable variations in the relative tide- influenced. by the effect of lunar variation (see p. 165) raising forces associated with spring tides. These include: Which tends to increase the orbital velocity of the Moon at (I) the diurnal inequality, resulting from a large declina- syzygy (and thereby lengthen the tidal day) and, as a tion of the Moon; (2) a coincidence of either position of function o .f lunar phase angle, the effects of priming and syzygy with (a) the summer or winter solstice, (b) the lagging which act respectively to shorten or lengthen the vernal or autumnal equinox, (c) other times at which the tidal . day. Moon and Sun reach the same declination, or (d) the time at which the Earth reaches its closest annual approach to Concepts of Tidal Priming and Lagging the Sun (perihelion) ; and (3) a large zenith distance of Although the,mass of the Sun is 27,070,000 timesthat the Moon. Since, however, these same fa 'ctors may also act to modify perigean spring tides, none of these variable of the Moon, the average distance of the, Sun from the influences may be considered as distinguishing ordinary Earth is 389 times that of the Moon. The comparative spring tides from the former type. tide-raising forces of the Sun and Moon are directly As in the case of all higher-than-usual tides, ordinary proportional to the relative masses of the Sun and Moon spring tides are subject to the action of sustained onshore and inversely proportional to the cube of their respective winds in lifting the greater water levels produced onto the distances from the Earth. The effective tide-raising force land. Although spring tides usually possess a much smaller of the Moon is, therefore, 11/7ths that of the Sun, or the flooding potential compared with tides of the perige .an tide-raising force of the Sun is only %iths that of the spring type, it must be recognized that they, too, have Moon. In all tidal actions, the Earth's tidal waters accord- played .a definite, although considerably less prominent ingly more closely follow the position, angular motion, and consistent role in major tidal flooding over the course and relative distance of the Moon, but are modified by the of history. Despite the emphasis given in the present corresponding solar factors. volume to perigean spring tides as a heavily documented Lunar Phase Effects- contribi-iting cause to coastal flooding as well as the special Qualitative Evaluation object of study, there is no intent to detract from the Sig- In terms of the elongation, or changing angular distance nificance of the ordinary spring tide as an additional between Sun and Moon in the sky consequent upon the source of such flooding, given the necessary supporting lunar phases, this same tide-raising principle applies. The conditions of very intense, sustained onshore winds. major axis of the Earth's hypothetical tidal force envelope However, in objecti 'vely evaluating the flooding poten- is always directed toward a position which is the resultant tial of ordinary spring tides compared with that'of peri- of the gravitational force influences of both the Moon and gean spring tides, certain definite astronomical factors the Sun. Except at-times-of conjunction (new moon) and exist which favor the latter for the production of severe opposition (full moon), when the directions of the Sun coastal flooding when appropriate wind conditions pre- and Moon come into coincidence in longitude (or right vail. These astronomical differences between ordinary spring tides and perigean spring tides will now be ascension) the orientation of the resultant force vector in the direction of the combined gr @ i ational attraction considered. avit It has been repeatedly pointed out in previous chapters of the Moon and Sun always lies between these two that one of the factors increasing the potential for tidal bodies as seen from the Earth, but closer to the longitude of the Moon by a factor proportional to its greater tide- flooding in the case of perigean spring tides is a greater raising influence. length of time during which the enhanced gravitational forces of Sun and Moon can act, associated with a loriger Priming and Lagging as Shown tidal day. As has been shown, the principal lengthening of in Tide Curves the tidal day is due to the increased velocity of the Moon The repeating maxima and minima in the two com- at lunar perigee. By definition, a true ordinary spring tide posite sets of tide curves (figs. 44a-44b) showing the Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 303 variations in the length of the true tidal day may readily angle of separation (the elongation) between them is be explained by an analysis of the changing phase rela- re'duced. The gravitational influence of the Sun is added tionships of the Moon with respect to the Sun. increasingly to that of the Moo'n and in a direction more As the result of the annual orbital motion of the Earth nearly corresponding to that of the Moon as the two around the Sun, the Sun appears to move around the bodies. come 'into closer alignment. From last-quarter celestial sphere at the same, speed as the Earth and in the phase to new moon, therefore, the tidal day is continually same counterclockwise direction as viewed from the north shortened and reaches a minimum at new moon. Exactly pole of the ecliptic. As seen on the va .ult of the sky, this the same situation prevails between first-quarter phase apparent movement of the Sun duplicates the 360' of and full moon, since the tidal force action is exerted along the Earth's revolution in 365.25 days, at an average speed the line of syzygies. This phenomenon (called lunar of slightly less than 1' per day. The apparent motion of Ccpriming") accounts for the successive minima in the the Sun is also in the same direction as the actual motion length of the tidal day shown idfigs. 44a-44b. of the Moon in its orbit around the Earth. Whereas the Sun's apparent motion is approximately V/day, the 2. Tidal Lagging Moon's orbital motion ranges from about , 11.78' to 15.37'/day, and the Moon therefore achieves -two succes- The greater relative speed of the Moon in its orbit sive alignments with the Sun from one syzygy position compared with the apparent daily motion of the Sun (new moon) to the next (full moon) in about 14-15 days. likewise explains the opposite phenomenon which in- At last-quarter phase, the Moon is 90' to the west creases the length of tidal day following the syzygies and of the Sun in celestial longitude but, in its eastward between new moon and first-quarter and full moon and motion in orbit, the Moon reduces this angular separa- last-quarter phases, respectively. Since the Moon is tion at a rate of some 14'/day. Between last-quarter traveling faster than the Sun at each instant, the latter phase and new moon, the configuration of Earth, Moon, is effectively falling behind the position of the Moon. and Sun is such that the Sun lies ahead of the Moon (at The major axis of the Earth's tidal force envelope which, a greater right ascension or longitude) and the Moon as previously explained, follows the Moon's position far is overtaking the Sun. Because the Sun leads the Moon more closely, is in this case continually displaced away in the sky, the position of maximum amplitude of the from the Sun. This displacement now is in the same di- Earth's tidal force envelope resulting from the combined rection as that of the Moon's revolution, and that in gravitational attractions of the Sun and Moon is dis- which the Earth is rotating on its axis. A catch-up time placed to a position in advance of a line joining Earth is required in the Earth's rotation. Thus, following the and Moon b Iy a considerable but rapidly lessening minima occurring at new moon and full moon, the tidal amount. day is progressively lengthened between the new moon Each day, the Moon further closes the angular dis- and first quarter and full moon and last quarter, re- tance in elongation separating itself from the Sun, and spectively. This relationship is clearly indicated in the the major axis of the tidal force envelope in turn swings curves showing changing lengths of the tidal day in figs. continuously. into closer alignment with the Moon (i.e., 44a-44@b. The shortening process thereafter resumes, as in a direction opposite to the orbital motion of the Moon noted under section 1, above. and the rotational motion of the Earth). 'The period required for any position on the rotating It is important to observe that the lengthening of the Earth to align itself twice with the major axis of the tidal tidal day produced by the phenomenon of tidal lagging force envelope represents the length of the tidal day. occurs prior to neap tides, when the tide-raising forces Since, with the major axis of the tidal force envelope of Moon and Sun are directly opposed and minimized. moving in a direction opposite to the Earth's rotation, it The extension of the tidal day resulting from this cause takes. any point on the Earth's surface somewhat less does not, therefore, provide a meaningful contribution time to reach alignment with this force-axis, the tidal day in augmenting the daily range of the tides as in the case is shortened proportionately. of: (1) decreased lunar distance of the Moon from the 1. Tidal Priming Earth at perigee-syzygy; (2) an extreme proximity of the Moon to the Earth at lunar proxigee; or (3) the in- It has been shown that, following last-quarter phase creased motion of th-c Moon in right ascension when it and with the Moon rapidly catching up on the Sun, the is at higher declinations. 304 Strategic Role of Perigean Spring Tides, 1635-1976 F-68 (a) VARIATION IN DECLINATION OF MOON AND SUN-1939 -2U 4k Z-10F 0 Z, 0o .................... .............. ............... ....... ................... ............ .................... .......... .............. 75 -1 0c -20' 0 0 0 Y 0 A 0 9 A 0 Y *A A A 80 ASTORIA, OREGON C*4 1939 W 8 70 C/) W D z 6 2 0 z 50 LL 0 40 ----- -- ----- z W 6 Z z LU 30 2 i LU Cr L) Z 201 JAN FEB MAR APR MAY JUN 1 7 14 21 .28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 FIGuRE 44a.-Variation in the length of the tidal day during 1939 January-June, shown as a function' of the increment to be added to the time of the previous day's higher high water to establish the time of occurrence of HHW on the current day. The graph for an entire year is presented in figures 44a and 44b. A detailed analysis of these variations is con- tained in the main text. r, Classification, Desigmation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 305 F-68 (b) VARIATION IN DECLINATION OF MOON AND SUN-1939 -20' '-%j Z.J& 0 z 0 ........... . .................. . ....................A ........ ................. ................... 141................... ................ .............. ................... .................. U IIt ItI LU %%61 1 -20P 11 Y OA OY Y 0 A* Y 0 A 0 Y OA A yo A 80 ASTORIA, OREGON 1939 Uj 70 U) LU z 60 E Z 50 LL 0 --- --- ------ 0 40 z LLI 18 15 12 Z z uJ 30 LLJ Cr U Z 20 JUL AUG SEP OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FIGuRE 44b.-A graph containing data of the same nature as figure 44a, plotted for 1939 July-December. The technical in- terpretation of the changing maxima and minima of these curves is given in the text. 202-509 0 - 78 - 22 118 8 306 Strategic Role of Perigean Spring Tides, 1635-1976 QUANTITATIVE ANALYSIS OF THE EFFECTS Relative Tide-Raising Forces at Quadratures and Syzygies OF TIDAL PRIMING AND LAGGING The instantaneous magnitude of the combined lunisolar force during each lunation is primarily a function of the As in previous cases, the use of an actual example will phase angle of the Moon with respect to the Sun-varying serve to illustrate the various quantitative relationships in- from a minimum at quadratures (when the Moon's gravi- volved between neap tides, ordinary spring tides, and per- tational force on the Earth is imposed at right angles to igean spring tides, as well as the modifications introduced by that of the Sun) to a maximum at the syzygies (when the tidal priming and lagging. Restating the earlier qualitative vector forces of the Sun and the Moon are applied along description, the direct cause of these latter phenomena is the the same axis in space to reinforce each other). These con- addition of two vector components indicative of the separate ditions result in neap and spring tides, respectively. (See fig. gravitational forces of the Sun and Moon, rather than that 3, appendix.) of the Moon alone. This vector sum representing the com- Column 7 of tables 20 and 21, in which the relative mag- bined gravitational forces of the Sun and Moon and varying nitudes of the resultant forces of the Sun and Moon have with the lunar phase is hereafter referred to as the resultant been computed for various times in a lunar cycle, shows force vector. A meaningful evaluation of the effects of these this relationship clearly. For the purpose of convenience, two phenomena may be achieved by reference to figs. 45 and the tide-raising force of the Moon is assumed to be unity, 46, and tables 20 and 21. In the two diagrams, vector arrows and that of the Sun to have its comparative value of 5/1, indicate, for each succeeding day, the directions and magni- or 0.455 that of the Moon. Thus, at quadratures (neap tudes of the combined gravitational forces of the Sun and tides), the vectorial combination or resultant of the two Moon. The composite of these resultant force vectors (each forces approximates 1.03 to 1.19 and at the syzygies (spring symbolizing a mean daily magnitude and direction) serves to tides) is the simple sum of the two, or 1.455. (See the note define the shape of the total tidal force envelope. at the end of the following section.) It should immediately be pointed out that this tidal force The numerical values of the forces specified above are envelope representing the combined gravitational attractions only relative for any given angular orientation between Sun, of the Sun -and Moon on the waters of the Earth during the Earth, and Moon. In terms of a quantitative evaluation, the course of the lunar month is not identical with the envelope particular value of these figures is to show the increase in lunitidal forces occurring between the situation producing of gravitational forces responsible for the instantaneous dis- *des and that producing spring tides. It must be borne position of tidal high and low waters and their movements nean t, in mind that the absolute magnitude of this resultant force over the surface of the Earth during each tidal day. Both of will be modified by the many factors of changing distance, these force envelopes are ellipsoids, and both are delineated declination, etc., between Earth, Moon, and Sun as these by force components, but the larger force envelope shown in bodies shift in relative position. figs. 45 and 46 involves the changing pattern of lunisolar forces over an entire lunarmonth. The smaller ellipsoidal Confirmation of the Extended Duration of Peak Tide- figure immediately adjacent to the Earth in these same fig- Raising Forces at Perigee-Syzygy ures (and also shown in fig. 2 of the appendix) represents However, column 7 also serves to reinforce one very impor- the combination of all gravitational force components act- tant principle In regard to perigean spring tides-namely, ing instantaneously on the tidal waters. This force envelope the extended period of time within which .the stronger com- sweeps daily around the rotating Earth. With certain excep- bined forces of the Sun. and Moon at pengee-syzygy are ef- tions of nonastronomical nature subsequently to be discussed, fective in producing higher-than-usual tides vulnerable to the major axis of this second force envelope is aligned ap- wind attack and potential tidal flooding. proximately with that of the Earth's envelope of tidal waters. Such a direct analysis of the basic lunisolar forces acting Although the tidal waters themselves do not actually "ro- is possible through a comparison of the normal perigee- tate" around the Earth due to the many inertial and geo- quadrature situation occurring on 1962 June 24 (table 21), graphic restraints imposed to their passage, the force enve- with the close perigee-syzygy situation contributing to the lope does so rotate onceeach tidal day. It is in this latter sense great coastal flooding of 1962 March 6-7 (table 20). In the first example, with perigee occurring at quadrature, syz- that it is safe to use the expression "diurnal rotation" in con- ygy is necessarily more than 5 days away and, under the nection with the smaller ellipsoid (shown in elliptical pro- terms of reference previously established, the ensuing tides file) in figs. 45-46. With the passage of each succeeding day, at new moon are defined as ordinary spring tides. In this the major axis of this smaller force envelope shifts continu- case, the resultant maximum force of Moon and Sun defined ously to follow the instantaneous orientation of the resultant by the peak value of 1.455 lasted only I day, and this force vector in the larger force envelope, representing one maximum value stands out singularly from a lesser valueon monthly lunation. Although certain other modifying factors either side. During the coastal flooding of 1962 March prevent an exact coincidence between the instantaneous ori- 6-7, which (as noted later in this chapter) continued for entations of the resultant force vectors of these two ellipsoids, five successive high tides, maximum or near-maximum their orientations are obviously very closely related for any forces of Sun and Moon (1.452 to 1.455) prevailed through- given position of the Moon and Sun in the monthly cycle of out a 2-day period and even longer. (Note: In order to phases. standardize the trigonornetric-vectorial reductions involved, Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 307 DIRECTION APOGEE -QUADRATURE SITUATION OF MOON'S FQ AS OF 1962 ORBITAL MOTION JUNE 18 -JULY 10 THE SHIFTING FORCE-AXIS IN THE HYPOTHET- icAL LUNISOLAR TIDAL FORCE ENVELOPE, COM- BINING THE GRAVITATIONAL ATTRACTIONS OFTHE MOON AND SUN. SEE ALS046,BELOW. THE ELLIPTICAL PROFILE OF THE TIDAL FORCE ENVE- LOPE REPRESENTS ONLY THE GENERAL DISTRIBUTION OF FORCES PRESENT, SINCE THE INSTANTANEOUS MAG- NITUDE OF THE COMPOSITE FORCE VARIES WITH LU- NAR DISTANCE AND MANY OTHER FACTORS. THIS TID- AL FORCE ENVELOPE SHOULD NOT BE CONFUSED WITH THE DAILY-R.OTATING ELLIPSOID REPRESENTING ACTUAL TIDAL WATER LEVEL (STIPPLED AREA). 18 E 2 TO FM --------- -------------- A LINE OF S)@XYGIES N M R - ------------ W-57 ------ 3 SUN T lop, ------- 19 3 H 1 29 20 S. % 30 -N_-_-27 % 25 \% 21 29 9 28 22 10 '25 2 27 24 LO 26 PERIGEE -OUADRATURE NOTE: THE DAILY LUNAR MOTIONS SHOWN POSSESS APPROPRIATE RELATIVE ANGU- LAR INCREMENTS AND DE'CREMENTS, BUT ARE NOTDRAWN TO EXACT SCALE SINCE .INCREASINGLY DIVERGENT RADIUS VECTORS OCCUR BETWEEN PERIGEE AND APOGEE. _j FIGURF 45.-Graphical representation of the basis for lunar priming and lunar lagging, as these phenomena affect the length of the tidal day. The situation depicted is that at perigee-quadrature. A detailed discussion and quantitative 3 analysis of these effects form part of the main text. 308 Strategic Role of Perigean Spring Tides, 1635-1976 TO SUN PERIGEE-SYZYGY 7 N M 6 8 5 7 6 9 4 10 9 4 /11 3 2 it 12 13 13 EARTH 28 F 0- ----------------------- LO DIAGRAMS 45 AND 46 SHOW THAT, AS A LUN ISOLAR EFFECT RELATED TO LUNAR PHASE, A DECREASING ANGULAR MOTION OF THE FORCE-AXIS OCCURS IN THE TIDAL FORCE ENVELOPE BETWEEN FO AND FM AND LO AND NM. THE SAME MOTION INCREASES FROM NM TO FO AND FM TO LO. WHEN COMBINED WITH THE EARTH'S DIURNAL ROTAT ION, THESE VARIATIONS RESULT IN A MINIMUM LENGTH OF THE TIDAL DAY AT THE SYZYGIES. THIS EFFECT IS PARTIALLY OFFSET AT PERIGEE- SYZYGY. SEE EXPLANATION IN TEX DIRECTION SITUATION OF MOON'S FM AS OF 1962 ORBITAL MOTION APOGEE-SYZYGY FEB 28-MARCH 13 FiGURE 46.-Partial compensation of the effects of tidal priming and lagging at perigee-syzygy, in relationship to these same effects represented in figure 46 at perigee-quadrature. The corresponding amounts of acceleration or deceleration in the force-axis of the tidal force envelope in these two cases, both at and between the various phases of the Moon, may thus be intercompared. TABLE 20.-Elects of Tidal Priming and Lagging (at Perigee-Syzygy) (2) (3) (4) (5) (6) (7) (8) (9) (10) Lunar Moon's Daily change Sun's Moon's Magnitude of Vector angle Daily change Angle between C) Date phase or apparent in longitude apparent true resultant of resultant in resultant Moon and configuration longitude of Moon longitude elongation tidal force tidal force force vector resultant cl@ force vctor 1962 0 0 0 0 F 0 0 0 Feb. 27. 0 LQ 240.1170 337.9209 -97.8039 1.041 -72.1645 25.6394 12.8803 -9.9487 28.0 252.9973 338.9254 -85.9281 1. 127 -62.2158 23. 7123 13.2594 -9.6888 Mar. 1.0 266.2567 339.9295 -73.6728 1.209 -52.5270 21.1458 1?1 13.6826 -9.5754 9@ 2.0 279.9393 340.9333 -60.9940 1.284 -42.9516 18.0424 14. 1251 -9.5647 3.0 294.0644 341.9365 -47.8721 1.348 -33.3869 14.4852 14.5503 -9.6185 4.0 308.6147 342.9394 -34.3247 1.399 -23.7684 10.5563 14.9119 9.6976 5.0 323.5266 343.9418 -20.4152 1.433 -14.0708 6.3444 15. 1614 -9.7690 6.0 338.6880 344.9436 -6.2556 1.453 -4.3018 1.9538 6.5 P-S(NM) 346.3157 15.2585 345.4444 0.8713 1.455 0.5988 -9.8049 0.2725 7.0 353.9465 345.9451 8.0014 1.452 5.5031 2.4983 15. 1837 9.7937 8.0 9. 1302 346.9459 22. 1843 1.431 15.2968 6.8875 14.9449 9.7406 9.0 24.0751 347.9462 36.1289 1.393 25.0374 11.0915 14.5763 9.6689 10.0 38.6514 348.9459 49.7055 1.340 34.7063 14.9992 14.1274 9.6117 11.0 52.7788 349.9451 62.8337 1.273 44.3180 18.5157 13.6508 9.6112 @9 12.0 66.4296 350.9436 75.4860 1.198 53.9292 21.5568 z: 13.1917 9.7144 13.0 FQ 79.6213 351.9414 87.6799 1.115 63.6436 24.0363 Ito 12.7820 9.9657 14.0 92.4033 352.9387 99.4646 1.028 73.6093 25.8553 Note: In columns 3 and 5, although the accuracy of the data on celestial longitudes of the Moon and Sun given in The American Ephemeris and Afautical Almanac for 1962 is suf- ficient to carry these figures to five decimal places, in degrees, they are rounded off to four places here and elsewhere in the volume in teram of adequacy for the immediate purpose. In the computations for column 7, the tide-raising force of the Moon is assumed to be unity, and the tide-raising force of the Sun 0.455 that of the Moon. W CD TABLE 21.-Elects of Tidal Priming and Lagging (at Ordinag Syzygy) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Lunar Moon's Daily change Sun's Moon's Magnitude of Vector angle Daily change Angle between Date phase or apparent in longitude apparent true resultant of resultant in resultant Moon and configuration longitude of Moon longitude elongation tidal force tidal force force vector resultant force vector 1962 0 0 0 0 C 0 0 0 June 24. 0 348.9209 92.0131 -103.0922 1. 189 55.0367 21.8711 P-.Q-(LQ) 14.1996 10.3923 25.0 3. 1205 92.9669 -89.8464 1. 100 65.4290 -24.4174 14. 1780 -10.6149 26.0 17.2985 93.9206 -76.6221 1. 190 54.8141 -21.8080 14. 1218 -10.0337 1@2. 27.0 31.4203 94.8744 -63.4541 1.270 44.7804 -18.6737 14.0258 -9.5859 Q 28.0 45.4461 95.8281 -50.3820 1.337 35. 1944 -15.1876 13.8851 -9.2248 29.0 59.3312 96.7819 -37.4507 1.389 25.9696 -11.4811 10 13.6974 -8.9214 30.0 73.0291 97.7357 -24.7066 1.426 17.0483 -7.6583 13.4680 -8.6587 July 1.0 86.4971 98.6894 -12.1923 1.447 8.8396 -3.8027 13.2051 -8.3491 2.0 NM 99.7022 99.6432 0.0590 1.455 0.0406 0.0184 12.9243 8.2369 3.0 112.6265 100.5969 12.0296 1.448 8.2775 3.7521 19 12.6438 8.0851 4.0 125.2703 101.5506 23.7197 1.428 16.3625 7.3572 12.3825 7.9850 5.0 137.6528 102.5043 35.1485 1.396 24.3475 10.8010 12.1586 7.9497 6.0 149.8114 103.4579 46.3535 1.354 32.2972 14.0563 11.9875 7.9953 7.0 161;7989 104.4115 57.3874 1.303 40.2925 17.0949 11.8814 8.1403 8.0 173.6803 105.3650 68.3153 1.242 48.4328 19.8825 A 11.8491 8.4107 9.0 185.5294 106.3185 79.2109 1.173 56.8435 22.3674 11.8955 8.5859 10.0 FQ 197.4249 107.2719 90.1530 1.100 65.4295 24.7235 Note: In columns 3 and 5, although the accuracy of the data on celestial longitudes of the Moon and Sun given in The American Ephemeris and Nautical Almanac for 1962 is suf- ficient to carry these figures to five decimal places, in degrees, they are rounded off to four places here and elsewhere in the volume in terms of adequacy for the immediate purpose. In the computations for column 7, the tide-raising force of the Moon is assumed to be unity, and the tide-raising force of the Sun 0.455 that of the Moon. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 311 the force magnitudes shown here do not contain any extra angle separating the Moon from the direction of the result- allowance above lunar force unity to accommodate this ant force vector also continuously increases. Between either perigee-syzygy situation. Accordingly, in,this purely vectorial position of quadrature and the ensuing syzygy, the reverse analysis, the maximum tidal force value at perigee-syzygy occurs and both the elongation and the angle between the calculated with this simplification does not exceed that at Moon and the resultant lunisolar force vector diminish in ordinary syzygy as is actually the case.) value. (See cols. 6 and 10 in tables 20 and 21.) This is one clue to the phenomena under consideration. Examples of Tidal Priming and Lagging The situation is exactly akin to that of the converging step However, the principal function of these tables is to per- increments by which a function approaches zero as a limit mit a quantitative verification of the manner in which the in the integral calculus. Between'either position of quadra- resultant lunisolar force vector either precedes or follows ture and syzygy, each day's orbital motion of the Moon the position of the Moon in its orbit in the respective phe- results in diminished angle between the Moon and the nomena of priming and lagging. Although these relation- resultant fdrce vector, approaching zero at syzygy. The in- ships are shown graphically in figs. 45 and 46, it is impos- cremental variations in those angles (second differences) sible because of the continually changing proportions of an themselves proceed toward increasing values between quad- ellipse to represent the appropriate angular motions to a rature and syzygy, and toward decreasing values between sufficiently accurate degree at the published scale. For de- syzygy and quadrature., Accordingly, the Moon is closing up scriptive purposes only, it is possible-by a smoothed con- faster on the resultant force vector the nearer i 't gets to solidation of the data appearing in tables 20 and 21-to in- syzygy. By taking differences between the successive values dicate theresultant force vectors in figs. 45 and 46 in at in col. 10 (tables 20, 21), it will be seen that this daily close- least approximately their correct positions either ahead of up rate is also noticeably greater at perigee-syzygy than at or behind the instantaneous position of the Moon, and ordinary syzygy. with due regard to the phase and apsides relationships of The rise and fall of the tides is very closely related to the the Moon at the time considered. The next step is to eval- times at which the Moon (and by extension, the lunisolar uate the effect of differences in angular orientation of the force vector) transits the local meridian of any place on resultant force vectors upon the Earth's tides. the Earth's surface. The above-mentioned nonuniform dis- 1. Application to Ordinary Spring Tides placements of the resultant force vector with respect to the position of the Moon therefore are of considerable signifi- With reference to the tide-influencing aspects of the cance in establishing not only the times of arrival of high and Earth's diurnal rotation, the "catch-up" principle has been low water but also the total periods of time in which tide- thoroughly described in previous pages. From an analysis raising forces of maximum intensity operat6. As the resultant of this principle, it has been determined that any influence force vector moves ahead of the Moon's position through which tends to accelerate the orbital motion of the Moon constantly decreasing angular values each day between quad- in the same direction as that in which the Earth is rotating rature and syzygy, the effect is a slowing down of the monthly will lengthen tl@e tidal day. Since it is the mass and the rotation of the axis of the combined lunisolar force so that it, gravitational force of the Moon rather than its geometrical in effect, "drops back" in a direction opposite to that of the fi-ure that is involved in the production of the tides, this rotating Earth. A shorter period of time therefore elapses principle can be narrowed to permit, in substitution for the between two successive transits of this force axis across the words "orbital motion of the Moon" above, the correspond- local meridian of any place. This results, in turn in a contin- ing motion of the line of gravitational force action extending ous shortening of the tidal day to a minimum value at the between the center-of-mass of the Moon and the Earth's lunar syzygy. surface. Conversely, any influence which tends to decelerate As, between syzygy and quadrature, the resultant luni- this line of force action *oining the Moon and the Earth- solar force vector falls behind the position of the Moon, in a thus increasing its effective displacement in a direction op- motion entailing steadily increasing angular values, the effect posite to that of the Earth's rotation-causes a shortening of is continuously to accelerate this movement in a direction the tidal day. which is the same as that of the Earth's rotation. A longer A close examination of figs. 45 and 46 and the accom- catch-up time is thus required for any place on the rotating panying tables 20 and 21 reveals the nature of this particular Earth to reach and pass this resultant axis of force. The pe- influence upon the tides. In proceeding from either of the riod of time between two successive transits of the lunisolar position of syzygy (NM or FM) toward the quadratures resultant force vector is increased, and the consequence is an (FQ or LQ, respectively) it will be observed that the lon- extension of the tidal day. gitude angle (measured from the center of the Earth) be- As pointed out above, although the orientation in space of tween the direction of the Moon and the direction of the the lunisolar resultant force vector and the major axis of the resultant lunisolar force vectors on successive days grows Earth's fluid envelope are not the, same, the two normally steadily larger. This follows logically from the circumstance accompany each other very closely. A circumstance thus that the Moon separates from the Sun through 90' of arises in which, between quadrature and syzygy, the Earth's elongation between syzygy and quadrature. The significant tidal bulge lies ahead of-and, subject to the Earth's rotation, fact, however, is that not only does the angle of separation reaches the meridian before-the Moon itself. This condition (elongation) between Sun and Moon grow larger, but the is known in tidal theory as pri .mi.ng. Between syzygy and 312 Strategic Role of Perigean Spring Tides, 1635-1976 quadrature, the tidal bulge transits the local meridian after curves in figs. 44a, 44b amounts-to as much as 18 minutes. the Moon, a phenomenon known as lagging. This difference represents the increase in the length of the The tidal day is generally defined as the interval of time tidal day accompanying a situation of close perigee-syzygy between the occurrence of two successive higher high waters. compared with a corresponding situation of apogee-syzygy The daily displacement of the lunisolar resultant force vec- in the same lunation. tor with respect to the Moon's position is in a forward direc- The uplift effect in the curve minimum at the time of tion near quadrature and retrograde near syzygy. Because perigee-syzygy and increased depression of the minimum the major axis of the Earth's tidal force envelope responds during the immediately preceding or following apogee- most closely to this motion, the tidal day acquires its greatest syzygy may be attributed to parallactic inequality. When length near tKe. quadratures, and its shortest length near the either new moon or full moon coincide with perigee, the syzygies. As the result of this decreasing length of the tidal shortening of the tidal day described earlier for the ordinary day between quadrature and syzygy and increasing length syzygy condition is offset. At such times, the Moon's orbital between syzygy and quadrature, the minimum length of the motion is accelerated by its proximity to the Earth, and the tidal day from this single cause is established at syzygy. This, Earth's rotational catch-up motion increases the length of then, is the situation as it exists at the time of ordinary spring the tidal day. Conversely, the recession of the Moon to its tide, without any additional tide-raising influence being ex- greatest monthly distance from the Earth at apogee reduces erted by perigee. the Earth's gravitational attraction for the Moon and slows its orbital motion, decreasing the length of the tidal day and 2. Application to Perigean Spring Tides producing a deeper curve minimum. It is important in terms of the classification of perigean A complete contrast exists in the case of the ordinary spring tides given below to note that, in the case of ordinary spring tide. When perigee coincides with quadrature, and spring tides, the greatest gravitational attraction produced either full moon or new moon is 90' removed from perigee, by the combination of Sun and Moon (at syzygy) occurs at the average orbital speed of the Moon is only about 13' per a time when the tidal day has its shortest length. Also, in figs. day compared with a value which may reach more than 15'. 44a, b it will be seen that the peaks of the curves (which rep- per day in the case of perigee-syzygy. The resulting con- resent the maximum lengths of the tidal day at quadratures) siderably shorter length of the tidal day in the case of ordi- are much more uniform in height when at least 5 days nary spring tides is further decreased by the effect of tidal separate syzygy and perigee-the classification criterion priming previously described, and lacks any compensating adopted in this work for an ordinary spring tide. In all cases, increase as in the case of perigean spring tides. the peaks are separated by raised minima (resembling valleys between high mountains) which, however, are subject to a A Pro osed New System for the Quanti- greater elevation in height when the length of the tidal day p (e.g., at a time of perigee-syzygy) becomes greater. tative Designation of Perigean Spring A further enlightening feature concerning the nature of perigean spring tides is the direct contrast between the shal- Tides lower depths of the curve troughs representing ordinary spring tides and the troughs of perigean spring tides imme- diately preceding or following an uplifted maximum asso- It is obvious from the step-by-step analysis of the very ciated with the latter type of tide. In the case of perigean numerous astronomical factors which may influence the spring tides accompanying a close alignment of perigee- amplitude and range of perigean spring tides as outlined syzygyl an apogee-syzygy situation must immediately precede in previous chapters that various degrees and grades of or follow, within one-half a lunation, the corresponding con- these tides exist. Consequently, it becomes desirable for dition of perigee-syzygy. In terms of the tide-raising force on scientific purposes to establish a meaningful system for the Earth, at apogee-syzygy, the gravitationally enhanced tidal effect resulting from the Moon's alignment with the classifying these tides based upon the particular astronomi- Sun at syzygy is partially offset by the increased distance of cal circumstances which both create them and determine the Moon from the Earth at apogee. At the time during the relative heights of the water they produce. In a suc- which this reduced gravitational force acts, the Moon's ceeding section, the development of a suitable coefficient orbital velocity is also reduced, due both to its greater dis- tance from the Earth and to its approach to syzygy, shorten- or index of tidal flooding potential also will be undertaken ing the tidal day. The considerably greater net shortening for these various classes of perigean spring tides, assuming in the length of the tidal day consequent upon both of these them to be accompanied by the necessary meteorological causes provides an excellent basis for comparison with the conditions. shortening produced primarily by the syzygy effect in the case In this terminology-assigning process, certain new ex- of an ordinary spring tide. The lengthening of the tidal day and uplifting of the curve minima at perigee-syzygy provides pressions, not presently in the language of either astronomy a Still further contrast. It will be seen that the difference in or tides, will be introduced which it is felt may, be deserv- amplitude (in units of time representing the length of the ing of consideration in order to fill in an existing gap tidal day) between the lowest and highest minima of the created by many years of comparative neglect of the sub- Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 313 ject area-and, in any event, to make the analysis of these these components, the increased lunar parallax, and the tides more understandable. greater speed of the Moon in orbit. The angle of the Basis for the Classification of Moon's orbital motion with respect to the Equator is also Perigean Spring Tides considered. As has been seen, all these factors are of con- sequence in the differentiation between perigee-syzygy The common denominator of all such tides, as fre- situations of varying tide-maximizing ability. And it must quently emphasized in the foregoing chapters, is the small be emphasized again in terms of a later discussion of time interval between perigee and syzygy, which leads- hydrographic and oceanographic influences that purely through solar perturbations of the lunar orbit-to the astronomical data are involved in the general classifica- resulting close proximity of the Moon to the Earth, tion scheme for perigean spring tides which follows imme- and a considerable increase in the tide-raising force. The diately below. (See also figs. 47A, B, C, D, and table 22.) reduced lunar distance from the Earth at times of perigee- syzygy is expediently (but in a mathematically inverse 1. Maximum Perigean Spring Tides (or Ultimate- relationship) indicated by the geocentric horizontal Maximum Proxigean Spring Tides); Maximum parallax (r) of the Moon. It will become clear in connec- Proxigean Spring Tides tion with both astronomical and meteorological factors The theoretically largest possible value of the geocen- later to be discussed that the lunar parallax alone -is in- tric horizontal parallax which the Moon can attain is sufficient substantively to evaluate the various categories 6 V3 2. 0" (see fig. 41 ). The conditions necessary to achieve of perigean spring tides in terms of their potential flooding this very high parallax presume that the full moon shallbe ability if they become subject to continuous, strong, on- simultaneously at proxigee-syzygy, with P separation- shore winds. However, this quantity is suitable for a selec- interval, at one of the lunar nodes (i.e., coincident with tive classification of such tides, based solely upon astro- the ecliptic, and with the Earth precisely at perihelion. nomical parameters. (See pp. 203, 219.) Because this combination has not In the subsequent analysis of tidal flooding potential, occurred any time in the past five centuries and will not a practical numerical coefficient will be derived which occur again until A.D. 3300, it may be described as one represents the instantaneous value of the rate of change of maximum perigean spring tides (or, for consistency in of the Moon's true anomaly at the time of perigee-syzygy the present classification scheme, as an example of as a function of the small separation-interval a between ultimate-maximum proxigean spring tides. The designa- ' It is important to note that the difference between perigee and tion of maximum proxigean spring tides is appropriately syzygy can be indicated either as an angular distance or in hours given to those astronomical tides produced under a condi- of time. Because of this dual quantification, the expressions separa- tion of proxigee-syzygy in which the resulting lunar paral- tion-time and separation-interval have both been used in this work- the first primarily in part II, chapter 4 and earlier where the. time lax lies below its ultimate value, but within a range of 1.3". difference was critical, the second in the present chapter and The use of the word "proxigean" in preference to the later. The term separation-interval, while at first glance seemingly word "perigean" to distinguish such cases of unusual close redundant, is actually the more meaningful, since its two elements are representative of either arc or time. proximity of the Moon to the Eaxth results from the TABLE 22.-Proposed Classification System for Perigean (Including Proxigean) Spring Tides Range* in lunar geocentric hori- Definition zontal parallax at mean epoch of perigee-syzygy 1. Ultimate maximum proxigean spring tides 61'32.011 �0.111 Maximum proxigean spring tides >61'30.711<61'32.011 3. Extreme proxigean spring tides >61'29.0"<61'30.711 4. Proxigean spring tides >61'21.0"<61'29.0" 5. Perigean spring tides >60'20.0"<61'21.0" 6. Pseudo-perigean spring tides >59'00.0"<60'20.0" 7. Ordinary spring tides >55'00.0"<59'00.0" *Because of the complexity of dynamic forces and conditions present, some exceptions to these arbitrarily established parallax ranges may exist on the part of tides otherwise responding to the average daily amplitude variations which occur within these individual categories. co 0 a 0 0 Z z z m lz a) Z z C 4 m 03. m lz Z m 0 > 0 2 , z Too 0 @ - @ a " m 0 Z, 9 Z- 0 OZO,Ozxc 0 o ozzox@ m m M@zw,zm.al Zqj m mo C) -,C*.Z-* M zo 2.@, z z Z 00:10.mom M>z ..Oz 30002m@m ;[email protected]@@<Zm mo T ml @- *1 1. 1 rc) M.N , 1. @p 0 0,-@ 7" z z3zz, N M@o N i'om , @ C) @;@MTM 000 zcm X,x 11 mr m 0 Co 0.... C, m cy@ C', w I I 0 -10 m molm C) 0 z Z. 0! 0 m m 10 z, 1. 10 i 23. 11" m 0 m 00 o r om z T 0 X 0 r-- m - - - -- - ------- 0 0 BYZYGIES SUN Z x m m -4 Z w X 0 0 1.0 -xr m 10 'OoOE; I.m.>Xm -z A. @,mmT !o mmm,w ow). 0 >lm ul mE; Z-@ rj)'.!2zz m z I. x,v m C,w m 0 0,0 0' 0 0 m;_ol z w,x m C, > 4 Iz, 0 -mo 0 ;x 1. 0 @O,x ml-,,o m@oxoc z z m 'm o XZX M-wc; w i i [email protected] -Z mm>m ow m cm,omm@;w> m@zm Z@t m 0,.G)). 0 oc,@, Y. 0 ;.m 0 X, A- T ouK 0@ r@. a @ m > - of@ m m m O..mgc... zt,r,.X. m , c z r) X m -m zo, 0'. 0 )@Gz> .50 mmx@lwa 5D Mmw.omr m m m> Z-1. ox 30 0,. C@ T 'm -'o ozo 71mri> r 3ro z E)m oz .0 1 j MI-901 's9P!,L ful.ItIE uv9ffz.,Od 10 010?1 .92291MIS tic Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 315 degree of selectiveness of the Latin and Greek prefixes definitely not peculiar to either language and their inter- involved in these respective terms. In a secondary usage lingual mixture should provide no major concern. to its more familiar concept of "around" (i.e., "circum- To drive this point home, a brief summary (table 23) is scribing"), the Greek prefix peri also has a connotation appended herewith containing representative examples from among a large number of similar cases present among Eng- of "near." The suffix gee (from the Greek gj) designates lish scientific and technical vocabularies. This abbreviated the Earth, so that the expression perigee properly implies table shows clearly that-especially among the words of nearness of the Moon to the Earth. In this sense, the word modern-day origin but formed variously from Greek, Latin, defines the point of the Moon's closest monthly approach English, French, Spanish, and Arab roots-prefixesand suf- to the Earth in its elliptical orbit around it. fixes are joined almost indiscriminately. This is particularly true of more recent additions to the scientific vocabulary However, this single term permits no indication of the where the restraints imposed by the origin of a word by any relative closeness of the perigee position itself which, as one country are no longer necessary. has been seen, may vary within significantly wide limits subject to solar perturbations. For more accurate nomen- TABLE 23-Examples of scientific and technical terminology in the clatural purposes, the suggested words "proxigee" and English language involving interlingual combinations of prefixes "proxigean," with prefix proxi from the Latin superlative and suffixes form proximus meaning "nearest," connote both a posi- Greek-Latin Latin-Greek tion and an instant of unusual proximity of the Moon to peri/martium semi/logarithmic the Earth. Without altering the time-honored concept of peri/jove co/logarithm the word "perigee," the additional term "proxigee" allows peyi/saturniurn super/adiabatic for the more selective designation of a situation involving pseudo/conglomerate super/panchromatic pseudo/fluorescence non/mathematical a particularly close perigee. Supplementary descriptive thermo/pile extra/atmospheric modifiers then complete the classification scheme. thermo/couple bi/chloride thermo/electric bi/chromate di/sulphide bin/oxide One factor of immediate note in this connection is that the dyna/motor bin/iodide use of the prefix proxi together with the suffix ge (e) brings a hyper/space electro/lyte Latin and a Greek root immediately into apposition, a pro- auto/mobile electro/kincties meso/tron (meson) electro/phorus cedure which might be frowned upon.by those concerned photo/electric spectro/bolometer with the origins and orthography of scientific terminology. hemi/demi/semi/quaver spectro/heliograph An alternate choice for proxi might be the use of the prefix epi, which is itself a Greek root. However, because this prefix Latin-Middle Latin-French possesses such a wide range of possible meanings-including (or Old) English (or Middle or Old French) 44on" (or "upon"), cc at," "besides," "after," "over," cc outer," sub/giant electro/jet and "anterior," all in addition to "near to7'-it is not nearly infra/red gravi/meter as suitable, in -a semantic sense, as is the prefix proxi. The flux/gate multi/stage prefix epi lacks in every way the fine points of distinction multi/foil French- Greek-Middle Latin which go with the prefix proxi, whose exact meaning is so Satur/day familiar both to scientific and general audiences in the words counter/glow kilo/par/sec cc ultra/high proximal ... .. proximate," and "proximity." (frequency) Greek-French A thorough review of unabridged dictionaries and of thermo/nuclear words forming, for the most part, a complement of the Latin-Arabic photo/gravure international scientific vocabulary (ISV) reveals the very alt/azimuth (instrument) photo/montage large number of early, middle, late, and new Latin words co-/azimuth micro/fiche which have come down to the modem period from original Latin-Spanish Greek sources. Thus, in a very great number of cases, it (or Old Spanish) would appear to be senseless to distinguish between their circum/zenithal (arc) primary Latin or Greek origins, since the words have super/cargo appeared, at the same or different times, in both languages with but slight modifications in spelling. Such words are FiGuRE 47, A,B,C,D.-A comparison of four different astronomical configurations and alignments which result-both through the combined lunisolar gravitational force action and an increasingly more exact orientation between the lines of syzygies and apsides--in proportionately higher tides. 1n conjunction with table 22, a suggested classification scheme for various amplitudes of perigean spring tides is also represented by this composite chart. 316 Strategic Role of Perigean Spring Tides, 1635-1976 Without in any way advocating the introduction of such a possess certain of the same force-amplifying elements as surficial inconsistency other than by the statement that the those described in the preceding section. However, neither use of the prefix proxi in every logical way "belongs," it may the lunar parallax produced, nor the accompanying astro- readily be seen from the table that ample precedent exists nomical tides, achieve the absolute maximum values as- for such apparently discrepant prefix-suffix combinations where the combination involved is more meaningful. sociated with this first category. It is important in consideration of the specialized and Through an analysis of all cases recorded in the 400- valuable roles of both chemical handbooks and unabridged year printout, the lunar parallaxes characteristic of this dictionaries to include one further comment. Actually, if a group range between > 61'29.0" and <61'30.7". The true adherence to a consistent policy is used, such chemical greatest separation-interval between proxigee and syzygy radicals as chloride, chromate, oxide, or iodide, which origi- nate from Greek words designating the chemical elements encountered among the 39 examples bounded by these chlorine, chromium, oxygen, and iodine, respectively, should parallax limits in table 13 is zL5'. Of considerable im- possess the corresponding Greek prefix di rather than the portance to the creation of the large parallax values, Latin prefixes bi or bin(i) which they now have. Similarly, therefore, is the very consistent, close alignment of proxi- the word sulphide, originating from the Latin word for sul- gee and syzygy in all cases. phur should, for the sake of consistency, possess the Latin prefix bi instead of the Greek di. But a second, strongly contributing factor in this cate- In the proposed new classification, the position of extraor- gory of tides is the circumstances that the tide-raising dinary recession of the Moon from the Earth along the line forces of the Sun and Moon are also exerted in the same of apsides 180' from proxigee (either preceding or follow- declinational plane in each example, thus reinforcing the ing) would be termed exogee (from the Greek prefix exo, gravitational effect of alignment in longitude between meaning "far from" and suffix gj, "Earth") as the counter- part of apogee. the two bodies at proxigee-syzygy. The result of these concurrent lunisolar alignments in two coordinates is to It is emphasized that the preceding two classes of tide increase the eccentricity of the lunar orbit and thus also require the reinforcement of an extremely close proxigee- the lunar parallax. The proxigee distance of the Moon syzygy alignment by the other astronomical factors noted from the Earth is diminished in proportion. As indicated in the first paragraph of this section in order to achieve on page 199, the further location of the Moon at full the maximum lunar parallax range cited, in excess of moon and near solar perigee also play a significant role 61'30.7" (the upper limit of the next tidal category). in this force-enhancing situation. Although the coplanar This circumstance has occurred (at instants of proxigee) alignment of the Moon and Sun may ordinarily occur on only 14 times in the past 376 years. Appropriately, there- either the same or opposite sides of the Earth, in the fore the use of the word "maximum" serves to distinguish latter case the two bodies are 180' from each other, re- between these tides produced by the combination of ex- sulting in the force differences previously noted (see p. tremely favorable circumstances and those belonging to 214). Although the maximum negative solar declination the succeeding category of tides. (solstitial) is -231/2', as seen in table 13 such ap- By contrast, the tides of this next group are in no way proximately coplanar gravitational reinforcements can related to the position of the Moon at a lunar node. They take place at slightly higher positive declinations of the are, in fact, produced by an entirely different set of astro- Moon, especially when the nearly coplanar relationship nomical circumstances which results in an extraordinarily occurs close to the time of perihelion. large value of the lunar parallax. As will be seen, these above-normal tides may be generated even with the 3. Proxigean Spring Tides Moon at rather high celestial latitudes, so long as it is At about 18-month but irregular intervals of time, a in the same declination plane with the Sun. more exactly commensurable relationship between the 2. Extreme Proxigean Spring Tides synodic and anornalistic months creates a separation- Of considerably more consistent, but still infrequent interval between perigee and syzygy which is considerably occurrence (see table 13) among the 400-year tabular less than average. This in turn -results in an especially printout represented by table 16-and in no wa 'follow- close distance (here termed proxigee) of the Moon from y ing a regular chronological pattern-are those perigean the Earth and a substantially increased lunar parallax. spring.tides which, for lack of any existing classification The arbitrarily established values of the parallax for system are, in this volume, designated as extreme proxi- this category lie between < 61'26.5" and <61129.011. The gean spring tides'. In manner of dynamic origin, they limiting value of the separation-interval is I oh. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 317 As will be.seen by comparison with the immediately The mechanism of production of this general category succeeding category, a condition of proxigee-syzygy there- of perigean spring tide has been explained both in the fore represents, by definition, a particularly, close ap- Technical Commentary accompanying part I, chapter 1, proach of the Moon to the Earth and, by implication, in and elsewhere throughout the work and need not be order to cause this, an unusually close alignment of peri- repeated here. The arbitrary limits of parallax for this gee-syzygy. The tides of exceptional amplitude which category, established from a detailed analysis of table 16 result from this reduced distance of the Moon from the as well as the tidal flooding events encountered in the Earth and the correspondingly increased gravitational present study, are from > 60'20.0" to <61'26.5". The attraction of the Moon on the Earth's tidal waters- perigee-syzygy separation-interval which. seems optimally coupled with the pull of the Sun at syzygy-are referred to represent the average situation in this category suscep- to throughout this work as proxigean spring tides. In the tible to tidal flooding (emphasizing again not the most computer printout (table 16) covering the 400-yearpe- severe cases) ranges from !5:L10h to ::-::@LW. riod 1600-1999, a qualifying value of the parallax (at The computer printout of table 16, with an upper the time of proxigee) and corresponding proxigee-syzygy limit of -L 24', does not include all of the perigee-syzygy situation occurs, based on an actual average, once in each alignments within :i-36' responsible for pvrigean spring 1.46 calendar years. tides according to the present classification system. From an evaluation of the historic record, this particular cate- 4. Perigean Spring (or Perigee-Spring) Tides gory of tides-when accompanied by the appropriate These are the technical expressions which traditionally winds-appears realistically to account for the great have been used to designate tides (possessing approxi- majority of cases of coastal flooding (exclusive of those mately 40 percent greater mean range) that result from caused by hurricanes). The addition of a 12-hour exten- any condition of near-alignment of perigee and syzygy. sion to the present printout data over a period of 400 Either of these alternate terms as heretofore used collec- years would, however, make the list prohibitively long tively encompasses all of the other categories discussed in for publication. this list. 5. Pseudo-Perigean Spring Tides For the purpose of the present classification, the term is confined to tides produced by an astronomical con- This designation has been given in the present work dition involving a relatively close'@ but not unusual align- to a group of tides whose perigee-syzygy interval lies just ment of perigee-syzygy. If the separation-interval between beyond the upper limit for perigean spring tides. How- perigee and syzygy is chosen as � 24 hours, such tides oc- ever, they are produced close enough to even a compara- cur, on the average, three or four times in each tropical tively wide alignment of perigee-syzygy to acquire some (ordinary) year. Two of the associated perigee-syzygy of the general characteristics of perigean spring tides in alignments are invariably closer than the other two, and terms of increased amplitude and rapidity of tide growth. the tides raised are slightly higher in these cases. Some of the other tide-amplifying factors mentioned in Perigean spring tides could, therefore, be regarded as previous chapters such as coplanar alignment of Moon the generic model, of which the other examples included and Sun, etc.) may provide additional support to the in the present classification system are special adaptations. weaker perigee-syzygy effects present. This category-because of the far greater frequency in Given sufficiently strong and lasting accompanying the number of cases represented which offer the possi- onshore winds, some surprisingly high tides and asso- bility of simultaneous combination with strong, persist- ciated coastal flooding events have occurred among the ent, onshore winds-is responsible for by far the greatest examples of this type of tides listed in tables I and 5. number of cases of tidal flooding, but by no means the The parallax limits for this category have been set, for most severe cases, unless accompanied by a hurricane. the purpose of consistency throughout this work, as be- As a matter of comparison, the separation-intervals and tween >59'00.0" and <60'20-0"'. The corresponding lunar parallaxes are given in tables I and 16, while news separation-interval which seems best to define these cases accounts of the relative severity of tidal flooding are is from :!@ --L361 to :_!@ 4-841. Some few exceptions of an provided for many cases in table 5. The predominance hour or so in excess of the upper limit have been permitted of major tidal floods at proxigee-springs and the greater where the particular characteristics of the tide appear frequency in the number of cases of tidal flooding at to dictate the logic of these minor extensions beyond the perigean spring tides are thus easily verified. arbitrarily chosen limit. 318 Strategic Role of Perigean Spring Tides, 1635-1976 6. Ordinary Spring Tides motion in the same direction and to achieve an alignment Finally, the category of ordinary spring tides is used to in celestial longitude between the Earth, Moon, and Sun define that situation in which perigee is separated from at times of new or full moon. syzygy by more than =L 84' and up to --f: 120'. At a posi- The actual difference between the synodic month and tion more than 5 days away from perigee, an existing the anornalistic month is syzygy condition will generally converge toward, and be 29.530588-27.554550=1.976038 mean solar days gravitationally weakened by, the increasing lunar distance In consequence, once each synodic month, or lunation, at the immediately following or preceding position Pf the synodic month gains approximately 2 days on the apogee. An apo ,gee-syzygy alignment ultimately results. anomalistic month. This means that, following a situation The true spring tide, to be completely unaffected by in which the Moon, Earth, and Sun are closely aligned the influence of either perigee or apogee (including at perigee-syzygy (assumed, for this present case, to occur factors consequent upon both the lunar distance and at new moon) the difference between the lengths of the velocity in orbit) must be separated by the entire 5 days anomalistic and synodic month will cause the positions from perigee and approximately 8-9 days from apogee. of perigee and new moon to diverge gradually from each (The interval between perigee and apogee is one-half of other. an anomalistic month, or 13.7774 days, but the Moon In each synodic month, the mean moon revolves moves faster over the portion of its orbit closest to perigee and the distances from perigee .and apogee are thus through 360' of arc with respect to the position of con- unequally divided in terms of time.) junction, at an average rate of The parallax limits for this category of tides correspond 360- / 29.530588 = 12.19074947'/day roughly to a range from > 55'00.0" to <59100.011. However, this mean daily motion of the Moon does not reveal the wide variations in the Moon's angular velocity Periodic Relationships previously discussed, and caused by parallactic inequal- ity, solar perturbations, and other factors. The various astronomical relationships governing rep- During each anomalistic month, the mean 'moon also etition of the phenomenon of perigee-syzygy will now be revolves through 360' with respect to the position of discussed. perigee, at an average rate of The Mean- Period Between Successive 360'/27.554550= 13.06499290'/day Occurrences of Perigee-Syzygy Since this value has been observationally established, it According to the origin selected from which to meas- includes the effect of an assumed mean revolutionary ure the motion of the Moon, this body may have several motion of the lunar line of apsides (and hence perigee itself) in the same direction as the revolutionary motion different periods of revolution around the Earth. De- of both the Moon and Earth (see p. 177). tailed explanations of the synodic and anornalistic months The daily angular gain of the anornalistic revolution have been included on pages 126, 130 and will not be re- over the synodic revolution is peated. Ile length of the synodic month is 29.530588 13.064992900 - 12.190749470 = 0.87424343'/day mean solar days. It is the period of time required for the mean moon to orbit from conjunction to conjunction, Since the synodic period is 29.530588 days, at a time ap- assuming it has a constant, average daily motion relative proximately 0.5 month or 14.765294 days after new to the position of conjunction. However, this position is moon, full moon will occur. In this same 2-week period, itself subject to small variations caused by perturbations the gain of the Moon's position over the line of apsides will in the lunar orbit, and the above period is an average for be the equivalent of many circumstances, including the effects of parallactic 0.87424343*/day X 14.765294 days 12.9084610 inequality. The length of the anornalistic month is 27.554550 which is less than one day's motion for the Moon. Subject mean solar days. It represents the period of time it takes to the previously stipulated conditions, the Moon, in its the Moon to revolve in its orbit from one perigee to the orbital revolution, cannot attain a position much more next. The anornalistic month is shorter than the synodic (and quite possibly less) than this amount ahead of the month because of the extra time required in the latter position of apogee' When the new moon occurs within case for the Moon to catch up with the Earth's orbital less than a day of perigee, the succeeding full moon will Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 319 normally fall within less than a day of the next following anomalistic months increasing considerably more than the apogee. The perturbational motion of the line of apsides synodic months under such circumstances (see table 17). itself may be disregarded as of minor consequence during During those anomalistic months whose lengths are in- this lunar half-revolution since, over this interval between creased to more than 28.5 days by virtue of a close perigee- perigee and apogee, the motion is partially forward and syzygy alignment, the mean motion of the Moon is reduced partially retrograde. to 360'/28.5' or 12.6' per day with respect to the mean For this daily gain to add up to the equivalent of one position of perigee. (In the remaining anomalistic months revolution of 360* requires of the lunar year, whose lengths are usually >I to <5 3600/0.874243430/day = 411.7846216 days days shorter than the synodic month, the mean motion of the Moon with respect to perigee varies from about 12.70 The full 411.78-day cycle is known as "the evectional to 14.5' per day, on the average.) The previously noted period in the Moon's parallax," and since an early time daily angular gain of the anomalistic month over the has appeared variously throughout computational pio- synodic month is thus decreased from 0.87'/day to cedures for the tides, in connection with the synodic 0.5'/day at times of close.perigee-syzygy alignments. periods of the semidiurnal and diurnal tidal constituents. Because the daily angular gain of the anornalistic mo- (See, for example, page 163 in Manual of Harmonic tion over the synodic motion is less, the lengths of the Analysis and Prediction of Tides, USC&GS (NOS) Spe- corresponding months come more nearly into agreement. cial Publication No. 98 (1941 also table 2 of "Auxiliary In addition, the length of time required for this daily gain Tables for the Reduction and Prediction of Tides," page to add up to the equivalent of one full revolution of 360' 194 in the annual Report of the Superintendent of the U.S. is greater, and the actual minimum period between the Coast and Geodetic Survey for 1894, Part II). This inter- closest occurrences of perigeip-syzygy is shortened with re- val of 411.78 days represents the average period of time spect to the previously computed mean value of 205.- required for a perigee-syzygy alignment of Sun, Earth, 892318 mean solar days. This conforms with the observed and either new moon or full moon, once having been facts, (see table 17 attained, to occur next again at the same phase. It is also important to note that, for reasons explained But since a near-concidence between perigee and in chapter 6, once the position of perigee-syzygy occurs syzygy which takes place at new moon results in a second with a minimum separation in time between the two close alignment between the line of syzygies and the line components, it may be accompanied in immediately of apsides before the Moon returns to its new phase, suc- preceding or following months by similarly close, but cessive occurrences of perigee-syzygy and apogee-syzygy gradually diverging, perigee-syzygy alignments. These alternate. Alignment of perigee and syzygy at new moon is will, as a rule, take the form of wider spaced perigee-syzygy followed by alignment of apogee and syzygy at fun moon. or pseudo-perigee-syzygy situations. At cine perigee-syzygy alignment in each sequence, the .It has been established above that, subject to an as- two components converge toward a least separation. After sumed constant angular speed of separation, a period this smallest separation-interval is attained, the. interval of 411.78462 days is required for the position of perigee, increases with each lunation for some 3 months, then again \ continuously falling behind the position of conjunction, decreases. Thus, the minimum time for a recurring near- to complete a full revolution of 360' around the lunar coincidence between perigee and either conjunction or orbit. At the end Pf this period, any previously existing opposition is, on the average coincidence between perigee and conjunction will repeat 411.7846216/2=205.892318 mean solar days itself again, but will not usually occur a second time in succession according to this exact time interval. Because (pf-, table 39, "Synodic Periods of Constituents," in there are numerous disturbing influences affecting the Manual of Harmonic Analysis 'and Prediction of Tides.) Moon's orbital motion, the immediate repetition of this This average period of time assumes that the mean cyclical period will usually be broken. values for the s@nodic and anomalistic months previously specified possess a 'constant and invariant value. The Short-Period Cycles of Repetition lengths of these individual lunar months actually vary of Perigean Spring Tides considerably. As has been noted in chapter 6, those syn- It is obvious that, from the standpoint of winter storms, odic and anomalistic months which contain the phenom- the greatest astronomically induced potential for tidal enon of perigee-syzygy are the longest, but with the flooding will exist in those years in which the calendar 320 Strategic Role of Perigean Spring Tides, 1635-1976 arrangement of near-coincidences between perigee and over short periods of time (e.g., one recurring cycle). Over syzyzy permits the greatest number to occur within the longer periods, the effect of individual variations will more most common period of winter storms from November 1 nearly average out, and a comparison of the actual and to April 1. the mean intervals of time between perigee-syzygy align- The exact number of occurrences of perigean spring ments will show smaller residuals. The assumed periodic tides in any one year (3-5 having a perigee-syzygy relationships will, for the same reason, more nearly apply. sepa.ration-interval of _�:24') is a function of the number Thus, the mean epoch of the proxigee-syzygy alignment of close alignments between perigee and syzygy in that of 1974 January 8.49 (e.t.), is connected through the calendar year. The number of these close alignments is, 205.89-day perigee cycle (2X205.89=411.78 days) in turn, a function of the slow but continuous revolution with a proxigean spring tide occurring on 1972 Novem- of the line of apsides (connecting the positions of perigee ber 20.98 (e.t.) (a Julian Day difference, at mean syzygy, and apogee) around the Earth in a period of 3,231 days of dt=413.40). In the chain of cyclical interrelationships, (8-85 years). Other controlling factors include the the January 8.49 date is also directly related through the Moon's revolution around the Earth from perigee to 205.89-day cycle (2lX205.89=4,323.7 days) with perigee in a period of 27.554550 days, the lunar revolu- another proxigean spring tide associated with the proxi- tion from new moon to new moon in 29.530588 days, the gee of 1962 March 6.375 (e.t.) (dt=4,326.2), in which apparent motion of the Sun around the Earth in an ordi- the extraordinary high waters were further augmented by nary (tropical) year of 365.242199 days, and certain an intense, wind-driven storm surge to produce extensive additional astronomical variables. The numerical inter- flooding along the mid-Atlantic coast (see item 4, later relationships between these various periods determine the in this chapter). frequency of occurrence of the different classifications of The 1972 November 20.98 proxigee-syzygy date like- perigee-syzygy alignments. wise forms an integral number of multiples of 205.89 As the result of the relative movements of. the Earth, (15X205.89=3,088.4 days) with a close perigean spring Moon, and Sun, the repetition of tides of similar phase and situation on 1964 June 10.08 (e.t.) (dt-3,086.0 days). amplitude-including those of perigean spring origin- Coastal flooding associated with perigean spring tides takes place in certain well-defined periods averaging occurred at Atlantic City, N.J., on 1967 April 27 and 28.981403, 162.502866, 191.484268, 355.022184, and December 3, near the mean perigee-syzygy dates April 384.003587 days,' as well as in the previously- discussed 24.15 and December 1.13 (e.t.). These dates are sepa- astronomical cycle of 205.892318 days representing the rated by a 221.98-day period, which is approximately average motion of perigee around the Earth. Various com- equivalent to one 191.48- and one 28.98-day cycle (the binations of, these cycles also occur (e.g., 28.981403 sum=220.46 days). + 162.50286 '6=191.484269 days). The 205-892318-day Similarly, all four of the previously mentioned perigee- cycle is the principal one affecting perigean spring syzygy dates form part of a long-period astronomical re- tides; the others are subordinate. lationship extending backward over 31.010 tropical As has beeii evidenced in chapter 6, a considerable years (11,326 days) or 55 cycles of 205.89 days (11,324 deviation is present between the lengths of the actual and days). These individual perigee-syzygy dates in 1974 are mean values of both the anomalistic and synodic months almost exactly repeated at the end of this long cycle, in in those months containing a close perigee-syzyky align- ment. -The magnitude of this deviation increases as the each case only 2 calendar days after the perigee-syzygy separation ,interval becomes smaller. Accordingly, any as- dates which occurred 31 years previously on 1943 Janu- sumed value involving an average period of time between ary 6, February 4, July 17, and August 15. More will be perigean spring tides also will least adequately represent said concerning this 31-year period in the immediately the actual period -between these tides when the perigee- following section. syzygy alignments are especially close. The deviation from Over an even longer period, the four dates of proxigean a mean, period also will be the greatest, percentagewise, and perigean spring tides in 1974 also are commensurate with (i.e., an integral number of cycles removed from) b Cf., R. A. Harris, Manual of Tides, part V, Currents, Shallow- proxigean spring tides which were accompanied by severe Water Tides, Meteorological Tides, and Miscellaneous Matters, flooding along the New Jersey coast on 1861 November 2, as Appendix No. 6 in the annual Report of the Superintendent of the Coast and Geodetic Survey for 1907, Washington, D.C., U.S. 113 years earlier (see page 78). The 1861 November Government Printing Office, 1908, p. 492. 2.69 (G.m.t.) date is separated (dt=40,973.7 days) Classification, Designation, and Periodicity of Perigean @gpring Tides; Recent Tidal Floodings. 321 from the 1974 January 8.49, (e.t.) date by 199 cycles of September. In order to make possible the determination of 205.892318 days (total 40,972.6 days). any desired statistical probability of occurTence incorpo- And, as a final example in this representative list, there rating this double threat of hurricanes and high tides, a are 225 cycles of 162.50 days, plus 3 cycles of 28.98 compilation is included in table 24 of all cases of proxigee- days (total-36,649.4 days) between the 1861 November syzygy or, perigee-syzygy (P-S <::L24) occurring be- 2.69, (G.m.t.) proxigee-syzygy date and that of 1962 tween 1600 and 1999 in the month of September. In con- March 6,375 (e.t.), accompanied by severe flooding 101 sequence of the purely astronomical factors expressed in years later (dt=36,647.5 days). this table, the augmented tide levels resulting are vulner- able to any type of intense offshore coastal storm occurring The 31-Year Cycle of Perigee-Syzygy in this month. The resulting susceptibilities to tidal good- A very significant relationship exists in the 3 1 -year cycle ing apply, therefore, to either hurricanes or winter storms. of iteration which governs close perigee-syzygy align- Although the data are tabulated for the single month of ments. For greater emphasis on the meaning of this re- September, the purpose of this tabulation is to discover lationship in terms of recurrent tidal flooding, the astro- the cyclical relationships between successive close perigee- nomical factors responsible for a periodicity in tidal ex- syzygy alignments, regardless of their calendar positions. tremes will be established by an analysis of ephemeris The periodicities revealed may involve any month of the data. This will be followed by correlations between the year, depending upon which month is selected as a start- cyclical data obtained and examples of repeated coastal ing point and whether the repeating cycles are exactly in- flooding from past history. Coincidentally, in followup tegral ones. to a previous section, consideration will be given to the In table 24, col. I contains the date of syzygy; col. 2 unusually hazardous flooding situation which prevails lists the corresponding Julian Date, including in order whenever landfalling hurricanes occur on the same dates that the differences between successive dates of syzygy as those on which markedly elevated perigean tides exist. may be taken over long periods without involving the com- Because of the inherent danger for extreme coastal flood- plexities of calendar months; those successive differences ing produced by the combination of a hurricane plus are tabulated in col. 3. Finally, assuming a synodic month proxigean or perigean spring tides, this becomes an es- having a mean period of 29.530589 days, col. 4 indicates pecially critical aspect in evaluating tidal flooding poten- the corresponding number of synodic months represented tial. by the figure,in col. 3. Cols. 5, 6, and 7 repeat the same It has been established over a long period of record data for the time of perigee. Some interesting facts emerge that the month in which the greatest frequency of hurri- from the detailed analysis of this table, and the investiga- canes occurs on the Atlantic coast of North America is tion of the anom@listic period is particularly productive. TABLE 24.-Short-Term and Long-Term, Cyclical Relationships Between Close Perigee-Syzygy Alignments Calendar date Julian Difference No. of synodic Julian Difference. No. of anomalistic of syzyg-y date of syzygy between syzygy, cycles (to date of perigee* between peri@ee Cycles (to dates (days nearest 0. 1) dates (days) nearest 0. 1) 9/ 5/1603 2306791.2 2306791.0 383.8 13.0 384.8 14.0 9/23/1604 2307175.0 2307175.8 1077.9 36.5 1076.2 39.1 9/ 6/1607 2308252.9 2308252.0 383.9 13.0 384.9 14.0 9/24/1608 2308636.8 2308636.9 1461.8 49.5 1461.1 53.0 9/24/1612 2310098.6 2310098.0 1816.1 61.5 1817.3 66.0 9/15/1617 M1914.7 2311915.3 1461.8 49.5 1461.2 53.0 9/15/1621 2313376.5 2313376.5 1461.7 49.5 1460.9 53.0 9/16/1625 2314838.2 2314837.4 1816.2 61.5 1817.5 66.0 See footnote at end of table. 202-509 0 - 78 - 23 322 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 24.-Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments-Continued Calendar date Julian Difference No. of synodic Julian Difference No. of anornalistic: -fsyzygy date of syzygy between syzygy cycles (to date of perigee between per' ee cycles (to dates (days) nearest 0.1) dates (day.1 nearest 0. 1) 9/ 6/1630 2316654.4 2316654.9 146.17 49.5 1461.0 53.0 9/ 7/1634 2318116.1 2318115.9 383.9 13.0 3B4.8 14.0 9/26/1635 2318500.0 2318500.7 1077.9 36.5 1076.3 39.1 9/ 8/1638 2319577.9 2319577.0 383.9 13.0 384.0 14.0 9/27/1639 2319961.8 2319961.8 1461.8 49.5 1461.2 53.0 9/27/1643 2321423.6 2321423.0 1861.1 61.5 1817.3 66.0 9/17/1648 2323239.7 2323240.3 1461.8 49.5 1461.1 53.0 9/17/1652 2324701.5 2324701.4 1461.7 49.5 1461.0 53.0 9/18/1656 2326163.2 2326162.4 1816.1 61.5 1817.3 66.0 9/ 8/1661 2327979.3 2327979.7 1461.8 49.5 1461.9 53.0 9/ 9/1665 2329441.1 2329440.9 383.9 13.0 384.8 14.0 9/28/1666 2329825.0 2329825.7 1077.9 36.5 1076.2 39.1 9/10/1669 2330902.9 2330901.9 383.9 13.0 384.9 14,0 9/29/1670 2331286.8 2331286.8 1461.7 49.5 1461.1 53.0 9/29/1674 2332748.3 2332747.9 1432.3 48.5 1432.6 52.0 9/ 1/1678 2334180.8 2334180.5 383.9 13.0 384.7 14.0 9/20/1679 2334564.7 2334565.2 1461.7 49.5 1461.1 53.0 9/20/1683 2336026.4 2336026.3 1461.8 49.5 1461.1 53.0 9/21/1687 2337488.2 2337487.4 1816.1 61.5 1817.3 66.0 9/10/1692 2339304.3 2339304.7 1461.8 49.5 1461.1 53.u 9/11/1696 2340766.1 2340765.8 383.9 13.0 394.8 14.0 9/30/1697 2341150.0 2341150.6 1432.2 48.5 1432.6 52.0 9/ 2/1701 2342582.2 2342583.2 1461.8 49.5 1461.1 53.0 9/ 3/1705 2344044.0 2344044.3 1461.8 49.5 1461.1 53.0 9/ 4/1709 2345305.8 2345505.4 383.9 13.0 384.8 14.0 9/23/1710 2345889.7 2345890.2 1461.7 49.5 1461.1 53.0 9/23/1714 2347351.4 2347351.3 1461.8 49.5 1461.1 53.0 9/24/1718 2348813.2 2348812.4 1816.1 61.5 1817.3 66.0 9/14/1723 2350629.3 2350629.7 1461.8 49.5 1461.1 53.0 See footnote at end of table. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 323 TABLF 24.--Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments-Continued -Calendar date Julian Difference No. of synodic Julian Difference No. of anornalistic ofsyzygy date of syzygy between syzygy cycles (to date of perigee* between peri ee cycles (to dates (days) nearest 0. 1 dates (day@j nearest 0. 1) 9/15/1727 2352091.1 2352090.8 1816.1 61.5 1817.4 66.0 9/ 4/032 2353907.2 2353908.2 1461.8 49.5 1461.0 53.0 9/ 5/1736 2355369.0 2355369.2 1461.7 49.5 1461.1 53.0 9/ 6/1740 2356830.7 2336830.3 383.9 13.0 384.8 14.0 9/25/1741 2357214.6 2357215.1 1461.8 49.5 1461.1 53.0 9/25/1745 2358676.4 2358676.2 1461.8 49.5 1461.1 53.0 9/26/1749 2360138.2 2360137.3 1816.1 61.5 1817.3 66.0 9/16/1734 2361954.3 2361954.6 1461.8 49.5 1461.2 53.0 9/17/1758 2363416.1 2363415.8 1816. 1 61.5 1817.3 66.0 9/ 7/1763 2365232.2 2365233.1 1461.8 49.5 1461. 1 53.0 9/ 8/1767 2366694.0 2366694.2 1461.7 49.5 1461.0 53.0 9/ 9/1771 2368155.7 2368153.2 383.9 13.0 384.8 14.0 9/27/1772 2368539.6 2368540.0 1461.8 49.5 1461.2 53.0 9/27/1776 2370001.4 2370001.2 1461.7 49.5 1461.0 53.0 9/28/1780 2371463.1 2371462.2 1816.2 61.5 1817.4 66.0 9/18/1785 2373279.3 2373279.6 1461.7 49.5 1461.1 53.0 9/19/1789 2374741.0 2374740.7 1816.2 61.5 1817.4 66.0 9/9/1794 2376557.2 2376558.1 1461.7 49.5 1461.0 53.0 9/10/1798 2378018.9 2378019.1 1461.8 49.5 1461.1 53.0 9/11/1802 2379480.7 2379480.2 1816.1 61,5 1817.4 66.0 9/ 2/1807 2381296.8 2381297.6 1461.8 49,5 1461.0 53.0 9/ 2/1811 2382758.6 2382758.6 383.9 13.0 384.9 14.0 9/21/1812 2383142.5 2383143.5 1077.9 36.5 1076.3 39.1 9/ 3/1815 2384220.4 2384219.8 383.9 13.0 384.5 14.0 9/21/1816 2384604.3 2384604.3 1461.7 49.5 1461.3 53.0 9/22/1820 2386066.0 2386065.6 1816A 61.5 1817.4 66.0 9/12/1825 2387882.1 2387883.0 1461.8 49.5 1461.0 53.0 9/13/1829 2389343.9 2389344.1 1461.8 49.5 1461.1 53.0 9/13/1833 23SO805.7 2390805.2 1816.1 61.5 1817.3 66.0 See footnote at end of table. 324 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 24.-Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments-Continued Calendar date Julian Difference No. of synodic Julian Difference No. of anornalistic ofsyzygy date of syzygy between syzygy cycles (to date of perigee* between penijee cycles (to dates (days) nearest 0. 1) dates (days, nearest 0. 0 9/ 4/1838 2392621.8 2392622.5 1461.8 49.5 1461.1 53.0 9/ 4/1842 2394083.6 2394083.6 383.9 13.0 3a4.9 14.0 9/23/1843 2394467.5 2394468.5 9/ 5/1846 2395545.3 1077.8 36.5' 2395544.6 1076.1 39.1 383.9 13.0 384.9 14.0 9/24/1847 2395929.2 2395929.5 1461.8 49.5 1461.1 53.0 9/25/1851 2397391.0 2397390.6 1816. 1 61.5 1817.3 66.0 9/14/1856 2399207.1 2399207.9 1461.8 49.5 1461.1 53.0 9/15/1860 2400668.9 2400669.0 1461.8 49.5 1461.2 53.0 9/15/1864 2402130.7 2402130.2 1816.1 61.5 1817.3 .66.0 9/ 6/1869 2403946.8 2403947.5 1461.8 49.5 1461.1 53.0 9/ 6/1873 2405408.6 2405408.6 383.9 13.0 384.8 14.0 9/25/1874 2403792.5 2405793.4 1077.8 36.5 1073.9 39.0 9/ 7/1877 2406670.3 2406869.3 383.9 13.0 385.2 14.0 9/26/1878 2407254.2 2407254.5 1461.8 49.5 1461.1 53.0 9/27/1882 2408716.0 2408715.6 1816.1 61.5 1817.3 66.0 9/17/1887 2410532.1 2410332.9 1461.8 49.5 1461.1 53.0 9/18/1891 2411993.9 2411994.0 1461.7 49.5 1461.1 53.0 9/18/1895 2413453.6 2413455.1 1816.0 61.5 1815.9 65.9 q/ 9/1900 2415271.6 2415271.0 1461.9 49.5 1462.5 53.1 9/ 9/1904 2416733.5 2416733.5 383.9 13.0 384,8 14.0 9/28/1905 2417117.4 2417118.3 1077.9 36.5 1076.2 39.1 9/10/1908 2418193.3 2418194.5 383.9 13.0 384.9 14.0 9/29/1909 2418579.2 2418579.4 1461.8 49.5 1461. 1 53.0 9/30/1913 2420041.0 2420040.5 1432.2 48.5 1432.5 52.0 9/ 1/1917 2421473.2 2421473.0 383.9 13.0 384.9 14.0 9/20/1918 2421857.1 2421857.9 1077.9 36.5 1076.2 39.1 9/ 2/1921 2422935.0 2422934.1 383.9 13.0 384.9 14.0 9/21/1922 2423318.9 2423319.0 1461.7 49.5 1461.0 53.0 9/21/1926 2424780.6 2424780.0 1816.2 61.5 1817.4 66.0 See footnote at end of table. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 325 TABLE 24.-Short-Term and Long-Term Cyclical Relationships Between Close Perigee-Syzygy Alignments-Continued Calendar date Julian Difference No. of synodic Julian Difference No. of anomalistic ofsy.ygy date of syzygy between syzygy cycles (to date of perigee* between perigee cycles (to dates (days) nearest 0. 1) dates (days) nearest 0. 1) 9/12/1931 2426596.8 2426597.4 1461.7 49.5 1461.1 53.0 9/12/1935 2428058.5 2428058.5 383.9 13.0 384.7 14.0 9/30/1936 2428442.4 2428443.2 1077.9 36.3 1076.3 39.1 9/13/1939 2429520.3 2429519.5 1816. 1 61.5 1817.4 66.0 9/ 2/1944 2431336.4 2431336.9 1461.8 49.5 1461.1 53.0 9/ 3/1948 2432798.2 2432798.0 383.9 13.0 384.8 14 0 9/22/1949 2433182.1 2433182.8 1077.8 36.3 1076.2 39.1 9/ 4/1952 2434259.9 2434259.0 383.9 13.0 384.8 14.0 9/23/1953 2434643.8 2434643.8 1461.8. 49.5 1461.2 53.0 9/23/1957 2436105.6 2436105.0 1816.1 61.5 1817.3 66.0 9/14/1962 2437921.7 2437922.3 1461.8 49.5 1461.1 53.0 9/14/1966 2439383.5 2439383.4 1461.8 49.5 1461.1 53.0 9/15/1970 2440845.3 2440844.5 1816.1 61.5 1817.3 66.0 9/13/1975 2442661.4 2442661.8 1461.8 49.5 1461.2 53.0 9/ 6/1979 2444123.1 2444f23.0 383.9 13.0 384.8 14.0 9/24/1980 2444507.1 2444507.8 1077.8 36.5 1076.1 39. 1 9/ 7/1983 2445584.9 2445583.9 383.9 13.0 384.9 14.0 9/25/1984 2445968.8 2445968.8 1461.8 49.5 1461.1 53.0 9/25/1988 2447430.6 2447429.9 1816.1 61.5 1817.3 66.0 9/16/1993 2449246.7 2449247.2 1461.8 49.5 1461.2 53.0 -0/16/1997 2450708.5 2450708.4 *Xote: It has been seen (part II, chapters 3, 4) that certain lunar perturbations are especially critical at times of perigee-syzygy. During the early course of the research for this project, it was discovered that the utilization of a substantial and presumably quite sufficient number of reduc- tion terms among the theoretical expressions for solution of the Moon's orbital position and motion was still quantitatively inadequate. The insuffi- ciency lay in the determination of geocentric horizontal parallax and the times of perigee and syzygy to the accuracy required for consistency with ephemeris data. A corresponding computer reprogramming was introduced, expanding from the partial sequence of analytic terms in table 16A to the full complement of terms given in table 16B. All tables in this monograph involving lunar positions and motions-including the data displayed in the computer printout of table 16-are now based either upon the full reduction expressions contained in table 16B, or upon The American Ephemeris and Nautical Almanac. However, table 24 already had been typeset from data computed on the basis of the initial, smaller number of analytic terms. The time differ- ences, perigee minus syzygy, may occasionally vary from 1-3 hours between the solutional accuracies of the short and long methods, if the individual differences are additive in the same direction. Thus the Julian dates of perigee in table 24 (which, as throughout this work, are represented as a function of their intervals from syzygy) may, in some few cases, differ by 0.1-0.2d from the more precise data obtainable from table 16. Because such slight differences do not materially affect the average values of the long-range cycles of recurrence of perigee-syzygy listed in table 24, these original values calculated from a smaller number of analytic terms have not been altered. The periodic relationships present are quite readily apparent. 326 Strategic Role of Perigean Spring Tides, 1635-1976 The various repeating cycles of anomalistic months moon and in declination from positive to negative values between successive perigee-syzygy dates as given in col. 7 between successive cycles should also be noted. are: 14.0, 39.1, (52.0 or 53.0), and 66.0. Assigning each The two cases of proxigee-syzygy marked with a solid cycle a serial number in this same sequential order it is star (*) were both accompanied by severe tidal flood- obvious that, with some few interruptions and irregulari- ing (see table 1). A slightly different situation exists ties (i.g., wherever 52 instead of 53 cycles occur), the for the two cases identified by an open star The two principal cycles which are systematically repeated great coastal flooding of 1869 Oct. 5 in New Brunswick, are 1-3-3-4-3-4-3-3 and 1-3-4-3-3-4-3-1-2. Canada (see page 112), was associated with a perigee- Adding the total number of cycles contained in each syzygy alignment on this same date ( -7rma.=6l'244", P - S = - 7 ") . However, the flooding occurred at the end of these repeating series gives 411.0 and 411.1 anornalistic of a 221.5-day interval (194 .0d +27.5") following the months, respectively. The average between these two 1869 Feb. 26 date listed in the above table. This is equiv- values is equivalent to 11,326 mean solar days or 31.010 alent to the normal period (7.5 months of 29.5') between tropical years. As noted in the preceding section, this is successive perigee-syzygy alignments possessing the small- also very nearly equivalent (11,324 days) to 55 cycles est P - S intervals in any one lunar year (see fn. p. 17 7 ). of the 205.89-day average period between ordinary peri- Obviously, therefore, this case was paired with the gee-syzygy alignments. February 26 date in the same 31-year cyclical relation- Using this 31-year cycle, it is now possible to establish ship responsible for a very close proxigee-syzygy align- an interesting relationship connecting several of the very ment and large parallax. In the same manner, the major major tidal floodings on the east coast of North America tidal flooding of 1900 Oct. 11-12 (maximum (see table 1 ) which have occurred at times of large paral- r = 61126. 1 ". P - S= - 7" on Oct. 8) occurred '221.5 days lax ( 7r) and close perigee-syzygy separations (P-S). after the closest P - S alignment in the year on 1900 These cases are starred in the list below. Mar. I as listed in table 25. Exactly the same reasoning applies to the influence of the 31-year cycle upon the TABLE 25.-Cases of Extreme Tidal Kroding Coincid:ng With 1900 Oct. I I - 12 flooding. To date, flooding events have Long-Term Astronomical Cycles of Close Alignment Between not been discovered which are related to the 1776, 1807, Perigee and Syzygy and 1838 dates. Lunar Date 7r P-S Attention. is drawn to the near-equatorial position of Phase (G.c.t.) (at proxigee) 0 h Sun and Moon, the large lunar parallax, and the classifica- tion of the astronomical circumstance as one of extreme NM 1776 Feb. 19 . . . 61'26.411 -12.0 +4 proxigee-syzygy on 1993 Mar. 8, should meteorological FM 1807 Feb. 22 . . . 61'30.211 +5.2 +2 conditions supporting tidal floodi .ng prevail within a pe- NM 1838 Feb. 24 . . . 61'27.111 -12.0 +2 FM* 1869 Feb. 26 . . . 61128.711 +10.1 + I riod of several days on either side of this date in lowland NM* 1900 Mar. I . . . 61128.211 -2.9 +1 coastal regions. This date is the next 31-year multiple FM* 1931 Mar. 4 . . . 61129.01' +9.3 -1 following the 1962 Mar. 6 coastal flooding catastrophe NM* 1962 Mar. 6 . . . 61'26.6" -8.2 0 on the mid-Atlantic coast. FM 1993 Mar. 8 . . . 61'30.111 +0.6 -2 Meteorological Aspects of Coastal Flood- It will be observed that all of the above are cases of ing), at Times of Perigean Spring Tides astronomical proxigee-syzygy (and hence associated with proxigean spring tides) according to the parallax limits it has been stated repeatedly throughout this work that of @_-61126.511 to <61'29.0" previously defined. (Strictly speaking, the first example is but negligibly below this perigean spring tides alone are not sufficient to cause major coastal flooding, but must be accompanied at the range; the second and the last are, in fact, well into the times of attaining one or more of their suc7cessive peaks extreme proxigee-syzygy range.). All have very low P-S of astronomical high water by strong, persistent, onshore values, and these are seen to converge to a minimum at winds. the time of the great 1962 flooding, event. The slight It is in no way the intention of the present volume to excess in period over an exact 31 years is responsible for enter into a 'detailed discussion of the nature of the the syste matic forward sliding of 2-3 days between cycles. meteorological factors contributing to each of the coastal The alternation in lunar phase from new moon to full flooding events enumerated in table 1. This would re- Classification, Desi@,anation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 327 quire another volume of equal lcng@th, and representative tation in chapter 8. Curves showing the actual rate of tide descriptions of the meteorological circumstances accom- growth subject to the combined effect of astronomical panying specific cases of coastal flooding attributed to -causes, plus wind, have been prepared for the 1962 storm tides" or "storm surges" are already available in March 6-7 tidal flooding event. Finally, aerial and ground the scientific literature (see hibliography--catcgories 18 photographs of the extent of structural and erosional and 42). damage resulting from various of the most recent of these It would, however, bc remiss to conclude the present coastal flooding events along the North American coast- study without providing the meteorological conditions line are included. acting on the tides in a representative group of coastal It must be brought out in the latter connection that re- flooding events. To provide a suitable comparison, these strictions to photography-even from the air-are often should be chosen chronologically and at random (see the imposed by the combination of the ocean waters intruding E'xplanatory Comments preceding figures 50-69) from over the land ''strong and gust@ winds, a turbulent atmos- the total number of cases in table 1. Such a purely rep- phere, intense precipitation and/or dark, heavy, and low rcsentative documentation of the statc of the weather ac- cloud cover generally associated with such storm-assisted companying cases of major coastal flooding which have tidal flooding events. Hence any closeup film documen- occurred at the times of perigcan spring tides is contained tation of the flooding effects often is not possible until the in the following pages. seawater has receded from the land, and meteorological Surface synoptic weather maps prepared by the U.S. conditions permit detailed photography. The photographs Weather Bureau (now the National Weather Service) , of final destruction caused,,taken after the waters subside, meteorological and climatolopcai records, cloud-cover do not in any sense reflect the total chaos nor the violent photographs taken from artificial satcllitc.,@, and other data conditions prevalent during the actua I period of flooding concurrent with these coastal fl ooding events are variously from the sea. presented for comparison with the flooding data. According to this plan, the surface synoptic weather Selection of Multidisciplinary I maps most closely accompanying each of 20 cases of Data Sources major tidal flooding occurring at times of perigean spring Because of the tremendous amount of information re- tidc-i are grouped together in succeeding pages of the searched and the profusion of data reduced and made present chapter (see table 26). To provide an effective available for graphic presentation, a'concept of diversifi- balance, these are followed by the 'synoptic weather maps cation becomes the most logical selection principle in for 20 cases of nonflooding which accompanied instances providing a balanced representation of such data suit- of very close alignment of perigee-syzygy, but in which able for interdisciplinary comparison. the necessary strong, persistent, onshore winds to support Seven of the lettered weather maps corresponding to the augmented astronomical high tide were lacking (see dates of perigean spring tides, for which news accounts table 27). Tables 28a-28b list, respectively, represent- of the accompanying coastal flooding are provided (see ative cas ses of (1) hurricanes concurrent with perigean table 5), and for which rate-of-tide-rise curves also have spring tides and (2) impairment of hydrological runoff been computed (see chapter 8), are among the cases by such tides. listed in table 26. These cases, which permit a full inter- There ensues a text discussion of an additional eight comparison of data, comprise a part of the first series.of cases of perigean/proxigean spring tides deserving of spc7 weather maps, arranged in chronological order. The spe- cial attention because of the special circumstances thereof cific cases involved arc A-43, B-50, C-51, F-68, G-69, and/or the very severe degree of accompanying tidal flood- H-72, and 1-83c. One case (M-98c,w) includes both a ing. (Table 29 lists the synoptic weather maps provided weather map and two individual tide 'curves, but has no for four of these cases.) Certain supplementary news- accompanying printed news articles. An additional seven paper account-, and quoted excerpts from report litera- cases among this first group of weather maps are repre- ture arc also presented for their topical value. Among sented by news summaries of the associated severe tidal other data included for these special instances of tidal flooding but, because of space limitations, do not possess flooding described in the text are the following: A curve matching tide curves. These cases are 25, 34, 35, 63, 64, plot showing the predicted rate of tide growth subject 74, and 94. to astronomical causes at the time of the 1931 March 4-5 Five cases of coastal flooding J-83e, J-85, 86, tidal flooding is introduced as a basis for further interpre- M-98w, and N-99) for which tide curves as we .11 as daily 328 Strategic Role of Perigean Spring Tides, 1635-1976 weather maps and published newspaper reports relative ing represented was associated with the perigean spring to the flooding are provided in this work-and two (F-68 tides which occurred on, or very near to, the date of one and 0-100), supplemented by newspaper excerpts but of these weather maps. The group of weather maps contained in table 26 there- no tide curves-appear separately in this chapter, where fore involves actual coastal flooding events in which (1) a detailed discussion of these major tidal flooding events close perigee-syzygy alignments (and resulting perigean is presented. Tide curves for other outstanding examples spring tides) as well as (2) strong, sustained, onshore winds of coastal flooding (D-57 and E-58) for which news (usually generated by offshore low pressure centers) joined accounts are available-but this time with the omission to become the cause of coastal flooding. As in all examples of the full-page weather maps--are also included in chap- used, the incidents of tidal flooding were selected, without any systematic predetermination, from the catalog of 100 ter 8. Both a weather map and tide curves are published such representative events compiled in part 1, table 1 of for K-87 in the text, but because of the widely scattered chapter 1. and unusual nature of this event, U.S. Weather Bureau (b) A second, control group of 20 weather maps in table sources are used, and news articles are not included in 27, chosen with equal randomness in each decade through- out the same 90-year period, show the meteorological condi- table 5. Satellite cloud-cover photographs taken by night- tions at times of extreme close perigee-syzygy alignments. infrared and day-infrared cameras are also provided for The factors producing perigean spring tides also were se- event N-99. lected to include a variety of solar and lunar positional relationships representative of significant tide-amplifying The Correlation of Meteorological and forces and inequalities, as described in chapter 5. These Astronomical Data different circumstances are listed in the "Remarks" column As has been noted in both the first and present chapters of the table. The resulting astronomical tides were, as in of this work, meteorological factors may act either to su the first series of examples, raised to unusual levels, but p- no pronounced flooding was observed in these cases, due to port, or to reduce, the effects of astronomically induced the complete absence of persistent, strong, onshore winds tides. Because of the large area of coastal coverage, pro- at the time. vided by synoptic weather maps, including the adjoining The weather situations portrayed in this category are oceans and ship weather reports, these offer the most con- generally dominated by large high pressure systems, in which venient means of detennining both the continental and wind conditions ranging from light and variable breezes to a complete calm are common. The associated high baro- marine pre,;sure and wind patterns in existence at the metric pressure and/or offshore winds are both counter- time of perigean spring tide. The daily synoptic weather productive to the generation of additionally augmented and maps of the United States used as data sources through- flood-producing high tides. out this work are copies of those compiled and published (c) Although, for reasons given in part 1, chapter 1, the by the U.S. Weath@r Bureau (since October 3, 1970, consideration of coastal flooding resulting from the impact of hurricanes does not form a major part of the present the National Weather Service) as a part of its forecasting investigation, a few appropriate weather maps depicting analysis and historical record series. Tle oversize printed conditions in which hurricanes have quite closely coincided maps in all cases have been photographically reduced, with perigean spring tides are included in table 28a. and appropriate overlays and spellouts have been applied Together with the accompanying explanation in the text of the present chapter, these examples will help to substan- to emphasize the critical factors of wind direction and velocity (and the movement of relevant low pressure tiate the role of perigean spring tides, when acted upon by the onshore winds of a hurricane. The result is, by com- atmospheric pressure systems) as these variously affect parison, a much greater amount of water damage through the potential for tidal flooding in connection with peri- tide-supported flooding-in addition to the hurricane-in- gean spring tides. duced wind damage-whenever such hurricanes occur near the times of perigean spring tides. GROUPING OF THE WEATHER MAPS In an example at the opposite end of the scale, a typical case is also included in table 28b in which the unusually The series of synoptic weather maps contained on the high waters associated with perigean spring tides-because following pages consists of four distinct sections, within of the influence of strong, onshore winds-became a major each of which the maps are chronologically arranged: factor in blocking hydrological runoff. Quite numerous in- . (a) The first section consists of 20 weather maps show- stances exist in which exceptional perigean spring tides ing-as closely as can be correlated-the meteorological (even without the support of onshore winds) have, through conditions accompanying a randomly selected group of ex- such blocking action, variously caused, contributed to, or amples of major tidal flooding. These were observed along severely aggravated coastal flooding associated with surface either the east or west coasts of North America (or on both runoff of heavy rainfall-or melting ice and snow. A num- coasts, simultaneously). Each such instance of coastal flood- ber of such examples are considered in the text. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 329 (d) Finally, a special series of eight weather maps repre- presented,. together with an appropriate discussion thereon, senting, like those in table 26, cases in which perigean in chapter 8. spring tides accompanied by strong, persistent, onshore The corresponding daily synoptic weather map for many winds have caused prominent coastal flooding, are listed in of these cases is included in a grouped series of maps fol- table 29. Together with four other examples of major tidal lowing these comments (table 26), or may individually flooding, they are of sufficient importance or uniqueness accompany the detailed discussion of representative exam- to be discussed individually in the text of this chapter. ples of major tidal flooding contained in the text of this Tables 26-29 thus list the weather maps available in each chapter (table 29). In addition, a compilation of newspaper of the above four groups. Immediately following the pres- articles covering 50 of the 100 representative cases of major ent discussion, a set of Explanatory Comments is provided tidal flooding itemized in table 1 graphically describes the summarizing the various symbols, descriptors, and techni- extent of the coastal flooding occurring in conjunction with cal data used on these synoptic weather charts. To determine these various cases of perigean spring tides. The latter com- the full implication of all meteorological factors, reference pilation comprises table 5 of part I, chapter I - also should be made to the text and cross-related graphic The procedure previously mentioned-involving a ran- materials of this and other chapters for the following per- dom sampling of the tremendous quantities of meteorologi- tinent topics: (a) the practical effects of strong, sustained, cal and tidal data available-makes practicable a coordi- onshore winds in driving the amplified waters of perigean nated investigation of the various related, interdisciplinary spring tides onto the coastline (chapter 7) ; (b) the value factors which enter into such cases of tidal flooding. This of coordination and intercomparison of these weather maps analysis is expedited through the intercomparison of those with the computed rate-of-growth tide curves illustrating various sources of data which, because of their common rela- the astronomically induced, rapid rise in water level at time tionship in time, bear the same alphanumeric designation in of perigee-syzygy which provides a natural setup condition the various index lists (tables 1-5, 26, 27, 28a,b, 29, 33). for wind-actuated onshore flooding (chapter 8) ; and (c) The first date given (in roman type) in the upper right- the possibility of assessing and grading the violence of the hand corner of each weather map is the date of the weather coastal flooding resulting from the combination of perigean map; each map has been chosen to accord as nearly as spring tides and onshore winds by means of contemporary possible with the date on which coastal flooding occurred. newspaper accounts of the,damage produced, as given in The. calendar date is immediately followed by the eastern table 5 (part 1, chapter I). standard time (e.s.t.) for which the weather map is plotted. [Subtract 3 hours to obtain Pacific standard time (P.s.t.) EXPLANATORY COMMENTS CONCERN- for cases of flooding on the west coast; Greenwich, civil time ING THE MANNER OF DESIGNATION (G.c.t.) may be obtained by adding 5 hours to e.s.t.1 OF WEATHER MAPS AND THE CON- The second entry (in italics) gives the date and time CURRENT PERIGEE-SYZYGY DATA (e.s.t.) of mean perigee-syzygy; this mean epoch of perigee- syzygy for any occurrence is obtained by taking half the The number in the upper left-hand corner of each difference between the respective times of perigee and syz- weather map is a serial number for ease in chronological ygy-in the sense perigee minus syzygy-and adding the re- comparison and evaluation of these maps. All maps con- sult algebraically to the time of syzygy. All time values are tain such a serial number. In addition, some of the weather rounded off to the nearest hour. The last number, in paren- maps are designated by a capital-letter prefix. This is a key theses, gives the algebraic difference in time, in hours, be- letter, to allow a ready intercomparison of a variety of tween perigee and syzygy (likewise taken in the sense perigee data-in some cases located at different places in the book- minus syzygy). but all pertaining to the same example of tidal flooding. Cases in which the difference in time between perigee Only significant cases of tidal flooding which are the subject and syzygy is less than 24 hours are tabulated in the com- of detailed investigation in the presen 't work are designated puter printout (table 16). In this table, the times are given by a key letter. In this system of computation of standard for syzygy (plus an additive or subtractive value, in hours, comparative data for master cases, one such example of to give the time of perigee). All times given are in ephemeris coastal floodin- associated with perigean spring tides has b time (e.t.)-which corresponds very closely with, and for been chosen, at random, in each decade from 1910 (at the present purpose may be assumed to be equal to, Green- which time 37 harmonic components replaced the previous wich civil time (G.c.t.). Although the times used (imme- 19 in Coast and Geodetic Survey tidal computations) down diately following the date) have been consistently rounded to 1970. These sample cases have purposely been selected off to-the nearest hour, they are sufficiently accurate for on both coastlines of North America, representing both semi- diurnal and ,mixed tides, and distributed throughout a wide reference use in connection with these weather maps. range of latitudes as well as varying astronomical, hydro- Wherever the separation-interval between perigee and b 0 syzygy is equal to, or greater than 24 hours, the difference graphic, climatological, and meteorological conditions. has been taken from The American Ephemeris and Nautical Appropriate tide curves based on predicted tide heights Almanac, or from astronomical data contained in annual at appropriate nearby tidal reference stations, and showing the accelerated rate of tide growth subject to the influence tide tables. All such values are similarly rounded off to the of perigce-syzygy, have been prepared in figs. 153-163 (table nearest hour, since th 'e time of perigee is now customarily 33) for 16 prototype examples of tidal flooding. These are oriven only to this accuracy. In earlier years, the times of 330 Strategic Role of Perigean Spring Tides, 1635-1976 both perigee and syzygy were tabulated to the nearest min- All of the weather maps shown were plotted subsequent -t. t-, 1 .1 - . . . I 332 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 26.-Surface Synoptic Weather Mapsfor Twen@y Representative Cases of Coastal Flooding Associated With Perigean Spring Tides and Strong, Sustained, Onshore Winds Key letter Weather map date and mean Perigee and serial No. perigee-syzygy date -syZygy Location of tidal flooding (e.s.t.) (in hours) 25 1895 February 8 8. Oh 4) Staten Island, N.Y.; Providence, Newport, R.I.; Cape Cod, New Bed- February 9 10.0h ford, Boston, Mass.; Bangor, Portland, Bath, Me. 27 1896 November 6 8. Oh (-15) Pictou, Nova Scotia November 4 19.5h 34 1901 November 24 8. Oh 9) Asbury Park, Sea Bright, Keyport, NJ.; Coney Island, N.Y.; New Haven, November 25 15.5h Stamford, Greenwich, Conn.; Chatham, Provincetown, Mass. 35 1908 February 2 8. Oh 8) Port aux Basques, Newfoundland; Harrington Harbour, Quebec February 2 O.Oh 41 1917 October 1 8. Oh (-27) Moncton, Sackville, Amherst Harbor, New Brunswick September 30 2.5h A-43 1918 April 10 8. Oh (-19) Sea Bright, Atlantic City, NJ.; Staten Island, Rockaway Beach, southern April 10 14.5h Long Island, N.Y. B-50 1927 March 3 8. Oh (+15) New England coast March 3 21.5h C-51 1927 April 2 8. Oh 6) Atlantic City, N.J.; Delaware April 1 20.Oh 63 1933 December 17 8. Oh (+ 9) Hoquiam, Cosmopolis, Aberdeen, Montesano, Wash. December 17 2.5h 64 1934 August 21 8. Oh (-24) Balboa, Malibu, Newport, and Laguna Beaches, Calif. August 24 3.Oh F-68 1939 January 4 7. 5h (+14) Aberdeen, Hoquiam, Neskowin, Wash.; Astoria, Marshfield, Coos Bay, January 5 23.Oh Delake, Oreg.; northern Calif. G-69 1940 April 21 7. 5h (-34) Boston, Minot's Light, Deer Island, Bassing's Island, Hull, Winthrop, April 21 7. Oh Quincy, Mass. H-72 1945 November 20 1.5h (-13) Eastport, Machiasport, Portland, Me. November 19 3.5h 74 1948 January 26 1. 5h (+ 4) Vicinity of San Francisco, Calif. January 26 4.Oh 1-83e,w 1959 December 29 1.0h (-18) Atlantic City, N.J.; Long Island, N.Y.; Hull, Boston, Provincetown, December 29 5.Oh Gloucester, Cape Cod, Barnstable, Mass.; Kennebunkport, Me.; San Pranciso Bay area, Calif. 84e,w 1961 January 15 1.0h (+ 1) Atlantic City, NJ.; Delaware; Ventura County, Calif. January 16 17. 5h 86 1962 October 13 1.0h 9) Local estuaries and bay locations, Oreg., Wash., and northern Calif. October 13 3.5h L-93e,w 1971 March 26 7. Oh (-10) Vicinity of Sewell's Point, Virginia Beach, Willoughby, Ocean View, March 26 9.Oh Norfolk, Sandbridge, Va.; Oxnard Shores, Calif. 94 1971 April 23 7. Oh (-34) Oxnard Shores, near Oxnard, Calif. April 24 6.Oh M-98e,w 1973 December 11 7. Oh (+21) Tokeland, Raymond, South Bend, Wash.; Seaside, Astoria, Newport, December 10 7.5h Oreg.; Halifax, Nova Scotia full-size monthly report- Storm Data (initiated January retical significance to this study because of its association 1959). Thus, detailed technical data concerning this with astronomical tides predicted to rise (at Boston) 6.3 case of coastal flooding are not available. However, the ft above mean tidal level at this location and, therefore, history and course of the atmospheric storm which added particularly vulnerable to wind attack. It is technically its effects to perigean spring tides to produce tidal flood- important because of the extremely close perigee-syzygy ing are included in an article appearing in the New York alignment which existed on this occasion (see reference Times for March 5, 193 1, which is reproduced, in partly note 4 to chapter 4, part II at the end of this volume) abbreviated form, below. (See figs. 95, 96.) and which was responsible for the greatly enhanced astro- This example is historically meaningful as an instance nomical high tides experienced. of perigean spring tides accompanied by widespread As an example, the value of the astronomically pro- coastal flooding. The March 5 flooding event is of theo- duced higher high water predicted for Boston, Mass. . . . . . . . . . . . . . . . . . . . . -!!MMM, I iH - -ing ju i i i M a@. fv N v jgp@ N YJ, N. piFi FN J' P eV IS-1 @h-- J, 7-e Ln M, cn,> 42 (D ggill..Tiu U M"M MU U, . ....... ... it lik1W UtW. 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ILI iij r- el".! 5 1 , 4 It a 41 4 0.11, it it A J,@ O_jf V., 'I u@ @z T 15 4 17 ur d @4 q., Tj @Fl iJ ci ZM4 VX ;5 r Pl 0@ M r, @q js@ @; m,47- JZ +7M, 5 t T" ti co Q14 "77f" AV Ns_@ r --- - ---------- c P. 9Z61-,CC9[ "SdP!1 -@Uz-"IS uvdD'Z-19J 910Y 92D viggg-p-nu ffiul' 'tg U all. h N pan o i N1 vtaL - ..; -a @i @t@ - @ T4 MI a-M ;P N, q @ I N1- grip" FjPq Ut"T "@_`WF 1"Un G UM ',9 jil ;I g3 115 c;[email protected] wt W@-i U H y' PINS Tj I'll, 2 k MUPH. P k 4@4 HU 0. let M7F ""A -2t, kv@ .'!'i MR.! lo W Y_ t 14. n v, van 91 'N' 'PION[-M ev, - Xel IR N 'pap, inig w 2112 -p @@rzu.&y We@. @igj IL, II ell 05 j., W-1 gli -M p"M MURgo @@wo g '@ov @ggnEoooi-- v pvpo@n .......... .. . ....... .......... .......... ..... ...... L .... ...... ....... . ............ ....... 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A IUR Fw R I A I I- r Jt 14 Oil -@K TE TH-K "A' . ..... .. . .... .. ... t t t 1t ------- ---- . . . . ............. . . .......... . . ...... 9461-fC91 'SdP!j @UU(fS UWD'111,9d 10 OJOY 9299JV.ZjS NO ffl- , 5 C, q f0- fin q" z z 41 q LI ,g,, -4sin"iw la RN t, i T,' t4 ,Qj 'it2 n 1:7F M, A) VIP P., -& 1, 4 I Ll Zt 7 ci t 'gX Rv 44- 'uw 4.: 2 P 0 rl lt4 A 05, 0 (D c > tN L s2uzpoolg lop!j p.-gay @Swp!j fful.111S uvaffz.&,gj 10 @jpzpouaj PUD luozlvuff?Sg(g lumpogys'VID 1948 JANUARY 26 1.5h. January 26 4. 0 h. (4) po U. S. DEPARTMENT OF COMMERCE V1 AVERELL RARRIMAN, S-.-, 2!7 WEATHER BUREAU A Ft, X b It"s 14 -7 7: ,j r jt PIN WT@ AS T 13 71 -t " ; . --!, ----, IN L-L '04 QN1 U, sv,@iv@ ED 0 im SEP N "T o" 7 V 4o, cx4> FIGURE 63 74@ F9 0 90 ol Is; 4o';/' "Ai Akl ......... . --'5e als, aa! np ................ W4 "Y' C/ @Jt 14r. k. ........... Mto" //I wo I@b cc N3 61 kA ORY NJ tl 4 4K SD'ul 001,q IDP!,L JUP.?.-Y @S'qp!'L guutfs YM-2229d 10 Xj!32POZj0d PUD 'UOjjVUgjS?(g 'UO7;V,?Y!SSVjD T 8 4 1961 JANUARY 15 1.0h. January 16 17.5h. (1) 00 "W-A @j Y' 'A bi') 4-, co) _ej fo g@ con v;, GIV I'," ZIP za 4"'', @ Z- @01 AINED 0 sus N SHORF,'@@ gr' f, c' 'ti WIND FZ -"1061 ye i a'4 F4 P) 0@ iz, M STIMIlarl AT-1; ft@. yi' E. S. If.. mcr'lul . ...... s-eTxrl K FioURE 65 1969 OCTOBER 13 1.0h. October 13 3.5h. (-9) S ... . ........ 0, el IIAM@ cr NO 25 'op Co. I @j W- 41 S;, P1 STRONG 440`@ ALONG R X V, 35, w6 wn ged @@ Jv@ , ".2 1 ... ron ....... .. jZ1 4S 001rw@ 37 W,A . ...... t 0h 2v Do S&RFACE WEATHER AND STATION WE AT 1:00 A. M, K S. . SPMMEN 00 0. too- 95. 85. Fic;uRE 66 V@-93o,vv 1971 MARCH 96 7.0h. March 26 9.0h. I". I'D' '051 Ica. 95, so, 351 Cal 51 7W G@@ ---- -------- f;@- lop", lot". I Or FL@ Ff 4 10 '-x-L "b A .9 6 EV 25 60 'd a it 4A 17"hIl/ (i4 @4 0@@O--" 7; s"O Ni ?I 12r@ "'It, P11 I, 'Pjj ct I @9 29 f), IPI@ r, X @'A- E X E 151 G lk: 8 an ;1' ? @ 11, @i Ilk @k "Y lilt;' C117 21 r -d@J PI'V @\S@r 1b 3v AP11% lif- F I D 41 0", 0i .W-",nA '4' -a AND GYA l.0-11ILt0- 11EIGHT C-TOU11S AT Y:00 E.S.Y. IT Too Ill Ei, Ili - - - .. --- .. - ---- 120' FiGuRB 67 1971 APRIL 23 7.0h. April 24 6.0h. (-34) 130. 12S* 12w 116, wv- ----95. 9w 05, W 75, W 65, 60 55, of! 1@12 1017 VOIG i-0;26r 00 3:j" 993 x Ft ;JO Wd- ft -a t-.t. 2 14@ 4@ OL cu., Z,. C, 39 "u, J6,1L f 40 '43 17, tj@ cl@ ji ak, /19 '6nA rA 25// rt" 2 V1 ct@ -J, Z YO j f A:T@ 'Al NV 'o, t-1 J, 46, It A Cz- A-I..;. 1E. S. Y. 5m-@, ".An AT 11'0M. EST SW.-Act vJCAYNE" @Ilfkllll 115 90, FiGuRB 68 1973 DECEMOER 11 7.0h. December 10 Z.5h. (2Y) r- 125. !?0* 1W 8Q. 7Y 65' Zn-rl- AL 1 1-16 1012 1012 0 004 100810121016 lb2og. 1024 7- -o 16 - r-,,e -jw % i ,,, 0 u Ai '6N F )WHORE ffiNns, MNOS S-1 Zvi 0". 0,4 z X 2;@ "s-j )8l 2-i v G-4 2@s W @Ovl' 4;A ab -ss Ml 9V@7 -18 -M"A.d @! @- - "s, 49 % a@ 'Co. IS 40" /A 1 Z55 P-14L 270 37 A SURFACE WEATHER MAP AND STATiON WEATHER AT 7: 00 A, M . E, S.T. @T 7.00 1;5 95. FIGURE 69 Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 353 TABLE 27.-Surface Synoptic We ather Maps for Twenty Representative Cases of Nonflooding Conditions Associated With Perigean Spring Tides Which Were Accompanied by Light and Variable Winds and High Atmospheric Pressure Weather map date and mean Perigee Serial No. perigee-syzygy date - syzygy Remarks 1. s. t. (in hours) 151 1893 December 23 20. Ch 2) Near-maximum parallax and declination, occurring at the winter solstice December 22 23. Ch and near perihelion. 152 1899 January 12 8. Ch (+3) Large parallax; close to perihelion. January I 1 19. 5h 153 1912 January 5 8. Oh (+6.5 min.) Near maximum parallax; occurring at perihelion; very close separation- January 4 8.5h interval. 154 1922 September 22 8. Oh (+0 Total solar eclipse; autumnal equinox; and Moon very nearly on September 21 0. 5h Equator. 155 1923 November 9 8. 0h (-27 min.) Large parallax; very close separation-interval. November 8 10. Ch 156 1928 November 28 8. Ch (+5) Large paralax and positive declination. November 27 6. 3h 157 1930 January 15 8. Oh (+2) Near maximum parallax and high positive declination, occurring near January 14- 18. Oh perihelion. 158 1935 September 13 8. Ch (-2) Very large parallax; Moon very nearly on Equator. September 12 14. Ch 159 1940 October 2 7. 5h (+3) Total solar eclipse; Moon near Equator. October 1 9. 5h 160 1944 October 2 1. 5h Moon very nearly on Equator. October 1 17. 5h 161 1950 May 3 1. 5h (+2) Large parallax; close separation-interval. May 2 1. Oh 162 1950 December 9 1. 5h (-8) Large parallax; very high negative declination (ascending node at the December 9 1. Ch vernal equinox). 163 1951 June 20 1. 5h Summer solstice and maximum declination of Sun (+) and Moon June 19 8. Oh close separation-interval. 164 1953 September 24 1. 5h (-15 min.) Autumnal equinox, large parallax, and Moon near Equator; very close September 22 23. Oh separation-interval. 165 1954 November 10 1. 5h Large parallax; close separation-interval. November 10 9. Ch 166 1966 September 14 1. Oh (-2) Large parallax. September 14 13. Ch 167 1967 March 27 1. Ch (+5) Moon near vernal equinox and on Equator. March 26 0. 5h 168 1968 December 19 7. Oh (-6) Large parallax and high negative declination. December 19 10. Oh 169 1972 December 20 7. Ch (-21) Near winter solstice; full moon at high positive declination, nearly co- December 19 18. 5h planar with negative declination of Sun. 170 1974 February 6 7. Oh (-24) Declination of full moon (+ 15 " 19') nearly coplanar with declination of February 5 6.0h Sun (- 15'39'). (Comnonwealth Pier) on 1931 MarcH 6 at 1243 h the predicted rate of tide rise (in ft/minX0.0001) at (e.s.t.) - 55 hours after the mean epoch of perigee-syzygy Willetts Point, N.Y., during successive lunations bracket- on 1931 March 4 at 0530h (e.s.t.)-was 11.0 ft. The ing 1931 March 4-5, is far more meaningfu1 in indicating maximum tidaL range on March 6 was 13.0 ft. These the potential for the tidal flooding which actually oc- values compare respectively with 10.3 ft for mean high curred. The use of such rate-of-growth tide curves of' water, springs and 10.9 ft (or 11.0 ft in the 1977 tide perigean spring tides and the determination of their,re- table) for the spring range of the tide at Boston. spective "windows for potential flooding" will be dis- It will be demonstrated in chapter 8 that the likelihood cussed furtHer in part II, chapter 8. of an increased amount of tidal flooding is associated, not The peaking of those portions of the tidal curve con- alone with the predicted amplitude and range of perigean taining perigean spring tides at a level considerably above spring tides, but. with their accelerated rate of growth in the baseline representing the average rate of tide growth reaching this maximum. Thus figure 96, which depicts throughout the entire year at this location is clearly evi- 202-509 0 - 78 - 25 V !I Ak le@ d-L. Ii@: Z L v In -:;@3,@%,, a co 7v% ti; Ir -------- --7 9U24S 10 ajoy R. i vu, j Hbi M- g E J k w 'R if A JI > 0 -"N ----------- Z4, cc '71 I t(-T@ eg CL 7 717 1, 75 n 1-4r nt-:, -,I., :J, ND It I I :,@ ........... ........... .......... SgUl 0012 jVP!j ?Ua.?dy !S,9p!l DUM@S UM922-19t7 10 XI!91 OZJ,9,g PUD 'UOIIvufzsg(g 'UO11vqY!Syvjo P p fir It Li I .13 u 04, i@ 2 1-4 If,- It zi, CO ;vlnm v [email protected] Lj uP t7l Aiv 7", '0 6 na, p! i Ln -71 Tr L 77- 9Z 6 I-,CCqj 'S.9p!,L OUUdS UV,9DUl-,j fO 91OL7 X29 JAZIS Xfii 44r i I d5j,@IHIJ MUL, 0", E, r i5l _11;@I! fiiilliw J 4,Y Dior PH; E 4- 2-ill R, H F, ft It -4@v FV_ g, Rlt H T4 L 00 Lip P tg@g It (j,\RF -Arn v z 71 4W, Lu %', V > N- M; 7t ci fir F", 7,j1 in@ t VA I a @ _4 47 tk, i T, 'A 46,/ 0i, MO@ u MMIRFM P 1;N gu g; ug vNif 9,flnvioff 91 _0 Nfi e-Frx A , i, 5 1 5 ri r .-PI-b ... 1w,m-D ov -E g.,Pvr;,g.% Pg: =Pgv -=Ms. ...... ........... *:.*.'..*:..a..'.+..+..'...+.+,::..i@'..,:.+.*@:.@@z;..:. bi ................... -T .-n ......... L. 17-1 Lo- 64 ..................... .............................. . ............. . .... ......................... 49E Sgul 007Z jVP!j juoooy fSOP!j guu4s UVRD'723d /0 (C*??POP9,f Puv 'uO?1v0!s19G 'vOzJv9Y!sSv1D T '_Lip F 1D ITO rs -i E61 M;l II ni __ Ri Ki , > _7 "Y @ R, co -77 ... ........ ...... . . .... qZ6j-,rC,Qj `S'gp@j @W.&@S UV92120,7 10 OJOY 9ZD'9jVZ?S 89E -iUD 7, d I Llvu, _j P ,@F@4 !1, tIll <7 ix 4 F,@tv@ q Rij, 6, -i@ iliw A. N4"- Lk -,R5 Aill! '0,4 1 W J@T 'a j it 41 4' r,C U1 !@4 ION 14 7, it 5 @J. 61@ OD 10 L J. 5 CID vyz j7 pj@ [Nhit ,LA' *-Lj .......... ----- - 1p 1@:+111 Ll@ . .. . ... A 69C SDU? P0012 7VP!,L JUd99y !S-9p!j UV,91@ .uaj 10 ((Ip .?P01119j puv cuolivuffugg cuozjv.?Y!SSvjD 1, Tm - Z-7 Eli a Is I Na"SIA d '111 HIRE Ili ir @4, mom @17 A, V SIR Iq iuY F; let'. oU Fj Ur- -5.'HuM.4 IVj 1; ir; 11 17 ;i R5 V, 74 5 Ng q RQ OD IVI Iffy Tq g on: F"k qI Man @q,@ A N-N" M U OU i;61 to ON , et VS 4 k4 ;j' ... ON Y@, . " , '4@ ON PPOOM ON ON, ...... ;V51 CD MINIM 4111 P 2-.- ... N-Nu 7 ......... ON= ... ON OOQ.--. ........ .... z= CIO a- NL ...... @N NNO-N ........ .NO. N.4- P. O-.N: . ..... 0 Nal NCOI 9Z6I-,CC91 'S'9P!j @UT.14S unql@yacf jo gloy UD N IN N 11fi-E, MUR it I 'Y' Elf n a ij f IN all, 74 Ld al -'@6'@ ,4 - f -p" 11 -7 @7 j Jj@ x@" f R-4 4o MA, @2mm' up - j'p I n 0i cl 1.7 R @N RIJ I-- @-A' V -7@- V 11d q o i"RWIPPIT Rn Plif'-` P. 90 z t4 @ @' - V-'L 3 eg gig 'fr mt . g "p, 40""p-M.- cr (D v;iP, W-me .......... .... ....... .......... ................ ........... ..... . . . . .... ............ . J, T SOUIPOOIg IDP!j JU9.99Y @Sgp!j gUZ114S UVaD'7.19,� 10 X1297pouad PUD luoljvu'@2saa 'uoIjvqy!swjD Lin 1T 7H, S, 'N' -Ay_ i@ J, El N oa I,q t7l Po co kk. @op AI dy 1 'Ji rl L4 It UV99U3j 10 djOy 919dPJjS 160 1944 OCTOBER 2 1.5h. October I 17.5h. (-11) or YX t,w 1W M, lee rw CII - rl- kip K lq, 6A, ny,! 31 lid If W@-:, V,,Z)r- 14 V3, tq v v CTK V., as* :3j Y-MT C% WMMM WORMA11ON FOMCA-STS AMD GEMM UMTW VATUS VMATM BUREAU. WASKINGTON, D. C. u. Wr FIGURE 79 61 1950 MAY 3 1.5h. May 2 1.0h. (2) 3 A\- al Ly I wl\ I E Arl H Da M TAT .. .... U. S. DEPARTMENT OF COMMERCE CHARLES SAWYM 8-0-Y V"\ A WE THER BUREAU i> lk 7, ct-, V -QU N@ % -@31 A, VAR( -T- 4= N61 Z 4- STAMN MODEL d*,p 24 ;4k ir FIGURF 80 162 1950 DECEMBER 9 1.5h. December 9 1.0h. (-8) -D DAMY VEMIHN2 M 1'w'T CHARLES SAWYER, 5 .... -y U. S. DEPARTMENT OF COMMERCE WEATHER BUREAU T-, @"A t"Z5 4 @, It kilt, VAM LEA 4 6h, Z"o J Z UP 'v, ti. nd, <@ A SIATION MODEL N -A 04 QL. .2,.r@m.@a .q __j FIGURE 81 G) Ul c 4 163 1951 JUNE 20 1.5h. June 19 8.0h. (1) MT Q@ 11 C."' i W'.',.A'fMXt C 0 MHM, Y CHAnLLS SAVIYU. 8--r A, 'NEATI-IrM BUREAU -Jf> G- MGM D VAN 5ADLE f 4@ VVL C") mms < C--Z % al 1A ZFM 73 OF, C@o MMON MOD-1 cp, Z4 FIGURE 82 16-4 1953 SEPTEMBER 24 1.5h. September 22 23.0h. (0) FREEONG U. S. DEPAIIT'"EIKIT OF CORM1.01RCE ivi SINCLAIR VILUICS, DI, 1 2, @W 7@ /W K - T' V, A WEATHER BURE-y 7@ 17 s ;2 vF j I'VIT @V- ,01-1 z/- AL ----------- J-- T 7 P 5, p. J, ZIL & @@jt m GQ nATION .'ODFL 4P, v N 4p MAP r H 1 FIGURE 83 w cl) 1954 NOVEM13ER 10 1.5h. Hovember 10 9.0h. co --25- ICY U. S. DEPARTMENT OF CO VNERCE SINCLAIR VIEErS, S-1.1y WEATHER BUREAU FR-,F < -'Zim, ILI - o" 4k, 4\ u. 7--r -1K Qiv V W z nllll@ -7 "A nor sx, g-5 "T ar MAP FOR 1:30 A.M., E.S.T.. ... . . . ....... ... . FiGURE 84 166 1966 SEPTEMBER 14 1.0h. September 14 13.0h. (-2) 7-%4 bo IAV 11 'q 4-b 'tot t.0 0 A -'sq uz:1 s"A Vol, lz VAWYA I'r WNW "u Py 4 Ct. 3w IIP 4bZ VIA i' r,,f _.- __ , I , t A, 0 35 4@6`4 A@ S4, V IN 4!s 4, '4, 144 SA I, 4b om. A Uy P Q.1 ....... IV, in, .. .. ........ -14 tc;l t 5t; r r24 or, k'L P-w- G@ %%-I a ? SURrACE WEA MR MAP C", AND STATION WEATHER -14 A 1:00 K M, t. S, T. t T 4 SPECI Ex I STATION ""L k,k,( 2v SCALE OF -L WLW AT TAR-I -TTIl- If A --. . - I - ...................... Iw FIGURE 85 1967 MARCH 27 1.0h. March 26 0.5h. (5) C-) G4, 4R @kN 7 N, V Ocl 4o, A" @@29\ @ I-- -Av 51 @X' Z14 2 4 44@ s 4"@A w. 4. Is, 7 @; Ali f SURrACE 1-VEATHIM NIAP Q, 14 ARD STATIO-ill IYEATHE@Ei 0) AT 1:00 A. M., r- S. T. GPM, WWSL If IV r llo@ FIGURE 86 160 1968 DECEMBER 19 7.0h. December 19 10.0h. (--6) 10 Mc j Al lb 41 4i 'L L vnn"b 4 f r 0 I Op - AP, V, "AQ I'AL @4 1. w > -Z@ Tp. ov 7 \Co' la" WEATHER MAP SURFACE AND STAT!ON WEATHER AT 7 00 A.M.- E S.T. IZ)k Fir,URE 87 w 169 1972 DECEMBER 20 7.0h. December 19 18.5h. (-21) - IV ) I It , - 1024 "@ I , 6* 0. '1 3@@ 1008 (Y" -1 Ir loSt Is 3.,2- C91 h 1 lot, A 0.11004 -7V X Ll, z @z7 25 -P@ vffl 3 3@7 W4 oll Q', GR4 w .3 CIO 2 % 6w N 00 1020 14 49 "'0 X SURFAC @@ -F..T.E" -A' AND STATION Ill..T.111 1008 2@.'j AT 100 AJA @ E.S,T, K@ FIGURE 88 170 1974 FEBRUARY 6 7.0h. Februory 6 6.0h. (-24) 140' so ss. 1024 O@ 0 1036 1 @1111032 'q2 1 8 109 984 028 2 .1012 10 8 vq 04 Q km, "ter"- A4 >@u zi 10 A H [@i V; ib Zb *73 1 gm. 9 @@qh-,r 4,ia - a i MN-i A Vie 0, -,AT 8, to 'A 2(t, o so 4 fZ',I J@.,sA 4b 14 0 -4 sa I 05p 016 0 2 a SURFACE WEATHER MAP AND STATION WEATHER AT 7:00 A.M.. E.S.T. 0 FIGURE 89 374 Strategic Role of Perigean Spring Tides, 1635-1976 TABLF_ 28a.-Surface Synoptic Tlv'eather 211apsfor Four Representative Cases of Hurricanes Occurring in iVear-Coincidence With Perigean Spring Tides Serial Weather map date and mean Perigee- No. perigee-syzygy date syzygy Region of impact (hours) 266 1878 October 23 1. Ch (-17) All sections of New ErIgland and the mid-Atlantic October 25 9. 5a States, Oct. 23-24, starting off the S.E. coast of Florida and the Carolinas, Oct. 21-23 268 1899 August 20 8. Oh (-7) Coasts of Virginia, Delaware, and New Jersey, August 20 20. 5h Aug. 18-19 283 1940 September 2 7. 5h (+26) Cape Hatteras, N.C., on Sept. 1, then northeastward September 2 12. Gh to eastern Maine and Nova Scotia 289 19M October 15 1. 5h (+21) Entire mid-Atlantic region and Carolinas, Oct. 15 (Hurricane Hazel) October 12 10. 5h TABLF, 28b.-Representative Surface Synoptic Weather Map at a Time During Which a Perigean Spring Tide Caused Blocking and Backup of Hydrological Runoff Serial Weather map date and Ferigee- No. mean perigee-syzygy syzygy Region of impact date (hours) 466 1936 March 21 8.017 (+5) Newburyport and tidewaters of Merrimack River, Mass. March 23 1. 5h dent. Where supporting winds are present, 'he vulner- O.C proxigean spring tides therefore substantiates, in every ability to tidal flooding on both Mam",@ 6-5 and April I way, the particular influence of such tides in causing at Willet's Point (and additional east coast locations coastal flooc.-,-g when reinforced by the prerequisite wind having similar tidal characterist-;cs) is diz-ect@y confirmed conditions. tLl-ereby. The coastiine near Boston, Mass. also L,@as been 2. The Tida@ Flooding o@ 1939 January 3-5 shown to be susceptible to tidal flooding at this time, if subject to the correct meteorologicaL conditmns. The next case of coastal flooding to come under con- As described in tlie accompanying newspaper account sideration from a combined meteorological-astronomical (fig. 95), the combination of both wind and astronomical viewpoint-that of 1939 January 3-5 (Key No. F.-68) effects lifted the tides at Boston on 1931 March 4 to an on the west coast-is notable because of the extent of its actual height of 13 ft 8 in. The tides a' the Naval Yard, occurrence, nearly simultaneous:y, from Long Beach, Portsmouth, N.H., were raised to a height of 13 ft 10 in. Calif., to Aberdeen, Wash. This fact substantiates the Region?-'- effects of these storm tides occurring near -3eri- effectiveness of perigean spring tides in producing coastal gee-syzygy are described both in. the other news articles re- flooding in various latitudes on either the east of west produced in figs. 95, 96, and in those of table 5, part 1, coasts of North America-wherever the correct tidal har- chapter 1. monic constituents, adequate tidal range, a. low-lying The circumstance of occurrence of a series of astro- coastline, and persistent, strong, onshore winds combine to nornica2y produced perigean spring tides related in ?- provide the conditions requisite to flooding. commensurable pattern to this 1931 March 4 flooding A surface synoptic weather map for the former map event, each of which was itself accompanied by tidal flood- plotting time of 043 Oh (p.S.t.) on 1939 January 4 is in- ing (Key Nos. 36w, D-57, E-58,59, and 60) already has cluded among the group of maps following table 26. As bten mentioned as of special consequence in reference indicated by the several newspaper accounts of this flood- note 4 supplementing part El, chapter 4. This example ing event which appear below and in table 5, part H, chap- C, 7 -I'r 3 Aq@ -4- t,-v, It 41 M, -17 ;T Z 7 7-- '1-" 0 M co x co co CIO '4 vF h7 NX Q opmup'? gm rooff kS LA lit ht- SDIU@Poojz IDP!l jugody !Sap!j fuylfs UVa2.Ij'q('7 fo Xj?.?!pO?.tqd PUD luolIV02sou Iuozjvqy!ssvjo cz 7, HIN 4-4 Rio N 114, 'I'll" 7@1 @fj it A @@Olv 11 5 fq co 10 10 12 I u "S, A@, t4 4 FRI 771 1 M, Lr MH ................... ......... ............... 14 9ZV-901 'sRPU gul-4S uvd,@?.'Od 10 0109 9204WIS 949 Co !R R rg Mi I 4@ I "COE Rtil RH a ft `9 1 1 NO I A ljfffflg;@ igi ;9651 -1-N. M p 14 qfil lHi 0 K 1v EIJI 00 V1 (D T) Y Q mooman- "MINTR OF -- r -AKIII 1215TOR "RIF , rl@', PIR RIMER, 0 1@ Fir MUM M-Q-1019571 mao.O.,02 VIUM K3 ..... . . .... ... . . .. . ..... I-.,- TJ@ SOUIP001Z IVP!l ;U,99ay fSgp!l 3M.41fS UVOD'U9,7 10 tcj!q2pouqd PUD UO?jvU21yqG uo2jvq@yyvjD 289 1954 OCTOBER 15 1.5h. October 12 10.5h (21) .... ..... DAXLY WEATHER MA_ li - U. S. DEPARTMENT'OF COMMERCE WEATHER BUREAU FREEZING _-A /. If R -M PAA@7_1Zp, ad. ".7, , - - mows amumm Q4 MG r Rr@ Y Al, p 'Z Ilk, `oZ MAP FOR 1:30 A.M., E.S.T. 7. FwURE 93 On all 1,2, 4-mill IlUip OIL 51 illi , f, I .@ ljj@ IN V HM JeL Vff 204! lu g MIR i"t -- -, I , I R L cn air Ili 4h@ IjjRk It @Juv A Dill M, ---- ---- - -------- 14MIURP OHL .@r 51) U I F1 Mg ILI 91 PR N6. AR, ,-N igai@. all u 0 k", um;l Cl 14z cn N m/ 5" 11,91EM7,101,11 'pafiR, 'Po M, .. .......... ............ 7... --1-- - - - w -- - - - - - d- L 7:z- - - -- .--t, 64E soulpoold IDP!l pdqay !Sap!j gul.14S UD,9222ad 10 dpolpouad PUD luollouffisa(ff uo?jv,?9PSvjD 380 Strategic Role of Perigean Spring Tides, 1635-1976 7ha Maui Veyk 7mam was so high over the pier that the gang- Nahant was turned into an island. Every- Thurs., @March 5, 1931 plank, when put down, was tilted at a where boat yards were endangered ... Page 20, Co@s. 3-6 crazy angle ... . . . At Hingham thousands of feet of . .. Last night remote shore villages in New lumber floated to sea when the yards of Jersey and on Long Island were still send- J. 11. Kimball & Co. and of E. B. Whitney B ing in reports of floods in the streets, boats were flooded to the tops of the piled S MKID 0 A R 5 carried to sea and homes undermined by boards. At Yarmouth. the town bathhouse, the tide ... town pavilion and town dock were distrib- ... EAST HAMPTON, L. I., March 4.- uted over several back yards. Iting Lardner's Summer home on the dunes With half of the Nanta8ket Beach Rail- Tide and storm had an interesting his- here was hanging over the cliff tonight way. undermined and destroyed, with prac- tory, with the Weather Bureau acting as after the high tide had undermined the tically every cottage and Summer resi- recorder. It appears that on the night of house, It is feared that the house will top- dence on the ocean side of the Nantasket Feb. 27 a little storm was cradled out in ple into the sea if a heavy tide rolls in peninsula damaged and with Hull cut off the open spaces of Utah. At first it tried tomorrow from communication, damage from Nan- its comparatively puny strength on the tasket to Pemberton was estimated at northeastern part of Mexico, whooped it HEkVY DAMAGE A7 BOSTON more than $1,000,000. up over the Gulf of Mexico and made a Gloucester suffered more heavily than vicious turn toward Tampa, reaching there at any time within recent years, with Monday morning. Loss From noaE and Waves Said waterfront streets submerged, train serv- to He Enormous. ice completely cut off and cellars flooded. Takes to the AtEzimtk. No trains operated between 9 A. M. and BOSTON, Mass., March 4-A huge tide 5:50 P. M. At Rockport a heavy surf Here it developed an extremely violent driven to heights unprecedented in two washed away the new sea wall completed temper and began to vent its wrath on the decades lashed the shores of New England a few months ago. Atlantic. By Tuesday morning it had ar- today, causing havoc among shore cottages, rived at Cape Hatteras, rolling tremendous demolishing sea walls and rolling up a waves before it, toward the shore, from damage which could not be estimated. The points as far as 1,0C0 miles out. Rushing tide rose three feet above normal. C= (3F LYNK HS a33Lk7ED northeast while growing to a sixty-mile Eighty-two structures were damaged in LYNN, Mass., March 4 (AP).-Lynn gale, it worked all Tuesday night and ves- Revere alone, seven of them being com- was virtually isolated by the storm and terday morning, driving the foaming green pletely wrecked and washed away. Seas tide. Transportation lines were paralyzed. water toward the coast. rolling through carried away all cottages, The harbor front was flooded. Children This continued drive from the east furniture, ripped up floors and undermined were taken from a flood-surrounded school would ordinarily have been enough to foundations. Damage at Revere was esti- in ambulances. create a high tide, but to make matters mated at $1,000,000. At Roughan's Point, worse, the moon is at full, exe in the Beachmont section, cottages were The adjacent town of Nahant was made rting its an island when the ocean waters rose maximum strength on the ocean. Thus, loosed from their locations and floated. to- above the isthmus for the first time since between the two, New York, New Jersey gether like packing boxes . . . 1909. The high waters swept into Lynn and other coastal States felt the power of sewers and breaking waves sent water the worst tide in four years ... The 2tevere Beach & Boston suspended operations for an hour before and nearly bursting out of manholes like geysers ... two hours after high water, at 11 o'clock. . . . At Swampscott, adjoining Lynn on the New Sersay R(283rts Bafteired. Two East Boston lines of the elevated north, the tide swept in over shore roads, Atlantic City, Margate, Ventnor City, were suspended for a time. The Portland bringing up dories and fishing equipment Ocean City and Sea Isle City received. a division of the Boston & Maine was held with it. tremendous battering from the tide and up nearly two hours by tracks under ?931 reported heavy damage. Rushing into the water. Sections of the New Haven tracks inlet and thoroughfare the waters spreac were washed out between Neponset and 5.5h 6.3.9. (0) out over the long meadows back of Atlan- ilton, and between Norfolk Downs and tic City, until they were completely sub- Atlantic. All communication between Lynn M-57 merged. Only the shore line trolley tracks and Boston was suspended during the remained clear. In Longport and the inlet flood tide. Whole sections of rail were T'he xwu V0711 urmse district the water was six inches deep in under water. Shore roads, washed by seas Mon., March 9, j931 the streets, marooning families in their or flooded entirely by the record tide, were Page 1, Cols. 1, 2 cottages and sloshing into cellars every- left impassable because of debris when the where waters receded . . . . . .Today's tide went to a height of 13 In-New York Harbor not only the ferry- feet 8 inches ... 11 1 _3 JIGH boats but the large ocean liners were ... From everywhere came reports of the affected. Commuters were delayed while the ferryboats maneuvered for the best appearance of myriads of sea rats, drtven out of the burrows near normal high tide position for the placing of gangplanks, and on the New Jersey side of the Hudson the marks by the rising flood. 3"i A T Vi R COAS57 tide was so high that passengers had to At Portsmouth Navy Yard the highest splash through several inches of water. level ever recorded was reported, 13 feet H@GH VDIES LASH SEACHIES Behind the Erie station in Jersey City 10 inches . . . automobiles and persons on foot virtually ... At Newburyport the 30,030 clam puri- In and about New York a high wind had to ford their way to cross the streets. fication plant was undermined by rushing that accompanied heavy rains and a high When the giant liner Europa docked high water and nearly wrecked. At Salis- tide caused at least seven deaths, scores of yesterday morning at the army base pier, bury, cement walks and miles of board- injuries and millions in property damage foot of Fifty-eighth Street, Brooklyn, she walk along the beach were washed away. . . . FIGURF, 95. Newspaper articles in connection with the 1931 March 4-5 tidal flooding in New England. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 381 METROPOLITAN AREA HIT HARD The gale, as earlier in the week, was a foot of the top of the sea-wall for the assisted by the waning moon, in rolling up first time in many years ... At least seven deaths, millions of dollars tremendous tides that gnawed away long in property loss and scores of injuries stretches of waterfront, undermined Sum- 1931 Mar. 4 were caused by the gale that scourged iner homes and flooded streets and high- 5.5h e.s.t. (D) New York and New Jersey Saturday night ways ... D-57 and all day yesterday. ... at the Battery the tide rose to within D-57 (a), E-58 (a) WILLETS POINT, NEW YORK 1931 8.4 8.3 8.6 8.9 9.0 8.7 8.2 OA y 0 *y 0 0 Y 0 AD Y 0 A 0 Y 0 A 0 A A 90 nWINDOW" FOR POTENTIAL TIDAL FLOODING 80 FL. FL. ....... ..... 3/4-8 4/1 7 0 AVERAGE 0 OF 0 .................................................. .. .......................................... ..... ........ ................................ ..... ....... ................. .......... . .... ... ......................................................................................................... 0 60 CURVE MAXIMA FOR 1931 z so LL 40 Li (n Cr. 30 22h 6 _22h 49 W u- 20 0 LU !a 10 cc UJ 0200 cc go 80 70 60 50 40 30 JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 FIGURE 96-Continuation of newspaper items relative to 1931 March 4-5 tidal flooding event. The appended graph also shows the 0 b accelerated rate of astronomical tide growth accompanying this event. The tidal enhancement is associated with an alignment of perigee-syzygy within 6 minutes at the mean. epoch of 1931 March 4.23 e.s.t. (See pt. II, ch. 8 for an explanation of these curves indicating rate of tide rise.) 382 Strategic Role of Perigean Spring Tides, 1635-1976 ter 1, tidal flooding of major consequence had begun circumstances, the first over Washington and the second along the Washington and Oregon coasts as early as Jan- in southern California. (See fig. 97). . uary 3. However, this weather map for the very next day, Numerous other examples of each type are contained midway in the tidal flooding period, reveals no deep low among the newspaper accounts of tidal floodings along pressure system, intense precipitation pattern, strong both the east and west coasts contained in table 5. On winds, or other active weather indicators either along the certain parts of the California coastline, notably from coast or offshore. Despite this, the tidal flooding was con- Point Conception south, a frequently 'Observed tendency tinuing along the Washington coast and beginning in exists for a channeling of a northeasterly directed swell- southern California. (It is important to remember in this apparently by similarly oriented bathymetric configura- connection that atmospheric fronts were not introduced tions on the ocean floor. This influence has been variously .on official U.S. Weather Bureau synoptic weather maps noted by marine engineers writing in Shore and Beach until August 1, 194 1.) magazine ', by coastal resource engineers in the Los An- The general summary of weather conditions over this geles District Office of the U.S. Corps of Engineers, and Pacific coast region appearing in the Monthly Weather by a beacliguard with many years of observational exper- Review for January 1939 solves the mystery of the me- ience at Imperial Beach, Calif. teorological contribution to this tidal flooding event. The The effects of the strong swell generated by a hurri- answer is inherent within a circumstance which occurs cane located even far to the southwest in the subtropical often along the Pacific coast of North America, but which regions of the Pacific can sometimes be felt as an active (before satellite weather photographs became available) series of ocean surges impacting on the California shore- confounded many an early weather forecaster in this area line. The swell may appear in an otherwise calm sea, un- attempting to determine the cause of such surging up- swept by wind or waves, under a perfectly clear sky, and lifts of water along the coastline-deten-nined as not due with no visible generating source, having been propagated to seismic sea waves (known alternatively as tsunamis). from its distant origin, losing little in flooding potential (Cf., for example, Key No. 64 in table 5.) on the way. A contributing element to such coastal inundations, es- From an astronomical viewpoint, while the perigee - pecially at times of perigean spring tides, can lie in deep syzygy alignment ( + 14') which produced the perigean atmospheric low pressure systems existing possibly many spring tides in case F-68 was not nearly so precise as in hundreds of miles at sea. These low pressure systems, with case D-57, the astronomical high tides resulting were of their associated steep atmospheric pressure gradients, pro- considerably augmented amplitude and range with respect duce very strong surface winds. The winds, in turn, gen- to their average values. erate an active swell on the sea surfare. The speed of On 1939 January 5 at 0802' (P.s.t.), for example, the movement of such a deep low pressure system can far ex- predicted higher high water at Los Angeles (Outer ceed that of the swell it generates. Thus the low pressure Harbor) was 7.0 ft. The predicted maximum tidal range center, accompanied by strong winds, can move rapidly for this same date was 8.6 ft. The latter value is signifi- onshore and be out of the area before the swell ever cantly in excess of either the diurnal range (that between reaches the coast. Conversely, a strong high pressure sys- mean lower low water and mean higher high water) of tem can block the forward movement of a low pressure 5.4 ft or the mean tidal range of 3.8 ft at Los Angeles. cell. As a result, the swell which the latter has produced At Aberdeen, Wash., the HHW predicted to occur at is propagated along the sea surface and may strike the 1218' (P.s.t.) on January 5 was 11.2 ft and the predicted coastline while the low center maintains its position many maximum range for this date was 12.7 ft. By contrast, hundreds of miles at sea. the diurnal range at Aberdeen is only 9.9 ft. In either case, if a very strong swell arrives along the At Astoria (Tongue Point), Oreg., the HHW predicted coastline at the same time that perigean spring tides rise for 1233' (P.s.t.) on January 5 was 9.8 ft and the maxi- to their greatest levels at high water, the reinforcing action mum range 11.2 ft, whereas the diurnal range at Astoria between strong swell and augmented tides can only cause is only 8.1 ft. These unusual tidal elevations, combined tidal flooding-while the apparent cause (lacking im- with the reinforcing influence of strong onshore winds, mediate strong winds) remains obscure. The present in- resulting high seas, and ground swell confirmed by the stance of coastal flooding seems to have involved both following general weather summary, could only produce Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 383 The Oregon Daily Journal But the Alamitos peninsula below Long roadbed and rails and ties strewn along Fri., Jan. 6, 1939 Beach was hardest hit. the Coast highway ... Page 1, Col. 7 William E. Ross, boat builder there. said the tide was the worst in his 96 -years' ex- ... The seawall was washed inland 50 to perience. 250 feet from Manhattan to Barview ... Mrs. D. H. Collins stood by and watched the tide carry her two-story dwelling into 13-Fact Tide Sea Unruly the Pacific . . . Recorded at Newport More than two feet of water roared Newport, Jan. 6-A 13-foot tide, one of in at some Sant'a Monica ba@ points, sweeping out the board walk along the the highest ever recorded here, washed the in (alifornia strand between Manhattan and Hermosa water fronts Thursday. Yaquina Bay was beaches . . . covered with heavy logs and timbers, kept moving away from boats and buildings by Three Homes Washed Into eoastguardsmen . . . Pacific; Others Damaged . . . Several hundred feet of the trestle Tillamook work of both jetties left standing by former contractors was washed to sea ... Long Beach, Cal., Jan. 6-(AP)-Three Area Raked ' modest beach homes in the Alamitos pe- . . . The surging breakers cut off lights, ninsula area southeast of Belmont shore water and traffic from the Bayocean pen- were washed to sea today as giafit break- By Sea Surge ninsula and washed out the highway at ers, riding in from the Pacific on high tide Oceanview, marooning those on the pe- ground swells. crashed over the low sea ninsula. The surf almost demolished the wall . . . Wheeler, Jan. 6-Devastation was left seawalls at Netarts by surging seas that hit Tillamook county ... The tide also brought extensive dam- beaches Thursday noon. High water marks 1939 Jan. 5 age to -Manhattan and Hermosa beaches, were broken. The Southern Pacific track 20h P.s.t. (-@14) where the highest water in years flowed at Barview, washed out Tuesday and re- as far as 180 feet inland. paired Wednesday, was torn from the F-68 FIGURE 97-Representative news articles relative to the tidal flooding of 1939 January 3-5 occurring in Washington, Oregon, and 0 southern California. the damaging tidal flooding along the coast which took "The easternmost Pacific storm was of unusual severity. Place. It was damaging on the Washington, Oregon, and California coast, from the standpoint of both heavy winds and high From: Monthly Weather Review, Vol. 67, No. 1, January seas, which continued with varying intensity from the lst to 1939 the 5th. At the entrance of the Strait of Juan de Fuca, the Swiftsure Bank Lightship reported winds of forces 9 to 10 F-68-COASTAL FLOODING OF 1939 JANUARY 5, CENTRAL on the lst, 2d, and 4th. At sea several vessels were delayed OREGON TO SOUTHERN CALIFORNIA in passage, and a number of passengers on the American "The early part of January may be characterized as one steamship Lurline were injured, according to press reports, of the stormiest periods in recent years on the North Pacific when a huge sea swept the decks. The American steamship Ocean. At the opening of the month low pressure extended Mauna Ala reported southerly winds of forces 11 to 12 an across the northern half of the ocean, with three distinct the 2d and 4th while proceeding southwestward some 100 and powerful centers, one east of Japan, another in upper to 200 or more miles west of the Oregon coast, lowest middle longitudes, and a third off the west coast of the barometer 29.08 inches, on the 2d. Much farther at sea, United States and British Columbia. In connection with near 43'N., 148'W. the Japanese motorship Genyo. Maru these specific storms and the generally unsettled weather encountered strong gales to hurricane winds, lowest barom- existing generally to the northward of the 30th parallel eter 28.71, on the 3d." during the 1st to 5th, gales, many of which were of hurri- cane or near hurricane intensity, occurred over wide areas, some being experienced' almost as far south as the 25th parallel. However, in east longitudes, the greater part of the 3. The Coastal Flooding of 1959 December 29-30 high winds reported occurred between latitudes 30' and This case of coastal flooding (1-83e,w) is the first 45'N., and in west longitudes, between 35' and 45'N., except along the American coast, where they were experi- among the present examples for which specialized in- enced also in much higher latitudes. formation as compiled in the U.S. Weather E@ureau (now 384 Strategic Role of Perigean Spring Tides, 1635-1976 the National Weather Service) publication Storm Data centered, at map time, over the Delmarva Peninsula, with is available. It also provides an example of two nearly its warm-front portion extending east-northeast along concurrent tidal floodings which resulted from perigean the entire southern New England coast. This'resulted in springtides produced on both the east and west coasts of a strong wind circulation from the east-northeast and North America. Although the respective floodings on op- hence directly onshore from the sea at coastal points to the posite coasts were separated by a day, in each case the north of the front-a typical setup condition for the event was a function of strong onshore winds acting upon familiar New England nor'easter in winter. the astronomically produced perigean spring tides. Other ne effect upon the rising perigean spring tides, whose such instances of near-simultaneous tidal flooding on both mean epoch occurred on 1959 December 29 at 0500h coasts exist in Key Nos. 56e,w, 84c,w, L-93e,w, and (e.s.t.) was also typical. Tidal flooding ranged along the M-98e,w. (See table 1.) coast from New Hampshire to Maine. The severe magni- A surface synoptic weather map plotted for 1959 De- tude of this tidal flooding and the associated damage in cember 29 at 0100' (e.s.t.) is included among the group New Hampshire, Massachusetts, and Maine are described of maps following table 26. This map clearly shows that in the following summaries from Storm Data. Further in- the meteorological factor which contributed to the east formation is available in the accompanying newspaper coast tidal flooding was a large low pressure system with articles (fig. 98), with an additional news account ap- two centers located just inland from the mid-Atlantic pearing in table 5. Considerable data in connection with coastline. The easternmost of these two centers contained this instance of coastal flooding, an event described by the a nonoccluded frontal wave. The peak of this wave was U.S. Coast and Geodetic Survey as produced by "the The Boston Herald Wed., Dec. 30,1959 Page C3, Cols. 2-4, 6-8 1959 Dec. 29 1-83e 5h e.s.t. (-78) South Shore Areas Lose Northeaster Lashes All Cape Cod Power; Streets Flooded 15-Foot Tides Smash A 100-foot section of the seawall at Lighthouse Point, near Rebecca road Provincetown, 'Barnstable where the Italian freighter Etrusco went aground in 1956 was washed away and homes on the point were isolated for sev- Storm tides 15 feet high crashed across road and isolated a big freezing plant. The eral hours. waterfronts of Provincetown and Barn- water receded before evacuation became Stores in the Scituate Harbor area were stable while the whole Cape Cod area was necessary. flooded, with a foot of water pouring both lashed with a heavy rain driven by north- Tit Provincetown the crashing tide sent in and out of the First National Store on east gale winds. spray roof-high over buildings on Mae- Front street. The street, main business Peak of the flood tides hit at 11 a.m. Milian Wharf and nearby piers. Crews of thoroughfare, was closed during the morn- and flooded scores of cellars in both towns fishing vessells were kept busy strengthen- ing. and washed out stretches of some high- ing moorings, In Marshfield, 50 families were evacu- ways and made others impassable for sev- In East Dennis, Bridge Street was ated for several hours from -the beach eral hours. washed out. It was repaired several hours areas at Rexhame, Ocean Bluff, Brant later by highway crews. In Wellfleet, the Rock and Green Harbor. VILLAGE THREATENED heaviest water damage hit Mayo's Beach road ... In Barnstable the sea flooded to within 50 yards of the main street of Barnstable Water breaking over the boulevard Village. In Provinectown, Commercial seawall on Western avenue, Gloucester, DIKE GIVES WAY street was hip-deep at one point and a drenched the area, and at Pavilion Beach, number of stores and dwellings were in the inner harbor, it climbed the back damaged. walls of a plant of the BirdsEye division Both Barnstable and Provincetown po- of General Foods. The bridge leading into The situation was particularly tense in lice estimated damage in the thousands of Annisquam was awash and cars were re- the Brant Rock area where the famed dollars but no injuries were reported. routed. esplanade was under three feet of water Police and firefighters stood by to evac- The water reached to within one foot of after a dike on the Green Harbor River uate 60 families in the Common Field area the windows of the Gloucester I-louse on gave way at 11 a.m.... of Barnstable as water flooded Commerce the Gloucester waterfront . . . FIGURE 98.-A newspape r account of the dual east-west coast tidal flooding of 1959 December 29-30, as it was experienced in the vicinity of Boston, Mass. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 385 highest tides in 108 years," are contained in the latter from the perigean spring tides was not nearly as con- article. sequential here as in the vicinity of Boston. The perigee-syzygy separation-interval at the time of this flooding was - 18'. The peak of the flood tides- indicated in the second of the immediately succeeding From: STORMbATA, Vol. 1, No. 12, December 1959 news articles as occurring in the vicinity of Cape Cod at 1-83e,W-COASTAL FLOODING OF: 1959 DECEMBER 29- 1100' on December 29-closely followed the predicted 31), MAINE, MASSACHUSETTS, NEw HAMPSHIRE; SAN high water for Boston (Commonwealth Pier) of 11.9 ft FRANCISco BAY AREA, CALIFORNIA at 10 16' (e.s.t. ) onthis date. The corresponding predicted maximum range was 14.1 ft. For comparison, the tide MAINE, level at mean high water springs is 10.3 ft, and the mean spring range is only 11.0 ft. Coastal ------- "Dec. 29-Abnormally high tides flooded waterfront along entire coast. Major These rising perigean spring tides reached A slightly damage south of Rockland over area with higher level of 12.0 ft at Boston at HHW (1109' e.s.t.) on eastward exposure to the sea. Coastal December 30 (as the result of the time lags introduced by streets and highways were flooded. Water phase age and parallax age), and then receded. poured into cellars of homes and busi- ness establishments. Five summer cot- tages were demolished by the huge waves On the west coast, the tidal flooding produced was in the Biddeford area. Small craft were occasioned by the same condition of perigean spring tides reported lost all along the coast. A num- that prevailed on the east coast, coupled with strong ber of roads were washed out. The tide onshore winds. To show the basis for these winds, the also backed up the Kennebunk River, synoptic weather map for 1959 December 30 would have flooding Dock Square at Kennebunkport. Hundreds of lobster traps were wrecked to be used, since the coastal flooding on the west coast or washed away. occurred on this date. However, on the 1959 December 29 map, a low-pressure trough is already seen to be moving MASSACHUSETTS from the south along the California coast, intruding be- Coastal ----- "Dec. 29-Unusually high normal tides, tween two high pressure cells--one off the coast and the strong to gale-force easterly winds, and a other centered over northeastern Nevada and southern full moon, combined to'produce the high- Idaho. est tides in at least 50 years, and possibly The strong winds produced over San Francisco Bay on as much as 108 years. Central and northern portions of the coast bore the brunt of the December 30 resulted from the steepening pressure gradi- tidal attack. Tidal flood waters engulfed ent associated with this low pressure system approaching all immediate coastal areas, and towering the mid-California coast from off the Pacific. Since no waves battered coastal installations and strong winds are indicated at San Francisco on the weather leaped seawalls. Water reached a depth of map of December 29, those mentioned in the Storm Data about 6 feet in the streets of Hull. At Nan- tasket Beach the waves tore out a 100 foot report must have been of relatively short duration, with section of parking area pavement to a the principal flooding effects being due to the augmented depth of 10 feet. Several thousand families perigean spring tide. were evacuated from their homes by the These tides reached their highest level of 6.9 ft at San Coast Guard, Harbor Police, or Fire De- h partments. Thirty families, were evacuated Francisco (Golden Gate) on 1959 December 29 at 1023 because of a flood-induced gas leak. Heavy (P.s.t.). The maximum range for this date was 8.4 ft. stones and debris were hurled onto shore The predicted higher high water at Golden Gate on De- areas by the giant waves. Plows were used cember 30 at 1112' (P.s.t.) was 6.7 ft, and the predicted to clear the affected area. Lobstermen lost many traps. Small boats were washed away, maximum range on this date was 8.2 ft. The correspond- and others were engulfed. Some beach ing values of mean higher high water and diurnal range areas were markedly eroded by the pound- at Golden Gate are 5.4 ft and 5.7 ft. ing surf. Flooded cellars crippled heating Because the onshore wind movement was neither sus- equipment in several thousand homes and caused heavy losses of inventory at business tained for a long period over San Francisco Bay, nor of establishments. Many homes were badly extreme intensity, the accompanying flooding damage damaged by flood and surf. 202-509 0 - 78 - 27 386 Strategic Role of Perigean Spring Tides, '1635-1976 NEW HAMPSHIRE factor induced by phase age and parallax age at times Coastal ----- "Dec., 29-Combination of spring tides and of perigee-syzygy. The separation-interval between prox- winds produced tide levels up to 14 feet igee and syzygy in this occurrence was only -31 minutes. above mean low water. Giant breakers The parallax of the Moon at the mean epoch of proxigee- smashed coastline. At Rye, wind-swept syzygy was 61'26.6". waters spilled over, damaging a seawall, The third fact of significance is the manner in which flooding roads, and hurling shale piles to a reinforcement was given to the high tides already present depth of 3 feet across a half-mile stretch at proxigee-syzygy by the merging of two atmospheric low of highway. Lobstermen and fishermen counted heavy losses from the abnormally pressure systems at a point midway along the east coast, high tides and surf. followed by the easterly movement of the combined system offshore, and its subsequent blocking by a strong, nearly CALIFORNIA stationary high pressure system which had moved south- San Francisco "Dec. 30-Strong winds combined wi.h ward off the east coast of Canada. Bay Area. high tides to flood low-lying areas of the The atmospheric pressures at the centers of both of the southern San Francisco Bay area. One man initially converging lows was 1,008 milibars. Although the was drowned when his small boat capsized. central pressure of the combined low was only 992 mb A painter lost his life when he was blown as it left the coast, the-cyclonic cell deepened and inten- from a scaffold at the sixth story of a Palo 0100h Alto building." sified after it left the coast. By on March 7, the cen- tral pressure had dropped to 984 mb. The process of successive buildup of this active wind- 4. The Tidal Flooding of March 6-7, 1962 producing system is shown in the series of three accom- The great.tidal flooding (Key No. J-85) which struck panying surface synoptic weather maps for 1962 March the entire coastline of the United States from South Caro- 5, 6, and 7, each plotted for 0100' (e.s.t.). (See figs. 99, lina to Maine (with the principal damage being experi7 100,101.) enced between Long Island, N.Y., and Hatteras Outer On the March 5 map, an extratropical low pressure Banks, N.C.) on March 6-7, 1962 is, without doubt, center with accompanying frontal wave is seen to be de- the most widespread nonhurricane-induced coastal flood- veloping off the southeast coast of the United States, ing which has occurred along the North American eastern centered at about 30'N. latitude and 75'W. longitude. A coastline during the entire period of coverage of this study, second low pressure system is centered at the same time 1635-1976. over southern Ohio. Falling pressures and the isallobaric So thoroughly has this event been documented since gradient indicate its projected movement to be almost its occurrence (cf., the reference source list opposite J-85 directly eastward. in table I ) that, with appropriate narrative excerpts in- The weather map of March 6 shows that the two low cluded from Climatological Data-National Summary pressure systems, on a collision course, have merged, with and Storm Data, it is additionally necessary only to assem- the center of the combined system being located at a point ble certain facts in r6surn6. some 100 nautical miles east of Chesapeake Bay. The pres- Of first importance is the consideration that, with the sure at the center of the new single low has deepened to initial severe flooding occurring in the dark of the Moon 992 mb, and the winds have intensified strongly,, with and in the early morning hours of winter predawn, as average easterly and northeasterly winds onshore from 32- well as under completely cloudy and snowswept skies, this .3 7 mph (28-3 2 knots) at map time, increasing as the day catastrophe resulted in the loss of 40 lives and property goes by, including isolated peak gusts to 81 and 84 mph damage estimated at 0.5 billion dollars. Incalculable loss (70 and 73 knots). was incurred as a consequence of coastal erosion. The weather map for March 7 shows that the center of .Second in significance is the very near coincidence of this the low pressure system has moved only slowly east-south- flooding event with a proxigee-syzygy alignment having eastward to an offshore location centered at about 35'N. a mean epoch of 1962 March 6 at 0430' (e.s.t.), just 3.5 latitude and 70"W. longitude. Its forward motion has hours before the initial peak reached by the inflooding become blocked by a strong, near-stationary high pres- tides at Sandy Hook, N.J., (see fig. 111 ) and some 28 sure cell which has intruded southeastward from off the hours before the highest tidal peak reached on the follow- Canadian coast and which, while not appearing on@ this ing day. This latter flooding included the normal delay weather map of t he United States and surrounding Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 387 TABLF, 29.-Surface Synoptic Weather Mapsfor Cases of Tidal Flooding Receiving Special Attention in the Text Key letter Weather map date and Perigee - and serial mean perigee-syzygy date syzygy Location of tidal flooding' No. (hours) J-85 1962 March 5 1. Oh (-31 min.) Entire mid-Atlantic coast from Long Island, N.Y. to Outer Banks, N.C. March 6 4. 5h J-85 1962 March 6 1. Oh (-31 min.) Do. March 6 4.5h J-85 1962 March 7 1. Oh (-31 min.) Do. March 6 4. 5h 86 1962 October 12 1. Oh (-9) Local estuaries and bay locations, Oreg., Wash., and northern Calif. October 13 3. 5h N-99 1974 January 7 7. Oh (-2) Santa Barbara, Santa Monica, and San Clemente; Newport, Capistrano, and Malibu January 8 7. Oh Beaches, Calif. N-99 1974 January 8 7. Oh (-2) Do. January 8 7. Oh N-99 1974 January 9 7. Oh (-2) Do. January 8 7. Oh 0-100 1976 March 16 7. Oh (+ 16) Beaches in Massachusetts, New Hampshire, and Maine, and northward to Halifax, March 16 6. Oh Nova Scotia. waters, lies over the Atlantic to the east of the blocked low. condominiums, are shown in figs. 102-109. The frontis- This low pressure cell has meanwhile expanded and elon- piece of the book also contains a very meaningful rep- gated along a southwest-northeast axis. The resulting resentation of the extent of damage that such severe tidal "fetch" of overwater surface wind movement directed, on flooding can cause. The various contemporary newspaper the north side of the low, from the sea onto the land, has accounts included in the present section and in table 5 thus been extended to several hundreds of miles. provide valuable supporting information in connection During the time that this offshore low pressure system with the 1962 catastrophe. had been deepening (979 mb being the lowest pressure A technical analysis of the time-rate of buildup of this actually recorded at sea) the barometric gradient had flooding event is also possible from a study of the accom- been steepening. Greatly strengthened, gusty winds re- panying graphs. Fig. 110 shows the progress of an ac- sulted, blowing onshore from directions originally north- celerated rise in the coastal flooding waters resulting from east over the North Carolina and Virginia coasts to final proxigean spring tides plus onshore winds at Atlantic east and east-northeast components over the New Eng- City, N.J., over a 5-day period bracketing the actual land coastline. Because of the imp-aired movement of flooding event. The various sets of broken lines in this the low pressure center, these intensified winds continued figure represent individual plots of observed (i.e., re- with little diminishment, but with changing locations of corded) hourly heights surrounding the time of each day's maximum onshore intensity, along the coastline for some higher high water in the period from March 5 to 65 hours, throughout five successive high tides. Although, March 9. (Note that the vertical tidal height is plotted as mentioned, peak gusts up to 84 mph (73 knots) were in meters as well asfeet.) For comparison, the two solid recorded, the average coastal onshore winds during the curves indicate the predicted, or purely astronomically height of the storm ranged from'about 21 to 49 mph (18 induced tide for March 6 and 7. In all cases, the appro- to 42 knots). priate curve is plotted for a 10-hour period in each day, The devastating effects of the severe offshore storm, centered on HHW. plus augmented proxigean spring tides, are illustrated in The accelerated rates of growth of these storm tides, various forms among the accompanying graphic mate- in excess of those which are astronomically induced, are rials. Representative scenes of extensive inundation of obvious from the shifting of the observed curves to the the coastline, severe beachfront erosion, flooding of both left of the predicted curves along the time scale of each suburban hom'esites and coastal industrial facilities, de- diagram. The considerably greater amplitudes of these struction And toppling of beach homes (and their trans- observed curves, in consequence of the sustained wind port to sea), and the complete demolition of waterfront action, and the resultant sharp peaks, rather than pre- J-85 1962 MARCH 5 1 R EA, TOR A ql) ks L R 7,\l 9 p @ss uil i @o a sh r.6, Pop aqd,! v r pr m on"' c 0., o-. A d- AJ NN Nis AAS N@. 'R SURFACE WEATHER Mlkp AND STATION WEATHER _AT 1:00 X M, S, T, "saai t. -x 211 'Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 389 %\ \0 I? IPA A 10 .0 cc Luj@ CY) LL 0 :74 IS j LLA > -7 4t 10 k, U 4 C4 - -- ---- 10 ANA 0j) . . .. . ... ... C6 cn IN ------ -4- cc ;3.6 A cc ........... gj P.- t C@ J@ 'I 2 w X@ 61 ACL, CA 04 M, v- LLI _j GO > FiGuRE 100. CA (D J-85 1962 MARCH 7 I.Oh. March 6 4.5h. (-I gon n socia stagg dee, ofts "A - w I -Wl 4 S W@ C: ti _q 'A A 0 - CD ir J7 5 -7 C', L',21 ,Y, "0 SUR@@"EATHER` MAP ggg;f 'T P 7@ $TAL Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 391' ---------- 7 @ 1- 0@ -_AL :7 x" Courtesy of U.S. Army Corps of Engineers (Philadelphia District) Courtesy of U.S. Army Corps of Engineers (Philadelphia District) FIGURE 102-The inundating effects of the great mid-, FIGURE 104-Beach homes at Rehobeth Beach, Del., Atlantic coastal storm and tidal flooding of 1962 March knocked over and reduced to rubble by the impact of the 6-7 upon the Grandview Beach section of the City of 1962 March 6-7 tidal flooding. Hampton, Va. A very close perigee-syzy y alignment oc- .9 curred on 1962 March 6.188 e.st. J -'I =K 4 7 Y t= ra - 0, W_ Courtesy of U.S. Army Corps of Engineers (Philadelphia District) Courtesy of U.S. Army Corps of Engineers (Philadelphia District) FIGURE 103-Devastation caused by the wind-driven tidal FIGURE 105.-Nearly total demolition of the Atlantic Sands assault of 1962 March 6-7 at Bethany Beach, Del. Note Resort Apartment at Rehobeth Beach, Del., by the 1962 the completely toppled homes. This aerial photograph was March 6-7 tidal onslaught. taken on March 11. 392 Strategic Role of Perigean Spring Tides, 1635-1976 IMF IZI _=70 Source U.S. Coast and Geodetic Survey (Aerial Photogrammetrie Survey) FIGURE 106-Severe erosion of the shoreline along the south coast of Long Island, N.Y., caused by the tidal flooding in- Courtesy of U.S. Army Corps of Engineers (Norfolk District) cursion on 1962 March G-7. 'The coastal highway was rendered impassable by huge, wave-transported mounds of FIGURE 108-Onshore encroachment of seawater at Nor- sand. folk, Va., associated with the 1962 March 6-7 tidal flood- ing. The area shown is on Moran Avenue between Princess Anne Road and Olney Road. r- Ar L 2- Source: U.S. Coast and Geodetic Survey (Aerial Photogrammetric Survey) Courtesy of U.S. Army Corps of Engineers (Norfolk District) FIGURE 107.-Portion of barrier beach south of Mecox Bay, FIGURE 109.-The Building 27 warehouse and pier at Fort near Southampton, Long Island, N.Y., breached by the Norfolk, Va., were extensively inundated by the 1962 tidal flooding of 1962 March 6-7. March 6-7 coastal flooding event. Note the top of the submerged car in the middle distance. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 393 10 GREAT MID-ATLANTIC COASTAL FLOODING -1962 3.05 PLOT OF OBSERVED AND PREDICTED HOURLY HEIGHTS (HHW) 9 ATLANTIC CITY, N.J. 6 LEGEND MARCH 5-9 7 2.74 OBSERVED ............ .......... Mar5 \'k Mar 6 ...... @- Mar 7 -------- Mar 8 8 ............... Mar9 244 PREDICTED Mar 6 May 7 213 U.1 LU 6 1W z tf ................ .............. .... ............. . .. ......... M LU __4 M 6 1.52 4 /* 1.22 3 "0.91 2 io i 03 04 05 06 07 08 09 10 11 12 13 HOURS OF THE DAY FwuRE 110. dicted plateaus, of tidal maxima on March 6 and 7 also Fig. 115a depicts tidal flooding of the streets in Nor- are clearly evident. folk, Va., during the earlier phase of the low pressure Fig. 111 illustrates the observed rapid buildup and less center's offshore -movement when the surface winds at rapid subsidence of the higher high water phase of the Norfolk were still directed onto the coast. tides at Sandy Hook, N.J., over 7 successive days from Appropriate newspaper accounts (figs. I t2-115) as March 4 through March 10. The considerable damage to the piers at Atlantic City well as official analyses from Climatological Data- caused by these repeated extreme rises in water level, and National Summary and Storm Data relative to the the hurling of ponderous masses of water against the piers meteorological circumstances accompanying this coastal by strong winds, is shown in fig. 113 a. flooding are included on the following pages. 394 Strategic Role of Perigean -Spring Tides, 1635-1976 GREAT MID-ATLANTIC COASTAL FLOODING-1962 10 3.05 PLOT OF OBSERVED HOURLY HEIGHTS (HHW) 7 SANDY HOOK, N.J. -_- 6 9 MARCH 4 - 10 //7 2.74 8 2.44 LEGEND 7 OBSERVED - M r 4 2.13 . . ............... M:r I Mar.6 X M LL) ......... Mar7 LU ------- -Mar 8 LL ... ......... Mar9 ...... . ........... X 9 6 Mario 1.83 S2 M M X M Z In 4 5 1.52 /* 4 1.22 .............. 3 0.91 2 0.61 02 03 04 05 06 07 08 09 10 11 12 HOURS OF THE DAY FiGuRE 111. Fig. 161 a in chapter 8 further represents the predicted was in no way predicted. (See the "Today's Forecast" rate of tide rise at Breakwater Harbor, Del., as a func- and "Five-Day Forecast" columns from the New York tion of the proxigean spring tide which-acted upon by Times in fig. 112.) Despite the very close proxigee-syzygy supporting winds precipitated this tidal flooding event. alignment ( - 31 minutes) accompanying this event, and It is especially noteworthy that this method of analysis the considerable potential for tidal flooding, the event reveals the March 6.19 proxigee-syzygy alignment to lie was later described in all public announcements only as centrally within a "window" of potential tidal flooding, being associated with "spring" tides. with the peak of the tidal growth curve well into the With the appropriate use of the data contained in potential danger zone. table 34, the computer printout of table 16, and the de- To conclude the'list of items under substantive review, velopmental predictor equation of chapter 8, such a seri- it is, therefore, also significant for the future in connection ous tidal flooding eventuality, it is to be hoped, can in the with such tidal floodings to note that this circumstance future be avoided. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 395 The New York Times Tues., March 6, 1962 Page 70 L+, Cols. 2-5 The Summary 2W7 V**WV Snow fell yesterday from the North Atlantic States to the Mississippi Valley and in the higher parts of the Pacific States. Rain fell in the North Atlantic States and the Pacific States. Low pressure will dominate the East 34 r 27 and the Pacific Northwest today. High pressure will extend from the Mississippi 4 Valley to the plateau region. ... .. . L i37 Snow is the forecast today for the north- 86 Ok ern plateau region. Snow mixed with rain 11085. will fall from the North Atlantic States to Famt the Appalachians. Rain will fall in the 60 western plateau region and the Pacific States. It will be colder in the Atlantic 01 29je .T - States, the Ohio and Mississippi Valleys and the lake region. OUTLOOK FOR WA Pod THIS FTRRXOOX,< , N b Aril % Today's Forecast J= M. raw United States Weather Bureau R@ PM 0@4wvm 'I1 (As of 11 P. M.) P_0C"_% 3W ONG fuumvc@ mpf NEW YORK CITY, NEW JERSEY, L JIM ISLAND, LONG ISLAND SOUND, wwo ROCKLAND AND WESTCHESTER "Q= 0. 0-.- 0-- 0-- o;z 0.- 0.- 0o'O.-O.- 0=0"O.- 00 0;= COUNTIES, SOUTHEASTERN NEW YORK, EASTERN PENNSYLVANIA AND CONNECTICUT-Snow today and tonight. highest temperature today in Figure beside Station Circle indicates cur- the action of the opposing wedges of cold air. the 30's, northeasterly winds 35 to 45 rent temperature (Fahrenheit); a decimal This lifting of the warm air often causes miles an hour; lowest temperature to- number beneath temperature indicates pre- precipitation along the front. night near 30. Cloudy and cold tomor- cipitation in inches during the six hours prior Shading on the above map indicates areas row. to time shown on map. of precipitation during the six hours prior to (As of 5 P. M.) Cold front: a boundary line between cold time shown. MASSACHUSETTS, VERMONT, NEW air and a mass of warmer air, under which Isobars (solid black lines) are lines of equal HAMPSHIRE ANj) NORTHEASTERN the colder air pushes like a wedge, usually barometric pressure and form patterns which NEW YORK-Snow, except snow or advancing southward and eastward. control air flow. Labels in . millibars and rain southeast portion today; snow Warm front: a boundary between warm air inches. north portion, snow or rain southwest and a retreating wedge of colder air over Winds are counter-clockwise toward the portion tonight. which the warm air is forced as it advances, center of low-pressure systems, and clockwise usually northward and eastward. and outward from high-pressure areas. Stationary front: an air mass boundary Pressure systems usually move eastward at Day's Records which shows little or no movement. an average movement of 500 miles a day in NEW YORK Occluded front. a line along which warm summer and at a rate of 700 miles a day in Eastern Standard Time air has been lifted from the earth's surface by the winter. Wind Temp. Hum. (M.P.H.) Bar. Midnight ........ 30 53 N 8 30.05 1 A.M ........... 30 56 N 6 30.04 2 A.M ........... 30 55 N 5 30.04 3 A.M ........... 30 56 N 6 30.02 4 A.M.. . @ ....... 30 56 N 6 30.02 5 A.M ........... 30 56 N 5 30.03 6 A.M.. . @ ....... 30 63 N 8 30.04 7 A.M ........... 31 61 N 8 30.05 8 A.M.. . , ..... 31 63 N 6 30.06 9 A.M ........... 32 66 NE 9 30.05 10 A.M ........... 35 67 NE 11 30.06 low temperatures are: Albany 39-21, At- 11 A.M.. ....... 36 69 NE11 30.05 Five-Day Forecast Noon .. ....... 36 72 NE 13 30.04 (March 6 through March 10) lantic City 46-33, Hartford 44-24, New 1 P.M ........... 36 79 NE 15 30.00 York 46-31, Philadelphia 49-33 and 2 P.M ........... 37 79 NE 16 29.98 Scranton 42-25.) Snow inland and snow 3 P.M.. . @ ....... 38 79 NE 17 29.95 4 P.M ........... 37 85 NE 16 29.93 SOUTHEASTERN NEW YORK, EAST- or rain along the coast today and rain 5 P.M.. ., .. .. _ .38 82 NE 16 29.98 ERN PENNSYLVANIA, NEW JERSEY Friday or Saturday may total more than 6 P.M... @ ....... 39 79 NE 17 29.98 7 P.M ........... 38 78 NE 18 29.98 AND CONNECTICUT - Temperatures one-half an inch melted. 8 P.M ........... 36 85 NE 19 29.93 will average near normal, except 2 to 4 9 P.M ........... 36 85 NE 21 29.93 10 P.M ........... 36 85 NE 23 29.91 degrees below normal in extreme south- 1962 Mar.6 11 P.M ........... 34 92 NE 25 2986 ections. It will be cold today and 4.5h e.s.t. (-31 min.) Midnight ........ 35 89 NE 27 29:82 ern s 1 A.M ........... 35 89 NE 27 29.81 tomorrow with warming toward the end. of the period. (Some normal high and J-85 FiGuRE 112. 396 Strategic Role of Perigean Spring Tides, 1635-1976, The New York Times Wed., March 7,1962 Page 24 L+, Cols. 1-4 (Continued from Table 5) Snow, Rain, Gales, Tides ... The Erie-Lackawanna ferry to Barclay between the Manasquan River and Barne- Street was closed from 7:25 to 10:30 A. M., gat Bay collapsed when racing waters un- Lash Mid-Atlantic States and again during evening high tide, start- dermined its pillars. ing at 6:55 ... Almost every house in Sea Isle City, (Continued from Page 1, Col. 3) N. J., which has 1,200 residents, was re- . . . The Jersey Central Railroad ferry ported flooded by four to five feet of The northeast storm developed with from Jersey City to Liberty Street was water. multiple centers, according to the Weather halted from 7 to 10:15 A. M. Flooding later Seventy-five families were evacuated Bureau. including one low pressure area halted the line at Jersey City and Bayway, from'Island Park, Oceanside, Bellmore and in Virginia and another southwest of Ber- so that until. noon, service ended at Bay- Seaford, L. L, when water rose two to muda. It stalled in the face of a cold, high- onne. Jersey Central normally handles 10.- three feet. Whid-driven waves twenty feet pressure area from Canada ... 000 passengers each morning. high stormed Fire Island, carrying away Ferry service was also suspended by the sand dunes on the ocean side and wreck- . . . Twenty-three persons in Far Rock- Jersey Central last night during high ing some Boardwalk and other facilities away and six in Breezy Point were evacu- tide ... . . . ated when high tides threatened their homes ... . . . Flooding in the Atlantic resort area . . . The barrier beaches of Long Island, and neighboring communities was exten- from Coney Island to Montauk Point, were ... Ferry service between Staten Island sive. A fifty-foot section at the end of the battered heavily. Many streets in Coney and Sixty-ninth Street, Brooklyn, was Steel Pier, used for a water circus, was Island were covered by up to two feet of halted from 8:15 A. M. until 10:26 A. M. washed away, and a thirty-foot section in water last night. because high tides made loading of ve- the midway portion of the pier was de- In Nassau County, flooding cut off see- hicles and passengers impossible . . . molished. So was a 200-foot section of the tions of Merrick, Baldwin Harbor, East boardwalk in the Inlet section while a Rockaway and Point Lookout. ... The Brooklyn-St. George ferry ceased sixty-five-foot boardwalk approach there High seas took a heavy toll of the dunes operations again during high tide last was washed across Maine Avenue . . . from Fire Island to Montauk. At West- night, starting at 7:30 o'clock ... hampton Beach, three luxurious summer ... The staff of The Atlantic City Press. homes were demolished . . . ... Flooding forced scores of families from a morning newspaper, worked with its homes in south shore communities. composing room and much of its editorial . . . In Fairfield County, Conn., several Sections of Franklin D. Roosevelt Drive, office covered by water at high tide . . . families were evacuated in shore homes the Belt Parkway in Brooklyn and the in Norwalk, Darien and Westport Hutchinson River Parkway in the Bronx Municipal offices in Asbury Park's were flooded and closed to traffic part of Convention Hall were flooded. Several hun- the day ... dred feet of the boardwalk were damaged as tide-driven sand niade the structure 1962 Mar. 6 ... High tides in the morning and evening bulge upward. 4.5h e.s.t. (- 31 min.) halted service on the railroad between the Loveland Town bridge over the In- Island Park and Long Beach ... land Waterwav Canal in Point Pleasant J-85 FIGURE 113. Source: U.S. Coast and Geodetic Survey (Aerial Photograni metric Survey) 4% AI le FIGURE 113a.-Aerial photograph taken.over Atlantic City, N.J. at 1030 e.s.t. on March 25, 1962, showing damage to Steel Pier by severe tidal flooding of March 6-7. Flight altitude, 10,000 ft; scale 1: 20,000. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 397 The Now York Times Thurs., March 8, 1962 Page 1, Cols. 6, 7 (Late City Ed.) At 7 o'clock last night the ocean broke 6 through Long Beach Island, cutting off Beach Haven. Storm Hits Coast 2d Da Police Chief Jerry Sullivan of Atlantic City predicted the damage would be "much more" than the $5,000,000 damage the city 27 Dead, Damage Heavy sustained in a hurricane in 1944. The re- sort city was swept by tides six feet high and winds that hit eighty-four miles an hour in gusts ... By Russell Porter The heavy storm that swept the mid- Atlantic states Tuesday struck again yes- TAUK terday with high tides and winds along MON -seven persons the coast. At least twenty were reported dead in its wake as the storm swept out to sea. CO N N -,t, Thousands of homes were wrecked or damaged from Virginia to New England SOUL"MPL ,On, and thousands of persons were evacuated. NEW 0, Hundreds were marooned without electric- -tking water, and food YORK ri'z ity, gas or drh ran G 0 Lon low. Rescuers used trucks, cars, boats, am- 14 0 Beach phibious vehicles and helicopters ... S 0 P, ... The Weather Bureau predicted that 5aqville abchoque strong, gusty winds and above-normal 0 ay Shor, tides would continue through the night, B but that the wind and water would sub- Babylon,` side today. lNew" 66m Tidal waters , in this area were expected to rise three to five feet above normal dur- C it, ing the night, and two to three feet higher Long 10____ MILE5 50: may be more flooding ... than usual in the early morning. There Beach 6V The New York Times March 8.1962 ... The New York metropolitan area was PerLh HAVOC: Storm swept hit hard yesterday by extremely high tides, heavy surf, violent winds, flooding Armbo Long Branch houses at (1) and (2) into and power failures. Perry, rail and high- ocean, inundated Rockaway way traffic was disrupted. Winds up to fifty miles an hour blew 6 Asburg Park area (3), routed Long Beach across the city. Streets in lower Man- ffian@35quan 0@ Island residents (4), and hattan, and sections of the East River @ N Drive, the Hutchinson River parkway and 2 pounded Atlantic City (5).. Toms the Belt parkway were closed by flooding. R@ver Coney Island was flooded and hotels and N EV4 Seas i de On Long Island, Suffolk County Ex- apartment houses in the Rockaways were ecutive H. Lee Dennison also said damage evacuated ... JERSEY was in the hurricane class. He asked Gov- ernor Rockefeller to declare the South 1962 Mar.6 LN Shore, along the Atlantic, a disaster area. 4.5h e.s.t. (-31 min.) zomo 9--AC" Mr. Dennison declared a state of emer- gency along the shorefront. He estimated property damage at more than $2,000,000. TulckerLon More than seventy houses, including thirty-five on Fire Island, were destroyed on the barrier beaches of the county. Fif- The New York Times teen summer houses on the dunes at West- Thurs., March 8, 1962 hampton Beach were undermined and Page 22 L++, Cols. 3-8 swept out to sea. About twenty other tlantic houses were lost in near@by coastal re- Cape May, Monmouth and Ocean cit!j sorts ... Counties declared states-of-emergency. All 700 residents of Long Beach Island were Most ferries stopped rumiing as the evacuated, and nine houses were seen morning rush hour started. because of floating in Barnegat Bay ... high tidal waters, heavy winds and power failures . . . . . .State officials in Trenton last night The rising tide forced the suspension estimated the damage in coastal areas at $30,000,000. Winds as high as forty miles of ferry service between Staten Island and an hour and abnormally high tides were 0 Cape May Manhattan between 8:05 and 9:18 P. M. still battering the coast. Two boats with about 2,000 passengers FIGURE 114. 398 Strategic Role of Perigean Spring Tides, 1635-1976 NEW YORK (Cont.) each stood off St. George, q. I., unable to a three-mile section from Fort Hamilton TIDE CYCLE AND WIND dock because of high water Parkway to Bay Parkway. The westbound lane was closed at 10:30 and the police BLAMED IN FLOODING ... Service on the Tubes was suspended said the road would be reopened after the again last night when high tides flooded tides diminished. WASHINGTON, March 7 (AP)-Winds the tracks between Newark and Jersey Some streets in downtown Manhattan from one of the worst winter Atlantic City. The rising waters also forced cancel- were also closed by flooding, including storms ever recorded, at a time of normal- lation of the Erie-Lackawanna ferry serv- Pearl Street from John Street to Maiden ly high tides, combined to produce the ice between Hoboken and Manhattan at Lane. The east side of Whitehall Street devasting high water today on much of 8:50 P. M. from the tip of Manhattan island to Front the East coast. The Greenwood Lake and Newark lines Street was under water. The main path of the wind, out of the of the Erie-Lackawanna Railroad were put The worst of the flooding in the city was northeast, was along a line extending from out of commission by flooding. The Penn- in the Rockaways and near-by sections. about 300 miles off Cape Cod to the Vir- sylvania Railroad reported some commuter Water covered the tops of parked automo- ginia-North Carolina coast. In a meteor- trains from North Jersey shore points de- biles in some areas. ologist's or sailor's term, this is a long layed by high water, some as much as fetch of about 600 miles. Such a long fetch thirty minutes . . . Water from Jamaica Bay was so deep gives time and opportunity for the winds at Howard Beach that commuters were to pile up water before them. The rush Power on the Long Beach line of the unable to wade through it to the subway of wind, pushing and dragging water, Long Island Rail Road was cut at 8 -25 and buses were unable to get to Hamilton came at a time when tides in the normal A. M. for the third time in two days as Beach. About 100 marooned families were course would have been high. third rails were flooded . . . evacuated from Breezy Point at the west In the twenty-eight-day moon cycle there . . .Service was resumed at 1 P. M. but end of the Rockaway peninsula . . . is a period when the gravitational forces was interrupted again last night by the of the moon and the sun, acting on the rising tide. It was expected to go back to . . . Flood waters inundated Wallops oceans, pull in opposite directions, dimin- normal when the tide receded. Island, Va., a launching site of the Na- ishing the tides. There is another period Aluch of the East River Drive was tional Aeronautics and Space Administra- when these forces pull together and give closed. At noon a foot of water covered tion. higher tides. This storm happened to come the roadway between Eightieth and Nine- In Chincoteague, Va., 1,000 residents in such a period ... tieth Streets . . . were evacuated after their homes began I to break up under the pounding of the 1962 Mar. 6 . . . The eastbound lane of the Belt was surf. At least five persons lost their lives 4.5h e.s.t. 31 min.) J-86 closed because of high tides at 9 P. M. over there . FIGURE 115a. anti 16E] T IN Q3 RE eXl@ Re R AP i_4 R U FIGURE 115a.-The corner of Bank Street and City Hall Avenue in downtown Norfolk, Va., showing the tidewaters reced- nil In ing after the great mid-Atlantic coastal flooding of March 6-7, 1962. Note the dark 3-foot highwater mark on the wall at the right. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 399 Abstracted from: Cooperman A. I., and Rosendal, H. E., ward northern New England, as the intensifying coastal "Great Atlantic Coast Storm, 1962, March 5-9," U.S. storm started to drift cast- northeastward. This resulted in Weather Bureau Climatological Data-National Sum- the LOW elongating in a roughly cast-west direction with a mary, vol. Ill. 1962, p. 137. very steep pressure gradient. . . . A long fetch of north- "A slow moving late winter coastal storm combined with easterly winds was set up by the configuration of this spring tides (maximum range) wrought tremendous destruc- elongated LOW. This pattern persisted from late on the 6th tion to coastal installations from southern New England to to the 8th, and the resulting strong northeasterly winds piled Florida on March 6-9. This storm, which consisted of a up additional water on top of the high spring tides and cre- series of LOWS, has been described as one of the most dam- ated mountainous seas which pounded savagely at the aging extratropical cyclones to hit the United States coast- coastline. line. Although gale-force winds and at times hurricane- ". . . [A sea-condition analysis revealed] a significant wave n 3 height of more than 40 ft at 0000 G.m.t. of the 8th. The force winds, accompanied the storm, this is not unusual for a cause of such high seas from the east ... was the slow move- North Atlantic winter extratropical cyclone. It was the long ment of the system and its elongated shape. Furthermore, the fet-h and the persistence of these strong northeasterly winds westward traveling seas were already set up, by the previous which raised the spring tides to near record levels. The tidal LOW, across the entire ocean to Europe, . . . [facilitating the flooding which attended this ston-n was in many ways more breakdown of the] ... easterly winds and rebuilding of waves disastrous than that which accompanies hurricanes. The traveling in the opposite direction. storm surge in tropical cyclones generally recedes rapidly-af- "The pressure gradient near the center of the system was ter one or two high tides, but the surge accompanying this not very steep, and the lowest pressure recorded was only storm occurred in many locations on four or five successive about 979 mb which is deep for an extratropical LOW in the high tides. In addition, many places reported runup of waves 20 to 30 ft high. western North Atlantic, but not too unusual. Within this "This successive onslaught of wave and tidal action for @"shallow" and fairly large region of the lowest pressures, two over two days weakened and undermined even the more or three separate low pressure cells could be detected during permanent shoreline structures, and after a period of time the first few days of the storm by analyzing the wind and some suffered structural damage and collapsed. . . . . pressure data received from ships in the area. These cells "The erosive effect of wave and tidal action changed the appeared to rotate within the primary system with the for- face of the immediate coastline, and on many of the well- ward one weakening and a cell toward the rear generating known beaches the most severe loss was often the sand of and taking over. This caused the movement of the system as the beach itself. In addition many new channels and inlets a whole to be rather erratic, and at times the storm appeared were cut in the shoreline. . . . to move backward or loop. Any single track is thus difficult "Preliminary estimates of damage total about $200 mil- to construct. lion; 1,893 dwellings were destroyed, 2,189 sustained major "Precipitation was heavy over the Middle Atlantic Coast damage, and 14,593 minor damage. Thirty-three persons are with interior portions of Virginia and Maryland receiving up known dead; 340 received major injuries and 912 minor to three feet of snow accompanied by some thunderstorm injuries. activitiy during the development stage of the storm. As the 41... This storm, although it first appeared as a wave on LOW became more mature, only light precipitation fell to the polar front on the 4th off the Florida coast, did not the north of it, and in New England the storm was known deepen to any extent until it reached the Hatteras area.... as a "dry northeaster." Much of the driving energy was prob- "When the coastal storm started to form as a wave on the ably caused by the transformation of potential energy stored polar front off the Atlantic coast of Florida on the 4th, the in the large warm HIGH into kinetic energy along the steep dominating features on the weather map were a strong block- pressure gradient of this LOW.... ina HIGH centered over the Canadian Arctic Archipelago "NEW ENGLAND.-Central and northern New England With a ridge extending south-southeastward over the Middle escaped relatively lightly the eff-cts of the coastal storm. Atlantic States and a moderate LOW located over the upper Seas came crashing over walls along all parts of the coast Mississippi Valley. On the 5th.the interior LOW with a very south of Portland, Maine. Low lying coastal highways were deep circulation aloft moved along the southern fringes of flooded and closed to traffic as tides ran up to 5 ft above nor- 'the Canadian HIGH to the Ohio Valley, where the surface mal. Damage to seawalls was slight along the, Maine coast LOW began to dissipate. In the meantime, a wide area of but was heavie 'r along the New Hampshire shore. Complete low pressure with several separate centers had developed be- sections of old seawalls were washed out at the New Hamp- tween the Carolina coast and the wave off the Florida coast. shire resort towns of Rye, North Hampton, and Hampton. The deep LOW aloft which was associated with the dissipat- Some structural damage to waterfront installations, mostly ing interior LOW continued its eastward movement, and by of minor nature, occurred in New Hampshire and Massachu- the 6th it was located over the Carolina coast. This triggered setts, and many cellars in low-lying districts were flooded. the intensification of the coastal LOW which still consisted Most damage in Connecticut and Rhode Island was con- of several ill-defined centers. The usual northeastward move- fined to beaches along the south coast and Block Island. mefit of such a system was retarded by the p Iresence of the There was some flooding in low susceptible places in Bridge- blocking HIGH which was now centered near Labrador. On port, East Haven, and Greenwich, and the Quinnipiac River the 7th and 8th this HIGH continued to move southward to- overflowed in North Haven doing some damage. An oyster 400 Strategic Role of Perigean Spring Tides, 1635-1976 boat and barge were sunk near New Haven. The highest ably prevented severe damage to inundated farmlands far- winds reported on the East Coast occurred at Block Island. ther inland or in the Bay areas. It is estimated that from 1.2 The Weather Bureau Airport Station recorded a peak gust to 1.5 million broiler chickens and an unknown number of of 84 mph and a sustained wind of 76 mph on the morning incubator eggs were lost chiefly due to power failures in the of the 6th. Delmarva production area. "Preliminary damage figures for the New England States: "Preliminary estimates on damage for the Delaware- Maine, $25,000; New Hampshire, $27,000; Massachusetts, Maryland shore are about $50 million. Seven deaths were $250,000; Rhode Island and Connecticut, $1 million. No reported in Delaware and three in Maryland. lives were reported lost in the New England area. "VIRGINIA.-The intense coastal storm brought as se- "NEW YORK.-The strong winds pushed the ocean vere damage to the Atlantic coastline of Virginia as any waters onshore, producing severe flooding. At the time of extratropical storm in modern times. The resort areas near high tides on the 6th and part of the 7th, the waters reached Virginia Beach in particular had heavy property losses. between 4 ft above mean sea level along the western end Many hundreds of homes on the beaches were totally de- .Of Long Island and 7 ft above in New York Harbor. On top stroyed and thousands were damaged. The fishing pier at of the high water the storm sent huge waves, estimated at Virginia Beach was destroyed. The largest pile driver in the 20 ft high in places, to break against beachfront installa- world, a $11/2 million machine, was turned over on its side tions. Damage was greatest on the south shores of Rich- in deep water. One of the communities hardest hit along the mond, Brooklyn, and Queens Boroughs in New York City, Virginia section 'of the Delmarva Peninsula was Chinco- and along the barrier beaches of Nassau and Suffolk County, teague Island. Extensive dariage was done to the fishing eastward to Montauk Point. On Long Island's South Shore boats and nets, homes and livestock. . . . Many ponies on about 100 houses were swept into the sea, 35 of them on Chincoteague drowned. More than 1,000 persons were air- Fire Island alone. Numerous other buildings suffered water lifted by helicopter to the mainland during the storm, The damage, and cellars, streets, and highways in waterside areas NASA installation on Wallops Island also suffered consid- were flooded. There was also wind damage to utility lines, erable damage. High tides inundated large areas inside the trees, signs, and windows, but these losses were compara- Bay, and sections of Hampton Roads were under several tively minor. feet of water. The 8.9 ft tide above mean low water, 5.6 ft "Preliminary and unofficial damage estimates are in above non-nal, was the highest tide caused by an extratropi- the $10-$15 million range. Fortunately, no loss of life or cal cyclone and the third highest of record. More than 1,000 injuries were directly attributable to the storm, 'although automobiles were flooded in the metropolitan area alone. many families were forced to evacuate threatened dwellings. The Chesapeake Lightship of the Coast Guard while on "NEW JERSEY.- . . . The major damage was re- station at 36'59'N., 75'42' W.., or 17 mi east of Cape Henry stricted to property facing the beach itself. The entire coast- Lighthouse was damaged by a 50-ft wave early on the 7th line and even the Delaware Bay area suffered from the high and forced to leave the station. At this time sustained winds tides. Highways along the coast were cut in many places were above hurricane force. or buried under several feet of sand. Thousands of homes "Damage in Virginia is estimated at $30 million; however, along the coast were damagea or destroyed. One of the the full extent is not known. In the city of Virginia Beach hardest hit areas was Long Beach Island. At Atlantic City alone, damage amounted to about $16 million. Five deaths the major damage was the cutting of the famed Steel Pier. were reported in Virginia. The storm swept away the quarter-mile section of the pier "NORTH CAROLINA.-The most destructive effects which connects the auditorium at the end of the pier with of the storm took place on Hatteras Island and northward. the mainland boardwalk. . . . On the entire stretch to the Virginia line, a large percentage "The storm did an estimated $80 million damage in New of the protective sand dunes along the ocean side of the Jersey. Deaths mounted to 14 with 12 other persons, in- elongated islands which constitute the Outer Banks were cluding nine aboard two fishing trawlers, missing and pre- washed flat. A 200-ft wide inlet was cut, by waves and sumed dead. strong currents at the change of the tides, across Hatteras "DELAWARE AND MARYLAND.-The Atlantic coast Island about 2 mi north of Buxton. The highway along the resort towns bore the brunt of the storm in these States. shore was destroyed or undermined in many places or cov- Four or five consecutive high tides with 20-30-ft waves ered with sand up to several feet deep. Many cars were right against the coast caused serious beach erosion and de- stranded with only the rooftops appearing above the sand. struction of shoreline property along the Delmarva Penin- Most of the damage to private property occurred in the Kill sula from Cape Henlopen and Cape Charles. At Rehoboth Devil Hills-Kitty Hawk-Nags Head area north of Oregon Reach, Del., and Ocean City, Md., complete destruction to Inlet where many motels and summer homes suffered. severe damage was inflicted to many resorts on the immedi- "Preliminary damage figures are estimated at $12 million ate coast while tidal flooding occurred farther inland. Tides which does not include the devastation to the land itself. at Ocean City were estimated to be 5 to 6 ft above nor- Two deaths were reported in North Carolina. mal. . . . The boardwalks were reduced to splinters early "SOUTH CAROLINA.-Damage from the coastal storm in the storm. . . . and in . . . resort areas much of the in this State was mainly limited to tidal flooding and some sand was washed away. . . . Less serious flooding occurred beach erosion. A few cottages along the beaches were de- in the Bay areas. The rain-soaked soil of late winter prob- stroyed and others damaged. All beaches along the coast Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 401 suffered in varying degrees from loss of sand in certain RHODE ISLAND sections. Folly Beach is estimated to have lost 100 to 200 ft in width for one-quarter mile in an uninhabited area Coastal "Mar. 6-7-Four successive high tides, near the east end . . . ... Sections. 2-4 feet above normal, with gale-force winds and gusts to 80 mph in southern sections of the mainland and hurricane winds with gusts to 85 mph on Block From: Storm Data, Vol. 4, No. 3, March 1962 Island, combined with surging waves to batter seawalls and destroy beaches as a J-86-COASTAL FLOODING OF: 1962 MARCH 6-7, EAST great storm moved eastward in the COAST OF U.S., MAINE-SOUTH CAROLINA Atlantic well south of Rhode Island. Strongest winds occurred on March 6, MAINE and highest tides on the morning of Coastal South of "Mar. 6-8-This area received fringe March 7. Considerable flooding in New- Portland. effects of a vast ocean storm that port, South Kingston, Bristol, Barring- wreaked havoc along coastal areas far- ton and Warren. Many piers and boats ther south. Flooding of coastal lowlands damaged. Heavy waterfront sand ero- and some road washouts were reported. sion and some 'property damage with 3-5 Slight damage was reported to seawalls. feet of sand being stripped from beaches between Point Judith and the Pawcatuck River. NEW HAMPSHIRE Coastal ------- "Mar. 6-8-This area received frinue CONNECTiCUT effects of a vast ocean storm that Shore Areas---- "Mar. 6-7-Four successive high tides, wreaked havoc to coastal areas farther 2-4 feet above normal, with gale-force south. A combination of wind-driven winds battered seawalls as a major storm tidal surges and spring tides brought seas moved eastward in the Atlantic well crashing over and damaging walls south of the State. Greatest damage due erected against them. Coastal lowlands to tidal flooding in Fairfield and eastern were flooded and some road washouts New London Counties with minor dam- were reported. Foundation of a beach- age along rest of Coast. Sand erosion front home was washed out. moderate along easternmost beaches. Wind damage confined to tree branches MASSACHUSETTS and downed powerlines. Coastal Areas- "Mar. 6-8-This area was relatively NEW YORK lightly affected by the vast ocean storm that wreaked havoc over coastal areas to Coastal sections "Mar. 6-8-A great Atlantic storm was the south. A combination of wind-driven extending centered off the Maryland-Delaware tidal surges and spring tides brought from the'New coast during the period. The extensive seas crashing over and damaging walls York City area intensifying storm finally encompassed erected against them. Complete sections throughout much of the North Atlantic and caused of some old seawalls were washed out. Long Island destructive winds, tides, and waves over Low-lying areas were flooded. Some and Montauk much of the Atlantic seaboard from structural damage to waterfront installa- Pt. southern New England to Florida. The tions occurred and many cellars were gale- to hurricane-force northeast winds flooded. About 100 residents of Ken- from this great storm pushed the ocean berma Park, Hull, Mass., were evacu- waters onshore during at least five suc- ated as a precautionary measure. Winds cessive high tides in an unprecedented. reached and maintained gale force for manner. On top of the near-record tides long periods on the 6th and 7th. How- was repeated wave action of heights be- ever,.wind damage was scattered and tween 20 and 30 feet. Great and un- mostly light and was generally limited to precedented damage was done to barrier broken windows and downed signs. dunes, beaches, and all types of shore Many flights out of Logan Airport, E. installations. Damage was greatest on the Boston, were cancelled because of the south shores of Richmond, Kings, and winds there and the weather at other Queens Boroughs in New York City, airports along the coast. A boy was in- along the barrier beaches of Nassau and jured when struck by a wind-blown Suffolk counties, eastward to Montauk storm door. Point. One hundred or more houses were 202-509 0 - 78 - 28 402 Strategic Role of Perigean Spring Tides, 1635-1976 MARYLAND swept into the sea. Many hundreds of Coastal Areas--- "Mar. 5-8-The storm deepened and buildings suffered water and structural nearly stagnated off the Virginia Capes, damages. Streets and highways, utility giving sustained northeasterly winds for lines and boats were severely damaged or over 24 hours. Ocean City Coast Guard wiped out. Much of the area lost its bar- reported 40-45 mph wind with gusts 55- rier dunes and beaches and left further 65 mph for 18 hours. The storm tide inland properties exposed to future piled on top of the high spring tides to storms. Property damage expected to be make the water up to 5 or 6 feet above well up in [the range from $5 million normal. Four or five such high tides with to $50 million.] 20 to 30 foot waves broke against the coast, causing serious beach erosion and NEW JERSEY destruction of shore property. Many Entire coastline "Mar. 6-8-A severe coastal storm, beach homes and commercial properties of State, in- moving very slowly, combined with high were damaged and destroyed. Other cluding Dela- tides on five consecutive occasions in a property was damaged by water and ware and Ra- three-day period, wrought tremendous sand. Nearly 1.5 million broilers and an ritan Bay. destruction to coastal installations. Hun- unknown number of incubator eggs were dreds of summer homes were demol- lost due to power failure. Salt damage to ished. The sand from beaches was flooded farmlands was minimized by the washed away, changing the shoreline in rainsoaked soil. Direct wind damage was many areas. Many new channels and small. Greatest and longest lasting dam- inlets were cut in the shoreline. High- age is to beaches where the sand was ways were cut in many places, or buried washed away. under several feet of sand. A Navy de- VIRGINIA stroyer, the MONSSEN, was beached about a half mile north of Beach Haven Eastern Shore "Mar. 6-8-The combination of the after breaking, its tow. The destroyer and Tidewater long fetch of strong onshore winds and was unmanned and was being towed to areas. the 'spring tides' caused greater wave Philadelphia from Bayonne Navy Yard. and surf damage and tidal flooding than Loss of life from the storm includes 6 any other coastal storm of recent'record. 'persons missing and presumed dead. The islands Chincoteague and Assa- Five of those six were aboard a fishing teague were completely covered with trawler off the New Jersey coast. Agri- cultural losses were chiefly due to flood- water and more than 1,000 residents ing of around 1,000 acres of Cumberland were evacuated by military helicopters. County, on Delaware Bay. Hundreds of homes on the beaches were totally destroyed and thousands were DELAWARE damaged; many residents were evacu- CoastalAreas___ "Mar. 5-8-The storm deepened and ated by boats and amphibious equip- nearly stagnated off the Virginia Capes ment. The fishing pier at Virginia Beach giving sustained northeasterly winds for was destroyed and the largest pile driver over 24 hours. The highest windspeed at in the world (a one and one-half mil- Delaware Breakwater was NE 72 mph at lion dollar mathine) was turned over 9PM on the 5th. The storm tide piled on its side in deep water. Hampton on topof the high spring tides to make Roads Harbor experienced the highest the water up to 5 feet above normal. In tide on record for an extratropicaI storm, addition, 20 to 30 foot waves broke that of 5.6 feet above normal, which was against the coast causing very serious less than a foot below the record tide beach erosion and destruction of shore- during a hurricane of 1963. All Eastern line property. Many beach homes and commercial properties were damaged or Shore' and Tidewater region was de- destroyed. In some places the beach clared a disaster area by the Governor. sand was completely washed away. Salt Removal of sand by waves and tide has damage to flooded farmlands in north- in many cases changed the configuration ern Delaware is considerable. of the shoreline. Classification, Designation, and Periodicity of -Perigean Spring Tides; Recent Tidal Floodings 403 NORTH CAROLINA Since an immediate question is raised as to why this case of perigee-syzygy, accompanied by a severe storm, did Northern Coast- "Mar. 6-8-Large and persistent low pressure storm caused greater alteration not produce the same marked degree of tidal flooding of coastline from Hatteras northward resulting from the very similar storm tide of March 6-7, than any previous known storm, includ- a detailed comparison is 'in order. The surface synoptic ing hurricanes. Miles of protective dunes weather map (fig. 66) for the date 1962 October 13 at destroyed and several breakthroughs 0 100' (e.s.t.) is included to make the analysis easier. (For entirely across Outer Banks from Ocean the-local tidal flooding effects observed around this date, to Sound. Completely new inlet 200 yards wide dividing Hatteras Island in see table 1. two parts will require bridging. Miles It is obvious from all evidence that the catastrophic of paved highway destroyed by washing effects of the 1962 Columbus Day storm on the Pacific out or buried in several feet of sand. coast were largely the result of wind damage rather than Hundreds of beach homes destroyed or any major tidal flooding. This event nevertheless is dis- damaged, hundreds of autos submerged in water or buried in sand. Many resi- cussed in detail here because of: ( I its local coastal flood- dents evacuated by helicopter. Two el- ing influences, including tidal impairment of hydrological derly persons died from excitement and runoff; and (2) the latent potential for extremely violent exposure due to rigors of the storm. Ship tidal flooding by the proxigean spring tides present, had broke in two 100 miles off Hatteras with the weather and wind been but slightly different. one person lost. Most of damage due to high water and pounding surf. Highest Considering first the atmospheric low pressure system recorded wind gusts near 70 miles per responsible for this storm, it is noteworthy that the deep hour, lowest 'barometer 29.20 inches at cyclonic system that was located just offshore along the Nags Head. Highest tides about ten feet northern California and southern Oregon coasts on Oc- above mean low water with seas of about tober 12 had basically a northerly component of move- 20 ft. height. Number, of persons in- jured estimated. ment and, further, that the storm center hugged the coast very closely. This low pressure center also possessed an SOUTH CAROLINA elongated north-south axis and moved very rapidly north- Coastal ------- "Mar. 7-9-The Great Atlantic Coast ward parallel to the coast. Storm of March 5-9, 1962 did limited This situation provided a limited fetch in wind move- damage in this state. Damage was mainly ment over the surface of the water. The coastal winds POS7 in the form of tidal flooding and beach sessed directional components primarily from the south erosion. Some beach cottages were de- (parallel to the coast) shifting only slightly to south- stroyed, others damaged. All beaches suf- fered from loss of sand." westerly components inland, with their directions still channeled strongly by the north-south oriented valleys 5. The Aborted Tidal Flooding of 1962 October 13 here. The tidal flooding of 1962 October 13 (Key No. 86) Those portions of the Oregon coastline which were is of definite parallel interest to the preceding discussion exposed to any onshore component of the wind are char- of the 1962 March 6-7 tidal flooding. This is because the acterized by cliff topography, with no lowland portions event is cyclically related to the latter perigean spring susceptible to flooding except in small bays and estuaries. tide through the 221.5-day average period of recurring In addition, the pressure gradient both in front of and alignments. The October perigee-syzygy alignment also behind the low pressure system was so steep, the alternat- occurred nearly simultaneously with a very active weather ing fall and rise in pressure as the system passed so rapid, disturbance along the Pacific coast now familiarly known gusting winds so prominent, and the whole system's move- in that,area as the "Columbus Day Storm of 1962." ment over the water comparatively so brief, that the Although some flooding damage was experienced in principal air-water interaction was evidenced in high connection with the near-coincidence of these events, it waves and spindrift rather than long-period onshore was nothing like that which accompanied the March 6-7 swells. catastrophe. Contradictingly, the associated storm on the The entire storm intensified and swept through coastal west coast was, if anything, much more. severe. An entire points, with winds shifting into directions parallel to the book has been written describing the widespread effects of coast and even offshore as the storm's center moved this natural disaster! slightly inland. The intense central core of the low pressure 404 Strategic Role of Pergean Spring Tides, 1635-1976 system was narrow and produced southerly winds along regions was recognized, should strong, persistent, onshore its eastern side and easterly winds along its northern winds simultaneously prevail. extremities as it moved inland. The strongest winds in the As noted in table 16, the mean epoch of extreme prox- Willamette Valley, Oreg., were from the south. The igee-syzygy in this case was 1974 January 8 at 1200' storm system and its associated atmospheric front moved (G.c.t.), 0700' (e.s.t.), or 0400' (P.s.t.). The astronomi- almost directly northward from the vicinity of Crescent cal alignment occurred at full phase of the Moon. The City, Calif., to Portland, Oreg., in less than 5 hours separation-interval between proxigee and syzygy was - 2', (traveling at something -less than 50 mi/hr). and the lunar parallax corresponding to this proxigee The stonn center with its cyclostrophic winds remained was 61'30.0". The parallax indicated is especially sig- just inland of the coastline during the early portion of nificant in that comparable values in table 16-either its passage, then erratically shifted offshore again in the equal to, or in excess of, this figure-have occurred only latter portion (see fig. 66). The entire course of this move- 29 times in the 373-year period (1600-1973) prior to this ment along the Pacific coast lasted barely 1.5 days. date, and 34 times in the entire 400-year period (1600- Thus, in recapitulation, the comparatively low flooding 1999) of the computer printout. (The instants of proxigee potential of this storm, despite the setup tidal condition are here compared, rather than the mean epochs, to present, is attributable to: ensure a maximum parallax in each case.) ( 1 ) The relatively small size of the low pressure center The predicted tidal ranges at representative stations and the fact that it did not intensify until just inland of along the east and west coasts of the United States, for the coast; those dates displaying the largest values of higher high (2) Its general south-north path, even recurving water resulting from this proxigee-syzygy alignment were: slightly offshore in the final phases of its movement up the Boston, Mass., January 8, 14.2 ft; Willetts Point, N.Y., coast; January. 9, 10.4 ft; Breakwater Harbor, Del., January 9, (3) The rapidity of movement, and corresponding 6.5 ft; Savannah, Ga., January 9, 10.8 ft; also, Aber- quickness of dissipation of this young storm system. deen, Wash., January 8, 14.1 ft; Astoria (Tongue Point), This combined situation is, by strong contrast with that Oreg., January 8, 11.7 ft; Los Angeles (Outer Harbor), of the relativ'ely slow-moving storm systems, responsible Calif., January 8, 8.9 1ft; and San Diego, Calif., January 8, for the extensive coastal floodings which occurred on 1931 9.8 ft. March 4-5, t939 January 3-5, and 1959 December 29 These ranges compare N%@ith corresponding values for (see the preceding discussions). Similarly, the 1962 Octo- spring ranges at the same east coast locations as follows: ber 13 storm is at sharp variance with the 1962 March 6-7 Boston, 11.0 ft; Willetts Point, 8.3 ft; Breakwater Harbor, storm on the mid-Atlantic coast. In consequence of a 4.9 ft; and Savannah, 8.6 ft. The matching diurnal ranges high pressure system which remained almost stationary for the west coast stations are: Aberdeen, 10. 1 ft; Astoria, over the North Atlantic on these latter dates, blocking 8.2 ft; Los Angeles, 5.4 ft; and San Diego, 5.7 ft. an active low pressure system over the ocean waters, a The buildup to this considerable increase in tide-rais- long fetch and strong onshore wind movement were ing force at time of proxigee-syzygy was further substanti- established for 2.5 days along the mid-Atlantic. coast. By ated by cyclically related tidal flooding (Key Nos. contrast, the Columbus Day storm on the west coast M-98e,w) occurring approximately one anomalistic traveled nearly 1,800 miles in 1.5 days. month earlier on 1973 December 11 on both the cast and 6. The Tidal Flooding of 1974 January 8 (N-99) west coasts. (See the news article of fig. 116 which follows, Perhaps one of the more interesting aspects in regard describing tidal flooding along the coast of Washington in to this case of tidal flooding on the west coast-produced connection with the perigean spring tides near this date.) in conjunction with a tide-amplifying astronomical ali The mean epoch of perigee-syzygy in this instance was gri- oh (P.S.t.). ment designated in table 22 as extreme proxigee-syzygy- 1973 December 10 at 1230' (G.c.t.) or 043 is that it was the first such tidal event whose indicated The lunar parallax at this time was 61"12.8", and the coastal flooding potential was verified according to the separation-interval was + 2 1'. principles enumerated in the present work. Confirming the increased eccentricity of the Moon's The astronomical situation involved was discovere'a orbit during the lunation containing the proxigee-syzygy during an early analysis of the data of table 16, and its alignment of 19 74 January 8, a total annular eclipse of the considerable potential for tidal flooding in lowland coastal Sun took place on 1973 December 24 at 1508 h (G.c.t.) Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 405 The Oregonian the seawall at Tokeland, Wash., leaving pushed a large trailer house out into a Wed., Dec. 12,1973 water a foot deep throughout town. street and washed another house off its Page 24, 3M, Cols. 4, 5 Flooding caused by the tide and winds foundation. also was reported at nearby Raymond and Waves breaking over the seawall near South Bend. rolice said water reached the general store and post office threw logs depths of four feet in the streets of-the against the store and littered the road Tidewaters floods two communities. No injuries were re- with rocks,- driftwood and debris. Washington towns; ported. The touchy period came between 2 and winds to ease off 3 p.m. at the peak of the high tide when 1973 Dec. 10 winds of 75 miles per hour were reported 4.5h P.s.t. (+21) Strong coastal winds Tuesday blew at Seaside. water from a near-record 16-foot tide over The wind-caused flooding at Tokeland M-98W FiGuRE 116. This failure of the apparent image size of the Moon to ological conditions which produce 'north-easters' or other cover the Sun because of the extreme lunar distance from offshore storms which, if combined with the unusual astro- Earth at the opposing exogee-syzygy position in the lunar nomical conditions, could prove hazardous to low-lying orbit occurred very close to the mean epoch of this latter areas. Other low-lying regions on the earth could be similarly affected. phenomenon (new moon on December 24 at 1507 h G.c.t., "A combination of unusual astronomical conditions will exogee on December 25 at 2200b G.c.t.). occur on January 8 and February 7. On these days the A suitable precautionary note to the public concerning moon, whose gravitational pull is the major influence on the the flooding potential of the astronomically amplified tides, will be full, causing 'spring tides,' a higher than nor- January 8 tides-carefully stressing the necessity of ac- mal rise in the water which occurs twice monthly. But companying winds possessing the characteristics to induce around these two particular days the tides will rise even higher than normal because of two phenomena: the moon coastal flooding-was felt desirable. The following NOAA will be 1137 miles closer to the mid-Atlantic coast on Jan- advisory article (with two slight clarifications added here uary 8 and on February 7 within 800 miles of the distance in square brackets) was released on December 26, 1973. it was on March 6, 1962. In addition, the sun, whose gravitational pull also influences the tides, will be in ap- UNITED STATES DEPARTMENT OF COMMERCE, proximately the same longitudinal plane as the moon. This WASHINGTON, D.C. 20230 alignment further enhances the 'astronomical effect on the tides. The earth will also be near its closest annual approach NEWS RELEASE: WEDNESDAY DECEMEER 2 6, 19 7 7 to the sun. Therefore, spring tides during these periods will be particularly high. East Coast tides to be unusually high on Jan. 8 and Feb. "The Coastal Environmental Studies Group of NOAA's 7; NOAA warns of coastal flooding if Atlantic storms oc- National Ocean Survey has, found that destructive high curthen. waters along the Atlantic coast occurred close to such ex- treme spring tides on April 27 and December 3, 1967 and "Unusual astronomical conditions will bring high tides have been traced as far back as November 2, 1861, Novem- on January 8 and February 7, 1974, the Commerce Depart- ber 1-2, 1877, and November 23-26, 1885. ment's, National Oceanic and Atmospheric Administration " 'Should a sustained onshore wind occur during these said today. high waters, a destructive water level could result around "Should these conditions be combined with severe At- January 8,' pointed out Fergus J. Wood, a research scientist lantic storms-a development which cannot be predicted at with the study group. 'The same could hold true also around this time-extreme flooding might strike low-lying coastal February 7.' Wood added that similar spring tide conditions areas. and wind-induced water crests could result in extraordinarily "By themselves, the astronomical tides will not produce high tides along coastal areas around July 19 and August 17 problems, weather being the controlling factor. However, next year, during the hurricane season. similar astronomical conditions, accompanied by an offshore "Wood said that his investigation reveals that in 1974 storm and onshore winds, generated much higher than usual there will be an above-average number [5] of longitudinal water levels on March 6 and 7, 1962, which resulted'in the alignments of the moon and sun which are associated with death of 40 persons and wrought an estimated $500 million close approaches of the moon to the earth. As a result, he damage from Long Island, N.Y., to the Outer Banks of stated, there will be a greater than usual number of extreme North Carolina. spring tide situations in 1974. "NOAA's National Weather Service alerted its forecast- "As a typical example, he cited predicted tidal conditions ers along the Atlantic coast to be especially aware of meteor- during 1974 at Atlantic City, N.J., which is being used as a 406 Strategic Role of Perigean Spring Tides, 1635-1976 representative test center for his studies. The [tide table] lustrations of the damage produced thereby---certain predictions are for 79 days of high tide, up to 1.3 feet higher information-disseminating procedures encountered in con- than the normal spring tide of 4V2 feet above mean low nection with this event are deserving of mention. The im- water, compared with 53 in 1954 and 1968, the greatest and mediate issue relates to the optimum manner of informing least number of days of such tides during the past two dec- ades. In 1973, the total will be 61 days and in 1975 it will those segments of the general public, maritme commerce, be 77. Twenty-four of these daysin 1974 are clustered and shoreline industry which are variously residing, va- around January 8, February 7, July 19 and August 17 when cationing, engaged in marine transportation, or conduct- the moon and the sun will be in approximately the same ing business activities within the coastal zone, in regard longitudinal plane. to such potentially hazardous or damaging tidal flooding "Wood noted in a report that 'from a statistical point of conditions. Environmental, coastal wildlife preservation, view, 1974 bears close watching.' The NOAA scientist added this 'careful reservation' that 'without the association of the and ecological interests are also deeply affected. necessary meteorological events producing sustained onshore As indicated in the preceding section, almost no ad- winds, only higher than usual high tides will be noted on vance information was made available to the public at these dates.' the time of the 1962 March 6-7 disaster. By contrast, in "At Atlantic City, in March 1962, the 5.2-foot spring consequence of the ensuing advances in knowledge of tide, reinforced by a 40-knot wind, with gusts to 70 knots, reached a total height of 9.5 feet above mean low water. The tidal flooding, an overwhelming media response (in- wind blew continuously from the sea for five consecutive cluding, unfortunately, some too terse misinformation) high tides over a 2Y2 -day period and that set up the condi- was directed toward assuring a general appreciation of the tions for the ensuing devastation. Waves as high as 20 feet potential flooding hazards involved in the 1974 January were recorded on the storm-lashed shore. 8 event. Somewhere between these two extremes, through "Wood stressed that the combination of unusually high a program of public education and enlightment, lies an spring tides and meteorological conditions could affect other coastlines around the earth to varying degrees. In the United optimum procedure for providing awareness of the neces- States, he added, this would be true along the West Coast. sary dependence of severe tidal flooding upon a variety of The danger would not be as great along the Gulf Coast, ex- meteorological contingencies in addition to predicted tidal cept durir@g the hurricane season, since the tides there are extremes. generally small. One of the principal aims of the present work has been A representative example of one of the conditional to delineate the very complex nature of a major tidal warnings of high tidal flooding potential which could oc- flooding and the numerous factors which go into its pro- cur in the event of supporting winds, as reported by the duction. It is virtually impossible to encapsulate any United Press International in the Los Angeles Times for proper explanation of these many variables within a neces- December 26, 1973, two weeks Wore the actual tidal sarily abbreviated news announcement just prior to the flooding which resulted, is given in fig. 117. A consider- tidal flooding. able number of similar rewrite articles, some not ade- Manifestly, it must become the responsibility of civil quately emphasizing the necessity for supporting winds; defense organizations, beacliguards, harbormasters, the others-apparently in the interests of sensationalism- Coast Guard, beach and coastal highway preservation positively stating that extraordinary tidal flooding would units, and other groups concerned with the coastal en- occur, were published in the news media on both the east vironment, as well as public safety therein, to acquaint and west coasts. themselves fully with the varying aspects of tidal flooding The major tidal flooding (Key No. N-99) which did potential. At the same time, these parties should become occur as the result of the combination of these proxigean intimately familiar with the use of marine advisory serv- spring tides and supporting meteorological conditions is ices providing other current or updated hourly data on graphically presented in the front page article from the the direction and velocity of coastal winds. These same Los Angeles Times of January 9, 1974, also reproduced sources also continuously monitor offshore storms which here (fig. 117). might combine with astronomically produced perigean spring tides to cause coastal flooding. A NOTE ON STORM TIDE ANNOUNCEMENT In this concept of providing continuing public en- EFFECTIVENESS lightenment both in the resource aspects and environ- Before proceeding with a more detailed discussion of mental problems of the coastal zone, the New England the nature and extent of the coastal onslaught associated Marine Resources Information Program (NEMRIP)- with this 1974 January 8 tidal flooding-including il- a Sea Grant project of the University of Rhode Island- Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 407 The Los Angeles Times Wed., Dec. 26,1973 Part 1, Page 4, Cols. 3-6 which also influences the tides-will be in about the same longitudinal plane as the caused 40 deaths and $500 million in flood moon, adding to the moon's effect. Further. Moon, Sun to Produce damage extending from Long Island, N.Y., the earth will be near its closest annaal to the outer banks of North Carolina. approach to the.sun. "Therefore, spring tides during these 2 Unusually High Tides Fergus J. Wood, a research scientist for periods will be particularly high," the the agency, said that without sustained agency said. A spring tide is higher than onshore winds, only higher than usual normal and occurs twice a month when WASHINGTON (UPI)-A rare rela- tides would occur on Jan. @8 and Feb. 7. the moon is full. tionship of the earth, moon and sun will He said there also would be more than the The agency said, other low-lying coastal cause unusually high tides on Jan. 8 and usual number of particularly high tide sit- areas also could be affected to varying Feb. 7, and forecasters have been alerted uations in the upcoming year and "from degrees, particularly along the Pacific to watch for Atlantic storms that could a statistical point of view, 1974 bears Coast . . . cause severe flooding along low-lying coast- close watching. al areas. The moon's gravitational pull is the The National Oceanic and Atmospheric major influence on the tides. On Jan. 8 Administration said Tuesday that similar and Feb. 7, the moon will be 1,137 miles astronomical conditions accompanied by closer to the mid-Atlantic coast than usual. 1974 Jan. 8 an offshore storm on March 6 and 7, 1972, In addition on those dates, the sun- 4h P.S.t. N-99 The Los Angeles Times Wed., Jan. 9, 1974 (CC Ed.) Part 1, Page 1, Cols. 2, 3 The high tides and battering waves also damaged beachfront homes in Los Angeles County, particularly in Malibu, where oc- Giant Waves Pound Southland cupants of two residences were evacuated ... Sheriff's deputies said earth fill was washed out from in back of two homes on Coast, Undermine Beach Homes pilings facing the ocean at 27036 and 27054 Malibu Colony Cove Road. Sandbag Barriers Ereded to Ward Off Tidal Assault; Heavy erosion was reported under homes at 25036 Malibu Road and 27308 Five-Day Storm Tapers Off After 7.69-inch Rainfall Escondido Beach Road, but the structures were not evacuated. Minor damage to sea walls, patios and BY DICK MAIN and TOM PAEGEL other outdoor improvements was reported Times Staff Writers to at least three structures in the Malibu Colony. Giant wind-driven waves riding on surg- In Orange County, supervisors proclaim- At Znma Beach, waves dug out much of ing high tides battered the Southern Cali- ed a "local emergency" for wave-battered the sandy beach, forcing lifeguards to fornia coast Tuesday, damaging homes and coastline sections . @. . move four portable lookout stations away flooding nearby areas. Part 1, Page 29, Cols. 2 from the surfline. Occupants of many beachfront homes . . . At least eignt homes in the Beach The high tide and waves uprooted more from Santa Barbara to San Clemente Road community of Capistrano Beach, than 20 old pilings from the abandoned erected sandbag barriers throughout the were damaged, as waves washed sand and often-burned Pacific Ocean Park pier day in preparation for the next high tide away !xposing or damaging seawalls, at Santa Monica. They were towed out at 10:08 a.m. today. foQations and pilings. to sea to prevent their crashing into Santa The wave and tidal assault came as Waves up to 8 feet high slammed into Monica Pier. rainfall from a five-day- storm tapered off Roger Pappas, National Weather Serv- some Orange County beaches during the ice forecaster, said winds which created after dropping 7.69 inches in the Los morning high tide Tuesday. Angeles Civic Center. Sheriff's officers and county firemen the towering waves during high tide early Mostly fair weather was forecast for were dispatched to endangered beach Tuesday should subside by this morning, .today and Thursday and chances of a properties and helped in sandbagging op- lessening chances of coastal damage. new storm Friday, feared earlier, appeared erations. A small-craft advisory warning of high to be remote. Breakers wiped out wide sections of winds between Point Conception and the Floodwaters and mud and rock slides many beaches, exposing the pilings of life- Mexican border was lowered at 8 p.m. continued to menace many low-lying areas guard headquarters at both San Clemente The National Weather Service earlier in. foothill and coastal valleys, however. and Newport Beach. said ocean swells were expected to drop 'A local emergency was declared for all Part of Pacific Coast Highway was from 4 to 6 feet during the night to 2 to 4 of Los Angeles County earlier Tuesday by flooded in Huntington Harbor and in New- feet today and Thursday. the Board of Supervisors. port Beach. A storm system in the mid-Pacific which "Conditions of extreme peril to the The morning tides are abnormally high had been expected to arrive in Southern r5afety of persons. and property have because the present alignment of' the California by Friday apparently has been arisen," the board said in its resolution. earth, sun and moon exerts a stronger blocked off by a high-pressure ridge ex- Board Chairman Kenneth Hahn said the than usual gravitational pull upon the tending southward from the Gulf of proclamation, which was forwarded to the ocean. Alaska, Pappas said . . . state director of the Office-of Emergency Tuesday morning's peak tide came at Services, may clear the way for state 9:22 a.m. and measured 7.1 feet. A 7-foot 1974 Jan. 8 financial assistance for storm damage to tide is expected this morning and Thurs- 4h P.s.t. (-2) public property. day's tide is expected to measure 6.5 feet. N-99 FIGURE 117. 408 Strategic Role of Perigean Spring Tides, 1635-1976 publishes a monthly bulletin of ocean-oriented facts titled lantic coastline resulted in 40 deaths and $5 hundred Information. In August 1975, this publication very ap- million property damage." propriately included a communicated explanation of why Finally, the important matter of dissemination of flooding conditions did not materialize on the east coast complete and accurate information-which includes the of the United States in connection with the 1974 Janu- various contingencies for tidal flooding7@was brought out, ary 8 perigee-syzygy alignment, although structurally reiterating and supporting the comments made several damaging tidal flooding conditions existed on the west paragraphs above: coast: "News accounts of [the] '74 prediction alarmed the "A continuous, strong, offshore wind tends to lower public unnecessarily . . . by oversimplifying NOAA's water level and negate the effects of a perigean spring press release and failing to stress that onshore winds as tide. The one which occurred on the northeast coast on well as high tides are required for flooding. They often January 8 [1974] ... was negated ... by a combination failed to mention, too, that only lowland coastal regions of offshore winds and an atmospheric high pressure sys- or those with a sufficiently large daily tidal range would tem. The atmosphere and the ocean ... act together like be affected' (Perigee-syzygy adds about 40 percent to an inverted barometer. As the atmospheric pressure rises, the tidal range.) Thus the entire coast of the Gulf of water level goes down; as atmospheric pressure dimin- Mexico and much of the southeastern coast of the U.S. ishes, water level rises. The adjustment in ocean level would not be in danger, except during hurricanes. in either direction is approximately 13 inches for each "Perigean or proxigean spring tides [likewise] do not change of one inch in barometric pressure. necessarily occur on the central day of perigee-syzygy, "Thanks to weather conditions, the east coast escaped ... but can show up within several days before or after flooding on both dates of predicted proxigean spring it." tides, but California did not. On January 8, 1974, giant DATA ON TIDAL FLOODING AND wind-driven waves combined with extraordinary high ASSO .CIATED DAMAGE tides battered the southern coast, creating a state of emergency." On-the-scene observations, scientific data, and photo- This article also pointed up the advantages of remain- graphs recorded in connection with this tidal flooding ing actively alert to the possibility of tidal flooding under circumstance were obtained from various sources located such conditions, and of taking precautionary measures in the coastal area between San Clemente and Ventura, when necessary: Calif., which felt the greatest impact of the destructive "Damage would have been far greater if local officials tides. Some of the most graphic illustrations showing the hadn't heeded NOAA's warning and taken defensive extent of the damage produced (figs. 118-131), as well measures. Because the action of tides is world-wide, origi- as extracts from official and nonofficial reports concern- nating from the same astronomical positions, the proxi- ing the protective measures taken in an attempt to pre- gean spring tide that pounded Southern California rose vent this damage, have been included on the following four days later off the English and Scottish coasts. (Ocean pages. water has a specific period of resonance that creates a a. The Department of Harbors, Beaches, and Parks of time delay.)' Orange County, Calif., for example, provided the Na- "Coinciding with a strong onshore gale off the south- tional Ocean Survey with a copy of a preliminary but west coasts of England and Wales, it breached sea walls well-detailed report covering the January 8 tidal flooding. and caused widespread flooding there as well as in the Abstracting only the appropriate technical information outer Hebrides. On February 9 through 11, the second from this partially administrative report, the following summary is representative of the tidal flooding conditions period predicted for perigean spring tides, conditions a.t one of many similarly, affected coastal communities, were also propitious and southern England was clobbered Capistrano Beach. It also demonstrates the effectiveness again. of well-organized protective measures applied to counter "In 1962, residents of the mid-Atlantic United States tidal flooding. It was practicable to place these into had not been as lucky as they were in 1974 ... fsince] early operation in consequence of the 1973 December 26 there was no warning that conditions could be ideal for NOAA information release-with 2 weeks' advance indi- disaster on March 6 and 7. As it happened, proxigean cation of the potential flooding threat. The prevention spring tides prevailed and the flood waters along the At- of extensive flooding damage despite high tides which Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 409 Ak V*V -7 Courtesy of U.S. Army Corps of Engineers (Los Angeles District) Courtesy of U.S. Army Corps of Engineers (Los Angeles District) FiGURE 118.-Workers filling sandbags at Newport Beach, FIGURE 120-Backfilling of the shoreline at Newport Beach, Calif., in consequence of NOAA forewarning of tidal Calif., to create sand barriers during the buildup of the flooding potential resulting from the extremely close tidal onslaught of 1974-january 8. perigee-syzygy alignment of 1974 January 8. T 7Z 1`7 'ROM ::zw 41 74 4-1 ------ Courtesy of Marine Safety Department City of Newport Beach, Calif. Courtesy of U.S. Army Corps of Engineers (Los Angeles District) FicURE 121-The perigean spring tides contributory to the Fic.URF 119.-Sandbags being emplaced at Newport Beach, 1974 January 8 coastal flooding event completely cover Calif., as protection against the predicted extreme peri- the beach and begin to intrude onto the Dory Fleet's gean spring tides of 1974 January 8. Beachfront fish market facility, f4r above the normal high water mark. were already several feet above their mean value is clearly evidenced. This record als6-points up the fact that, de- Storm-Surge Damage at Capistrano Beach, Calif., Janu- pending upon location as well as meteorological and other ary 7-9,1974 circumstances, the flooding effects from perigean spring "The storms of early January were accompanied on tides may occur from one to several or more days on either occasion by strong winds. These winds were especially side of the epoch of perigee-syzygy (or proxigee-syzygy) strong on Friday, January 4 and again on the evening of @_ @A which is responsible for the astronomi.cal portion of the Monday, January 7, with gusts of 50 miles per hour re- unusual tidal uplift. corded at both Newport and Dana Point Harbors. 410 Strategic Role of Perigean Spring Tides, 1635-1976 _Q 314- - .@W Courtesy of Marine Safety Department City of Newport Beach, Calif. Courtesy of U.S. Army Corps of Engineers (Los Angeles District) FIGURE 122.-Scene showing the encroaching sea responsible FIGURE 124.-The complete destruction of the beach front for the extreme tidal battering experienced at Newport parking lot fronting the lifeguard station, Newport Beach, Beach, Calif., on 1974 January. 8. The municipal fishing Calif., caused by the pounding action of the surf accom- pier is in the background; the lifeguard station is at the panying the extreme tides of 1974 January 8. right. Note the severe damage to the thickly layered as- phalt parking lot in the foreground. @7 ? 0, 4- -7' o`1 T@ I'Y Courtesy of U.S. Army Corps of Engineers (Los Angeles District) FIGURE 123.-The wind-driven tidal assault of 1974 January 8 sweeps away sandbags emplaced at the lifeguard station, Newport Beach, Calif., and begins erosional breakup of the surfaced parking lot. "The strong winds were from the southeast, causing waves to strike the shore at an angle, commonly called Courtesy of The Orange Coast Daily Pilot, Costa Mesa, Calif. an upcoast angle. Indeed, in Newport Harbor, the waves FIGURE 125-Severe undercuttino, subsidence, and cracking 0' came in almost directly in the harbor mouth between of the marina wallkway at Newport Beach, Calif., caused the breakwaters . . . . by high waters associated with the tidal flooding of 1974 January 8. -a.>qtcatzon, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 411 @0 '4 Courtesy of The Loa Angeles Times FiGuRE 126.-Picture taken along the coast just west of Los Ang geles, Calif., at approximately 9 a.m. on 1974 January 8, coinciding with the time of the unusually high perigean it spring tide of this date, Courtesy of Department of the Los Angeles County Engineer FwuptE 128.-View from the landward side, showing ex @4 treme damage to the seawall at Malibu Beach, Calif., pro- duced by the wind-reinforced erosion, and undemutting of the seawall from the rear caused by these augmented high tides. 4 *L 'A" Courtesy of The Orange Coast Daily Pilot, Costa, Mesa, Calif. FIGURE 127.-The augmented perigean spring tides of 1974 January 8 break destructively against the El Moro Trailer Park between Corona del Mar and Laguna Beach, Calif. "The beach began to disappear at Capistrano Beach, and by January 7, waves were pounding against the seawalls in front of some homes there, Then on Tuesday morning, January 8, one of the highest tides of the year occurred. The approximate +7.4 foot tide was fortu- nately not accompanied by large waves, but because the Courtesy of. Department of the Los Angeles County Engineer seawalls had previously been exposed, the battle was on. FIGURE 129.-Dislocation of an access stile surmounting the The waves damaged some sections of the wall, and ap- seawall at Malibu Beach, Calif., as the result of underinin- PCared to be undermining other sections. ing and toppling of the wall by storm-amplified perigean spring tides on 1974 January 8. 412 Strategic Role of Perigean Spring Tides, 1635-1976 able erosion had occurred behind the- walls, in some cases clear up under the beach side of a home. "Due to the fact that another high tide was expected the next day and storm conditions were forecast which could result in big waves on top of the tide, it was decided A @-j that protective measures must be taken. Residents got together and obtained sandbags from the County Fire De- partment and began sandbagging, and also called a con- tractor to deliver and place large rocks in front of the sea- walls. The residents also requested County assistance .... "Things then happened fast. The County Departments of Communications, Road, Flood Control, Fire Protection and Sheriff were contacted. Communications dispatched a mobile communications van to the site with complete radio and telephone service, as well as portable electric generators. The Road Department sent dump trucks and Courtesy of Department of the Los Angeles County Engineer drivers, which, on the way, stopped at a sand and gravel FicURE 130.-View of a section of the beachfront at Malibu plant and picked up 50 tons of sand. Fire Protection dis- Beach, Calif., following the tidal flooding of 1974 janu- patched trucks and crews for filling sandbags. Harbors, ary 8, showing the extensive darnaue to the seawall caused Beaches and Parks sent men, trucks and a tractor. Flood- by wave overtopping. A closeup of the rear portion of this ing Control sent thousands of sandbags and the Sheriff's same seawall at a point in the center distance is included Department provided deputies for security and crowd in figure 128. control. "Almost immediately telephone lines at the District Headquarters began to ring with reporters asking ques- tions. Eventually, crews from all three television networks would visit the site and film reports. Coverage by news- A papers was complete .... "An approximate 7.2 foot high tide arrived at 10: 20 a.m. Pacific daylight time, on January 9. The sea was very 0", calm, waves only 2-4 feet. 7 "Approximately 13,000. sandbags had been placed in front of approximately 12 homes. Generally, the bags were placed behind wooden seawalls which already existed. The day before, the sand behind the seawalls had been .@A 14W eroded away. In some cases, it was necessary to cut holes in wood decking or patios to gain access to behind the sea- wall for sandbag placement. "One section of seawall had to be cut down, as it had Courtesy of Department of the Los Angeles County Engineer been damaged to the point where the 1/9 high tide could FiGURE 131.-Detail of the breaching of the seawall at be expected to break it loose, and then it would become a Malibu Beach, Calif., by the perigean spring tides of 1974 battering ram tossed about by the surf. This section was January 8. The deep cavitation behind the wall is pro- the width of one lot, fortunately the lot was vacant. During duced by erosional action resulting from the overspilling seas. the night of 1/8 crews replaced this wall with a sandbag barrier, several bags deep and approximately 7 feet high. "At this point, some of the residents called the Harbor "In addition, some homeowners contracted for the de- Patrol for assistance. A representative was dispatched livery and placement of large granite boulders in front of to investigate the situation. At first, it didn't look too their seawall. Many had been put into place before the bad, but when the tide receded and it was possible to high tide of 1/9, witill more, to be put in after the tide walk in front of the seawalls, it was found that consider- recedes. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 413 "The high tide of 1/9 resulted in no further damage. All Marine weather observations obtained at 20 stations, seawalls and sandbags remained in place. As the waves ranging from Point Arguello on the north to San Diego rolled in, they would send surges of water to the seawalls, on the south show the maximum swell height reached but they and the bags held . . . ." (at Avalon Harbor at 2000' (P.s.t.) on January 7) to b. In addition, official data were obtained from the be about 7 ft; the average swell height at all other points Los Angeles office of the National Weather Service rela- was 4-5 ft. The peak-velocity ESE to SE winds experi- tive to the prevailing wind velocities and directions, and enced along the southern California coastline in advance state-of-the-sea at the time of the tidal impact. Damage of the eastward-moving low pressure center were strong reports from coastal communities were also compiled by and gusty, but their duration of movement over the water the Los Angeles weather station on the basis of reports was relatively brief. Their velocities built up slowly during from local beacliguards or similar authorities which are the morning and afternoon of January 7 to an average summarized below: range of 15-30 knots at various locations, with continuing As can be seen from the synoptic weather maps of the rain throughout the day. United States for 1974 January 7, 8, and 9 at 0400' By 2000' on January 7, practically all of the marine (P.s.t.) in figs. 132, 133, and 134, the contribution of weathtr stations reporting indicated wind velocities of 20 wind to the unusually high tides already present was the knots and greater from S to SE components, with addi- result of a fairly shallow low pressure system (central tional gusts to 30-35 knots, and with the barometric pressure, approximately 1004 mb) approaching the south- pressure reduced to 999-1,005 rubs. During the late night west coast of California from off the Pacific Ocean. of January 7, the maximum wind velocities were attained The January 7 weather map indicates a warm front at Avalon on Catalina Island and were carried over to extending southeastward from the low pressure system. other coastal points. Fortunately, this period coincided However, the absence of either an open or an occluded with that of an extremely low water accompanying the wave, as plotted, seems to indicate that this frontal ex- proxigean spring tides. tension did not forin part of a series of "feeder" waves The astronomical higher high water was predicted to which often impinge on the southern California coastline, reach 7.1 ft at Los Angeles (Outer Harbor) on January 8 one after the other, during the winter season. at 0822 h (P.s.t.). The maximum tide height actually The satellite weather photos in figs. 135, 136 show the reached here, as reduced from marigram records, was 7.8 offshore situation to better advantage, and reveal that this ft, corresponding very nearly to the time 0800' (P.S.t.) weather front was (on January 7) an extension of an on January 8. This value is 2.6 ft above that of mean intense occluded frontal system over the southeast Pacific, higher high water (5.2 ft) at Los Angeles. and probably, indeed, part of a feeder-wave system. In a telephoned communication from' the harbor- The counterclockwise rotation within this low pressure master at Avalon on Catalina Island to the Los Angeles center, with the surface winds blowing in northerly and weath--r station, the extreme height of the tides on the northeasterly directions on the eastern side of the low, ac- morning of January 8 was confirmed. It was stated that, counts for the prevailing winds from southerly and south- at this time of higl@er high water, the anchor lines of the easterly components during the entire period of onshore mooring buoys to which many. small boats were tied movement of the system. (ordinarily containing some slack cable and hence in- As shown on the January 8 map, the warm front has clined in the water) were standing straight up, with the moved very rapidly eastward and has been modified into buoys resembling "buttons ready to pop." It was affirmed that, had the high winds of the previous night occurred an occluded front. It is the strong, gusty, surface winds instead during this period of morning high tides, a dis- associated with the passage of this front which were re- astrous situation might have resulted. With the water- sponsible for the meteorological contribution to the storm piling action of the winds added to the unusually high surge experienced along the southern California coast. astronomical tides, many of the small boats unquestion- However, neither the surface waves nor the sea swells ably would have been snapped from their anchor cables produced along this coast were very high, nor was their and have been released to drift freely around the harbor, maximum height of long duration. It was the already collide with eac h other, or smash on the shore subject to extraordinarily high tides, driven en masse against the the strong winds and currents present. coastline by these short-lived but powerful winds, that Onshore, where strong winds and very high astronom- caused the ensuing damage. ical tides did more nearly coincide (fig. 126), problems 414 Strategic Role of Perigean Spring Tides, 1635-1976 f?"O CO F'M" lN 04 "r U 7'@ .at S, 1, v7'hK'Vlll` P7 @l z v < "AOEm"'U'N.@ @JA- 0 pt QN, A, -11-1 " , -1'11 @-'@.'q",v':' N"Y' V"A' tw !%' TT 1, '? '1-1 " @ @ - 171 '@.'W W,I ,S@ D 4'@ mo dA Ct V110 .423 S14 @g '@Z MW I'D 57 W.? ul, N, o' IN t'. Mrl'@ Ol FIGURE 132. N-99 1974 JANUARY 8 7.0h. Jonuory 8 7.0h. (-2) C) V 70' 65. 1024 102V 1028 1024 1 t c" A PN b "J, @'A fll"@ 4 41- -P :7z; 1-4 71@ 100 ill Mof W SURFACE WEA HER MA Q AND STATION EATHER uw AT 7:00 A E.S.T. Ln N-99 1974 JANUARY 9 7.0h. January 8 7.0h. (-2J o 4- 4 4C"13 MX- -4 -@N 'cl Ct, @7 low @i4 T- zt y Ai HS S, @U@UA6L@@ LAIHE A P,, 2 ANV@STATION, WE R W, E@ AT 7@:OO_A T. IT,:j, -J': FIGURE 134. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 417 NQAA-@! N HIR NIGHT OR13 I T5G24 1/ 7/74 20S,3z ORB 1 T51335 1 B/74 1807Z a To 44, % 40 45 iiAi so_t4 J'6_-;A T?W Y 049' CIO COT @4j a COT d .1; W1, @A K Source: National Environinental Satellite Service, NOAA FiGuRE 135-This composite mosaic of Northern Hemisphere cloud cover was compiled from infrared "night photog- raphy" images secured by a NOAA weather satelliteduring the period between 1974 January 7 1259 P.s.t. and 1974 January 8 1007 P.s.t. The approximate times corresponding to the geographic positions of satellite photography are indicated around the equatorial margin of the grid overlay. The situation represented off the Pacific coast of North America as of January 7 2248 P.s.t. shows an intense low pressure system marked by a strongly occluded frontal wave, with an associated cloud cover extending from Hawaii to the Gulf of Alaska. The southeasterly extending warm front portion of th6 occlusion merges into a long, recurving cold front. This joins a second warm front and to- gether they form a second, rapidly eastwardly moving "feeder wave" whose cloud-cover effects are already noticeable over northern Baja California. (See also figs. 132-133.) Astronomically induced proxigean spring tides, raised during the early morning hours of Januarv 8, reached their maximum heigb@s locally along the southern Cali- fornia coast between approximately 0800 and 1000 P.s.t. The southerly and southeasterly winds encircling this sec- ond low-pressure system prior to the onshore arrival of the warm front (shifting to strong southwesterly winds with passage of the front) further raised the proxigean spring tides to coastal flooding conditions. Moderate swells also had been generated many miles at sea, adding to the tidal flooding potential. 202-509 0 - 78 - 29 418 Strategic Role of Perigean Spring Tides, 163@4976 NOAA,2 N H IR WIrHT ORBIT 5636 11 8/74 20012 ORBIT S640 11 5114 1%12 0-10 00- 4) 40-45 LAT &L 21, A 0-90 TEMI, "Y' 64U C111 1048 GMT@ Ti 7""V q7', 13'r 7 -_10014,41 X G648 C111 1440 GMT J p 1@44T VMT Source National Environmental Satellite Service, NOAA, FIGURE 136-Approximately 24 hours after the meteorological situation depicted in figure 135, the large,offshore oc- clusion is still essentially stagnant, but the rapidly moving feeder wave which contributed to the coastal flooding already has moved over Arizona. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 419 of another sort had arisen. Since the maximum height of (c) A one-half mile stretch of beach also was the sea swell running at this time was estimated by vari- eroded back a distance of 75 ft. ous observers as 4-5 ft, this means that the crest of the (3) Malibu Cove Colony, Malibu swell would ride 2.6+4.0 or 6.6 ft above the level of mean higher high water. Assuming any seawall would be (a), Erosion occurred along one-half mile of the built with its base at the level of MHHW to afford maxi- waterfront, including overspilling and undercutting mum protection against tidal flooding, the .wall would of 700 ft of seawall from the rear. have to be at least 6.6 ft high to keep the sea from surg- (b) Structural damage also was caused to this ing over its top. same seawall. As attested by the previous report in connection with (4) Malibu Film Colony, Malibu Capistrano Beach, by various among the illustrations of the 1974 January 8 tidal flooding which conclude this (a) An estimated $20,000 in damage to home chapter, and the summary of tidal damage at southern prop-crties resulted through seawater penetration, California coastal communities which immediately fol- sand leaching, flooding of cesspools, downing of lows, such a violent overspilling and breaching of sea- power poles, and overtopping of protecting bulk- walls actually did happen, with consequent damage to heads. beach homes. (b) The erosion around, and saltwater corrosion c. The estimated amounts of damage caused by the to, the steel foundation beams of two condominiums unusually high tides of 1974 January 8 at various loca- required $20,000 for their replacement. tions on the southern California coast, (See fig. 151A.) (5) Mission Beach as obtained (together with related information) by Na- A 1.7 mi. stretch of beach was eroded back a dis- tional Weather Service forecasters at the Los Angeles tance of 100 ft. office, were as follows: (1) Newport Beach (6) South Laguna Beach (a) The first floors of 20 homes were. inundated A 200-ft section of beach was eroded back a dis- by tidal resurgence within Newport Bay, with tance of 25 ft. corresponding structural damage to plaster walls, (7) San Clemente etc. - A seashore gas main was broken by attrition due . (b) A 300-ft portion of a concrete seawall to the strong tidal action; four or five house trailers collapsed. in a coastal trailer park were lost in the fire resulting (c) A 500-ft section of, the shoreline was eroded therefrom. back a distance of 120 ft along an elbow of the bay. d. As, noted in the NEMRIP bulletin quoted in an (d) An asphalt parking area on the seaward side of the lifegu Iard station was severely broken up by earlier portion of this same section, no promine 'nt coastal wave erosion and undercutting. flooding accompanied the proxigean spring tide of 1974 January 8 on the east coast of the United States. The (e) The total structural damage to the area was reasons are made very clear by reference to the daily estimated at $100,000. synoptic.weather map of the United States for this date (f) Additional damage occurred to a boat of the (fig. 133). Dory Fleet and to the beachf ront fish market facility. I A very large high pressure cell (central pressure 1,028 (g) The measured maximum tides in this area mb) was centered over the Great Lakes. The 1,024-mb throughout the period of tidal onslaught were 7.7- isobar of this cell reached -eastward as far as the Atlantic 8.3 ft above mean lower low water. coast and extended along it from Long Island to central (2) Capistrano Beach South Carolina. The associated clockwise circulation (a) Structural damage was incurred to 12 around a high pressure system in the Northern Hemisphere homes, involving especially that caused by erosion resulted in a light offshore wind movement at all coa 'stal beneath concrete foundations and damage to points from the Chesapeake Bay north to the Gulf Of wooden patios. St. Lawrence. Those winds along the coast from the Chesa- (b) The total loss due to structural damage in peake Bay south to Flori& likewise possessed relatively the area was estimated at $25,000. small velocities. with comDonents parallel to, or directed 420 Strategic Role of Perigean Spring Tides, 1635-1976 just off the shoreline, and (in the extreme south) having (2). An increase in atmospheric pressure prior to and/ gentle landward components. or during the period of the enhanced astronomical tidal In addition, the eastward movement of a high pressure uplift tends to depress the tide by virtue of the added (1,024-mb) ridge over the middle and southern portions weight of the overlying atmospheric column. At this same of the Atlantic coastline caused the pressures here to rise time 'such a rising barometric pressure-as the result of from that of an atmospheric "col" (1,012-1,016 mb) on gradual "filling" of the system and production of asmaller the previous day. This circumstance tended slightly to atmospheric pressure gradient from the high pressure depress the rising tides, by approximately .1.3 in. for each center outward-is accompanied by a reduction in surface 0.1 in. rise in barometric pressure (0.1 in. of mercury wind velocities. rise==4.06 mb). The January 9 synoptic weather map Subsidence of the air within the high pressure system shows that the im-noving 1,024-mb isobar was still along rather than a vortex uplift motion which frequently the coast at map time on this date, but subject to the ad- occurs in an atmospheric low also tends to stabilize the vance of a rapidly moving, dual low pressure system and air mass present and to resist the effects of cyclogenesis two associated cold fronts over the eastern portion of the and frontogenesis associated with a low (both conducive country (fig. 134). to strong surface winds). In the Pacific Northwest, where certain lowland por- (3). As mentioned in part 1, chapter 1, the addition of tions also are susceptible to tidal flooding, a moderate outlying breakwaters, organized and renewable coastal high pressure system (central pressure 1,020 mb) re- berms, dikes, dunes, and groins (artificial barriers built mained relatively stationary over eastern Oregon and out perpendicular to the shoreline to resist alongshore Washington between January 7 and January 8. Light and current movements) have, in more recent years, reduced variable winds prevailed on this portion of the coast much of the severe damage caused by the combination of throughout the foregoing period. strong onshore winds and astronomically amplified tides. Consequently, despite the unusually high astronomical The planting and maintenance of appropriate species of tides present, no reinforcement by strong, onshore winds saltwater-tolerant spartina grass on the slopes of barrier conducive to tidal flooding was provided either in the sand dunes located above the mean high water mark also Pacific Northwest or along the Atlantic coast on Janu- have served as an aid against irremedial coastal erosion ary 8. A case of ordinary perigean spring tides followed by these tides. this proxigean spring event of 1974 January 8 by approx- imately one anomalistic month. Although its . perigee- 7. Tidal Flooding in the British Isles on 1974 syzygy separation-interval was a full -2411, it was January 11-12 and February 9 - closely watched for tidal flooding propensities. Again, how- The foregoing instance of tidal flooding on the west ever, high pressure systems prevailed on both the east coast of the United States on 1974 January. 8 was di- and west coasts, shoreline winds were light and variable, rectly related through the astronomical perigee-syzygy and flooding was not induced in the considerably height- cycle to two other tidal floodings on the west and south ened astronomical tides around February 6-7 (fig. 89). coasts of Great Britain. These incidents occurred in con- In summary, three principal factors can greatly re- nection with the same proxigee-syzygy alignment of 1974 duce, or even cancel out the rather severe damage threat January 8, having a mean epoch of 1200' (G.c.t.), and a to a coastline posed by the astronomical production of a second perigee-syzygy alignment of February 6 at 1100' proxigean spring or similar extraordinarily high tide (G.c.t.). which is subject to further uplift through the action of The actual, floodings occurred on January 11-12 and intense and persistent onshore winds: February 9-11, with the already amplified astronomical . (1). The substitution of a strong, sustained, offshore tides being reinforced by the necessary strong onshore wind, resulting in a negdtive storm surge, or partial de- winds on these dates. This delay in the rise of maximum pression of the existing astronomically raised tidal waters. astronomical tides experienced in the British Isles to a This occurs as the result of the amplified tidal waters being date approximately 3 days later than that in which these distributed toward the deeper, more open sea rather than same amplified tides became evident on the east and west landward, involving runup over shallow bottom slopes coasts of the United States is caused by a dynamic and channeling into constricted coastal passages. phenomenon. Simply put, the ocean waters in each given Light to calm surface winds also usually exist in a high locality possess a specific resonance response to their local- pressure, system. Such winds have very little effect in mov- ity which, in this instance, results in the maximum tidal ing (or raising) the surface waters of the oceans. effects of the proxigee-syzygy (or penigee-sy zygy) align- Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 421 A-Z 40-4S LAI T 4 46 L,"- A u"I Source: National Environmental satellite Service, NOAA FIGURE 137-This photomosaic is compiled from "daytime infrared" images of global cloud cover obtained by a NOAA weather satellite between 1974 January 11 0754 G.m.t. and 1974 January 12 0654 G.m.t. (a malfunctioning signal is responsible for the blank, saw-toothed area off the east coast of the United States). A large, bed-back frontal oc- clusion associated with a deep low pressure center is seen to be approaching the west coast of Great Britain along a southwest-northeast track. In the eastern portion of this low pressure system, because of its steep pressure gradient strong winds would subsequently blow from the south against the southern English coast; in the warm front section of the occluded wave, winds would likewise blow from the southwest and west, directed onshore along the west coast of England. This atmospheric storm system, and the proxigean spring tides simultaneously present, were together respon- sible for the active coastal flooding experienced -along the western and southern lowland shores of Great Britain during high tides on January 11-12. 422 Strategic Role of Perigean Spring Tides, 1635-1976 NOAA-2 N.H. SR vis ORBIT 5667 1/11/74 07542 ORBIT 5679 1/12/14 065,4Z 01 2248 EMT 4B CMT Jr 4 IF, ,411' 18.40 Ct@T 48 CMT 'IX "k RUN DATE 01/12/74 Source: National Environmental Satellite Service, NOAA FIGURE 138-As subsidiary weather satellite coverage useful in nephanalysis, a Northern Hemisphere "visual image" photo- mosaic is included here, covering the same period of record as figure 137. This mosaic also illustrates the somewhat greater sensitivity of infrared photography in representing diffuse and peripheral cloud cover compared with photography in the visual range of the spectrum. Note the considerably sharper delineation of cloud boundaries (altl@ough cloud areas of cor- respondingly smaller extent) in the present figure compared with figure 137. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 423 N"s Aa 51, Ga - i P - I lyna), (A." h. is J191 V Courtesy of The Stornoway Gazette, Ltd., Stornoway, Courtesy of The Guernsey Press Co., Ltd., Guernsey, Channel Islands, Isle of Lewis, Scotland Great Britain FIGURE 139.-Tidal flooding at North Beach Street quay, FIGURE l4l.-Surf breaking over the seawall at Guernsey in Stornoway, Scotland, on January 11, 1974 produced by a the Channel Islands off the south coast of Great Britain on wind-driven storm surge accompanying perigean spring January 11, 1974, in consequence of strong onshore winds tides on this date. With the quay inundated, the boats have combined with augmented tides produced by the close been lifted to-the level of the over-street flooding. perigee-syzygy alignment of 1974 January 8. The arrival of the maximum perigean spring tides is affected by a com- posite delay resulting from approximately 3-day phase- and parallax-lags at this location. (See chapter 6.) 71 7ZI; MR 5 Courtesy of The Stornoway GazetteLtd. Co urtesy of The Stornoway Gazette, Ltd. FIGURE 142.-Seawater lifted by the perigean spring tides of January 11, 1974 extends inland onto the wooded area at FIGURE,140.-As a major spillover from the inner harbor Porter's Lodge, entrance to Lady. Lever Park on Lewis into South Beach Street, Stornoway, caused by the storm- Castle Grounds, Stornoway, Scotland. Such an extraor- amplified perigean spring tides of January 11, 1974 begins dinary incursion by tidal flooding was reported by The to recede, business traffic resumes. The photograph was Stornoway Gazette to have occurred for only "the second taken about 10: 30 a.m. time in living memory." 4- 41,k- 424 Strategic Role of Perigean Spring'Tides, 1635-1976 ment being felt about 3 days later in the British Isles than panying low pressure system) was carefully monitcred as on the southern coast of California. its center moved northward from the New Jersey coast, Since it is not the purpose of this treatise to intrude on some 50 miles at sea. The storm system deepened steadily the analysis of tidal waters in other areas than the United in intensity as it proceeded, causing onshore winds (to States and, to a very limited extent, Canada (many other the north of the low) of increasing velocity along the New more definitive works having been produced, with far England coast (fig. 143). greater local knowledge, by experts in the countries in- By the time the northern edge of the low pressure cen- volved) this instance will be summarized in very brief ter had reached a point opposite Massachusetts, the com- terms. I bined tide-amplifying and storm surge effects were begin- The extreme bent-back atmospheric occluded front and ning to be felt in lowland coastal areas. Likewise, in sand the very deep low pressure system which produced strong embankment regions along the coast from Plum Island, onshore winds along the entire west and south coasts of Mass., to Saco and Popham Beach, Me., cottages and Great Britain on January 11-12, 1974 is distinctively summer homes built on pilings overlooking the water had marked by the cloud-cover pattern approaching the their foundations undercut by erosion, dropping the houses southwest coast in the weather satellite photographs taken onto the lower beach or into the sea. at 6754' (G.c.t.) on January I I (figs. 137-138). With Tidal flooding and erosional damage was reported from these winds arriving at the same time as the amplified, such coastal communities as Marblehead, Newbury, and astronomically produced proxigean spring tides, flooding Provincetown, Mass.; New Castle, Rye, Hampton Beach, of low-lying coastal regions was inevitable (figs. 139- and Portsmouth, N.H.; and Ogunquit, Popham Beach, 14.2). Saco, and Kennebunkport, Me. At Saco, the tidal flood- Seawalls were breached along the western coasts of both ing washed out a coastal road, destroyed a seawall, and England and Wales, and tidal flooding extended from caused an estimated $102,000 in damage to property. the District of Lewis in the Outer Hebrides on the north Even on the afternoon of March 16, hurricane-force to Guernsey in the Channel Islands on the south. The ' winds were predicted off Narragansett Bay. By the time effects of such rampaging storm surges were felt at Mine- the low pressure center reached Halifax, Nova Scotia, in head, Somersetshire; at Appledore in north Devonshire; its northward movement, the central pressure had and at Amroth in Pembrokeshire. Coastal flooding also dropped to about 962 mb. The system continued to in- occurred in Devonshire at Ilfracombe, Bideford, and tensify as it proceeded northward over Newfoundland. Lynmouth. The town of Barnstable described the. flooding With storm surge effects due to the intense winds adding there as the worst in 25 years, while in Stornoway, Outer to the already high perigean spring tides, the eastern sides Hebrides, the tidal inundation covered a considerable of bays and harbors near Halifax were subjected to active section of a coastal airfield. tidal flooding from the strong westerly winds in the south- A similar tidal inundation occurred on the southern ern portion of the low. coast of England between February 9-11, 1974, as on- As quoted from the front page of the Halifax Chron- shore winds reinforced perigean spring tides raised around icle-Herald for March 18, 1976: these dates. ". . . Unusually high tides recorded along the eastern side of Halifax@ Harbour and at Eastern Passage caused 8. Tidal Flooding of 1976 March 16-17 unestimated damage, with roads, fishing wharves, and a This coastal flooding event (Key No. 0-100) is sig- number of houses flooded and isolated. The high tide sub- nificant as the second test case in which an accurate con- merged some areas under 5 feet of water. firmation was madet of the princi 'pies of tidal flooding ". . . Ferry service between St. John, N.B., and Digby potential enumerated in this work. Advance warnings also as well as sailing of the ferry Bluenose from Yarmouth for were released to responsible agencies in this instance, and Bar Harbor, Maine, were cancelled . . . The South appropriate flooding-protection measures were taken. (Cf. Korean oil tanker Ocean Park was unable to dock at the The Boston Globe, March 17, 1976, p. 1, cols. 2-6, and Gulf Oil Refinerv at Pt. Tupper because of high tides and especially p. 42, cols. 1-6.) heavy wind The associated perigee-syzygy alignment (P-S= The rapid northerly movement and deep intensification + 16') had a mean epoch of 1976 March 16 at 0600h of this low pressure system over the waters of the North (e.s.t.). Between March 16 and March 17, the progress Atlantic are described in the accompanying abstract from of a strong, swiftly moving offshore storm (with accom- the Mariners Weather Log for September 1976. 0-100 1976 MARCH 17 7.0h. March 16 6. Oh. 16) 140' 135' 130. 125. 120- lis- 1 I(Y- 106- loo- 95- 1. 85* so 75. 70' 65- 55- t. 3r 9929% / - --- N 1 0" 1004 Chu"hIl 50- 45- E 'Oe l'O' 45- O'Cl ;2 k 40- ..c"laso L.% IS, .57, k 100 127 LA "fold I ', IV 40. -a4 W .@O,d City Plerr" 45 llo' \25 5111 X- a b@z CA, C A <G IN m..'.. 00 4 3 A. Lw North Pli it. i Ps. hill.... @-JL. 117 Oy I .10 1p Gr @*rmr I Y' I-, \11 '@$ 4 Cb 35- 0:v ? '@V-oh -,y.7. Ib or OMM11, @3 AV J 30' 13 if ftdr.@ 38 1 -j C., t 0, -A117- -1 ZI "'L I sr. .00 -17 76- \01 A 30- _34 'ot, % 10 10 -5\- v C% M If _,41 lill 41 0% xA- 25* 22 torm X 110 -P Chih,ah,a IN. Corp., -6 25- Lii,.d. N- 012 2 48 R@ I, --C :to, WALK NAUTIVAL MILES AT VARIOVS LATI-DES -34 .V. 34 100 to. 'I00 loo HER A 10.1 p 31 20'1 VEATHER 16 1020 5 -X'111'12i@ T 7:00 A.M., E.S.T 120' 115- 1 105- too- 95, 90- 85' 8 rQ FIGURE 143. 426 Strategic Role of Perigean Spring Tides, 1635-1976 From: Mariners Weather Log, Vol. 20, No. 5, September "At 0000 on the 18th, the 957-mb LOW was near Corner 1976 Brook, Newfoundland. Four ships reported 40-kn winds from Cape Cod northward. St. Pierre measured 60-kn 0-100-COASTAL FLOODING OF: 1976, MARCH 16-17, Winds. A ship at 51' N, 50' W, reported 60-kn winds just MAINE To NOVA SCOTIA prior to passage of the occlusion. The ATLANTIC CHAM- "This storm moved out of New Mexico as a frontal wave PAGNE, at 400 N, 510 W, and east of the cold front, was tossed by 20-ft seas and 28-ft swells. At 0000 on the 19th, It did not develop until late on the 16th as it approached the center was approaching Kep Farvel with a pressure of the U.S. East Coast, By 1200 on the 17th, it was 962 592 mb. Ocean Weather Station Charlie measured 50-kn near Yarmouth, Nova Scotia. On the afternoon of the 16th, winds and 26-ft seas. Waves were forming on the front south storm warnings were issued for the New England coast with of the center and moving northeastward around the perim- hurricane-force winds in the Narragansett Bay area. Up to eter. Forty knots was the strongest wind on the chart, but 14 in. of new snow accumulated in some areas of Maine, the ANNA WESCH reported 33-ft s.wells near 50' N, with 20 in northern Maine. Boon Island, along. the coast of 420 W." Maine, reported gusts to 75 mi/h. Ships off the east coast were observing 40- to 50-kn winds with the highest being Miscellaneous scenes of perigean spring tides, photo- measured as 52 kn by the BIBB near 42.20 N, 65.2' W. Seas graphed at both extreme high and low water, and the dam- and swells of over 30 ft were reported by four ships with the age caused by such augmented astronomical tides in asso- highest of 35 ft by the BALTIMORE TRADER near 37.4' ciation with severe onshore winds and/or sea swell, are N., 72.6- W. shown in figs. 144-151, on the following pages. 4; to, -t!2iA6X&- U V t t t I I Jt Courtesy of The Pacifica Tribune, Pacifica, Calif. Courtesy of The Pacifica Tribune, Pacifica, Calif. FIGURE 144-The extreme low water occurring during the FIGURE 145.-A matching scene photographed from the negative-amplitude phase of perigean spring tides on 1962 same location during the extreme high-water phase of October 13. The scene is photographed from offshore at these perigean spring tides. Despite a protecting seawall, Pacifica, Calif. The vastly greater amount of beach ex- 'the beach cottage shown already has been flanked by the posed at such extreme low waters is a boon for marine incominc, tide and is in'danger of serious flooding. biologists, marine archaeologists, beachcombers, and certain engineering projects. At the same time, however, very shallowly submerged reefs, rocks, and bottom slope present a hazard to navigation. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 427 7; j AV- Rif Courtesy of The Paciflea Tribune, Pacifica, Calif. Courtesy of County of Ventura, Calif., Public Works Agency FIGURE 146-A second view looking slightly to the left of FIGURE 148-Representative damage to porch and front of figure 144 during the extreme low water on this same date, beach home at, Oxnard Shores, Oxnard, Calif., caused by showing the large extent of foreshore uncovered. The wind-impelled waves and swell piling on top of perigean existing stream drainage channel in the foreground is spring tides resulting from a perigee-syzygy alignment on seen to be completely unimpaired, permitting free hydro- 1971 March 26. logical runoff of rainfall or other surface waters to the sea. -77 "K 'M D- Courtesy of The Pacifica Tribune, Pacifica, Calif. FIGURE 147-Corresponding view from the same position as Courtesy of The Orange coast Daily Pilot, Costa Mesa, Calif. figure 146, photographed during the high-water phase of the tides. The drainage outlet to the sea is now completely FIGURE 149.-Damage to the seawall and protecting parapet covered and blocked by the incoming tide. Thus, whereas at Capistrano Beach Club, Capistrano, Calif., consequent sometimes perigean spring tides do not result in actual salt- upon the wind-reinforced amplification of already high water inundation, the impairment of strong hydrological waters produced in association with the perigee-syzygy runoff by such extraordinarily high tides can cause the alignment of 1962 February 5. (See table 16.) backup and/or overflow of normal drainage channels into surrounding areas. 428 Strategic Role of Perigean Spring Tides, 1635-1976 @2' Courtesy of The Orange Coast Daily Pilot, Costa Mesa, Calif. FIGURE 150.-Detail of destruction of the concrete walkway and driveway at Capistrano Beach Club resulting from erosion and attrition of the underlying foundation ma- terials by storm-amplified perigean spring tides occurring around the 1962 February 5 date. 'A5131- -7/1 iAo 17 NZ W law, .0 N. Courtesy of County of Ventura, Calif., Public Works Agency FIGURE 15 IA.-Section of the coastline in Ventura County, Calif., photographed on January 8, 1974 during the coincident ar- ' q rival of wind-driven surf and perigean spring tides associated with the close perigee-syzygy alignment of this date. Note the extensive log debris in the foreground and the fact that waves are pounding against fenced areas non-nally well above the waterline. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 429 It is significant in terms of a further verification of the beaches. (See The Evening Tribune, San Diego, Janu- principles of tidal flooding potential enunciated in this ary 9, p. 1, col. 5; p. 6, cols. 1-2.) These initial instances work to include four other examples of severe tidal flood- of tidal flooding were succeeded on January 9 by further ing which took place subsequent to preparation of the tidal inundation at Malibu, Rincon, and Solimar beaches preceding text covering the period 1635-1976. These as well as, further north, at Seacliff State Beach and more recent examples are especially noteworthy since, in Capitola. (See the Los Angeles Times, January 10, pt. 1, appropriate pairs, they occurred nearly simultaneously on p. 1, cols. 3-4; p. 3, col. 4; p. 19, cols. 1-4.) the east and west coasts of the United'States, exactly one Because of the average 0.5'-1.5' phase- and parallax- ages on the east coast, perigean spring tides prevailed here anornalistic month apart. The respective cases, happening on January 9. And, successively, along the entire Atlantic in 1978, are outlined below. Additional information re- coast from Virginia to Maine, these tides were accom- garding the full extent of the flooding damage sustained panied during the period of their rise by strong onshore and the exact times and locations of these flooding events winds produced in the northern portion of a deep low may be had from the newspaper sources cited in each pressure system which moved up the coast from the south. instance. Tidal flooding and/or severe erosion of the coastline 9. The Tidal Flooding of 1978 January 8-9 was felt prominently at Provincetown, along Cape Cod, and at Revere Beach, Mass., during the times of high On 1978 January 8-9, severe coastal flooding obviously tides on January 9 (see the Boston Evening Globe, Jan- related to perigean spring tides was experienced, in turn, uary 10, pp. 1, 8); also at Southampton, Long Island, along both the coast of southern California and the south- and the Rockaways, Queens, N.Y., and in various other east coast of New England-and, 3 days later, on the west coastal lowland regions between Virginia and Maine. coast of Great Britain. Interestingly, this circumstance (See the New York Times, January 10, p. 20, cols. 2-6; was, in the latter respect, very nearly a repetition of the p. 25, cols. 5-8). tidal flooding of 1974 January 8 described earlier in this In keeping with the individual resonance factors pecu- same chapter. liar to the west coast of Great Britain noted in example 7 The 1978 flooding event was directly associated with of this same chapter, the effects of these augmented an alignment between perigee and syzygy having a mean perigean spring tides, raised further by strong onshore epoch of January 8 at 15001, (e.s.t.), for 'which P-S winds, were felt 3 days later in various coastal regions. =-16', 7r=61'18.2". As the result of the particular The gale- to near-hurricane force winds (gusting to 82 oceanic resonance factors appropriate to the west coast. mph at London) were produced by a steep atmospheric compared with the east coast, major tidal flooding oc- pressure gradient between a 1,032-millibar high pressure curred in connection with these perigean spring tides one system in the eastern North Atlantic and a 892-millibar day earlier in the former location, aided by coincident low pressure cell over the north of Europe. (See The strong onshore winds. These winds were generated in con- Times, London, England, Thursday, January 12, p. 2, junction with a long, southward-exteniding, cold-front cols. 5-7.) portion of an occluded atmospheric wave centered in a High tides breached seawalls at Cleethorpes in Hum- deep low pressure cell over the Gulf of Alaska. berside, and invaded the town. A portion of a road at Particularly hard hit by tidal flooding in the lowland Ilfracombe on the north Devon coast was washed into the coastal regions of southern California were the beaches at sea by the combination of high tides and heavy rainfall. El Segundo and Manhattan, as well as numerous others Other tidal flooding occurred at Rhos-on-Sea in Colwyn between Malibu and Ventura. At many such locations, Bay, Clwyd, and at Llanfairfechan, Gwynedd. A coastal sandbagging was resorted to, but failed to stem the in- road at Sandgate in Kent was closed by the coastal coming tides and storm-raised surf on January 8.. Very innundation. (See The Times, London, January 12, p. 1, extensive damage was caused to seawalls, homes, and cols. 5-6.) Elsewhere, the effects of these exceptionally beachfront property in these areas. (See the Los Angeles high astronomical tides, coupled with strong storm winds, Times, Monday, January 9, pt. 1, p. 1, col. 4; p. 3, cols. were observed on the Thames River, England, which 1-4.) Considerable flooding damage also was experienced came within 19 inches of breaching its floodwalls, and in at Mission, South Mission, La Jolla, Ocean, and Del Mar wave and tidal flooding which surmounted dikes in Bel- 430 Strategic Role of Perigean Spring Tides, 1635-1976 gium. (See the Reuters dispatch in the Los Angeles Times, flooding damage likewise was heavy along the southeast- January 13, pt. 1, p. 7, cols. 5-6.) ern coast of Maine. It has 'been estimated that, through- out the entire coastal region of New England, 11,000 per- 10. The Tidal Flooding of 1978 February 6-7 sons were forced to leave their homes due to the flooding Yet another confirmatory instance of coastal flooding waters. [See The Boston Herald American, February 9, produced by perigean spring tides in conjunction with p. I (entire page) ; p. 2, cols. 5-6 (pictures) ; p. 3, cols. supporting onshore winds-which is also indicative of a 1-4; p. 4 (entire page); also this same newspaper's series relationship between such tidal flooding events and Storm Souvenir Edition under "The Flooding," pp. 7-13 the times of successive perigee-syzygy alignments-came, (pictures. Cf., further, The San Diego Union, February significantly, exactly one anornalistic month later, on 1978 9, p. A-3, cols. 1-4 (pictures) ; p. A-14, cols. 4-8.] February 6-7. Again, the situation is made more mean- This tidal flooding on the east coast was matched on the ingful in strengthening previous evidence with regard to west coast on February 6-7 by major tidal flooding re- the significant role of perigean spring tides in coastal sulting from exceptionally high tides coupled with pound- flooding by a nearly coincident occurrence of tidal flood- ing waves and surf. The latter two conditions were created ing on both the east and west coasts of the United States. by successive storm fronts associated with a series of In this case, a pseudo-perigean spring tide (defined ac- inmoving meteorological "feeder waves" from off the cording to the terms of reference given earlier in this Pacific Ocean. And, in a manner similar to that demon- chapter) was produced by a perigee-syzygy alignment strated one anornalistic month earlier, the astronomically whose mean epoch was 1978 February 6 at 13001, (e.s.t.), elevated tides, reinforced by gale-force winds, swept over with P - S = - 42". This astronomical circumstance was protecting sandbag barriers at Surfside, Sunset, and Seal accompanied, on the east coast of the United States, by a beaches, Calif. Tidal flooding also occurred along Balboa violent storm which has been variously described as every- Penins Iula, on Balboa. Island, and at Pacific Beach. Severe thing from "the worst stormin 30 years" to "the most tidai erosion was encountered at South Mission Beach. severe storm ever to strike New England," depending (See the Los Angeles Times, February 8, pt. I, p. 1, col. upon the particular location affected. At Cape@ Cod, wind 5; p. 32, cols. 1-3.) velocities as high as 92 mph were recorded. As in the Such recurring coincidences between perigean spring January 9 case,, the shoreline flooding consequent upon tides and violent coastal storms possessing strong onshore wind-driven high tides was felt in coastal lowlands from winds capable of supporting severe tidal flooding-as Virginia to Maine on February 6-7. (So severe was the evidenced throughout history, and often occurring on both resulting damage that, for some days, local newspapers coastlines simultaneously-is a scientifically intriguing cir- were unable to publish or distribute their regular editions. cumstance. From evidence at hand, these coincidences But cf., the Los Angeles Times, Wednesday, February 8, appear to exceed a normal probability distribution, con- pt. 1, p. 1, col. 1; p. 29, cols. 1-5; February 12, pt. I, p. 1, sidering the far greater number of 'occasions within each cols. 1-2; p. 6, cols. 1-3.) year when such strong onshore winds could occur other The sections hardest hit by tidal flooding were those than ir the relatively narrow "windows" of perigean spring around Revere, Scituate, (See fig. 151B.) Hull, Salem, tides. The seemingly above-average frequency of such con- and Winthrop, Mass. In Revere alone, an estimated current events raises the question whether some possible 2,000 homes were flooded. At Monmouth Beach, 85 interrelationship between the respective astronomical families were evacuated, and at Winthrop, 50 families (gravitational) and meteorological phenomena might had to be reached by amphibious vehicle. At Revere, exist which has not as yet been established. From the 20-ft tides topped the seawall, and were prevented from available, documente d occurrences, a certain statistical returning by the rising high waters. Also feeling the relationship also seems to hold between the most severe flooding effects' of the high tides on February 6-7 were cases of tidal flooding and the second or third alignment Falmouth, East Falmouth, Woods Hole, Eastham, and in a given perigee-syzygy series. Under these latter circum- Rockport, Mass. Otl@er extensive tidal flooding occurred stances also, repeated flooding events often occur within at Belman, Sandy Hook, Sea Bright, and Monmouth consecutive anomalistic months. These and other yet un- Beach, N.J., and at Coney Island, N.Y. The Cape Cod proven astronomical-geophysical issues will receive further coastline suffered very damaging beach erosion. Tidal attention in chapter 8. Classification, Designation, and Periodicity of Perigean Spring Tides; Recent Tidal Floodings 431 41e. "r 9- 41* 010 N A '7' Photocredit: The Boston Herald American FIGURE 151B.-Section of shoreline at Scituate- Marshfield, Mass., showing the extensive tidal flooding damage to homes caused by the combination of strong onshore winds and the elevated perigean spring tides of February 6-7, 1978 0 associated with the pseudo-perigee-syzygy alignment of 1978 February 6, P - S 421. (See item 10.) Chapter 8. Tidal Flooding Potential, and the Relationship of Perigee- Syzygy to Other Oceanographic and Geophysical Factors and Influences The data of table 1, the news accounts contained in In columns 5-6 and 11-12 of table 16, four sets of table 5, and the detailed evidence of chapter 7 provide figures have been included for each case of perigee-syzygy ample support to a strong positive correlation between whose meaning has not yet been fully explained. These perigean spring tides and coastal flooding, when these tides data, examined analytically, incorporate the effects of at are accompanied by the correct conditions of wind. The least the majority of the above-mentioned factors and, in many examples of tidal flooding previously cited also in- so doing, provide a quantitative measure of the gravita- dicate that a considerable multiplicity exists -among the tional forces tending to amplify the astronomical tides. astronomical conditions of perigee-syzygy which are capa- Grouped in consecutive pairs, they constitute the astro- ble of raising tides to the point of vulnerability to attack nomical portion of an index of tidal flooding potential. by strong onshore winds. An unusual proximity of the Moon to the Earth, to- The changing right ascensions, declinations, orbital an- gether with a corresponding variation in the tide-raising gular velocities, and distances of the Moon, when subject force inversely as the third power of the distance, is the to correspondingly varying dynamic conditions imposed most important single determinant in raising the tides during each revolutionary period and the perturbations to a significantly higher level. However, the use of the produced in the lunar orbit by the Sun, themselves result geocentric horizontal parallax of the Moori is not the in a diversity of tide-raising forces at times of perigee- most representative astronomical indicator of tidal flood- syzygy. ing potential. Moreover it has been repeatedly pointed In addition, the reinforcing gravitational forces of both out that an increase in the interval of time during which the Moon and the Sun are involved in the production o,,- these near-maximized forces act also plays a contributing unusually high tides at these times. Add to the Moon's role in augmenting the tide-raising influence. It thus be- complexities of motion (1) those of the Sun's apparent comes necessary to select, as an appropriate coefficient, motion due to the annual revolution of the Earth, and (2) some indicator which combines the distance, velocity, further modifications affecting the attraction of the Sun declination, and relative inclination of the Moon's motion upon the Moon caused by the Earth's changing heliocen- with respect to the celestial equator (thus allowing for tric distance in its elliptical orbit-and the variety of cir- amplified tidal duration effects) and which includes the cumstances of perigee-syzygy builds up accordingly. The influence of the Sun's gravitational attraction as well. Such magnitude of the combined lunisolar tide-raising force a composite astronomical index to tidal flooding potential, also can vary at perigee-syzygy alignments occurring at known as the Aw-syzygy coefficient (or Aw-S) will be different times of the year. Finally, the fluctuating veloc- proposed in the present chapter. In this particular usage, ity of the Moon at different points in its orbit, and the par- Aco represents a comparative measure of the changing or- ticular component of this velocity measured parallel to the bital angular velocity of the Moon, selectively referenced Earth's Equator, are of importance in the production and to (I) perigee, and (2) the vernal equinox, and including duration of perigean spring tides. the effects of numerous other astronomical factors. 433 202-509 0 - 78 - 30 434 Strategic Role of Perigean Spring Tides, 1635-1976 Certain necessary qualifications and restrictions on the syzygy in a closely matching fashion. However, this quan- universal application of such a coefficient, related to the tity as tabulated in the ephemeris does not represent the existing type of tides, a limited dai:y range, or a predomi- corresponding effects of changing orbital velocities of nant solar modification of the harmonic constituents at a the Moon with distance from the Earth, the influence of given locality-as well as other special exceptions resulting the changing lunar declination in this same connection, from geographic and hydrographic considerations-are nor the combined (coplanar) tide-raising actions of the also presented. Moon and Sun. Neither does it in any way indicate the corresponding requirements for catch-up motion by the Development of a Numerical Index Desig- rotating Earth, and resulting extensions in the duration nating the Astronomical Potential for of time over which stronger gravitational forces act, con- Tidal Flooding sequent upon any given perigee-syzygy alignment. Simi- In establishing some quantitative measure of the pos- larly, the value of p, the radius vector from the center of sibility of any one perigean spring tide producing coastal the Earth to the center of the Moon, which is numerically flooding when accompanied by the requisite wind condi- equal to cosecant 7r , is not a useful indicator for the pres- tion,s-and hence the flooding potential of one perigean ent purpose. spring tide compared with another-the astronomical cir- 1. The Need for Combined Lunisolar Representa- cumstances present must be individually evaluated. The tion four principal conditions affecting the production of all In assigning some quantitative measure to the increased categories of perigean spring tides are: (I ) a closer prox- potential for tidal flooding resulting from the astronom- imity of the Moon to the Earth as a result of (a) solar ically amplified higher waters at times of perigee-syzygy, perturbations of the Moon's orbit when the Sun in its the preceding factors and failings must be taken into ac- apparent motion approaches coincidence with the line of count. It is obvious that it is necessary to find some coeffi- apsides (in this case, specifically, the perigee position) cient which includes the dynamic effects of both the Moon and (b) a smaller separation between perigee and syzygy and Sun, since the gravitational forces of both are in- produced by a closer commensurability between the syno- volved. The increase in tidal range due to the alignment dic and anomalistic months under certain conditions; (2) of Moon and Sun at syzygy has been shown to be about the effect of changing declination upon the Moon's com- 20 percent, and that due to the approach of the Moon to ponent of motion in right ascension; (3) the longer in- the Earth at perigee amounts to another 20 percent. Ac- terval of time required for a point on the rotating Earth cordingly, the combined gravitational forces of the Moon to catch up with the physically advanced positions of lunar and Sun at times of perigee-syzygy are, on the average, transit resulting from accelerated orbital motions of the responsible for an increase in tidal range of about 40 per- Moon at the time of perigee-syzygy; and (4) the retro- cent above the mean spring range. grade motion of perigee at this same time. As derived from The American Ephemeris and Nauti- The varying distance of the Sun from the Earth is also cal Almanac, daily apparent angular velocities of the relevant in terms of the increment of force acting on the Moon and Sun in celestial longitude (A) or in right ascen- Earth's waters at perihelion; however, as has-been seen, sion (a) are basically a function of: (1) their respective at solar perigee the Moon's orbital velocity is decreased and the Earth's necessary rotational catch-up motion is parallaxes; (2) their instantaneous and changing declina- reduced. tions (8), and (3) the actual or real (as well as pertur- Among all of the tide-raisin .factors present, the Moon's bationally disturbed) motions of the Moon and the Earth, 9 respectively. All three of these factors are among those distance from the Earth has the greatest influence in pro- whose effects are being sought after for consolidation in ducing a significantly amplified rise of the tides. It might a single index of enhanced tide-raising activity. The daily readily be assumed, therefore, that the use of the Moon's motions of the Moon and Sun in celestial longitude must, instantaneous parallax as interpolated from The American therefore, be regarded as useful indicators in the task of Ephemeris and Nautical Almanac for the various occa- finding such a meaningful index of amplified astronomi- sions of close perigee-syzygy might be the most logical cal tide-raising force and associated tidal flooding poten- single indicator of tidal flooding potential associated with tial. Of even greater significance in the first case, however, such astronomical alignments. This is not the case. is the angular motion of the Moon in its own orbital An increased value of the lunar parallax does represent Plane. The daily apparent ml otion of the Moon in right the reduced distance of the Moon from Earth at perigee- ascension becomes an equally valuable indicator for the Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 435 present purpose, since the Moon's angular motion is there- (The magnitude of this component of the Aw-S coeffi- by referred to the plane of the celestial equator. Sig- cient therefore bears a direct relationship with the in- nificantly, this is also a plane perpendicular to the axis creased values of the lunar parallax at times of perigee- of the Earth's rotation-and that plane in which the syzygy.) frequently described catch-up effects of the Earth's rota- b. The motion of perigee: Of particular importance tion must occur. is the maximum retrograde motion of perigee which oc- curs as the Moon reaches the position of perigee-syzygy. 2. Significance of the Aw-Syzygy Coefficient This effect will be evident as an increase in the rate of In the light of all aspects of the preceding discussion, closure between the Moon and perigee, since the two are it is apparent that the necessity exists for the establishment moving in opposite directions. The relative velocity is, of some quantitative indicator which represents not only therefore represented by the vector sum of the two ve- the increased gravitational effects of' the Moon on the locities, 'whose magnitude will always have its greatest Earth's tidal waters caused by the reduced separation value at the time of perige'e-syzygy (see pp. 177-182). between them at the time of perigee, but also: ( 1 ) the .c. The solar parallactic effect: This negative velocity combined gravitational forces of the Moon and Sun at of perigee is further augmented at the time of perihelion (perigee-) syzygy; (2) the increased tide-raising force of by an added lunar proximity to the Sun and an increase the Sun exerted at solar perigee; and (3) the enhanced in the perturbational influences consequent upon the tidal forces introduced by a coplanar alignment of the heightened solar gravitational force present. The value Moon and Sun in declination. It must also include the of the rate of closure. will increase accordingly, providing various effects, at perigee-syzygy, tending to lengthen the an indication of the effect of solar perigee. periods of time during which the previously mentioned d. The effect of the annual equation: Conversely, the augmented gravitational , forces exert their influences, reduction in the Moon's velocity near the time of solar and the special significance of the retrograde motion of perigee caused by perturbational influences will, of its perigee. Such a numerical quantifier is achieved, in own accord, be reflected in a diminished relative velocity part, through the determination of the rate of closure between Moon and perigee. Thus, in its total effect, of the Moon's angular motion in orbit with respect to the proximity to solar perigee will be represented by the net position of perigee. Because the Moon's velocity of revo- difference between c and d. Since the Ieffect of c is always lution is always far greater than the angular motion of larger, the resultant influence will always be an increased perigee along the orbit as the result of solar perturba- value of tions, the Moon will in every case be catching up on the e. Coplanar lunisolar alignment: A coplanar align- position of perigee. Expressing the appropriate angular ment of the Sun and Moon in declination, or the possible velocities as differential rates of motion in one day of time, joint alignment of these bodies in declination and longi- as a first component of the total expression for Aw-S, the tude at the equinoxes, are both conditions which. create relative motion Aw, of the Moon with respect to perigee increased gravitational forces. The corollary production is given by: of an augmented lunar parallax is manifest, in turn, by an increase in orbital velocity of the Moon, and hence where iz(r represents the rate of angular motion of perigee a larger value of the Aw,-S coefficient. (or rate of angular change in the true anomaly) and V'([ the Thus, in each of the above cases, the Awi.-S coefficient rate of angular motion of the Moon. Both motions, ex- responds directly to, those factors whose existence pro- pressed in degrees per day, occur along the Moon's orbital duces an enhancement of the tide-raising forces on the plane. Earth's waters. A large value of the Awi-S coefficient is directly indicative of conditions which are conducive The selection of these particular parameters permits to an increase in such tide-raising forces. representation of: Of considerably less consequence in its influence, and a. The lunar parallactic effect: The increased orbital subsequently so weighted, a second component of the angular velocity of the Moon as a function of close prox- total AcB-S coefficient is required in order to include the imity to the Earth at the time of perigee- (or proxigee-) effects of a lengthening of the period of increased gravi- syzygy-this reduced separation being caused by the solar tational force associated with each alignment of perigee- perturbational influences exerted on the Moon's orbit by syzygy. Such prolongations of the intervals of tide-raising ,the perigee-syzygy alignment. force application result from the necessity for equivalent 436 Strategic Role of Perigean Spring Tides, 1635-1976 catch-up motions by the rotating Earth to compensate that by far the greater number of cases of a large lunar for increased orbital motions in right ascension at the parallax occur with the Moon at a relatively large declina- time of perigee-syzygy, especially when the Moon's tion-especially when the Moon 's also coplanar with the declination is large. Sun. The resulting closer approach of the Moon to the Earth (with the accompanying tide-raising force increasing This second component involves the actual daily rate inversely as the cube of the distance) caused by the orbital of motion of the Moon in right ascension. The influences perturbations becomes of considerable significance. The coin- of (a) a closer approach of the Moon to the Earth at cidence of the Moon and Sun on the celestial equator can- perigee-syzygy, with a resulting larger parallax and faster not occur at solar perigee (i.e., perihelion) because the Sun lunar motion and (b) a large lunar declination, will al- is then near its maximum negative declination. It is less cogent that the Moon's presence on the celestial ways be reflected in a correspondingly high value of equator is manifest in a reduction of its apparent angular AC02-S. As in the case of Awi-S, therefore, a higher velocity in right ascension (i.e., in the value of &([) by about value Of AW2-S indicates the presence of factors produc- 2'-4'/d compared with the value of &([ when the Moon is tive of enhanced tide-raising forces. As will be seen on at or near its maximum declinations of � 23.50 to � 28.50. following pages, the two components A(,),L-S and A(,)..-S Because of the weighted reduction formula for the total Aw-S coefficient, this relatively small decrease in the value of are added (with proportionately far less emphasis on &,[ is more than offset a the time of a close perigee-syzygy AO)2-S) to obtain the 'most meaningful astronomical alignment by the corresponding increase in the angular coefficient of tidal flooding potential. velocity of both the Moon and perigee and the consequent Supplementary Note: larger value of Awl. The effect of the Moon's greater tide-raising action when 3. Evaluation of the Aw-S Coefficient the Moon and Sun are both on the celestial equator is also worthy of attention. Although the Moon passes through 0' In the computational procedure for determining declination twice each lunar month in the same manner that it reaches a position of maximum (positive and negative) the numerical equivalent of Aw-S, the values of the declination twice a month, very few of the 100 cases of tidal angular rate of motion of the Moon with respect to flooding enumerated in table I took place with the Moon on perigee at the respective instants of perigee and syzygy or very near the, celestial equator. Many examples of tidal must first be obtained. These two values can readily flooding have occurred with the Moon at or near its position be established as a computer output by use of a of greatest declination. Fortran formulation of the equation given in para- The Sun is on the celestial equator only twice each year, at the vernal and autumnal equinoxes. Thus, the possibility graph 3 of table 16B (p. 225). for a combination of solar and lunar gravitational forces Since the angular separation in longitude of the exactly in this plane occurs only 2 times a year-with the Moon from perigee is defined as the true anoma@y, chance for coplanar alignment existing at either new moon it only becomes necessary.to differentiate or full moon. This small number of possible occurrences of thie algorithmic expression for true anomaly in the reinforcing coplanar lunisolar tidal forces at 0' declination form of a series expansion to determine its time rate must be compared with the far greater frequency of cases of augmented lunar motion in right ascension when the Moon of variation ;([. The resulting quantity may then be is at a high declination (e.g., >z!::181, approximately). evaluated for any one instant of time without involving Above this declination, a graph of declination as the ordi- the individual differences between @([, the rate of nate versus right ascension (or time) as the abscissa re- angular motion of the Moon, and r@([ the rate of curves more rapidly toward the horizontal (figs. 44a, b), angular motion of perigee (both motions being ex- indicating a proportionately larger component of motion pressed in 0/d in a. , and both occurring in the plane of The latter motion creates the necessity for a corresponding the lunar orbit) - catch-up motion by the rotating Earth, and results in a It should be reiterated at this point that the single longer interval of amplified gravitational force action if value of,;([ = - 1.6' /d at perigee-syzygy, computed on the high lunar declination is coincident with perigee- page 180, is purely a representative figure for an aver- syzygy. age circumstance of perigee-syzygy, and is subject to The greater number of cases of such coplanar forces considerable variation corresponding to different occurring at larger lunar declinations (up to � 28.50) com- values of the separation-interval between these com- pared with those occurring at or very near declination 0* likewise increases the statistical probability for coincidence ponents. A basic tenet of the present evaluative pro- of these high declination cases with meteorological condi- cedure is, in fact, that the same variable solar forces tions of strong, onshore winds contributory to tidal flooding. which produce different amounts of perturbations in It has been amply demonstrated in table 13, and can be the lunar orbit also produce varying maxima in the even more fully corroborated by an analysis of table 16, height of the tides. It is upon this relationship that the Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 437 use of these parameters in the astronomical portion of constituents, tidal range, and various meteorological a coefficient of potential tidal flooding is based. circumstances as well. Since, vectorially, in a graphic and analytic evaluation of b(c, the instantaneous angular Establishment of a Combined Astronomical- velocity of the position of perigee (negative around the Meteorological Index to Potential Tidal time the Moon reaches perigee) must be algebraically Flooding subtracted from the velocity of the Moon at this same The. speed of the wind, its direction, and duration time. The latter, direct motion is always positive. The of overwater movement are, of course, further aspects vectorial sum thus yields an increased angular velocity of importance in the production of tidal flooding. Strong of the Moon (still positive) relative to perigee. winds, onshore winds, and th e ith a long fetch-or The individual values of this relative velocity at the 0s w instants of (a) syzygy and (b) perigee are tabulated in total distance of airflow over the sea surface-are all con- columns 5 and 11, respectively, of table 16. Because a tributing factors to coastal flooding when added to astro- purely dimensionless coefficient is to be established, nomically amplified tidal conditions. Offshore winds pro- the units of angular velocity in 0/11 are dropped, per- vide a negative or subtractive effect. Low pressure mitting an otherwise incongruous combination of atmospheric systems create an additional rise of water level values possessing completely. variant units in the by an amount equal to about 13 inches for each inch of several parts of the subsequent evaluating formula.- barometric depression (i.e., approximately 1 centimeter In determining the second component, Ace,-S, the per millibar), while high pressure systems cause a- reduc- values of the instantaneous rate of change of the tion in water level by the same amount. Meteorologically, Moon's motion in right ascension (including the therefore, a correction must also be applied to account effects of declination) are computed by use of the for any deepening or filling of the overlying atmospheric expression for &,: given in paragraph 4 on page 226.@ pressure system during the 3-hour period since the preced- These values, corresponding to the instants of syzygy ing synoptic weather map. and perigee, appear in the computer printout of table With consideration to the foregoing and other factors, 16 in columns 6 and 12, respectively (the time units of it is now possible to develop a single equation incorporat- right ascension being reduced, for consistency, to 0/d). ing the various astronomical, meteorological, physical, and It is obvious that a further measure is necessary to hydrographic elements which together serve to establish establish the relatively greater importance assignable to a greater or lesser potential for tidal flooding. Specifically, the tide-raising forces resulting from the close lunar these elements include: ( 1 ) the effect of a perigee-syzygy proxim.ity to the Earth at perigee-syzygy (indicated by alignment in increasing the tide-raising forces present, Awl-S) compared with the effect of the prolongation represented by the Aw-syzygy coefficient; (2) the response of these forces at the same time (indicated by AW2-S) of the local tide to the semidiumal lunar influence, which The procedure used also serves to define a more explicit is that most prominent in connection with perigean comparative influence of lunar proximity over the range spring tides, and here expressed for mathematical conven- between apogee-syzygy, perigee- or apogee-quadrature, ience by the term M2- 1; (3) the value of the mean spring perigee-syzygy, and proxigee-syzygy. It further main- (or diurnal) range of the tides at the place under con- tains an appropriate relative perspective between astro- sideration, representing a further aspect of local dynamic nomical contributions to tidal flooding and the hydro- response to astronomical tide-producing influences, and logical and meteorological factors which follow. From incorporating as - well a quantitative indication of the empirical considerations, the data of columns 5 and 11 degree of constriction of tidal estuaries, shallowing of the are multiplied by 4, with those of columns 6 and 12 being ocean floor, and other variables; (4) the average velocity left the same. of the strong (usually > 25. knots), persistent, and direc- The total expression for the Ao)-S coefficient then tionally steady wind movement over the sea surface neces- idal flooding. The effects of the wind ac- becomes: sary to support ti tion on the sea surface are manifest in waves produced in the shallow waters immediately adjacent to the coastline, The sum of these two tenns will subsequently become but may Ialso persist in the form of swell hundreds of the astronomical portion of a multiparameter empirical miles from the coastline (the total distance of such uninter- formula applicable to the evaluation of tidal flooding rupted wind movement is known as the fetch); (5) the potential-which includes the effects of local harmonic angle-of-attack of this overwater wind movement with 438 Strategic Role of Perigean Spring Tides, 1635-1976 respect to the shoreline, measured by the angle 0 between D=the duration of a strong, sustained, on- the direction from which the wind is 'blowing and a shore windflow over the body of water lying normal or orthogonal line to that immediate section of -directly seaward (but with no limit on its coastline under consideration; (6) the duration.of the total outward extent) from the coastal overwater wind movement, expressed as a time factor a station (in hours) rather than in terms of distance, as in the case of the fetch; AP=the change in barometric pressure at the and (7) the atmospheric pressure gradient during the past coastal weather station, during the past 3 hours. 3 hours (in millibars) A meaningful index quantifier describing the active Thus, where: potential for coastal flooding resulting from the com- II=a combined astronomical-meteorological bination of astronomical and meteorological causes coefficient of potential tidal flooding (the may be represented by: capitalized symbol is derived from the first letter of the Greek word 7rX@Mupa meaning H=AW-S+(M2-1)+ I "flood-tide" or "inundation," and should G._5 +V cos O+D-34 (�AP) not be confused with the lower-case symbol ir universally used for astronomical par- The final coefficient, 34 millibars, is approximately allax throughout this volume). (As a nu- equivalent to an atmospheric pressure change of I inch merical index only, II is dimensionless.) of mercury-that required to raise or lower the water b(C=the rate of angular change in the Moon's level bv I foot. For simplification, the small effect of. a true anomaly at the instant of syzygy (or rapidly' moving atmospheric pressure system in itself perigee) (Vectorially, The altering the level of the sea surface is ignored in the above units of all three quantities are O/d.) equation. The remaining numerical constants are @C @ the rate of angular motion of the, Moon in arbitrary ones, based both upon empirical data and its orbit analytic convenience in establishing an average index ii@(C=the rate of angular motion of the lunar value centered around 100. perigee along the orbit 'The units in which the individual functions comprising @C:@the rate of lunar angular motion in right this equation are customarily derived are specified in the ascension (i.e., as projected on the celestial preceding legend, but are not carried into the computa- equator) at the instant of syzygy (or tions associated with this formula. Since the index is itself perigee) dimensionless and constitutes a purely relative measure, Aco-S=4bC+L(C the various components of the equation may be' safely M2 =the principal lunar semidiurnal component combined, with their different units being ignored. of .the tides at the location under consider- In this equation, it will be seen that the first term on ation (in feet) the right-that expressing the effect of a perigee-syzygy R,,@the mean spring (or diurnal) tidal range alignment-is always positive. So also, in successive order at the same local station (in feet) V=the mean velocity of the surface wind are M2, Rs, and V, the magnitude of the wind velocity. during at least a 3-hour period at a nearby The cosine 'function in the fourth term automatically reference coastal weather station (in knots) takes care of the tide-raising or tide-reducing effects O@the angle measured between an axis ex- created by onshore or offshore components of the wind, tended to seaward perpendicular to the respectively. The corresponding additive or subtractive general coastline and the direction from functions are indicated by the algebraic sign customarily I assigned to this trigonometric function in the quadrant which the wind is blowing (in degrees of . The value of D is again always positive, but arc) concerned 'The reason for use of the dimensional unit of time rather than the algebraic sign of the last term varies respectively from distance is obvious when an actual example such as the great mid- plus to minus with rise or fall in atmospheric pressure Atlantic tidal flooding of 1962 is considered. Because of stagnation of (the corresponding correction being taken care of by the the offshore low pressure center, the distance of overwater wind minus sign in front of the parentheses) . movement remained relatively constant. However, the onshore wind- The greater the arnount by which the numerical value flow persisted timewise through 2.5 days and 5 successive high tides, during each of which continuously height-accelerating effects were felt. of this index is in excess of 100 (representing an average Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 439 condition) the greater is the potential for tidal flooding. gations of hurricanes and storm surges, N. Arthur Pore, Examples demonstrating the application of this index to Chester P. Jelesnianski, and others (see bibliography- the determination of tidal flooding potential, and showing category 18) have derived various theoretical, empirical, in the relative magnitude of II a very close agreement with and modular formulae for predicting the height of waves, the severity of the flooding conditions actually encountered wave setup conditions, swell, and storm surges.under con- are given in table 30. These and other desired historical ditions of strong, onshore winds. These formulae are based examples for which II has been evaluated may be upon such factors as wind stress vectors, offshore surface- compared with the extent of tidal flooding described for pressure fields, maximum storm winds, and the magnitudes specific cases in chapter 7 and in the newspaper accounts and distributions of these and related meteorological ele- comprising table 5 of part 1, chapter 1. ments within rectangular grid systems covering the coastal This index to potential tidal flooding is presently in waters. Such formulae will prove more satisfactory for an analytic stage of development and largely dependent detailed analytical evaluations, bearing in mind an earlier upon correlations with empirical data. Appropriate ad- clarification that a storm surge analyzed for meteorological justments within the individual portions of the formula purposes does not necessarily imply coastal flooding will undoubtedly occur as additional comparisons are potential. made with future coastal flooding events. With this un- The numerical evaluation of II is designed to provide derstanding, the expression for II is to be regarded as a an expedient and, where appropriate, a timely forewarn- provisional one, pending the realization of such a definitive ing of astronomical tidal flooding potential should critical indicator. meteorological conditions also prevail. A more compre- The incorporation of the various contributing causes hensive evaluation is achieved when most of the terms to tidal flooding in such a single numerical index is in- in the expression are employed. However, where certain tended principally to achieve -a generalized descriptor term elements are lacking-or in the exigencies of the mo- leading toward an awareness of the increased tidal flood- ment-a, partial indication of any pending tidal flooding ing potential occasioned by tide-amplifying astronomical threat to the shoreline may be secured by the combined conditions, where supporting meteorological conditions utilization (or separate analysis of) all parameters in the are also present. In connection with meteorological investi- equation which are immediately available. ' TABLE 30.-Examples involving the Use of the Aw-S Coefficient in Establishing a Combined Astronomical-Meteorological Index (11) of Potential Tidal Flooding The astronomical coefficients are computed for the mean epochs of perigee- (proxigee-) syzygy and are combined with the most representative meteorological data available for the cases evaluated.* Astronomical-Tidal Parameters Meteorological Parameters Potential for tidal flooding Key Date; flooding location (or that No. of the nearest tide station) AW-S M,- I I Vcos 0 D Index coefficient (table 19) 3.5 (kt) (h) 34 (�P) II Intensity rating (table 16) (table 19) D-57 193 1, Mar. 4-5, New York (The 82.178 1.138 0.5 52 36 ........ 17 1. 8 Extreme. Batte@y), N.Y. F-68 1939, Jan. 3-5, Aberdeen, Wash. 84.056 2.425 .9 43 48 ........ 168.4 Severe. -I-83e 1959, Dec. 29, Boston, Mass.. .. . 84.105 3.422 3.1 56 20 ........ 166.6 Severe. J-85 1962, Mar. 6-7, Entire mid- 83.025 .916 .4 30 65 ........ 179. 3 Extreme. Atlantic coast (Breakwater Harbor, Del.). N-99 1974, Jan. 8, Malibu Beach (Los 84.611 .693 .5 35 24 144.8 Strong. Angeles, Calif.): (Willets Point, N.Y.) ........... 84.611 2.619 1.4 -8 0 80.6 Insignificant. 0-100 1976, Mar. 17, Halifax, Nova 82.371 1.046 .5 43 10 ........ 136.9 Moderate. Scotia. Intensity rating scale: *Note: Precise values for the rates of barometric pressure change in II>170-Extreme, . II>120-Moderate. the past 3 hours at local stations are best obtained from original I15160-Severe. Il 5; 1 00-Slight. hourly weather data in each case and, accordingly, have not been R 5- 140-Strong. 11< 100-Insignificant. inserted in the above table. 440 Strategic Role of Perigean Spring Tides, 1635-1976 One further requirement for extensive tidal flooding i 's, Among such predicted tidal data, a second practical of course, the involvement of a lowlying coastal area, indicator of perigean spring tides exists in the large daily whose mean elevation is only some few feet above the level ranges usually displayed by this type of tide (with certain of mean high water spring tides, and in which any upward exceptions listed under "Diurnal Tides" in table 19). The slope (positive gradient) extending inland from the sea maximum daily tidal range is obtained as the simple differ- is also small. ence between the height of higher high water. and the immediately preceding or succeeding lower low water. Empirical Support for the Validity of the Again, however, the tidal range is closely affected by the Delta Omega-Syzygy Coefficient Provided diurnal inequality, a lunar declinational influence whose by Predicted and Observed Tidal Height observed effects are more commonly associated with the Data tides of the Pacific Ocean than those of the east coast of Comprising the next step in an evaluative process to North America (except for Atlantic coast locations at high determine the reliability of the Aw-syzygy coefficient as one latitudes). factor in a multiple-parameter indicator of tidal flooding Some other more consistent parameter available from potential, it is desirable to subject this coefficient to appro- tide tables which is indicative of the relative tidal flooding priate quantitative tests. In this process, certain cases of potential of perigean spring tides when these are rein- perigee-syzygy alignment possessing unusually high Aco- forced -by appropriate meteorological conditions is ob- syzygy coefficients computed directly from the data in viously needed. table 16 are compared with predicted tidal data for the The Lengthened Tidal Day as an Indicator same dates contained within official. government tide ta- bles. Dates on which tidal flooding has been observed of Increased Tidal Flooding Potential to occur are selected for such analyses. Such an indirect indication of tidal flooding potential In this comparison with examples of known tidal flood- is obtainable through the analysis of the predicted times ing, the objective is that of discovering all consistent rela- of higher high waters. A consideration of the daily differ- tionships between the Au)-syzygy coefficient and predicted ences between these times of higher high water provides or observed tide data which either give support to, or con- a valuable corroboration for the validity of the purely tradict, the interpretations made from the previously con- astronomically derived Aw-syzygy coefficient. This tempo- sidered, purely astronomical data. ral relation also provides support to an emphasis given A necessary preliminary to the establishment of factors earlier to the increased length of the tidal day as an im- of correlation between the astronomically related Aw- portant adjunct of perigean spring tides. syzygy coefficient and corresponding tidal.data is the dis- In the columns of tide tables immediately to the left covery of a suitable common-response parameter. A study of those indicating the predicted heights of high and low of the individual items published in tide tables giving the waters, the times of the highest high water in each day times and heights of the tides reveals that no one of the (specified in hours and minutes) can be found. If the quantities published is, in its present form, directly suit- time opposite the highest high Iwater for each day is sub- able for the desired correlations. However, through ad- tracted (with proper attention to the sexagesimal system ditional analysis, several of these can be made useful in used in timekeeping) from the corresponding value for this regard. the following day, the desired difference in time between The above-average water levels predicted for the times consecutive higher high waters is obtained. ,of perigean spring tides are, of course, a clear indication This interval will always be slightly more than 24 that increased gravitational tide-raising forces are active hours, and represents the length of the tidal day which, at these times. However, when the values of tide height although not precisely the same in its possible range of close to perigee-syzygy are compared with those occurring values, is directly related to the lunar day, defined as the in certain cases of unusual uplift producedby other than period of time between two successive upper transits of the perigee-syzygy conditions, the high waters predicted for Moon across the local meridian of any place. these latter cases may, in some instances, be equal to, or Tables 3 1 a,b,c,d and figs. 15 2a,b, appliGable to Break- sometimes even greater than, those predicted for perigean water Harbor, Del.., illustrate the graphical procedure spring tides. For reasons which will later be shown, pre- used in determining the effect of the lengthened lunar dicted tide height alone is not, therefore, a totally reliable day upon perigean spring tides. This effect is additive indicator of tidal flooding potential. to that of the increased gravitational forces of the Moon Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 441 TABLE 31a, b, c, d.-Data Used in Evaluating the Increased Length of the Tidal Day at Perigee-Syzygy (Made Comparatively More Effective by the Greater Gravitational Force at These Times) as Plotted on the National Ocean Survey Tide Tablesfor Breakwater Harbor, Del., januar@-December, 1962 74 BREAKWATER HARBOR, DEL., 1962 Times and Heights of High and Low Waters JANUARY FEBRUARY MARCH --!@Ime Ht. Time Ht. -- -,rime fft. Time Hf.-- - Time Ht. Time Ht. DAY DAY DAY DAY DAY DAY --h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. h. m. ft. M 1 ?35g 3 T16 0504 4.4 T 10504 4.5 F16 0631 4.4 T 1 0330 4.2 F16 0515 4-.0 00 0:9 1124 0.3 1125 0.2 1253 0.3 0954 0.4 11-38 0.5 1612 3.5 1727 3.6 1725 3.5 1855 3.5 1558 3 3 1747 3.4 51 2217 0.2 56 2320 0.1 S4 2323 -0.2 44 63 2158 0:1 so 2334 0.5 T 2 0450 4.1 W17 0600 4.6 F 20558 4.8 S17 0041 0.2 F 2 0433 4.4 S17 0605 4:.1 1102 0.4 1222 0.2 1220 0.0 0715 4.4 Ca 105? 0.2 1223 0.4 1704 3.5 1822 3.5 1820 3.7 1333 0.2 1701 3.5 1832 3.5 48 2304 0.0 49 S2 @ 39 1936 3.6 60 2300 -0.1 44 W 3 0538 4.4 118 0010 0.1 S 30016 -0-4 S18 0123 0.1 S 3 0533 4.7 S18 0021 0.3 1155 0.2 0649 4.7C 0650 5.1 0754 4.5 1155 -0.1 0649 4.2 1755 3.6 1312 0,1 *AF 1312 -0.3 1408 0.1 1800 3.9 1301 0.3 47 2352 -0.2 44 1911 3.6 S1 1913 4.0 36 2012 3.? S6 2359 -0.4 39 1910 3.7 T 4 0625 4.8 F19 0057 0.0 S 40109 -0.6 M19 0202 0.0 S 4 0629 5.0 M19 0102 0.2 1245 T733 4.7 7 5 3 T830 4 5 1248 -0.4 0728 4.2 843 9:17 N 355 0.1 T408 -0:5 443 0:1 1854 4.2 1334 0.2 1954 3.6 2003 4.2 2046 3.8 1945 3.9 47 41 49 34 53 34 F 5 0039 -0.4 S20 0139 0.0 M 50201 -0.8 T20 0239 0.0 M 5 0054 -0.7 T20 0140 0.0 0712 5.0 0814 4 7 0830 5.5 IrM 0904 4.4 0722 _5 2 0802 1.3 133.3 -0.2 1434 0:1 NM1451 -0 7 IF 1516 0.1 1338 0:6 A1407 0.1 47 1932 3.8 38 2034 3.649 2054 4:4 34 2120 3.9 S1 1947 4.5 34 2017 4.0 S 6 0127 -0.5 S21 0220 0.0 T 60254 -0.9 W21 0317 0.0 V 0148 -0.9 W21 -0217 -0.1 0759 5 0852 4.7P 0919 5 0938 4.3 0813 4.3 1511 0.10 _ " A FrAO836 S 1421 0:43 FM 1539 0:8 1548 0.1 1427 -0 1439 0 0 47 2020 4.0 37 2111 3.6 so 2144 4.5 3S 2154 3.9 TA2036 4:08 X3E2050 4:2 S 7 0215 -0.6 M22 0300 0.0 W 70346 -0.8 T22 0355 0.0 W 7 0241 -1.0 T22 0254 -0.1 NMO846 5.4 0929 4.6 1009 5.3 1013 4.2 0902 5:3 E0909 4.2 1510 -0.5 1547 1627 -0.7 1622 0.1 1514 -0 9 1511 0.0 2109 4.0 2148 9:16 2236 4.6 2229 4.0 2126 5.0 2123 4.2 48 36 S2 36 49 35 M 8 0305 -0.7 T23 0339 0.1 T 80439 -0.7 F23- 0434 0.1 T 8 0333 -1.0 F23 0331 -0.1 M 5 4 1005 4 5 11?1 5 1049 4 1 0943 4.1 00 0:6 1623 0:1 17 6 -0:06 E 1657 0:12 E 0196502 -50-18 1545 0.0 so 2200 4.1 38 2225 3.6 53 2330 4.6 37 2307 4.0 so 2215 5.0 36 2158 1.3 T 9 J358 -0.6 W24 0419 0.1 F 90535 -0.4 S24 0515 0.2 F 9 0425 -0.8 S24 0409 -0.1 p 1024 5.3 1043 4 3 1154 4.6 1126 3.9 1041 4.8 1018 3.9 64Q -0.5 1700 0:2E 1806 -0.4 1735 0.2 1649 -0.6 1620 0.1 S3 2253 4.1 38 2304 3.6 S6 41 2348 3.9 S2 2307 4e9 40 2234 1.3 W10 0451 -0.5 T25 0501 0.3 S10 0026 4.4z S25 0600 0.3 SIO 0519 -0.5 S25 0450 0.0 ill? _5 1121 4.1 0634 -0.2 12o? 3.6 1133 4.4 1056 3.7 1741 0:04 A 1738 0.3 1250 4.2 1817 0.3 1738 -0.4 1658 0.1 se 2349 4.1 41 2344 3.6 so 1900 -0.2 47 5S 41 2314 4.3 T11 0548 -0.2 F26 0545 0.4 S11 0126 4.3 M26 0034 3.9 S11 0001 4.? M26 0534 0.1 1213 4.7 1202 3.9 0738 0.1 0650 0.4 0615 -0.2 1137 3.5 1834 -0.3 1818 0.3 1351 3.8 1254 3.4 1228 4.0 1740 0.2 S8 44 65 1958 0.1 52 1904 0.3 57 1829 -0.1 48 F12 0050 .4.1 S27 0030 3.6 M12 0231 4.2 T27 0126 3.9 M12 0058 4.4 T27 0000 4.2 E 0651 0633 0 5 8 0.3 0747 0.5 0716 0.1 0623 0.3 1311 40:04 E 1246 3:7,FQ01445:87 3.5 1349 3.3 1328 3.6 1225 3.3 1931 -0.2 1901 0.4 2059 0.2 1958 0.4 1927 0.2 1828 0.3 62 48 67 60 62 S2 S13. 0152 4.1 S28 0118 3.7 T13 0338 4.2 W28 0226 4.0 T13 0200 4.2 V428 0052 4.2 0758 0 2 0726 0 6 0959 0 4 0850 0 5 0822 0 4 0720 O.A FQ1414 4:0 1334 3:5 1607 3:4 LQ1451 3:2 FQ1435 3:3 1321 3.2 2029 -0.1 154 1949 0.4 2201 0.3 2056 0.3 67 2029 0.5 60 1925 0.4 66 65 64 S14 0258 4.2 M29 0212 3.8 VJ14 0443 4.2 W14 0307 4 1 L9 0152 4.1 0908 0 3 8 1107 0.4 0933 0:5 0822 0.4 1520 3:8 LQO 24 0-7 Q 1429 3.4 1712 3.3 1546 3.2 1426 3.2 2128 0.0 2040 0.4 2301 0.3 2134 o.6 S2028 0.3 65 37 so 67 67 M15 0403 4.3 T30 0309 3.9 T15 0541 4.3 T15 0414 4.0 F30 0259 4.2 1018 0.3 0925 0.6N 1205 0.4 N 1041 0.5 0926 0.3 1626 3.6 1527 3.3 1807 3.4 1652 3.2 1535 3.4 61 2225 0.1 so 2134 0.3 so 2355 0.3 61 2238 o.6 67 2135 0.2 W31 0407 4.2 S31 0406 4.4 1026 0.5 1030 0.1 1627 3.4 1641 3.7 S7 2228 0.1 64 2241 0.0 Time meridian 75* W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. 442 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 31a, b, c, d.-Data Used in Evaluating the Increased Length of the Tidal Day at Perigee-Syzygy (Made Comparatively More Effective by the Greater Gravitational Force at These Times) as Plotted on the National Ocean Survey Tide Tablesjor Breakwater Harbor, Del., _7anuary-December, 1962 BREAKWATER HARBOR, DEL., 1962 75 Times and Heights of High and Low Waters APRIL MAY JUNE '11me Ht. '11me Ht. DAY DAY DAY Ti Te-fft.- DAY 11me Ht. DAY Ti@me Ht. DAY Time Ht. h. m. ft. h. m. ft. h. 7n. ft. ---h. m. ft. h. m. ft. h. m. ft. S 1 0510 4.6 M16 0613 3.9 T 1 0545 4.5 W16 0001 0.3 F 1 0108 -0.5 S16 0056 0.1 1129 -0.2 1218 0.3 1155 -0 5 0713 4.1 0655 3.6 1741 4.1 A 1836 3.9 1818 4:8 E 0610 3-7 1207 0.2 1307 -0.5 1246 -0.1 S7 2343 -0.4 35 51 37 1835 4.2 47 1941 5.3 42 1919 4.8 M 2 0607 4.8 T17 0036 0.2 W 2 0027 -0.5 T17 0043 0.1 S 2 0200 -0.5 S17 0139 -0.1 1222 -0.5 0652 4.0 0640 4.6 0650 3.8 0803 4.1 0738 3.6 1836 4.5 1253 0.2 p1245 -0.7 1245 0.1 1355 -0.5 1328 -0.2 SS 3S 1911 4z. 1 so 1909 5.1 36 1912 4.5 4S 2028 5.3 42 2001 5.0 T 3 0041 -0.7 W18 0114 0.1 T 3 0121 -0.7 F18 0124 0.0 S 3 0250 -0.5 M18 0223 -0.2 0702 0729 4.0 0732 4.6 0729 3 8 3.6 1312 -50-70 E -8 NMO853 3-9 FMO 21 327 1333 -0.8 1322 0.0 1442 -0.4 1 1412 -0.3 51 1928 4.9 33 1946 2:'3 47 1959 5.3 37 1948 4.6 4S 2113 5.2 44 2o43 5.1 .135 -0.9 T19 0152 -0.1 F 4 0213 -0.8 S19 0203 -0.1 N 4 0338 -0.4 T19 0308 -0.3 D753 5.0 03 4 M0822 4.5 0807 30 0941 3 8 S 0906 3.7 V400 -0.9 T401 0-00 N 1420 -0.7 1400 -0.1 1528 -0:2 1459 -0.3 49 E2017 5.2 3S 2019 4.4 47 2046 5.4 38 2025 4.8 46 2158 5.0 46 2127 5.1 T 5 0227 -1.0 F20 0229 -0.2 S 5 0304 -0.8 S20 0245 -0.2 T 5 0424 @0.3 W20 0355 -0.3 842 5 38 0 0911 4 3 0846 _3 1029 3.6 0953 3.7 447 _O 0 FMO8 4 FM NW, :9 1435 0:0 1507 -0:6 1438 0:17 N 1615 0.1 1547 -0.2 48 2106 5.3 3S 2054 4.5 47 2133 5.3 41 2103 4.9 47 2244 4.7 so 2213 5.o F 6 0319 -0.9 S21 0307 -0.2 S 6 0354 -0.6 M21 0327 -0.2 W 6 0511 0.1 T21 0442 -0.3 0931 4.7 0914 3.9 1001 4.1 0926 3.6 1119 3.5 1044 3.7 1534 -0.8 1510 0.0 1553 -0.4 1520 -0.1 1703 0.3 1639 -0.2 49 2154 5.2 37 2129 4.6 49 2220 5.1 44 2144 4.9 - 2331 4.4 S4 2303 4.9 S 7 0410 -0.8 S22 0347 -0.2 M 7 0444 -0.4 T22 0412 -0.2 T 7 0558 0.1 F22 0532 -0.3 1021 4.5 0950 3.7 1051 3.8 1009 3.5 1209 3 4 SS 1138 3@7 1R1 -R.5 154? 0.0 1641 -0.1 1603 0.0 1753 0:5 1734 0.0 52 n 3 .1 42 2206 4.6 - 2308 1.8 49 2228 4.8 48 - 2357 4.7 S 8 0502 -0.5 M23 0429 -0.1 T8 0535 -0.2 W23 0459 -0.1 F 8 0019 4.1 S23 0624 -0.3 1112 4.1 1030 5 S 1058 3.5 0645 0.3 1236 3.8 1708 -0.2 1627 30-61 N 11174304 03: 2 1652 0.0 1303 3.3 1835 0.1 - 2335 4.8 47 2248 4.5 52 - 2317 4.7 so 1847 0.7 S7 M 9 0555 -0.2 T24 0515 0.0 a 9 0000 4.5 T24 0549 -0.1 S 9 olog 3 9 S24 0054 4.5 1206 3.7 1114 3.5 0627 0.1 1151 3.5 0733 0:4 P 0719 -0.2 1800 0.1 1712 0.2 1240 3.3 1746 0.2 1356 3 .3 1338 3.9 54 - 2335 4.5 54 1824 0.5 S4 S3 1945 0.8 61 1940 0.2 TIO 0029 4.5 W25 0604 0.1 T10 0054 4.2 F25 0011 4 6 SIO 0202 3.7 M25 0155 4.2 0653 0.1 1204 3.3 0723 0.3 0643 0: Q 0822 4 8 -0.2 3.4 1803 0.3 1340 3.2 1250 3.0 F LQO 16 1306 5 1450 3 4 1443 4.1 58 1855 0.4 S4 58 1923 0.7 S9 1847 0.2 S3 2043 0.8 6S 2048 0.2 011 0127 4.2 T26 0029 4.,j Fil 0152 3.9 S26 0110 4.4 M11 0255 3.6 T26 0300 4.1 N 0755 0.4 07 1 0 2 0819 0.4 0?41 0 9 4 0913 -0.2 411 3.2 S 13003 3:3 1442 3.2 1355 3:60 A 090 0: E 1 1541 3 6 1546 4.4 64 1956 0.6 60 1902 0.3 S9 2026 0.8 64 1954 0.3 48 2140 0.? 61 2157 0.1 T12 0231 4.0 F27 0129 4.3 SIZ 0251 3.7 S27 0214 4.3 T12 0349 3.5 W27 0403 3.9 FQ0901 0 5 0801 0.2 F Q0914 0.5 L Q 0840 -0.1 0956 0.3 1009 -0.2 1520 3:2 1409 3.4 1540 3.3 1502 3.9 1629 3.8 1647 4.6 2102 0.8 2008 0.3 2129 0.8 2103 0.2 2233 0.6 2302 0.0 66 66 se 66 4S 62 F13 0337 3.8 S28 0235 4.3 S13 ?349 3.2 M28 0320 4.2 Va3 0439 3.5 T28, 0505 3.8 1002 0.5 4 0 1 003 0 b 0939 -0 2 1040 0.3 1104 -0.3 1622 3.3 LQ 090 1632 3:5 1605 4:2 1?14 4.1 1743 4.8 1518 3 6 60 2206 0.7 68 2118 0.2 4S 2225 0.7 S7 2210 0.1 43 2323 0.4 52 S14 0437 3.8 S29 0343 4.3 M14 0441 3.7 T29 0424 4.2 T14 0526 3.5 F29 0003 -0.1 1056 0.5 1004 -0.1 A 1049 0- 4 E 1035 -0.3 1123 0.2 0603 3.8 1714 3.4 1623 3.9 1717 3.8 1704 4.5 1757 4.3 115? -0.3 S1 2304 0.6 63 2225 ox 41 2316 0.5 S6 2314 -0.1 41 so 1835 5.0 S15 0528 3.9 M30 0446 4.4 T15 0528 3.7 1,130 0524 4.2 F15 0010 0.2 S30 0058 -0.2 1140 0.4 1102 -0.3 1130 0.3 P 1128 -0.4 0611 3.5 0658 3.8 1759 3.? 1723 4.4 1758 4.0 1800 4.9 12o4 0.0 1247 -0.3 4S 2354 0.4 5S 2328 -0.3 37 51 41 1838 4.6 46 1925 5.1 T31 0013 -0.3 0620 4.2 1219 -0.5 1851 5.1 so Time meridian 75' W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 443 TABLE 31a, b, q d.-Data Used in Evaluating the Increased Length of the Tidal Day at Perigee-Syzygy (Made Comparatively More Effective by the Greater Gravitational Force at These Times) as Plotted on the National Ocean Survey Tide Tablesfor Breakwater Harbor@ Del., .7anuary-December, 1962 76 BREAKWATER HARBOR, DEL., 1962 Times and Heights of High and Low Waters JULY AUGUST SEPTEMBER Time Ht Time Ht. Time Time Ht. Time Time Ht. DAY DAY DAY DAY DAY DAY h. m. ft. h. m. f t. h. m. ft. h. m. ft. h. m. f t. h. m. f t. S 10148 -0.3 M16 0115 -0 1W 10255 -0.1 T16 0223 -0.6 S 1 0331 0.0 S16 0330 _0 9 0749 3.7 0711 3 6 NMOB59 3 7 FM 0828 4.3 0941 4.0 0946 5:1 1334- -0.2 1303 -0:3 1446 O:o 1427 -0.7 1542 O.o 1558 -0.8 44 2011 5.1 46 1938 5.1 38 2114 4.6 47 2053 5.3 3S 2157 4.2 S2 2209 4.8 k 20235 -0 3 J7 0201 -0.3 T 20332 0.0 F17 0310 -0.8 2 G403 0.0 M17 0417 -Oo8 M0836 3:7 0759 3.7 0937 3.7 P 0917 4.5 4 1016 4.0 1038 5.0 1421 -0.2 1352 -0.4 1528 0.1 1519 -0.8 IL-1622 0.1 1652 -0.6 2055 5.0 2024 5.2 2152 4.5 2140 5.2 38F-2232 4.0 2302 4.4 42 @m 37 so S4 T 30319 -0.2 W18 0247 -0.4 F 30408 Ooo S18 0357 -0.8 M 3 0439 0.1 T18 0506 -0.5 0921 3.6 0847 3.9 1015 3o7 1007 4.6 1054 4.0 1132 4.9 1506 0.0 1442 -0.5 16@9 @.2 16 3 -0.7 1703 0.2 1749 -0.3 2137 1.8 2110 5.3 22 9 .3 W 5.0 2309 3.7 2357 4.0 41 48 38 52 41 58 W 40402 -0.1 T19 0334 -0.5 S 40444 0.1 S19 0445 -0.7 T 4 0516 0.2 W19 0558 -0.2 1004 3 6 2936 4 0 1100 4.6 1135 4 0 12 4.7 1551 0:1 533 -0:5 12'5t 'O:K E 1708 -0.5 1748 0:4 18 0 0.0 2218 4.6 2158 5.2 2307 4.1 2322 4.6 23P0 3.5 43 so 40 5S 45 63 T 5T442 F20 421 -0 6 S 50521 0.2 M20 0534 -0.6 W 5 0556 0.3 T20 0058 3.7 049 9:05 P T027 4: 1135 3.7 1155 44 1220 3.9 0655 0.1 2 1626 -0 1 A 1636 0. .4 1736 0.4 1805 -0.2 1837 0.5 1333 4.4 42 2301 4.4 52 2248 5.0 - 2347 3.9 60 so 68 1959 0.2 F 60523 0.1 S21 0510 -0.5 M 60600 0.2 T21 0017 4.3 T 6 0036 3.3 F21 0205 3.4 1134 3.5 1121 4 2 1218 3.7 0626 -0.3 0642 0758 0 3 _ 3 1823 0.5 1255 4.5 1310 0-4 LQ 1722 0.4 1722 0: E 3.9 1441 4 3 2343 4.1. 2340 4o7 1908 0.0 1933 0.6 2111 0.4 43 63 S6 68 S 70603 0.2 S92 0601 -0.4 T 70030 3.6 W22 0117 3.9 F 7 0129 3.1 S22 0319 3.2 1219 3.5 1218 4.2 0642 0722 -0 0733 0 4 0905 0.5 1810 0.5 1821 -0.1 1: 0-3 LQ :1 FQ : N 9@5 3.7 1358 4 4 1406 4 0 1549 4.2 1 4 0.6 2017 0.2 2033 0.6 2220 0.4 45 57 53 66 62 63 S 80028 3.9 M23 0037 4.4 W 80117 3.4 T23 0222 3.6 S 8 0229 3.1 S23 0429 3.3 '2646 0654 -0 3 72? 0 4 0822 Ool 0831 0.4 1012 0.5 A 307 9-53 E 1318 4:3 ?357 3:8 1504 4.4 1508 4.1 1652 4.2 1902 0.7 1925 0.1 2010 0.7 2129 0.3 2136 0.5 2319 0.3 47 59 S4 68 61 S3 M 90115 b.7 T24 0136 4.1 T 90208 3.3 FZ4 0333 3 4 S 9 0334 3.1 M24 0527 3.4 0731 0 3 0750 -0 2 816 0.4 0926 0:2 S 0931 0 3 1112 0.4 E1356 3:6 LQJL421 4:3 FQ01451 3.9 1612 4 .4 1609 4:3 AE1745 4.2 48 1957 0.7 6S 2033 0.2 S7 2109 0.7 61 2239 0.3 S8 2235 0.3 4S Tlo 0203 3.5 W25 0240 3.8 Flo 0305 3.2 S25 0441 3.3 M10 0437 3.3 T25 0005 0.2 0817 0 4 0848 -0 1 09GS 0.3 1029 0.3 1032 0.1 0614: 3.6 F Q 1448 3:7 1526 4:4 1548 4.1 1713 4.4 1707 4.6 1203 0.3 S2 2054 0.7 63 2143 0.2 5S 2207 0.6 S3 2340 0.2 S6 2331 0.0 40 1830 4.2 Val 0257 3.4 T26 0346 3.6 Sli 0404 3.2 S26 0542 3.4 Tll 0534 3.7 W26 0045 0.1 0904 0.3 0946 0.0 1002 0.2 1128 0.2 1130 -0.2 0655 3.8 1540 3.9 1629 4.5 1643 1.3, N 1806 4.5 1803 4.8 1246 0.2 S6 2150 0.7 59 2251 0.2 53 2305 0.3 46 S1 36 1910 4.3 T12 0351 3.3 F27 0452 3.5 S12 0502 Zo3 M27 0032 0.1 W12 0023 -0.3 T27 0119 0.1 0952 0.3 1045 0.0 1058 0.1 0634 3.5 0628 4.0 0730 3.9 1630 4.1 1.728 4.7 1736 4.6 1219 0.2 1226 -0 5 1325 0.1 49 2245 0.5 S4 2353 0.1 S1 2359 0.1 42 1854 4.5 so 1854 5:1 36 1946 4.3 F13 T443 3 3 S28 0552 3 5 M13 0557 3.5 T28 0114 0.1 T13 0110 -0.6 F28 0150 0.0 040 0:2 1140 0:0 S 1151 -0.2 0718 3.6 0718 4.4 0802 4.1 1719 4.3 1822 4.8 1827 4.9 1304 0.1 1319 -0.7 1402 0.0 45 2337 0.3 49 49 37 1936 4.5 48 1944 5.2 33 202o 4o2 S14 0534 3.4 S29 0047 0.0 T14 0049 -0.2 W29 0151 0 0 F14 0157 -0.8 2 0221 ooo 11180284 04'.06 N .0646 3.5 0649 Z.8 0757 3:8 FM 0807 4.7 NMO836 Ir 4.2 1232 0.0 1243 -0.4 1345 0.0 1412 -0 1439 - 0.0 1911 4.8 1916 5.1 2013 4.5 2032 5:2 2053 4.1 48 44 48 36 49 9 12 S15 0027 0 1 m3o o134 ox W15 0136 -0.4 T30 0225 OoO S15 0243 -0.9 S30 0253 0.0 0623 3.:5 0735 3.6 0739 0832 3.9 P 0857 5.0 0908 4.3 1319 0.0 1335 -'-0 NM 1216 -0.1 0.6 1425 0 0 1504 -0.-9 1516 0.0 1852 4.9 1955 4.8 2004 5.3 2049 4:4 E2121 5.1 2125 4.0 46 41 49 34 48 3S T31 0216 -0.1 F31 0259 0.0 0819 3.6 0906 3.9 1403 0.0 1503 0.0 2036 4.7 2123 4.3 39 34 Time meridian 75' W. 0000 Is midnight. 120o Is noon.. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. 444 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 31a, b, c, d.-Data Used in Evaluating the Increased Length of the Tidal Day at Perigee-Syggy (Made Comparatively More Effective by the Greater Gravitational Force at These Times) as Plotted on the National Ocean Survey Tide Tablesfor Breakwater Harbor, Del., january-December, 1962 BREAKWATER HARBOR, DEL., 1962 77 nmes and Heigbts of High and Low Waters OCTOBER NOVEMBER DECEMBER Time Ht. - Time Ht. Time Ht. Time Ht. ISim- Ht. I "me Ht. DAY h. m. ft. DAY h. m. ft. DAY h. m. ft. DAY h. m. ft. DAY h. m. ft. DAY h. m. ft. M 10326 o.o T16 0351 -0.8 T 1 0404 0.1 F16 0506 0. 0943 4.3 1016 5.3 1029 4.5 0 S 1 0425 0.0 S16 0532 0.3 1139 4.7 1054 4.7 1203 4.3 1555 0.0 1636 -0.6 1656 0.1 N 1808 0.0 1725 0.1 1828 0.2 3S 2159 3.8 52 2242 4.2 4S 2250 3.3 se so 2320 3.4 51 T 20400 0.1 W17 0439 -0.5 F 2 0447 0-2 S17 0014 3.4 S 2 0515 0.1 M17 00,39 3.4 1018 4.3 1108 5.o 1114 4 4 0600 0.3 1144 4.6 0625 0.5 1635 0.1 1732 -0.3 1744 0:3 1235 4.4 1816 0.1 1254 4.0 40 2236 3.6 se 2337 3 ..8 49 2338 3.2 60 1905 0.2 S6 S3 1918 0.3 W 30437 0.2 TIS 0531 -0.1 S 3 0534 0 3 S18 0117 3.3 M 3 0015 3.4 T18 0134 3.3 1058 4.2 1204 4.7 .5 1203 4:3 0659 0.6 0612 0.2 0723 0.7 1719 0 3 1831 0.0 1838 0.3 1335 4.1 1240 4.4 1347 3.8 2316 3:4 2004 0.3 1911 0.1 2008 0.4 44 61 S9 62 CIO T 40517 0.2 F19 0038 3.5 S 4 0034 3.2 SS 1142 4.2 0627 0.2 0630 0.4 M19 0222 3.2 T 4 0117 3.5 W19 0230 3.4 0803 0,.7 0716 0.3 1 9% 0822 0.8 1807 o.4 N 1305 4.4 1302 4.3 LQ1437 3.9 1340 4.3 m-'04 1442 3.6 soI.,- CA 1936 0.2 63 1937 0.3 S9 2103 0.4 es 2009 0.0 S4 2058 0.5 F 50002 3 2 S20 0146 3.3 M 5 0137 3 2 T20 0324 3.3 W 5 0223 3.7 T20 0325 3.5 0602 0730 0.5 0734 0:4 0909 0 3 0921 0.8 1232 04.14 LQ1411 4.1 F Q-41405 4.2 0-8 FQ08P,4 : E 1536 3.7 1445 4 2 3.5 1902 0.5 2044 0.4 2038 0.2 2155 0.4 2108 -0 .1 2145 0.4 S8 Go 67 S3 64 51A1536 S 60057 3.1 S21 0258 3.2 T 6 0245 3.4 W21 0418 3.5 T 6 0329 4.0 F21 0416 3.7 0657 0.4 0838 0.7 0843 0 3 1010 0.7 0933 0.2 1017 0.7 1330 4.1 1519 4.0 1512 4:3 1629 3.7 1549 4.2 1627 3.5 64 2003 0.5 61 2148 0.4 63 2137 0.0 47 2240 0.4 62 2204 -0.3 47 2230 0.3 7 0200 3.1 M22 0403 3.3 W 7 0351 3 7 T22 0505 3.7 F 7 0431 4.4 S22 0503 3.9 0759 o.4 0946 0.7 0951 0:1 1103 0 6 1039 0 0 WS1110 0.6 1434 4 1 1620 3 9 1615 _4 4 1716 3:7 E 1651 4:2 1715 3.5 1 2106 0:4 2244 0:4 2234 0:2 65Q S3 M 41 2320 0.3 S7 2259 -0.4 43 2313 0.2 M 80308 3.2 T23 0459 3.5 6 0452 4.2 F23 0546 4.0 S 8 0528 4.7 S23 0546 4.2 4 1047 0.6 .1056 -0.1 1149 0.4 1141 -0.2 1158 0.4 T999 0 1713 3.9 1714 4.5 A 1759 3.7 1749 4.2 1801 3.5 62 2206 0.2 46 2328 0.3 SS 2326 -0.5 3SE2357 0.1 54 2352 -0.6 42 2354 0.1 T 92414 3.5 W24 ?5" 3.7 F 9 0547 4:6 S24 0624 4.2 S 9 0622 5.1 M24 0628 4.4 010 0.1 138 0 5 1155 -0 4 1641 4.5 1759 4: E 1231 0.2 0 1238 -0.4 1243 0.2 58 2303 -0.1 39 0 S2 1809 4.6 37 1837 3.7 0S2 1844 4.2 39 1643 3.5 W10 0513 3-9 T25 0005 0.2 S10 0016 -0-7 S25 0033 0.1 M10 0042 -0.7 T25 0035 0.0 1112 -0.2 0624 3.9 0639 5.0 0701 4.4 0714 5.3 0707 4.6 1739 4.7 1222 0.3 1251 -0.6 1310 0.1 1332 -0.5 1325 0.1 S3 2355 -0.4 35 1838 4.0 S1 1901 4.6 3S 1915 3.7 48 1936 4.2 41 1925 3.5 T11 0607 4.4 F26 0039 0.1 S11 0103 -0-9 M26 0107 0.0 T11 0130 -0.7 W26 0115 -0.1 1210 -0.5 o659 4.1 P 0730 5.3 0736 4. 0802 5.4 0748 4.8 1832 4.9 1301 0.1 13" -0.8 1350 0.60 FM1424 -0.6 1406 0.0 S1 33 19 .13 4.o 48 1952 4.6 36 1952 3.7 49 2027 4.1 '40 2004 3.6 F12 0043 -0.7 S27 0111 0.0 M12 0151 -0-9 T27 0144 -0.1 W12 0218 -0.6 2@0156 -0.2 0658 4 0732 4.3FM 0818 5 5 812 4.7 0851 5.4 0828 4.9 1304 -0:88 E 1337 0.0 14.37 -0:8 NMO1430 0.0 1515 -0.5 1451 -0.1 48 1923 5.0 33 1948 4.0 49 2042 4.4 37 2029 3.6 47 2116 4.0 k4 2046 3.6 S13 0129 -0.9 S28 0143 0.0 T13 0239 -0.8 W28 0220 -0.1 T13 0305 -0.5 F28 0239 -0.3 0748 5 1 0805 4 4 0907 5.5 0849 4 0938 5.2 0908 5.0 1358 _O 9 1414 0 0 -8 N E 1528 -0.7 1511 -0.1 1603 -0.4 1534 -0.2 P 2011 5.0 2021 3.9 2132 4.2 2107 3.5 2204 3.8 2129 3.7 49 34 49 38 47 44 S14 0216 -1.0 M29 0217 -0.1 W14 0326 -0-6 T29 0259 -0.1 F14 0354 -0.3 S29 0324 -0.3 FMO837 -5 4 0839 4.5 0956 5.3 0927 4.8 1025 5.0 0952 5.0 1450 0:9 NM1452 0.0 1620 -0.5 1553 0.0 1652 -0.2 1618 -0.2 49 2101 [email protected] 34 2056 3.8 so 2223 3.9 2147 3.5 2254 3.6 2215 3.7 M15 0302 -0.9 T30 0251 -0.1 T15 0414 -0A 41 49 46 0926 5.4 - F30 0340 -0.1 S15 0442 0.0 S30 0411 -0.2 0913 4.6 1046 5.0 S 1008 4.8 1114 4.6 .1038 4.9 1543 -0.8 1531 0.0 1713 -0.3 1637 0.0 1739 0.0 1704 -0.2 2150 4.5 2131 3.6 2317 3.7 22,31 3.4 2346 3.5 2304 3.7 so 36 S3 46 49 49 W31 0326 0.0 M31 0502 -0.1 094:9 4.6 1127 4.7 1612 0.0 1754 -0.2 40 2208 3.5 1 Time meridian 75' W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 445 and Sun at perigee-syzygy, which act to produce aug- curve trough between two crests is clearly due to the com- mented high waters and thus enhance their susceptibility pensating effect of perigee in speeding up the Moon's to tidal flooding. Accordingly, its influence should be re- orbital velocity, increasing the necessary catch-up time of flected in the calculated value of the Aw-syzygy coefficient, the rotating Earth, and thus lengthening the tidal day. if this is to become a meaningful index of astronomical Further, the large 7r defines a condition of proxigee. tidal flooding potential. . The maximum increase in the tidal day at proxigee- One of the worst instances of tidal flooding in recorded syzygy (NM) on March 6.1975 (e.s.t.), compared with history occurred along the mid-Atlantic coast on 1962 that at exogee-syzygy (FM) on March 20.3944 (e.s.t.) is March 6-7. The unusually high proxigean spring tide 16m. The difference involved is larger than that for any created at this time, assisted by an increased tidal day, was other lunation except that containing the date September raised to severe flooding proportions by strong, persistent, 14.2374 (e.s.t.), when another perigee-syzygy alignment onshore winds which lasted through five successive high occurs at full moon. This case has a separation-interval of tides. (See chapter 7 for the flooding details published in 11.8" with an accompanying parallax of 7r=61'22.233" newspaper accounts of this catastrophic event, as well on September 14.2. The difference.in the length of the as associated weather maps, pictures of the flooding, and tidal day between perigeeand apogee is again 16- (fig. hourly height tide data corresponding to the dates in- 152b). volved.) The astronomical contributions to this extremely The incremental values of 15M on February 5.2541 vulnerable tidal flooding event are revealed among the (e.s.t.), and April 4.1406 (e.s.t.), correspond to two other various data and graphs covering this case. The evaluation perigee-syzygy dates in the year, with separation-intervals of the flooding potential 11 is shown in table 30. Table of 21.8" and -22.8", respectively. The third 15 n, incre- 32a gives thepredicted tide heights. Fig. 161a depicts the ment on October 13.1156 (e.s.t.) is associated with yet corresponding rate-of-growth tide curves. Similar data another perigee-syzygy alignment in this same unusual are provided for the rest of the year in tables 32b,c,d and year, having a separation-interval of -9.6" and a value fig. 161b to provide a controlled basis for comparison. of 7r=61'25.808" on October 12.8 (e.s.t.). In this example, an extremely close proxigee-syzygy The corresponding values of the Aco-syzygy coefficients alignment which occurred at a mean epoch of March for each of the above dates, as derived from table 16, are 6.1975 (e.s.t.), having a separation-interval of only all above average. Thus, the Aw-syzygy coefficients not - 3 1 m, resulted in a lunar parallax value of 7r = 6 1'26.6" only indicate very accurately the times of production of on March 6.19 (e.s.t.). The position of perigee (labeled P perigean (or proxigean) spring tides but (as a direct func- in table 32a) occurred at March 6.1868; syzygy (labeled tion of their magnitudes) denote, in relative degree, the NM in the same table occurred at March 6.2083 @e.s.t.). amplified heights of the high waters which result. The highest high water (5.3 ft at Breakwater Harbor) Various other astronomical influences resulting from was predicted for 0813 (e.s.t.) on March 6. The next succeeding higher high water (of the same height) was the changing interrelationships of the Moon and Sun predicted for 0902 (e.s.t.) on March 7. The difference may be studied in detail by the combined use of tables between these two times is 49- which, when added to the 31a,b,c,d and figs. 152a,b. In these tables, the follow- 24" of elapsed time between the consecutive days, ex- ing symbolic designations are used: presses the total interval separating the peaks, of immedi- S = the date on which the Moon is at its greatest ately succeeding higher high waters. This period is equiva- declination south of the Equator lent to the length of the tidal day. E@the date on which the Moon crosses the In fig. 152a, it will be noted that this increment of 49' Equator represents the minimum value in a curve trough located N@ the date on which the Moon is at its greatest between two peaks. As described in the discussion on declination north of the Equator similar tide curves (p. 303), each minimum in the series P= the date of perigee (or proxigee) of which this is a part is due to the effect of tidal priming A = the date of apogee (or exogee) in reducing the tidal day. However, among the total array NM=new moon of, minima appearing throughout the year, it will be ob- FQ=first quarter moon served that those occurring close to a time of perigee- FM=full moon syzygy are located farthest above a baseline corresponding LQ=Iast quarter moon to the next succeeding apogee-syzygy. This uplifting of a VE =the vernal equinox 446 Strategic Role of Perigean Spring Tides, 1635-1976 J-85 (a) VARIATION IN DECLINATION OF MOON AND SUN-1962 +20r Z+Icr 0 fill It If lit z a ............... .................... ....................i................... 'A ................ ................ ................ ...................A.................. ................... if ........... r C) -1 Cr .20f *A 0 y Y 0 A* Y 0 A 0 Y 0 A 80 BREAKWATER HARBOR, DELAWARE 1962 70 V) w z 60 Z 50 LL 0 F- 0 40 z Z y z LU 230 cc U z 20 JAN FEB MAR APR MAY JUN 1 7 14 21 281 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 281 7 14 21 28 FIGURE 15 2a.- (Discussed in text.) Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 447 J-85 (b) VARIATION IN DECLINATION OF MOON AND SUN .1962 20f. Z'i a 11 it lot %\ 0 It It it z Ai ................ .................. %................... ..........% .....................%...................L..........I............... Of i ............I% 1 1% 1 1 III It w 11 It -1 op -20P Y OA 0 Y 0 ey 0 yO Y AO 0 A A 80 BREAKWATER HARBOR, DELAWARE w 1962 8C 70 w Z 2 60 Z 8 50 ----- ---- ---- ----- ---- - --A ---- ---- ----- ----- ---- ---- ---- ----- ----- LL 0 13 16 16 z 40 U.1 w 230 w cc L) Z 20 JUL AUG SEP OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21- 281 7 14 21 281 7 14 21 28 FIGURE 152b.- (Discussed in text.) 448 Strategic Role of Perigean Spring Tides, 1635-1976 SS= the summer solstice In contrast with the previously constructed curves involv- AE =the autumnal equinox ing the length of the tidal day, however, the present curves WS= the winter solstice utilize the average rate of tide rise at a given station during any day of the year as the ordinate value. Depend- The symbols used in figs. 152a,b are indicated in the ing upon the characteristic type of tide found at the legend accompanying fig. 153a. At the top of each of station, one of two different procedures is used in the these composite diagrams, the continually varying decli- ensuing analysis. nations of both the Moon and Sun are plotted to the same scale as that used for the changing lengths of the 1. Semidiurnal Tide tidal day in the bottom portion of the diagram. A direct To achieve the appropriate curve-plotting values in this analysis of any contribution to the length of the tidal day case, the difference (in feet or meters) is taken between made by the changing lunar declination, or by the the predicted level of the lowest low water for any given declinational influence of the Sun, is thus possible. date and that of the highest high water next following An obvious disruption of the otherwise uniform, double it (even if this HHW occurs early in the'moming of the crests of the curves which occur individually near the next succeeding date). As will be explained in the next Moon's semimonthly positions of quadrature is evident section, if-as frequently happens on the west coast of at the time of the summer solstice. The resulting curve North America-the lower high water (LHW) sequen- irregularities are clearly due to a superposition of the tially follows the lowest low water, a slightly different diurnal influence of the Sun, exerted at a time when the procedure is used. Negative low-water values (indicating solar body is at its maximum positive declination (i.e., water levels below the standard chart datum) are, of at its greatest incursion into the Northern Hemisphere) course, treated algebraically in making the subtraction while the Moon is at a large southern declination. leading to the total maximum rise in water level. (See In fig. 152a, a bifurcated curve peak occurs shortly tables 32a, b, c, d.) after the summer solstice on June 21, 21'24-. This is To obtain the average rate of rise, it only remains to followed by a jagged and not readily identifiable mini- subtract the time of LLW for any date from the time mum about the middle of July as the Moon and Sun of the next succeeding HHW, and to divide the difference again move to nearly maximum opposing declinations. into that giving the corresponding change in water level This effect is not as pronounced when the Sun reaches over this same time interval. The resulting quotient is its maximum negative declination at the winter solstice plotted against the appropriate date on the abscissa axis (December 22, 08'15m). Since the Sun is then in the of the diagram. Southern Hemisphere, its influence on the Northern Because of the sizable task of extracting and plotting Hemisphere tides is somewhat reduced. these differences and quotients in each case for 365 days With the Sun and Moon nearly at the same declina- in the year, various representative examples from among tions and crossing the Equator on March 21 and 22, re- the 100 cases of tidal flooding noted in table I have spectively, the heights of the two adjacent crests on either been used to show the resulting correlations. Table 33 lists side of these dates are very nearly equal. As the dates of appropriate standard tide-prediction stations either at the the summer and winter solstices are approached, the scene of the flooding or close thereto. The principal. re- heights of any two contiguous peaks become the most quirement in the selection is that these examples be vari- disparate. ously typical of observed tidal flooding conditions. The examples are randomly distributed in time, including one Accelerated Rate of Tide Rise as an Indica- from each decade over the 56-year period from 1918 to tion of Increased Tidal Flooding Potential 1074, in latitudes ranging from Halifax, Nova Scotia The most significant of the empirical factors giving (44'40" N.), to Los Angeles, Calif. (33'43' N.), are lo- credibility to the use of the A--syzygy coefficient is its cated on both the Atlantic and Pacific coasts of North close relationship with a significantly increased rate of America, occur during all winter months of the year from tide rise at times of perigee-syzygy. Curves of rapidly ac- October to April, and at various times of the day and celerating tide growth may, in turn, be demonstrated to night. have a very real positive correlation with actual tidal Tables 32a,b,c,d show a sample of the method of tak- flooding events. ing the requisite time differences (the tidal height differ- The point of departure for verifying this relationship ences are similarly established for these same intervals) - is, again, basic data abstracted from the annual tide tables. Figs. 153-163 depict the predicted curves of astro- Ti dal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 449 TABLE 32a, b, c, d.-Data Used to Determine the Accelerated Rate of Tide Rise at Times of Perigee-Syzygy, Superimposed on the National Ocean Survey Tide Tablesjor Breakwater Harbor, Del., January-December, 1962 74 BREA1(WATER HARBOR, DEL., 1962 Times and Heights of Hijh and Low Waters JANUARY FEBRUARY MARCH 'nme Ht. Time Ht. nme Ht. Time Ht. Time Ht. Time Ht. DAY DAY DAY DAY DAY DAY h. m. ft. h. m. ft. h. m.' ft. . h. M. ft. h. m. ft. h. m. ft. M 1 ?35 T16 0504 4 4 T 1 0504 4.5 F16 0631 4.4 T 1 0330 4.2 F16 0515 4.0 009 '0:9 1124 0:3 1125 o.2 1253 0.3 0954 0.4 1138 0.5 1612 3.5 1727 3.6 1725 3.5 1855 3.5 1558 3.3 1747 3.4 99 2217 0.2 113 2320 0.1 127 2323 -0.2 107 109 2158 0.1 92 2334 0.5 T 2 0450 4.1 W17 0600 4.6 F 2 0558 4.8 S17 0041 0.2 F 2 0433 4.4 S17 0605 4.1 1102 0.4 1222 0.2 1220 0.0 0715 4.4 1057 0.2 1223 0.4 1704 3.5 1822 3.5 1820 3.7 1333 0.2 1701 3.5 1832 3.5 112 2304 0.0 115 140 113 1936 3.6 122 2300 -0.1 101 W 3 0538 4.4 1-18 0010 0.1 S 3 0016 -0.4 S18 0123 0.1 S 3 0533 4.7 S18 0021 0.3 1155 0.2 0649 4.7 0650 5.1 0754 4.5 1155 -0.1 0649 4.2 1755 3.6 1312 0.1 1312 -0.3 1 0 1 1800 _3 9 1301 0 3 02 3 7 2359 0 4 1910 3 7 127 2352 -0.2 119 1911 3.6 isi 1913 4.0 116 20 : 138 104 T 4 0625 4.8 F19 0057 0.0 S 4 0109 -0.6 M19 0202 0.0 S 4 0629 5.0 M19 0102 0.2 5 733 4.? ?741 5 3 830 4 5 1248 -0.4 072B 4.2 18,43 9:9 H55 0.1 40 -0:5 T443 0:1 1854 4.2 1334 o.2 137 119 1954 3.6 162 2003 4.2 114 2046 3.8 lS2 113 1945 3.9 F 5 0039 -0.4 S20 0139 0.0 M 5 0201 -0.8 T20 0239 0.0 M 5 0054 -0.7 T20 0140 0.o 0712 5.0 0814 4.7 0830 5.5 - 0904 4.4 0722 5.2 0802 4.3 1333 -0.2 1434 0.1 1451 -0.7 1516 o.1 133B -0.6 1407 0.1 148 1932 3.8 120 2034 3.6 164 2054 4.4 113 2120 3.9 161 1947 4.5 lie 2017 4.0 S 6 0127 -0.5 S21 0220 0.0 T 6 0254 -0.9 W21 0317 0.0 T 6 0148 -0.9 W21 0217 -0.1 0759 5.3 08.52 4.7 0919 5.4 0938 4.3 0813 5.3 0836 4.3 1421 -0.4 1511 0.1 1539 -0.8 1548 0.1 1427 -0.8 1439 ox 153 2020 4.0 lis 2111 3.6 159 2144 4.5 ill 2154 3.9 165 2036 4.8 115 2050 4.2 S 7 0215 -0.6 M22 0300 0.0 W 7 0346 -0.8 T22 0355 0.0 W 7 0241 -1.0 T22 0254 -0.1 0846 5.4 0929 4.6 1009 5.3 1013 4.2 0902 5.3 0909 4.2 1510 -0.5 1547 S.1 1627 -0.7 1622 0.1 1514 -0.9 1511 0.0 2109 4.0 2148 .6 2236 4.6 2229 4.0 2126 5.0 2123 4.2 lS7 114 149 107 161 lis M 8 0305 -0.7 T23 0339 0.1 T 8 0439 -0.7 F23 0434 0.1 T 8 0333 -1.0 F23 0331 -0.1 2g34 5 4 5 4 5 1101 5.0 1049 4 1 951 5 1 0943 4 1 00 -0:6 12% 0:1 1716 -0.6 1657 0:2 3602 -0:8 1545 0:0 2200 4.1 2225 3.6 2330 4.6 2307 4.0 2215 5.0 2158 4.3 lS3 109 132 100 149 112 T 9 2358 -0.6 W24 0419 0.1 F 9 0535 -0.4 S24 0515 0.2 F 9 '0425 -0.8 S24 0409 -0.1 024z 5.3 1043 4.3 1154 4.6 1126 3.9 1041 4.8 1018 3.9 1649 -0.5 1700 0.2 1806 -0.4 1735 0.2 1649 -0.6 1620 0.1 142 2253 4@1 100 2304 3.6 126 so 2348 3.9 131 2307 4.9 112 2234 4.3 W10 0451 -0 5 T25 0501 0.3 SIO 0026 4.4 S25 0600 0.3 310 0519 -0.5 S25 0450 0.0 1117 5:0 1121 4.1 0634 -0.2 1207 3.6 1133 4.4 1056 3.? 1741 -0.4 1738 0.3 1250 4.2 1817 0.3 1738 -0.4 1658 0.1 127 2349 4.1 93 2344 3.6 117 1900 -0.2 9s 133 94 2314 4.3 T11 0548 -0.2 F26 0545 0.4 S11 0126 4.3 M26 0034 3.9 S11 0001 4.7 M26 0534 0.1 1213 4.7 1202 3.9 0738 0.1 0650 0.4 0615 -0.2 1137 3.5 1834 -0.3 '1818 0.3 1351 3.8 1254 3.4 1228 4.0 1740 0.2 1958 0.1 1904 0.3 1829 -0.1 116 86 104 94 116 105 F12 0050 1.1 S27 0030 3.6 M12 0231 4.2 T27 0126 3.9 M12 0058 4.4 T27 0000 4.2 0651 0.0 0633 0.5 0847 0.3 0747 0.5 0716 0.1 0623 0.3 1311 4.4 1246 3.7 1458 3.5 1349 3.3 1328 3.6 1225 3.3 1931 -0.2 1901 0.4 2059 o.2 1958 0.4 1927 0.2 1828 0.3 113 as 100 93 102 102 S13 0152 4.1 S28 0118 3.7 T13 0338 4.2 W2B 0226 4.0 T13 0200 4.2 VJ28 0052 4.2 0758 0.2 0726 0.6 0959 0.4 0850 0.5 0822 0.4 0720 0.4 1414 4.0 1334 3.5 1607 3.4 1451 3.2 1435 3.3 1321 3.2 *2029 -0.1 1949 0.4 2201 0.3 2056 0.3 2029 0.5 1925 0.4 ill 89 97 99 90 96 S14 0258 4.2 M29 0212 '3.8 W14 0443 4.2 W14 0307 4.1 T29 0152 4.1 0908 0.3 0824 0.7 1107 0.4- 0933 0.5 0822 0.4 1520 3.8 1429 3.4 1712 3.3 1546 3.2 1426 3.2 109 2128 0.0 90 2040 0.4 100 2301 0.3 as 2134 0.6 100 2028 0.3 M15 0403 4.3 T30 0309 3.9 T15 0541 4.3 T15 0414 4.o F30 0259 4.2 1018 0.3 0925 o.6 1205 0.4 1041 0.5 0928 0.3 1626 3.6 1527 3.3 1807 3.4 1652 3.2 1535 3.4 2225 0.1 2134 0.3 2355 0.3 2238 0.6 2135 0.2 113 99 104 so 107 L,131 0407 4.2 S31 0406 4.4 1026 0.5 1030 0.1 1627 3.4 1641 3.7 2228 0.1 2241 0.0 ill 118 Time meridian 75' W. 0000 is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. 202-509 0 - 78 - 31 450 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 32a, b, c, d.-Data Used to Determine the Accelerated Rate of Tide Rise at Times of Perigee-Syzygy, Sup@rimposed on the National Ocean Survey Tide Tablesfor Breakwater Harbor, DeL, .7anuary-December, 1962 BREAKWATER HARBOR, DEL., 1962 75 Times and Heights of High and Low Waters APRIL MAY JUNE Time Ht. Time Fit. Time Ht. Time Ht. Time Ht. Time Ht. DAY DAY DAY DAY DAY DAY h. m. ft. h. m. . ft. h. m. ft. h. m. ft. h. m. ft. m. ft. S 1 ?510 4.6 M16 0613 3.9 T 1 0545 4.5 K6 0001 0.3 F 1 0108 -0.5 S16 0056 0.1 129 -0.2 1218 0.3 1155 -o.5 0610 3.7 0713 4.1 0655 3.6 1741 4.1 1836 3.9 1818 4.8 1207 0.2 1307 -0.5 1246 -0.1 13S 2343 -0.4 103 isi 114 1835 4.2 148 1941 5.3 132 1919 4.8 M 2 0607 4.8 T17 0036 0.2 W 2 0027 -0.5 T17 0043 0.1 S 2 0200 -0.5 S17 0139 -0.1 1222 -0.5 0652 4.0 0640 4.6 0650 3.8 0803 4.1 0736 3.6 1836 4.5 1253 0.2 1245 -0.7 1245 0.1 1355 -0.5 1328 -0.2 1911 4.1 1909 5.1 1912 4.5 2028 5.3 2001 5.0 ISO ill Ise 119 143 138 T 3 0041 -0.7 W18 0114 0.1 T 3 0121 -0.7 F18 0124 0.0 S 3 0250 -0.5 M18 0223 -0.2 0702 5.0 0?29 4.0 0732 4.6 0729 3.8 0853 3.9 0821 3.6 1312 -0.7 1327 @.l 1333 -0.8 1322 0.0 1442 -0.4 1412 -0.3 1928 @4.9 1946 .3 1959 5.3 1948 4.6 2113 5.2 2043 5.1 162 116 iss 127 133 139 W 4 0135 .-0.9 T19 0152 -0.1 F 4 0213 -0.8 S19 0203 -0.1 M 4 0338 -0.4 T19 0308 -0.3 J?53 5.0 gl@03 4.0 0822 4.5 080? 3.7 0941 3.8 0906 3.7 400 -0.9 1401 0.0 1420 -0.7 1400 -0.1 1528 -0.2 1459 -0.3 2017 5.2 2019 4.4 2046 5.4 2025 4.8 2158 5.0 2127 5.1 164 119 lS3 130 118 13S T 5 0227 -1.0 F20 0229 -0.2 S 5 03Q4 -0.8 S20 0245 -0.2 T 5 0424 -0.3 W20 0355 -0.3 C642 5.0 0838 4.0 0911 4.3 0846 3.7 1029 3.6 0953 3.7 1447 -0.9 1435 0.0 1507 -0.6 1438 -0.1 1615 0.1 1547 -0.2 Ise 2106 5.3 121 2054 4.5 142 2133 5.3 130 2103 4.9 106 2244 4.7 133 2213 5.0 F 6 0319 -0.9 S21 0307 -0.2 S 6 0354 -0.6 M21 0327 -0.2 W 6 0511 .-0.1 T21 0442 -0.3 0931 4.7 0914 3.9 1001 4.1 0926 3.6 1119 3.5 1044 3.7 1534 -0.8 1510 0.0 1553 -0.4 1520 -0.1 1703 0.3 1639 -0.2 147 2154 5.2 121 2129 4.6 127 2220 5.1 125 2144 4.9 89 2331 4.4 123 2303 4.9 S 7 0410 -0.8 S22 0347 -0.2 M 7 0444 -0.4 T22 0412 -0.2 T 7 0558 0.1 F22 0532 -0.3 1021 4.5 0950 3.7 1051 3.8 1009 3.5 1209 3.4 1138 3.7 M 1 -E:5 154Z 0 1641 -0.1 1603 0.0 1753 0.5 1734 0.0 3 1 220 N 2308 4.8 2228 4.8 2357 4.7 129 lis 100 122 93 110 S.8 0502 -0.5 M23 0429 -0.1 T 8 0535 -0.2 W23 0459 -0.1 F 8 0019 4.1 S23 0624 -0.3 1112 4.1 1030 3.6 1144 3.5 1058 3.5 0645 0.3 1236 3.8 1708 -0.2, 1627 0.1 1730 0.2 1652 0.0 1303 3.3 1635 0.1 2335 4.8 2248 4.5 2317 4.7 1847 0.7 105 112 110 84 lie M 9 0555 -0.2 T24 0515 0.0 W 9 0000 4.5 T24 0549 -0.1 S 9 0109 3.9 S24 0054 4.5 1206 3.7 1114 3.5 0627 0.1 1151 3.5 0733 0.4 0719 -0.2 1800 0.1 1712 0.2 1240 3.3 1746 0.2 1356 3.3 1338 3.9 2335 4.5 1824 0.5 77 1945 0.8 .107 1940 0.2 113 95 114 T10 0029 4.5 W25 0604 0.1 T10 0054 4.2 F25 0011 4.6 S10 0202 3.7 M25 0155 4.2 0653 0.1 1204 3.3 0723 0.3 0643 0.0 0822 0.4 0816 -0.2 1306 3.4 1803 0.3 1340 3.2 1250 3.5 1450 3.4 14-43 4.1 97 1855 0.4 106 82 1923 0.7 110 1847 0.2 82 2043 0.8 117 2048 0.2 011 0127 4.2 T26 0029 4.4 F11 0152 3.9 S26 0110 4.4 1111 0255 3.6 T26 0300 4.1 0755 0.4 0701 0.2 0819 0.4 0741 0.0 0909 0.4 0913 -0.2 1411 3.2 1303 3.3 1442 3.2 1355 3 6 1541 3.6 1546 4.4 86 1956 0.6 103 1902 0.3 75 2026 0.8 los 1954 0:3 89 2140 0.7 121 2157 0.1 T12 0231 4.0 F27 0129 4.3 S12 0251 3.7 S2? 0214 4.3 T12 0349 3.5 W27 0403 3.9 0901 0.5 0801 0.2 0914 0.5 0840 -0.1 0956 0.3 1009 -0.2 1520 3.2 1409 3.4 1540 3.3 1502 3 9 1629 3.8 1647 4.6 76 2102 0.8 103 2008 0.3 76 2129 0.8 114 2103 0:2 96 2233 0.6 128 2302 0.0 F13. 033? 3.8 S28 0235 4.3 S13 J03049 3:9 M28 0320 4.2 V413 0439 3.5 T26 0505 3.8 1002 0.5 0904 0.1 3 0 0939 -0.2 1040 0.3 1104 -0.3 1622 3.3 1518 3.6 1632 3.5 1605 4.2 1714 4.1 1743 4.8 2206 0.7 2118 0.2 2225 0.7 2210 0.1 2323 0.4 79 106 as 123 104 133 S14 0437 3.8 S29 0343 4.3 M14 0441 3.7 T29 0424 4.2 T14 0526 3.5 F29 0003 -0.1 1056 0.5 1004 -0.1 1049 0.4 1035 -0.3 1123 0.2 0603 3.8 1714 3.4 1623 3.9 1717 3.8 1704 4.5 1757 4.3 115? -0.3 86 2304 0.6 120 2225 0.0 9S 2316 0.5 13S 2314 -0.1 117 136 1835 5.0 S15 0528 3.9 M30 0446 4.4 T15 0528 3.7 W30 0524 4.2 F15 0010 0.2 S30 0058 -0.2 1140 0.4 1102 -0.3 1130 0.3 112e -0.4 0611 3.5 0658 3.8 1759 3.7 1723 4.4 1758 4.0 1800 4.9 1204 0.0 1247 -0.3 9S 2354 0.4 138 2328 -0.3 103 143 125 1838 4.6 134 1925 5.1 T31 0013 -0.3 0620 4.2 1219 -0.5 1851 5.1 1147 1 Time meridian 75' W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which Is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 451 TABLE 32a, b, c, d.-Data Used to Determine the Accelerated Rate q Tide Rise at Times of Perigee-Syz))gy, Superimposed on the National If Ocean Surve Tide Tablesjor Breakwater Harbor', Del., January-December, 1962 76 BREAKWATER HARBOR, IjEL., 1962 Times and Heights of High and Low Waters' JULY AUGUST SEPTEMBER Time Ht, Time Ht. Time Ht. Time Ht. Time Ht. Time Ht. DAY DAY DAY DAY DAY DAY h. m. it. h. m. it. h. m. it. h. m. ft. h. m. it. h. m. ft. S 1 0148 -0..3 M16 0115 -0.1 W 1 0255 -0.1 T16 0223 -0.6 S 1 0331 0.0 S16 0330 -0.9 0749 3.7 0711 3.6 0859 3.7 0828 4.3 o941 4.o ow 5.1 1334 -0.2 1303 -0.3 1446 0.0 1427 -0.7 1542 ox 1558 -0.8 132 2011 5.1 143 1938 5.1 lis 2114 4.6 157 2053 5.3 107 2157 4.2 152 2209 4.8 M 2 0235 -0.3 TV 0201 -0.3 T 2 0332 0.0 F17 0310 -0.8 S 2 0403 0.0 M17 0417 -0.8 0836 3.7 0759 3.7 0937 3.7 0917 4.5 1016 4.0 1038 5.0 1421 rO.2 1352 -0.4 1528 0.1 1519 -0.8 1622 0.1 1652 -0.6 123 2055 5.0 149 2024 5.2 108 2152 4.5 isi 2140 5.2 104 2232 4.0 140 2302 4.4 T 3 0319 -0.2 AS 024:7 -0.4 F 3 0408 0.0 S18 0357 -0.8 M 3 0439 0.1 T18 0506 -0.5 0921 3.6 0847 3.9 1015 3.7 1007 4.6 1054 4.0 1132 4.9 1506 0 0 1442 -0 5 16 9 2.2 1613 -0.7 1703 0.2 1749 -0.3 116 2137 4:8 148 2110 5:3 104 N9 .3 141 2230 5.0 100 2309 3.7 12S 2357 4.0 W 4 0402 -0.1 T19 0334 -0.5 S 4 0444 0.1 S19 0445 -0.7 T 4 0516 0.2 W19 0558 -0.2 1004 3.6 T936 4 0 125f 3:K 1100 4.6 1135 4.0 1.11230 4.7 1551 0.1 533 -0:5 5 0 1708 -0.5 1748 0.4 1850 0.0 2218 4.6 2158 5.2 2307 4.1 2322 4.6 2350 3.5 109 141 94 136 94 108 T 5 T442 0 F20 ?421 -0 6 S 5 0521 0.2 M20 05.34 -0 6 W 5 2556 0.3 T20 0058 3.7 049 3:9 027 4:1 1135 3.7 1155 4:6 220 3.9 0655 0.1 1636 0.2 1626 -0.4 1736 0.4 1805 -0.2 1837 0.5 1333 4.4 97 2301 4.4 132 2248 5.0 93 2347 3.9 123 90 99 1959 0.2 F 6 T523 0.1 S21 0510 -nO.5 M 6 0600 0.2 T21 0017 4.3 T 6 0036 3.3 F21 0205 3.4 134 3.5 1121 4.2 1218 3.7 0626 -0.3 0642 0.4 0758 0.3 1722 0.4 1722 -0.3 1823 0.5 1255 4.5 1310 3.9 1441 4 3 2343 4.1. 2340 4.7 1908 0.0 1933 0.6 2111 0:4 as 122 89 114 92 92 S 7 0603 0.2 S22 0601 -0.4 T 7 0030 3.6 W22 0117 3.9 F 7 0129 3.1 S22 0319 3.2 1219 3.5 1218 4.2 0642 0.3 0722 -0.1 0733 0.4 0905 0.5 1810 0.5 1821 -0.1 13 1358 9?5 3.7 4.4 1406 4.0 1549 4.2 90 120 87 1 4 0.6 107 2017 0.2 93 2033 .0.6 93 2220 0.4 S 8 0028 3.9 M23 0037 4.4 W 8 0117 3.4 T23 0222 3.6 S 6 0229 3.1 S23 0429 3.5 2646 Q.3 0654 -0.3 2727 0.4 0822 0.1 0831 0.4 1012 0.5 307 6.5 1318 4.3 357 3.8 1504 4.4 1508 4.1 1652 4.2 so 1902 0.7 lis 1925 0.1 89 2010 0.7 103 2129 0.3 101 2136 0.5 97 2319 0.3 M 9 0115 3.7 T24 0136 4.1 T 9 0208 3.3 F24 0333 3.4 S 9 03,34 3.1 M24 0527 3.4 0731 0 3 0750 -0.2 0816 0.4 0926 0.2 0931 0.3 1112 0.4 1356 3:6 1421 4.3 1451 3.9 1612 4.4 1609 4.3 1745 .4.2 84 1957 0.7 113 2033 0.2 95 2109 0.7 101 2239 0.3 114 2235 0.3 101 TIO 0203 3.5 W25 0240 3.8 F10 0305 3.2 S25 0441 3.3 M10 04,37 3.3 T25 0005 0.2 0817 0.4 0848 -0.1 0908 0.3 1029 0.3 1032 0.1 0614 3.6 1448 3.7 1526 4.4 1548 4.1 1713 4.4 1707 4.6 1203 0.3 91 2054 0.7 112 2143 0.2 102 2207 0.6 108 2340 0.2 127 2331 0.0 107 1830 4.2 W11 0257 3.4 T26 0346 3.6 S11 0404 3.2 S26 0542 3.4 T11 0534 3.7 W26 0045 0.1 0904 0.3 0946 0.0 1002 0.2 1126 0.2 1130 -0.2 0655 3.8 1540 3.9 1629 4.5 1643 4.3 1806 4.5 1803 4.8 1246 0.2 2150 0.7 2251 0.2 2305 0.3 1910 4.3 9S 117 113 109 1" 110 T12 0351 3.3 F27 0452 3.5 S12 0502 3.3 M27 0032 0.1 W12 0023 -0.3 T27 0119 0.1 0952 0.3 1045 0.0 1058 0.1 0634 3.5 0628 4.0 0730 3.9 1630 4.1 1728 4.7 1736 4.6 1219 0.2 1226 -0.5 1325 0.1 103 2245 0.5 119 2353 0.1 129 2359 0.1 112 1854 4.5 153 1854 5.1 ill 1946 4.3 F13 ?443 3 3 S28 ?552 3.5 M13 0557 3.5 T28 0114 0.1 T13 0110 -0.6 F26 0150 0.0 040 0:2 140 0.0 1151 -0.2 0718 3.6 0718 4.4 0802 4.1 1719 4.3 1822 4.8 1827 4.9 1304 0.1 1319 -0.7 1402 0.0 116 2337 0.3 120 140 lie 19.36 4.5 161 1944 5.2 112 2020 4.2 S14 0534 3.4 S29 0047 0.0 T14 0049 -0.2 W29 0151 0.0 F14 0157 -0.8 S29 0221 0.0 112B 0.0 0646 3.5 0649 3.8 0757 3.8 0807 4.7 0836 4.2 1804 4.6 1232 0.0 1243 -0.4 1345 0.0 1412 -0.9 1439 0.0 126 121 1911 4.8 IS2 1916 5.1 115 2013 4.5 1S9 2032 5.2 115 2053 4.1 S15 0027 0 1 M30 0134 0.0 W15 0136 -0.4 T30 0225 0.0 S15 0243 -0.9 S30 0253 0.0 0623 3:5 0735 3.6 0739 4.0 0832 3.9 0857 5.0 0908 4.3 1216 -0 1 1,319 ox 1335 -0.6 1425 0.0 1504 -0.9 1516 0.0 137 1852 4:9 120 1955 4.8 Iss 2004 5.3 113 2049 4.4 160 2121 5.1 114 2125 4.0 T31 0216 -0.1 F31 0259 0.0 0819 3.6 0906 3.9 1403 0.0 1503 0.0 2036 4.7 2123 4.3 1 119 1 1112 1 1 Time meridian 75' W. 0000 Is midnight. 1200 Is noon. Heights are reckoned from the datum of soundings on charts of the locality which is mean low water. 452 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 32a, b, c, d.-Data Used to Determine the Accelerated Rate of Tide Rise at Times of Perigee-Syzygy, Superimposed on the National Ocean Survey Tide Tablesfor Breakwater Harbor, Del., January-December, 1962 BREAKWATER HARBOR, DEL., 1962 77 nmes and Heights of High and Low Waters OCTOBER NOVEMBER DECEMBER rinme Ht. 'nme Ht. Time Ht. 'Bme Ht. Time Ht Time Ht. DAY DAY DAY DAY DAY DAY h. m. ft. . h. m. ft. h. m. ft. h. m. ft. h. m. ft. M 1 0326 o.o T16 0351 -o.8 T 1 0404 0-1 F16 0506 0-0 S 1 0425 0.0 S16 0532 0.3 0943 4.3 1016 5.3 1029 4.5 1139 4.7 1054 4.7 1203 4.3 1555 0.0 1636 -0.6 1656 0.1 1808 0.0 1725 0.1 1828 0.2 ill 2159 3.8 141 2M 4.2 109 2250 3.3 120 121 2320 3.4 102 . T 2 0400 0.1 W17 0439 -0.5 F 2 0447 0.2 S17 0014 3.4 S 2 0515 0.1 M17 00,39 3.4 1018 4.3 1108 5.0 1114 4.4 0600 0.3 1144 4.6 0625 0.5 1635 0.1 1732 -0.3 1744 0.3 1235 4.4 1816 0.1 1254 4.0 los 2236 3.6 122 2337 3.8 103 2338 3.2 104 1905 0.2 116 90 1918 0.3 W 3 0437 0.2 T18 0531 -0.1 S 3 0534 0.3 S18 0117 3.3 M 3 0015 3.4 T18 0134 3.3 1058 4.2 1204 4.7 1203 4.3 0659 0.6 0612 0.2 0723 0.7 1719 0.3 1831 0.0 1838 0.3 1335 4.1 1240 4.4 1347 3.8 104 2316 3.4 106 99 88 2004 0.3 108 1911 0.1 81 2008 0.4 T 4 0517 0.2 F19 0038 3.5 S 4 0034 3.2 M19 0222 3.2 T 4 0117 3.5 W19 0230 3.4 1142 4.2 0627 0.2 0630 0.4 0803 0.7 0716 0.3 0822 0.8 1807 0.4 1305 4.4 1302 4.3 1437 3.9 1340 4.3 1442 3.6 95 90 1936 0.2 97 1937 0.3 81 2103 0.4 104 2009 0.0 74 2058 0.5 F 5 0002 3 2 S20 0146 3 3 M 5 0137 3.2 T20 0324 3.3 W 5 0223 3.7 T20 0325 3.5 0602 0:4 07,30 0:5 0734 0.4 0909 0.8 0824 0.3 0921 0.8 1232 4.1 1411 4.1 1405 4.2 1536 3.7 1445 4.2 1536 3.5 94 1902 0.5 82 2044 0.4 103 2038 0.2 75 2155 0.4 102 2108 -0.1 78 2145 0.4 S 6 0057 3.1 S21 0258 3.2 T 6 0245 3.4 W21 0418 3.5 T 6 0329 4.0 F21 0416 3.7 0657 0.4 0838 0.7 0843 0.3 1010 0.7 0933 0.2 1017 0.7 1330 4.1 1519 4.0 1512 4.3 1629 3.7 1549 4.2 1627 3.5 94 2003 0.5 81 2148 0.4 112 2137 0.0 79 2240 0.4 106 2204 -0.3 84 2230 0.3 S 7 0200 3.1 M22 0403 3.3 W 7 0351 3.7 T22 0505 3.7 F 7 0431 4.4 S22 0503 3.9 0759 0.4 0946 0.7 0951 0.1 1103 0.6 1039 0.0 1110 0.6 1434 4.1 1620 3.9 1615 4.4 1716 3.7 1651 4.2 1715 3.5 101 2106 0.4 as 2244 0.4 112 2234 -0.2 86 2320 0.3 113 2259 -0.4 92 2313 0.2 M 8 0308 3.2 T23 0459 3.5 T 8 0452 4.2 F23 0546 4.0 S 8 0528 4.7 S23 0546 4.2 ygS4 @:3 1047 0 6 1056 -0 1 1149 0.4 1141 -0.2 1158 0.4 9 3 1713 3:9 1714 4:5 1759 3.7 1749 4.2 1801 3.5 113 2206 0.2 92 2328 0 .3 122 2326 -0.5 96 2357 0.1 131 2352 -0.6 102- 2354 0.1 T 9 ?414 3.5 W24 ?544 3.7 F 9 0547 4.6 S24 0624 4.2 S 9 0622 5.1 M24 0628 4.4 010 0.1 138 0.5 1155 -0.4 1231 0.2 1238 -0.4 1243 0.2 1641 4.5 1759 4.0 1809 4.6 1837 3.7 1844 4.2 1843 3.5 127 2,303 -0.1 98 130 106 146 109 W10 0513 3.9 T25 00()5 0.2 SIO 0016 -0.7 S25 0033 0.1 M10 0042 -0.7 T25 0035 0.0 1112 -0.2 0624 3.9 0639 5.0 0701 4.4 0714 5.3 0707 4.6 1739 4.7 1222 0.3 1251 -0.6 1310 0.1 1332 -0.5 1325 0.1 141 2355 -0.4 105 1838 4.0 149 1901 4.6 ill 1915 3.7 153 1936 4.2 117 1925 3.5 T11 0607 4.4 F26 0039 0.1 S11 0103 -0-9 M26 0107 0.0 T11 0130 -0.7 W26 0115 -0.1 1210 -0.5 0659 4.1 0730 5.3 0736 4.6 0802 5.4 0748 4.8 1832 4.9 1301 0.1 1344 -0.8 1350 0.0 1424 -0.6 1408 0.0 153 113 1913 4.0 160 1952 4.6 118 1952 3.7 156 2027 4.1 125 2004 3.6 F12 0043 -0.7 S27 0111 0.0 12 0151 -0.9 T27 0144 -0.1 W12 0218 -0.6 T27 0156 -0.2 0658 4.8 0732 4.3 0818 5.5 0812 4.7 0851 5.4 0828 4.9 1304 -0.8 1337 0.0 1437 -0.8 1430 0.0 1515 -0.5 1451 -0.1 iss 1923 5.0 lis 1948 4.0 165 2042 4.4 124 2029 3.6 IS3 2116 4.0 130 2046 3.6 S13 0129 -0.9 S28 0143 0.0 T13 0239 -0.8 W28 0220 0?48 5.1 0907 5.5 -0.1 T13 0305 -0.5 F28 0239 -0.3 0805 4.4 0849 4.8 0938 5.2 0908 5.0 1358 -0.9 1414 0.0 1528 -0.7 1511 -0.1 1603 -0.4 1534 -0.2 168 2011 5.0 120 2021 3.9 162 2132 4.2 126 2107 3.5 145 2204 3.8 136 2129 3.7 S14 0216 -1.0 M29 0217 -0 1 W14 0326 -0.6 T29 0259 -0.1 F14 0354 -0.3 S29 0324 -0.3 0837 5.4 0839 4:5 0956 5.3 0927 4.8 1025 5.0 0952 5.0 1450 -0.9 1452 0.0 1620 -0.5 1553 0 0 1652 -0.2 1618 -0.2 164 2101 4.8 123 2056 3.8 151 2223 3.9 126 2147 3:5 136 2254 3.6 137 2215 3.7 M15 0302 -0.9 T.30 0251 -0.1 T15 0414 -0.4 0926 5.4 0913 4.6 1046 5.0 F30 0340 -0.1 S15 0442 0.0 S30 0411 -0.2 1543 -0.8 1531 Ox 1713 -0.3 1008 4.8 1114 4.6 1038 4.9 2150 4.5 2317 3.7 1637 0.0 1739 0.0 1704 -0.2 1S8 120 '2131 3.6 138 126 2231 3.4 117 2346 3.5 132 2304 3.7 W31 0326 0.0 M31 0502 -0.1 0949 4.6 1127 4.7 1612 Ox 1754 -0.2 2208 3.5 114 125 Time meridian 75' W. 0000 Is midnight. 1200 Is noon. 'Heights are reckoned from the datum of soundings on charts of the locality which is mean low water. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 453 TABLE 33.-Sixteen Instances of Maj'or Tidal Flooding Near a Time of Perigee-Syzygv, Represented (in Figs. 153-163) by Plots Showing the Predicted Rate of Rise of the Astronomical Tide at Nearby Tidal Reference Stations (Listed in the Table) Tidal reference station used Dates of flooding Key letter and serial No. SANDY HOOK, N.J., 1918 Part (a): Jan. 1 -June 30 4/10-12 A-43(a); 44(a) Part (b): July I-Dec. 31 11/18 A-43(b); 44(b) NEWPORT, R.I., 1927 Part (a): Jan. 1-june 30 3/3-4; 4/2 B-50(a); C751(a), 52(a) Part (b): July 1-Dec. 31 12/5 B-50(b); C-51(b), 52(b) PORTLAND, ME., 1940 Part (a): Jan. 1-june 30 4/21 G-69(a) Part (b): July 1 -Dec. 31 G-69(b) EASTPORT, ME., 1945 Part (a): Jan. I-june 30 H-72(a) Part (b): July I-Dec. 31 11/20 H-72(b) HALIFAX, NOVA SCOTIA, 1973-74 Part (b): Oct. I-Mar. 31 12/11 M-98e ABERDEEN, WASH., 1973-74 Part (b): Oct. I-Mar. 31 12/11 M-98W WILLETS, POINT, N.Y., 1931 Part (a): Jan. I-June 30 3/4-8; 4/1 D-57(a); E-58(a) Part (b): July I-Dec. 31 D-57(b); E-58(b) BOSTON, MASS., 1959-60 Part (a): Jan. 1-june 30 I-83e(a) Part (b): July I-jan. 7 12/29 1-83e(b) BREAKWATER HARBOR, DEL., 1962 Part (a): Jan. I-June 30 3/6-7 J-85(a); K-87(a) Part (b): July 1 -Dec. 31 11/10-14 J-85(b); K-87(b) ASTORIA, OREG., 1962 Part (a): Jan. 1-june,30 86(a) Part (b): July I-Dec. 31 10/13 86(b) LOS ANGELES, CALIF., 1974 Part (a): Dec. I-May 31 1/8 N-99(a) Part (b): June 1 -Nov. 30 N-99(b) 454 Strategic Role of Perigean Spring Tides, 1635-1976 A-43 (a), 44 (a) 5.5 5.5 5.7 6.0 6.1 5.9 200 Y *A 0 OY 0 Y 0 A* Y 0 As Y 0 "WINDOW" FOR 90 SANDY HOOK, NEW JERSEY PCFTENTIAL TIPAL FLOODING 1918 AVERAGE 0 F OF 0 80 ... . .............................................. . ................... ............................................. ..... ................................... j: ...... .... ............................................ ... ...................... . .. . ................................................................ F L. CURVE MAXIMA X 4/10--- FOR 1918 70 ` 60 H LL W -45 T 50 .2 -19 Cr. W 40 U. 0 W 30 tR cc Uj 20 cc W 10 100 90 80. JAN FEB MAR APR MAY JUN 1 7 14 21 281 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 N2!t@ The bracketed "windows" of potential tidal flooding A Lunar perigee 11.4 Maximum tide height in each lunation, in feet and tenths pertain only to the higher of the two peaks indicating above standard datum maximum rate of tide rise in each lunation, and their corresponding dates. The position of the line representing Lunar apogee -13 Difference, in hours, perigee minus syzygy the "average of curve maxima" is computed (see excep- tons noted in text) from a 13 lunar-month mean of the 0 Full moon "One-back" computation method involving tidal phases higher of these two monthly maxima. A perigee-syzygy series may thus overlap successive calendar years. 3 "Three-back" computation method involving tidal phases 0 New moon FIGURE 153a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 455 A-43 (b), 44 (b) 5.7 5.8 6.2 6A 6.2 5.8 200 0 Y 0 A 0 y 0 y 0 0 yo 0 y 0 AO y A A f A W1 NDOW FOR 90 SANDY HOOK, NEW JERSEY -@-POTENTIAL TID- AL FLOODING 1918 AVERAGE 080 ................................... . ........................................................................................... . ........... ... ........................................... ..... ........................ OF q FL. Cukvff**'M'A' X, 1, M-A x 70 11/18 FOR 1918 2@ M ;.-: 60 U. ui T 50 16 -6 -219 ,cc w 40- LL 0 w 30 cc w 20 cc uj 10 100 90 80' JUL AUG SEP OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FIGURE 153b. 456 Strategic Role of Perigean Spring Tides, 1635-1976 B-50 (a), C-51 (a), 52 (a) 43 4.3 43 4.6 4.8 4.8- 4.6 0 A 0 T *A ov 0 Y 0 A* Y 0 A 0 yo 50 NEWPORT, RHODE ISLAND 0 1927 0 "WINDOW" FOR POTENTIAL q 40 -,---TIDAL FLOODING AVERAGE 30 ................................................................... OF .........................../. .. ....................................... .%... .... ........................................... .... .............................................. ......... CURVE mAxf U. FOR 1927 20 FL ..... FL . ....... Lj 3/3-4 4/2 T cc w 10 -6 -30 u- 100 0 w !-1i 90 CC w 0< 80 cc 70 60 50' JAN FEB MAR APR MAY JUN 1 7 14 21 281 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 FIGURE154a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 457 B-50 (b), C-51 (b), 52 (b) 4.4 4A 4.6 4.9 5.0 4.9 Y 0 A 9 Y OA 0 Y ey Y9 Y 50 NEWPORT, RHODE ISLAND 0 1927 "WINDOW" FOR POTENTIAL 0 C! 40 TIDAL FLOODING @s FL AVERAGE 12/5 Z- 30 .................... OF CURVE MAXi-M-K ................................................................................. .............................................. .... ............................... . .......... .... ............................................ ... .................................... 20 FOR 1927 Ld 0 cc 10 6 -16 -41 uj U. 100 0 w t<- 90 cc UJ 0< 80 cc 70 60 50 JUL AUG SEP OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FIGURE 154b. 458 Strategic Role of Perigean Spring Tides, 1635-1976 G-69 (a) PORTLAND, MAINE 1940 10.7 10.8 10.8 10.9 10.7 10.4 0 ey 0 0 AO@ Y A 0 T A A A "WINDOW" FOR POTENTIAL 50 TIDAL FLOODING 40 FL. 30 4/21 AVERAGE OF ........................................... ............... ............................ ..... ........................................ ...... ........................................ .... ........................................... . ...................... *"*** ................................. 020 CURVE MAXIMA FOR 1940 10 ---@-300 u- Ld 36 12 -10 -34 090 cc w 0 80 u- 0 70 w t@ cc 60 uj cc w 50 i@xl 40 30 20 10 200 90 180 JAN -F-EB MAR APR MAY JUN -- 1 7 14 21 281 7 14 21 28 7 14 21 281 7 14 21 281 7 14 21 28 1 7 14 21 28 FiGup.E 155a. @36 @10 Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 159 G-69 (b) PORTLAND, MAINE 1940 10.2 10.5 10.7 11.0 11.2 10.7 10.6 0 A 0 T *A 0 v or T 0 A 9 Y 0 50 'WINDOW" FOR POTENTIAL TIDAL FLOODING 40 30 AVERAGE ................................... OF ............................................................... ..... ......................................... ...... .......................................... .... ........................................... . .................. ................................ 0 20 CURVE MAXIMA 0 FOR 1940 10 ;@!300 u- w D 90 26 3 -18 -45 Cr w 980 u- 0 70 w cc w 60 cc w 50 40 30 20 10 200 90 180 JUL AUG SEP OCT NOV DEC 1 7 14 21 281 7 -14 21 281 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 @3 @18 @45 460 Strategic Role of Perigean Spring Tides, 1635-1976 H-72 (a) 20A 21.3 21.7 22.0 21.8 21.1 y 4111 A 0 y *A OY 0 y 0 A* Y 0 IT 1P A 'WINDOW" FOR POTENTIAL 700 EASTPORT, MAINE TIDAL FLOODING -====>- 1945 80 60 AVERAGE OF 0 40 CURVE mAki C! FOR 1945 20 17 .5 c,-600 u- Lj U) 80 cc 960 u- 0 4 ui 0 !a cc w 20 0 cc uJ500 80 60 40 20 400 80 JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 281 7 14 21 281 7 14 21 28 1 7 14 21 28 Fic;up,E 156a. @17 @5 Tidal Flooding Potential; Perigee-Syzygy in Relationship to other Geophysical Phenomena 461 H-72 (b) 20.1 20.8 21.5 22.1 22.0 21.5 0 A 0 Y 0 A OA Y OA, *y YD A 700 EASTPORT, MAINE "WINDOW" FOR POTENTIAL 1945 TIDAL FLOODING 80 60 FL. AVERAGE OF ................................................................................ ................. . ............................................ .... .......................................... .... .......................................... ................................. 0 IMA 040 FOR 1945 q @5 20 31 8 3 LL ui Ln 80 cc 960 u- 040 Cr 20 ui cc W500 80 60 40 20 400 80 L AUG SE OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FIGURE 156b. @31 @8 Ju 462 Strategic Role of Perigean Spring Tides,' 1635-1976 M-98 e HALIFAX, NOVA SCOTIA 1973-74 7.2 7.5 7.8 7.8 7.5 7.3 70 Y 0 A 9 y OA 0 yo AO Y 0 OY YO 0 0 WINDOW" FOR POTENTIAL x TIDAL FLOODING AVERAGE OF 60 CURVE MAXIMA .............................................. . ........................ ................................... ........... .... ........ ................................ . . .. ........ . .. .... ................ 10/1/73-3/31/74 LL FL. ul 12/11 50 21 .2 LL 0 w !R 40 cc cc ui 30 3 20 OCT NOV DEC JAN FEB MAR 1 7 14 21 281 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 7 14 21 28 FIGURE 157. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 463 M-98 w ABERDEEN, WASHINGTON 1973-74 11.3 12.1 12.6 12.7 12.1 11A 50 V 0 A 0 Y OA 0 Y YO Y 0 AO Y 0 A, 40 "WINDOW" FOR POTENTIAL -<- TIDAL FLOODING 0 0.30 FL. AVERAGE 12/11 4 OF 20 ...................................................................... ..... ........................................... ...... .......................................... ...... ............................................. .............................................................................. CURVE MAXIMA- 10/1173-3/31174 10 48 21 -2 SQ 100 90 u- -24 0 80 cc w 70 w 60 so 40 30 OCT NOV DEC JAN FEB MAR 3 1 7 14 21 28 1 7 14 21 281 7 14 21 281 7 14 21 28 1 7 14 21 28 7 14 21 28 FIGURE 158. 464 Strategic Role of Perigean Spring Tides, 1635-1976 D-57 (a), E-58 (a) WILLETS POINT, NEW YORK 1931 8.4 8.3 8.6 8.9 9.0 8.7 8.2 OA 0 y 0 0 AC) Y 0 A 0 Y 0 A 0 loy A y 90 "WINDOW" FOR POTENTIAL -TIDAL FLOODING 80 FL . ...... FL 3/4-8 4/1 70 AVERAGE OF q 60 CURVE fix FOR 1931 z 50 U. 40 Ld D cc 30 22h 6m- -22h 9 w u- 20 0 w !R 10 cc w 0<200 ir w 90 80' 70 60 50 40 30' JAN FEB MAR APR MAY JUN 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 FrGURE 159a. @22h @6M Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 465 D-57 (b), E-58 (b) WILLETS POINT, NEW YORK 1931 8.3 &3 8.8 9.1 9.0 8.6 Y 9A 0 Y 0 YO 0 Y 0 A* Y 0 A OT Y A 90 WINDOW'FOR POTENTIAL TIDAL FLOODING 80 70 AVERAGE 0 OF ..... ......... .............. ................... .......................... ............ ................................ .... ....................... . ........ .... ... . ... ... . .................................... ... ................................................................................... 60 CURVE MAXIMA FOR 1931 z 50 40 Lj Cr 30 13h -gh w u_ 20 0 w !R 10 M w 200 cc w 90 80 70 60 50 40 130L JUL AUG SEP OCT NOV DEC 1 7 14 21 281 7 14 21 281 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FIGURE 159b. 202-509 0 - 78 - 32 466 Strategic Role of Perigean Spring Tides, 1635-1976 1-83e (a) 11.4 10.7 11.0 11.4 ltg 12.1 12.0 A 0 T 0 A 0 Y OA ey 0 ey Yq A 70 - "WINDOW" FOR POTENTIAL TIDAL FLOODING 60 BOSTON, MASSACHUSETTS 1959-60 50 AVERAGE OF CURVE ..................................... .................................................................... .................. ................... .... ........................................... ...... ........ .................. .............. ...... .......................................... ... .............................. 40 MAXIMA I/l/59-1/7/60 30 37 13 -8 -31 0 0 q 20 @5 2f U. -300 w CD w 90 u. 80 0 w !rc 70 w 60 Cr w so 40 30 20 10 200 go, JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7- 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 FiGuRE 160a. @37 @13 Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 467 I-83e (b) 11.8 11.2 10.9 11.4 11.9 12.1 12.0 r 0 AO T 0 A 0 Y 0 A 0 Y *A 0 A ov A 70 "WINDOW" FOR POTENTIAL TIDAL FLOODING -==@ ... r- 60 BOSTON, MASSACHUSETTS FL. 1959-60 12/24'-\ 50 AVERAGE OF CURVE .................................................. ......................................................................................................... ........ ............................................... .... ................................. .......... ..... ............................................ .... ......... 40 MAXIMA I/l/59-1/7/60 3 -18 30 0 0 @R @20 :!5 z 10 LL 300 Ld T 01 go w LL 80 0 w t-- 70 w @ 60 Cr 50 40 30 20 10 200 90 1960 JUL AUG SEP OCT NOV DEC JAN 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 FIGURE 160b. @-3 468 Strategic Role of Perigean Spring Tides, 1635-1976 J-85 (a), K-87 (a) BREAKWATER HARBOR, DELAWARE 1962 5.4 5.5 5.3 5.3 5.4 5.3 175 *A 0 y *A OY Yo Y 0 A* Y 0 A, 0 Y 0 1 0 0 WINDOW" FOR 165 [-<-==P-0TENTl`AL T1 FLOODING AVERAGE OF ... ....................................... .. .............................................. ............................. C.U.RVE MAXIMA ................................ ... ... ........ . .... ... .. 155 ... ....... FL. FOR 1962 3/6-7 LL -145 uj Cn cc 135 22 -23 w u- 125 0 w !@ 115 w 105 CC w 95 85 75 JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 28 FIGURE 161a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 469 J-85 (b), K-87 (b) BREAKWATER HARBOR, DELAWARE 1962 5.3 5.3 5.2 5.4 5.5 5.4 Y OA Y OA oy 0 ye 0 Y 0 AO Y 0 0 0 ley ;@175 0 A A A 0 WINDO " FOR - 0 165 -POTENTI'A'L TID AL FLOODING AVERAGE OF N I CURVE MAXIMA ........................ ... ............................................. ... ........................................ .. .... ................ ....................................................... ;E I @di@ 1962 u- FL. Lj145 11/10-14 T w 8135 13 -9 -32 P u- 125 .0 Lu tR115 cc ui 0< 105 cc ui 95 85 75 JUL AUG SEP OCT NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FIGURE 161b, 470 Strategic Role of Perigean Spring Tides, 1635-1976 86(a) 70 9.6 9.5 9.1 9.4 9.5 as 60 OA 0 y Y 0 A* Y 0 k 0 v 0 A i A oy Yo 50 ASTORIA, OREGON "WINDOW" -1962 - FOR POTENTIAL 40 TIDAL FLOODI NG AVERAGE 30 0 *F .............. .......... ... .... ............ ............... ... .............. ................. .......... CURVE MAXIMA FOR 1962 0 20 10 2! PERIGEE -2 -50 & , 0 22 -a5 -23 j..:20 EQUATOR LL Lj C/) 90 rx- ui 080 U. 0 70 uj 'Ic 60 ui cc 50 ui 40 30 20 10 100 JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 281 7 14 21 28 FiGuRE 162a. -50 Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 471 86 (b) 70 9.1 8.8 8.6 8.6 9.2 9.7 9.8 600 Y OA 0 Y 0 OY 0 ye AO Y 0 AO Y 0 A A I i 50 ASTORIA, OREGON "WINDOW" FL. 1962 FOR 10(13 POTENTIAL 40 TIDAL FLOODING AVERAGE OF 30 ... ............................. CURVE MAXIMA' . .. . .......... ....... ------ fOR 1962 0 20 R 10 13, .,9 32 2@ -Z'200 w LL U190 U) w In 80 U. 0 70 cc 60 w so Lu 40 30 20 10 100 JUL AUG SEP OCT - NOV DEC 1 7 14 21 28 1 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FiGURE 162b. @32 472 Strategic Role of Perigean Spring Tides, 1635-1976 N-99 (a) LOS ANGELES, CALIFORNIA 10 1973-74 7.1 7.1 6.8 6.1 5.9 6.4 0 0100 0 ey Y 0 AO A 0 Y 6 A 0 Y 0A. q A 90 "WINDOW" FOR POTENTIAL TIDAL FLOODING-====*- '-180 FL. AVERAGE 1/8 OF ............ .............. ........... ...... ......................................... ...... .......................................... .... ............................................................................................................................................. .................... Ln 70 CURVE MAXIMA cr 12/l/73-11/30/74 Lu .2 -24 40 C1 60 21 LL 050 w !R cr 40 w cc 30 20 3 101 DEC JAN FES MAR APR MAY 1 7 14 21 281 7 14 21 281 7 14 21 28 7 14 21 281 7 14 21 281 7 14 21 28 FIGURE 163a. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 473 N-99 (b) LOS ANGELES, CALIFORNIA 10 1973-74 6.9 7.1 6.9 6.3 6.6 6.7 YO 0100 0 v A OT A A A Y 0 Ae Y 0 A 0 Y C q X @ 90 'WINDOW" FOR POTENTIAL, z TIDAL FLOODING 80 u- AVERAGE Lj ............. .......... ............ ........... *- QE .......... T 70 CURVE MAXIMA cc 12/1/73- w 10 060 33 11/30(75 0 50 w cc 40 w 30 20 10 JUN JUL AUG SEP OCT NOV 3 1 7 14 21 281 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 281 7 14 21 28 FIGURE 163b. 474 Strategic Role of Perigean Spring Tides, 1635-1976 nomical tide growth at the times of 16 representative With one or two exceptions made to-avoid repetition cases of tidal flooding, plotted from such data. Where and conserve space, both of the "windows" in each year direct tidal predictions are not customarily made at the containing close perigee-syzygy alignments are included, location of the tidal flooding, the nearest standard (ref- for completeness, among the examples of figs. 153-163, erence) tide-prediction station has been chosen. The irrespective of the half-year in which tidal flooding growth rates on the- ordinate axis are given in ft/min actually occurred. It is quite obvious, however, that the (X0.000l). The abscissa axis represents calendar dates, observed tidal flooding was associated, in every single labeled at 7-day intervals. The average of the curve max- example represented, with the peak of a curve located ima for one lunar year is obtained by dividing the sum within one of these "windows," and hence with a situation of the values for the 13 peaks by 13 lunar months. Across of perigee-syzygy having a large Aw-syzygy coefficient. the top of each chart is indicated the height, 'in feet and The flooding event did not, in every case, coincide with tenths, of the highest tide in each calendar month. the highest peak in a "window," nor, in every case, with The symbols used on each chart are again those coded the absolute peak of the curve. But, without exception, at the bottom of fig. 153a and are inserted directly above the coastal inundation occurred near the time of one of the appropriate dates. Thus, a close alignment of perigee- these peaks. syzygy is indicated by the symbol of a new or full moon The reason that (despite repeat cases later to be noted) resting centrally on the narrow tip of the perigee symbol. tidal flooding did not occur at the other peaks in the A condition of apogee-syzygy is denoted by either of these "window" is, of course, the fact that no supporting strong, lunar symbols located within the upturned cup of the persistent, onshore winds were present at these times. From apogee symbol. As one of the lunar-phase symbols and the the standpoint of the unusually high astronomical tide perigee symbol draw further apart along a horizontal axis, generated, the conditions present at these times were the corresponding astronomical configuration changes entirely favorable to coastal flooding, but lacked the neces- from a proxigee- or perigee-syzygy alignment to the situa- sary associated meteorological factors. tion described earlier as pseudo-perigee-syzygy. Finally On the other hand, realistic support is given to the (as either the new or full moon becomes separated by its premise that such tidal flooding situations are a definite maximum angular distance from perigee), a condition of function of perigean spring tides when accompanied by ordinary syzygy (or spring tides) results. the previously noted conditions of winds through a consi- The plus or minus values located inside the highest of deration of the following facts: the curve peaks indicate the separation-intervals, in hours, (a) At Newport, R.I., in 1927, extreme tidal floodings between the time of occurrence of the two phenomena occurred on both March 3-4 and April 2, one synodic- involved-in the algebraic sense perigee minus syzygy. anomalistic month apart. The same relationship holds true To provide a totally representative basis for compari- for Willetts Point, N.Y., on 1931 March 4 and April I son, all of the data being evaluated at any given tidal sta- in conjunction with two consecutive occurrences of peri- tion are plotted for an entire lunar year of 13 lunations gee-syzygy. (resulting, in some cases, in an overlapping of successive (b) On 1933 December 11, in conjunction with a calendar years). common astronomical alignment of perigee-syzygy, tidal Those immediately adjacent curve peaks which pro- flooding occurred simultaneously on both the east and trude appreciably above the average line are, in keeping West coasts of North America-at Halifax, N.S., and with the context of the present investigation, bracketed Aberdeen, Wash. and labeled cumulatively as a "window for potential -tidal (c) Other examples of both of the above types are to flooding." At times corresponding to the highest points be found in table 1, and are appropriately designated in of each of the peaks within these bracketed intervals', the this table. tide is rising the most rapidly (the lower peak in each pair is, of course, automatically excluded). It will be ob- 2. Mixed Tides (Affected by the Diurnal In- served that, among all the examples plotted, these "win- equality) dows" of potential tidal flooding contain not only all On the west coast of North America, a secondary dy- of the highest peaks indicating maximum rate of tide rise namic factor often intrudes at certain locations to alter within the lunar year, but all cases of proxigee-syzygy, the tidal situation typical of the east coast where (with perigee- syzygy, and some cases of pseudo-perigee-syzygy. some few exceptions) tides of the semidiumal type pre- Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 475 vail. Diurnal inequality is common at many west coast In this respect, three further considerations are note- stations, and mixed tides result. worthy in connection with the foregoing analysis aimed Along the east coast, the tides are generally character- at establishing a positive correlation between perigean ized by two highs and two lows in each day. Although a (or proxigean) spring tides, accelerated rate of tide rise, higher high water and lower high water as well as a lower and astronomical tidal flooding potential. These items are low water and higher low water exist, within each pair of by way of qualification on the previous discussion: high waters and low waters the tides are not extraordi- (a) Between 1885 and 1911, only 19 harmonic constit- narily different in height. (It must be noted, however, uents were used in the computation and prediction of that at very high. latitudes the phenomenon of diurnal tides by the U.S. Coast and Geodetic Survey. These did inequality manifests itself to increase the difference in not include the 3 second-order semidiurnal and diurnal height between higher high water and lower high water.) constituents, the 2 smaller elliptic terms (semidiurnal and At certain stations on the west coast a tidal situation diurnal), the larger evectional diurnal term, the tridi- frequently exists in which, at the Moon's maximum dec- urnal constituent, and 3 overtide constituents, and in- lination, one high water is much higher than the other. cluded only I component in each case among 5 dealing This effect, occurring at large southerly or northerly lunar with compound tides and 5 representative of long-period declinations, almost disappears when the Moon crosses the tides. (See fig. 43). The 18 additional components were Equator. (See, for example, the general tide curves for introduced and first became a part of the hannonic solu- Los Angeles in fig. 164.) For those tide stations especially tions forming the basis for the tide tables published in subject to the influence of diurnal inequality, therefore, 1912. Accordingly, the use of the previously described when the Moon is located at a high declination at time of method for determination of rate of tide growth (which perigee-syzygy, allowance must be made for this phenom- is sensitive to a greater level of accuracy) is not entirely enon. In taking the previously noted differences between effective when tM tide data were published prior to this the times and heights of LLW and HHW in order to plot year. the curves of rate of tide rise, a slight modification in pro- (b) Sufficiently large mean spring ranges must be pres- cedure is necessary. Instead of subtracting from the height ent at the stations utilized in such computations to indicate of HHW (or the time thereof) the value for the low water a characteristic responsiveness to lunar influences and a immediately preceding it, the corresponding value for the corresponding rapid rate of tidal buildup. From. a large low water three entries back is used. variety of tidal growth curves plotted for both the east and This "three-back" method reduces the discrepancy en- west coasts, it is apparent that those tide stations whose countered if the method for semidiurnal tides is used, and mean spring range is less than 5 feet do not lend themselves more accurately assures the representation of a period of readily to this test analysis. By the same token, however, water level rise from lowest minimum to highest maximum such coastal locations are not strongly prone to tidal flood- in accordance with the above-mentioned principles. Not ing at times of perigee-syzygy. all west coast stations require this adjustment, but those (c) The determination of astronomical tidal flooding strongly subject to diurnal inequality (e.g., Los Angeles, potential by the above methods (employing the closely Calif.; Aberdeen, Wash.) definitely do. Some high-lati- corresponding Aw-syzygy coefficient) is, of course, not tude stations on the east coast (e.g., Halifax) also require possible for tides which are more responsive to solar than this special method of solution at times when the lunar lunar influences. declination is large. Among the examples of this type included in the ac- An Independent Check on the Validity of the companying group of rate-of-tide-rise curves, those cases Aw -Syzygy Coefficient using the "three-back" method (figs. 157, 158, 163) are Since first proposing the use of the Aw-syzygy coeffi- indicated by a boldface number 3 in the lower right corner cient as an indicator of vulnerability to tidal flooding con- of the chart. Examples using the "one-back" method are ditions, it has been left to substantiate that the daily rate similarly identified by a number 1. Figures 153-163 con- of lunar motion in right ascension-the secondary element taifi 11 examples of both types, covering the broad range of the Aw-syzygy coefficient-is itself a parameter accu- of coastal locations previously noted. rately representative of tidal flooding potential. It has been indicated that such rapid and extreme rates In the immediately preceding section, the conditions of tide rise are present and demonstrable only where the of predicted and actual flooding have been positively cor- type of tide involved is one aff.ected strongly by the Moon. related with the accelerated rate of tide rise associated 476 Strategic Role of Perigean Spring Tides, 1635-1976 N 0 A 31 E 0 N C E S P SEPTEMBER ID3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 IS 19 20 21 22 23 24 25 26 27 28 29 30 6 - MHWS 4 A A a il. I . I a III A A III A I I . I ..1 .1 iI.AA11 A Al A III II III Il 19 -A -A 'MHW 211HUMA Al 1111111] 111111 111,11NIPAIIANVI MAN W11111111111INflA OVIVIVfM 111HVIVU11 VVVVVVW1VYIV V;14vvv MLW* W 10. NE YORK -,MLWS 8 1 . I - . .1. 1. A A IA IA 1. MHWS 6A A A IA -A NA1111111111111 11 IIhIII III, A AJIAJI Ili Ili InIld .111. MHW 4 LITW 11 if 11111111111111111 MINA I r 1 11, 1V Mill Um VITI III -IM" MLW 2T MLWS 0 PORT ADELAIDE 12 MHHW 10 - .1 01 A I A I A A ElliIIIIIIIIIA11111 MHW a A A, Al h IN 11 A 11 IIAI At AN RAI R, A, It It 11111 0 tl U11111111HI _111 111-11. 6 V, I 1 11 Jill lill 11 in HE 111 11 11 1` 4 11 A 11 ill ill V @ [111 T I I HVIIII Ill 11 [11 Ill 11 [11 T 2 1 . L11 1 11 1 11 11' ill 11 1111 'It 11 MLW 0 MLLWO SEATTLE -2 6 4 A Al-A AW A A) A@ AiiIIA A A A A A A A I A A A A A I M'H1W"W 2 I`j 1, N tv "V IV IV IIJI101111IMNI VIVO IIIAI Ill 111111AILVI 41 0 JA 1 11 1 111111 'I'll V VI I @@ I aa -A I MLW LOS AIN116ELE@ -1- - 2 MHHW I A A Al Al ALAR A A AIA A A AILA A IA INA A 1 11, 111.11 A A A A A L IA -,It _LA@ MHW WL_ - - . V1VPVVVVVnLT"L WWO Hvilvill Vill VW T_W_@_ MLW 0- is- I @ I I I @ I c 16 A A Al nl I I I i A A A I A A A IA MHHW 14 A 12 10 AA 8 'U'll 6 Ir V I V 11 11 4 MLLW PAKH TCLLW 2 T@ -- - F _. 0 ---- L O,newmoon; 3,firstquarter, O,fullmoon; C.,Iastquarter; E, moon on the Equator; N, S, moon farthest north or south of the Equator; A,P, moon in apogee or perigee; Q@, sun at autumnal equinox. chart datum. S VTTLE FIGUPLE 164-Representative daily tidal curves of different types (see p. 298 and fig. 6 in appendix) at selected stations throughout the world. Note the individual, varying effects of the perigee-syzygy align- ment (plus proximity to the autumnal equinox) on September 23. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 477 with perigee-syzygy. To complete the circle of analysis, it is peaks in figs. 16 1 a and 16 1 b. The even greater significance finally necessary to demonstrate that the unusually rapid of this circumstance is that, whereas the first curves are rate of tide rise at times of perigee-syzygy can be directly plotted entirely from astronomical tables and the second correlated with the daily velocity (and hence change of from tide tables, the profiles of the respective curves are an position) of the Moon in right ascension. Such an analysis almost identical match for all dates throughout the year. can be accomplished by the use of figs. 165a and 165b. The close resemblance between the positions, shapes, and These diagrams, in their inherent nature, constitute a augmented amplitudes of the curves at times of perigee- parallel reconstruction of the tide curves contained in figs. syzygy is particularly noteworthy@. Since the lunar phase 16 1 a- 16 1 b, which represent the varying daily rate of tide relationships do not directly affect the Moon's daily mo- rise thoughout the year 1962. However, for comparative tion in right ascension as they do sensibly affect the tides, purposes, these curves are plotted entirely from astronomi- figs. 165a and 165b do not contain the series of dual maxi- cal data in The American Ephemeris and Nautical Al- ma (one of which is elevated) and minima shown in figs. manac and are, therefore, independent of any particular 1.61a and 161b. tidal stations. The ordinate values and curve amplitudes Finally, an item of major importance should be men- accordingly will not change from tide station to tide sta- tioned in connection with the search for a suitable coeffi- tion as in the fate-of-tide-rise curves, but the properties cient of tidal flooding. Throughout the entire series of of the purely astronomically derived curves can prove to curves representing a considerable variety of tide stations be very meaningful in relationship to the tide curves. Figs. in figs. 153-163, the only major tidal flooding events ob- 165 a- I 65b represent graphs of daily lunar motion in right served among the 56 years of record covered, occurred at ascension plotted with declination as ordinate against the one of the peaks exfending above the respective "average time as abscissa (indicated to exactly the same scale as of curve maxima" lines. that previously used). For correlation purposes, the present As an aid to the determination of astronomical cbndi- curves may be directly compared with the matching tions which are especially conducive to tidal flooding curves of figs. 16la-161b, plotted completely from tide when they exist concurrently with strong, persistent, on- table data. shore winds, all examples of perigean spring tides occur- Specifically, the ordinate axis in these present figures ring between 1977 and 1999 in which the perigee-syzygy represents the angular distance in right ascension through separation-interval is < 24 hours are summarized in table which the Moon appears to move on each day of the year 34. Those cases of proxigee-syzygy and extreme proxigee- in consequence of both real and apparent motions. The syzygy leading to the production of exceptionally high movement is expressed as a difference between the Moon's tides, and thus particularly vulnerable to severe coastal position in right ascension at 0' of date and its position at flooding when supported by the correct meteorological a time 24 hours earlier. The tabular differences calculated conditions, are identified for quick reference., from The American Ephemeris and Nautical Almanac are converted uniformly to minutes of time. The final reduc- Summary and Conclusions tion takes into account corrections for lunar declination (i/cos' 8) and for the effects of the Earth's diurnal rota- In su Immary, the following facts have been made evi- tion. The result is, therefore, the projection on the celes- dent throughout the preceding chapters: tial equator of the apparent daily motion of the Moon. The horizontal dotted line labeled "Average of Curve A. The Tidal Aspects of Perigee-Syzygy Maxima for 1962" is obtained by taking the mean of the Alignment ordinate values for all peaks throughout a 13-month pe- 1. The coincidence of perigean spring tides and strong, riod and dividing by 13. persistent, onshore winds must inevitably result in active The effect of acceleration of the Moon's apparent mo- coastal flooding, a statement amply confirmed by table 1 - tion in right ascension in increasing the length of the tidal By contrast, perigean spring tides alone, without support- day at times of perigee-syzygy is clearly manifest in the ing winds, are usually insufficient of their own right to fact that the peaks of the curves extend perceptibly above cause major flooding. (See table 27.) Because of this re- the average line at these exact times. quired combination of events, at no time has the word A further salient factor is the very exact correlation be- "prediction" of tidal flooding been used in this publication. tween the portions of these curves protruding above the The astronomically induced tides can be computed for line in figs. 165a and 165b, and the matching extreme thousands of years into the future with extreme precision. 478 Strategic Role of Perigean Spring Tides, 1635-1976 J-85 (a) VARIATION IN DECLINATION OF MOON AND SUN - +2Cf % IIt 14 fI It% 1, 1, It 11 Z 41 or %It ItI 6 ItI %ItI L) C@ ItI It I,./ 111 1It -26 W *A 0 y 0 YO A T A Y 0 AO Y 0 A 0 Y 0 A 58 57 A* ..... ....... FL. 2 3/6-7 Average Ik- Of 56 .............. ........ . ........ ................................ .... ........... .................... .. ............................... . ........... .......... . ..................... ........... ................... 0 for 1962 it - -j 55 z X 8 54 LL. 0 z 53 0 w rn LL z 0 0 Cn w z uj .52 < 0- ---1 P: z z 0 51 o = Cc :< Z: a W Z rc 2 so LU z = 0 w CL Ld LU 0 w LLJ 49 L) U- w Z' 0 (L LLI 0 X cc (n w LU CC 48 LL 0 0 0 LL w z a wu- < >1 w 47 w E, 0 LL 46 a w 45 w 44 43 EFFECT OF PERIGEE-SYZYGY ALIGNMENTS IN ACCELERATING THE MOON'S APPARENT MOTION IN RIGHT ASCENSION AND LENGTHENING THE TIDAL DAY -1962- JAN FEB MAR APR MAY JUN 1 7 14 21 28 1 7 14 21 28 7 14 21 28 1 7 14 21 281 7 14 21 281 7 14 21 28 FIGURE 165a.- (Discussed in text.) Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 479 J-85 (b) VARIATION IN DECLINATION OF MOON AND SUN -2a I 111NI II II I It It It It It, tit, 1 1, It It z or ...........k................... ...................A....................A....................I......... .4 ...... ....... ....................I...................L....................A ......... ................... ................ It 11 1% 1 11 1% 1 11 I I I I It I I I I I It of IIt 111 If It 11 1, Itt 1 0 -20f a Y 0 A 0 Y OA, 6Y OA YO AO, Y 0 k0 Y 0 58 57 2 Average . ... . ....................................... . . ..................... jp! ................................................ F- 56 ..... . ............. . ........ ........................... Curve Maxima 0 for 1962 w 55 z < , 0 X 0 < 54 LL LU z U- 53 U- w 0 z 0 0 U) - z w 52 LU < 1-- Z Z < 0 @ 51 Ln P CC z 0 LU Z - 50 z :r 0 uj 0. Uj Cn ULI W a Cn U - LL Uj 49 Z- Ow U.1 0 D_ cc cn x UJI cr uj 48 LL E2 0 0 U- U.1 z LL LL U.1 47 46 45 Uj 44 43 EFFECT OF PERIGEE-SYZYGY ALIGNMENTS IN ACCELERATING THE MOON'S APPARENTMOTION IN RIGHT ASCENSION AND LENGTHENING THE TIDAL DAY -1962- JUL AUG SEP OCT NOV DEC 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 1 7 14 21 281 7 14 21 28 FirURE 165b.- (Discussed in text.) 480 Strategic Role of Perigean Spring Tides, 1635-1976 TABLE 34. -A Checklistof the CentralDates (Mean Epochs) of PerigeanSpring Tides (P-S< �24') Occurring Between 1977and]999 [Proxigean spring tides are indicated by the letters "Pr." before the date, and extreme proxigean spring tides by the letters "Ext. Pr." See table 16 for full astronomical details.] Mean epoch of perigee-syzygy Perigee Mean epoch of perigee-syzygy Perigee n-dnus minus Year Date Hour SYzYgY Year Date Hour SYzYgY (e.s.t.) (b) (e.s.t.) 1977 5/3 1600 (+16) 1988 2/17 0730 (-7) 1977 6/1 1300 (-6) 1988 8/27 0900 (+6) Pr. 1977 12/10 1530 (+5) 1988 9/25 0630 (-15) 1978 1/8 1500 (-16) 1989 3/7 2000 (+14) 1978 6/20 2330 (+15) 1989 4/5 1830 (-9) 1978 7/19 1700 (-5) Pr. 1989 10114 1830 (+5) Pr. 1979 1/28 0300 (+4) 1989 11/12 1700 (-16) 1979 2/26 0230 (-'19) 1990 4/25 0530 (+13) 1979 8/8 0600 (+16) 1990 5/24 0230 (-9) 1979 9/6 0300 (-6) Ext. Pr. 1990 12/2 0430 (+3) 1980 2/16 1600 (+24) 199D 12/31 0430 (-19) 1980 3/16 1430 (+ 1) 1991 6/12 1300 (+121 1980 4/14 1230 (-21) 1991 7/11 0930 (-9) 1980 9/24 1430 (+13) 1991 12/21 1700 (+24) Pr 1980 10/23 1230 (-7) Ext. Pr. 1992 1/19 1630 (+ 1) 1981 4/5 0230 (+23) 1992 2/17 1600 (-22) 1981 5/3 2330 (+ 1) 1992 7/29 2100 (+12) 1981 6/1 2000 (-22) 1992 8/27 1730 (-9) 1981 .11/12 0030 (+13) 1993 2/7 5000 (+23) Pr. 1981 12/10 2330 (-9) Ext. Pr. 1993 3/8 0400 (-2) 1982 5/23 1100 (+22) 1993 4/6 0200 (-24) 1982 6/21 0700 (0) 1993 9116 0400 (+12) 1982 7/20 0300 (-22) 1993 10/15 0200 (-10) 1982 12/30 1200 (+10) 1994 3/27 1530 (+19) 1983 1/28 1130 (-11) 1994 4/25 1330 (-3) 1983 7/10 1800 (+22) 1994 1113 1400 (+10) 1983 8/8 1430 (+ 1) 1994 12/2 1300 (-12) 1983 9/7 1100 (-22) 1995 5/15 0100 (+18) Pr. 1984 2/17 0000 (+8) 1995 6/12 2130 (-3) 1984 3/16 2230 (-13) Pr. 1995 12/22 0100 (+8) 1984 8/27 0100 (+22) 1996 1/20 0100 (-14) 1984 9/24 2200 (0) 1996 7/1 0800 (+18) 1984 10/23 2000 (-22) 1996 7/30 0430 (-3) 1985 4/5 1000 (+6) Pr. 1997 2/7 1300 (+6) 1985 5/4 0730 (-15) 1997 3/8 1200 (-16) 1985 10/14 1000 (+20) 1997 8/18 1500 (+18) Pr. 1985 11112 0830 (- 1) 1997 9/16 1230 (-3) 1985 12/11 0800 (-24) 1998 3/28 0000 (+4) 1986 5/23 1900 (+6) 1998 4/25 2200 (-18) 1986 6/21 1530 (-13) 1998 10/5 2330 (+17) 1986 12/1 2100 (+18) Pr. 1998 11/3 2200 (-14) Pr. 1986 12130 2000 (-4) 1999 5/15 0830 (+3) 1987 7/11 0200 (+6) 1999. 6/13 0500 (-18) 1987 8/8 2130 (-15) 1999 11/23 0930 (+15) 1988 1/19 0800 (+16) Pr. 1999 12/22 0930 (-7) However, sea-surface winds--especially under the most Major tidal flooding is dependent upon such support- changeable o ffshore storm conditions, and with only ship ing wind action as well as the coexistence of high tides (in weather reports and weather sa:tellite photographs as the cases being investigated, further heightened by the in- guides--can rarely be accurately predicted more than sev- fluence of perigee-syzygy alignment). Accordingly, care- eral days in advance. fully chosen phrases indicative of this astronomical situa- Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 481 tion as "enhancing the dynamic potential for," or "in- tides-the principal damage sustained frequently is wind creasing the vulnerability of the shoreline to," severe tidal damage. The coincidence or near-coincidence of hurri- flooding in the presence of strong onshore winds have been canes and perigean spring tides inevitably have resulted in used. Severe erosion of the coastline in low, sandy regions extreme coastal flooding (see table 2). Interestingly, is an attendant factor in any situation involving the simul- although the range of tides at Galveston, Tex., is not suffi- taneous occurrence of intensified onshore winds and astro- ciently large to support a major astronomical height-in- nomically heightened tides. ducing influence at perigee-syzygy, the great historical 2. Hurricane winds in combination with any state of tidal flooding associated with the hurricane of September the tide are usually intense enough to cause coastal flood- 8, 1900 at Galveston, which drowned some 6,000 persons, ing. However, to a degree which is variable with the dis- occurred on the same day as a perigee-syzygy alignment tance of the hurricane's center from the coastline, the (P-S=14 h) . strength of the storm (i.e., the existing pressure gradient), 3. The coincidence of strong, persistent, onshore winds the actual wind velocities present, their angle-of-attack to with ordinary spring tides can cause major beach erosion the shoreline, the duration of their movement over the and seawall damage if the winds are sufficiently strong water, the time of a hurricane's landfall with respect to and occur very close to the times of high water. Unless the high water, and the daily range of the tides at the location velocity of the surface winds is high and the path of their in question, the severity of the flooding may vary over a onshore movement is long-continued over the water, the wide range. magnitude of coastal flooding produced is, however, Disregarding for the moment the high- and low-water never as large as that created by the same circumstances extremes produced by perigean spring tides, a hurricane of strong onshore winds, plus perigean spring tides.' entering the coastline at low tide-although causing ex- A considerable increase in tide-raising power occurs treme wind damage-will not cause as severe flooding as when the Moon reaches a position at or near perigee, be- one impacting the coastline at high tide. A landfalling cause of the proximity of the Moon to the Earth. How- hurricane will likewise, during any period of average tidal ever, for true perigean tides to occur, with the least rein- range, cause much more severe flooding than an offshore forcement from the gravitational attraction of the Sun, hurricane. they must be produced with the Moon at one of its quad- In the case of an offshore hurricane, the duration of rature positions (first or third quarter) when the gravita- onshore surface wind movement is not usually as long tional forces of the Moon and Sun are opposed. The addi- as that associated with an offshore winter storm, because tional tide-raising force at lunar perigee, although con- of the generally far more rapid forward movement of the tributory in enhancing the tides, is not as effective when hurricane in its recurving path at higher latitudes. An thus acting alone as when a simultaneous perigee-syzygy overwater, deep low pressure system of extratropical na- alignment occurs. If strong onshore winds coexist with a ture, accompanied by strong onshore winds, may be totally high phase of the tides produced at times of perigee-quad- blocked by the presence of a stationary high-pressure sys- rature, some minor flooding may result, but the principal tem and the winds may thus persist in onshore movement, damage is that created by wind and associated high waves creating a long overwater fetch. Because of the great ki- directly along the coast, without strong flooding inland. netic energy contained within a hurricane, it is rarely so [Cf., for example, the instance of the coastal storm of blocked, and rather than coming to a complete standstill, February 11-12, 1973 at Nags Head, N.C., and vicinity is only diverted in its path, split into components, or baro- described in Mariners Weather Log, vol. 17 (May 1973), metrically filled and weakened in intensity by the blocking pp. 188-189.] Theoretical analysis indicates that wind- high pressure center. induced coastal waves of the breaking type are raised to On the other hand, in the case of the coincidence of a ; b Pseudo-perigean spring tides, at their upper limit of perigee- hurricane with perigean spring tides, the extra rise in the syzygy separation (_-tBO), also merge rather indistinguishably into high water level accompanying this type of tide acts as an ordinary spring tides. A major destruction to seawalls and the piles astronomically produced setup condition, and provides a supporting beach homes and patios occurred at Malibu Beach, factor of consequence in the production of extreme coastal Calif., during the pseudo-perigean spring tides (P-S=-82h) of 1978 March 3-7. This occurrence was the third in a series of such flooding. destructive tides following upon the two already discussed at the In recapitulation, cases of record show that, when land- end of chapter 7. But the immediate and subsequent attritional dam- age by pounding, wind-driven surf piled on top of moderately above- falling hurricanes have arrived on the coast at times of average spring tides was not accompanied by significant tidal low water-or even in conjunction with moderately high flooding. 202-509 0 - 78 - 33 482 Strategic Role of Perigean Spring Tides, 1635-1976 greater heights the more intense is the wind action and, 5. Important practical and environmental influences somewhat anomalously, the shorter the duration of storm of perigean spring tides, even without the support of strong growth and period of wave rise [Cf., Geoffrey L. Holland, onshore winds, include their action in: (I) bringing salt- "Effect of the Rate of Storm Growth on Subsequent Surge water farther up estuaries, thus modifying or even destroy- Elevation," Journal Fisheries Research Board of Canada, ing the equilibrium conditions required by various forms 26, (@), 1969, pp. 2223-2227]. The frictional coupling of marine fauna and flora (the destruction of birds' nests action between the wind and the sea surface is also greater, in saltwater marshes or seacoast wildfowl sanctuaries also the steeper is the windward slope of the waves produced. may result from the insurging water) ; (2) hastening the [See also the bibliography, category ( 18).] breakup of river ice in consequence of their strong associ- 4. Yet another coastal flooding influence of considerable ated currents; and (3) facilitating navigation through consequence is the combination of perigean spring tides coastal shoals and over rivermouth bars. All these factors with hydrological runoff from near-coastal uplands. This are well substantiated by examples cited in chapters 2-3. circumstance may cause severe flooding of coastal regions Other miscellaneous influences, both adverse and utili- as the result of an impairment of non-nal river or drainage tarian, have been suggested in these same chapters and runoff to the sea during a period of unusually high tides. are further amplified below. The increased water levels produced at times of perigee- syzygy may provide such an effective barrier to hydrolog- B. The Subsidiary Effects of Extreme High ical runoff and force the rising waters to flood over the and Low Waters and Strong Tidal Cur- banks of rivers or drainage channels leading to the sea. rents at Times of Perigee-Syzygy The necessarily intense initial watershed drainage is, Several practical. but-because of the complex accom- of course, created by the melting of thick layers of panying circumstances-not always directly provable con- snow and ice at higher elevations, by heavy and sustained sequences of p@rigean spring tides will next be considered. precipitation, and by the especially rapid and unimpeded Among these are: (a) the possible contribqtions of the runoff of water from slopes denuded by strip logging and extreme low-water phase of such ti des to instances of ship mining. Freshets and flash floods axe the result. Aque- grounding; (b) the increased chance of ship collisions im- ducts, storm sewers, and natural feeder channels sufficient posed by the strong currents associated with such tides; to take care of ordinary drainage situations may, under and (c) the effects of the accompanying extreme high such conditions, prove entirely inadequate to accommo- and low waters and intense tidal currents upon marine date the intense runoff which, in encountering the rising life in the intertidal zone. tide, is caused to back up into gutters and streets [Cf., table The same gravitational forces responsible for unusually 5, key no. 7 9 ( 2 ) col. 21. This is especially true if the peri- high waters in conjunction with perigean spring tides also gean spring tides, lifted further by strong onshore winds, produce extremely low waters at the opposite tidal phase. rise to the actual height of the outlets which compris@ the There is no question but that an inherent danger exists in sewer and drainage outfalls to the sea, thus physically pre- regard to ship grounding at such times of excessive low venting the effluent discharge. Significantly, however, an waters. This is especially true since the actual water level effective blocking action of extreme hydrological runoff is then considerably below the levels of mean low water or can occur as the result of perigean spring tides alone, with- mean lower low water on which chart datums (in the out the coincidence of strong onshore winds provided in United States) are based. Closer inshore, in the tidewater this same respect that intense and persistent offshore winds belt, entire schools of fish also can be left stranded by the do not prevail. unusually low water. Proper awareness should be observed by climatologists Because of the large number of possible alternative rea- to any coincidence between years of heavy snowfall and sons for ship groundings5 such as pilot's or navigator's years of proxigean tides (as defined earlier in this volume), error, adverse weather ' failure of navigation equipment, mechanical breakdown of the engines or rudder, confusion and attention should be given by hydrologists to the possi- of warning signals, etc., it is manifestly implausible to des- bility of runoff from snowmelt or heavy precipitation on ignate this critically reduced low water as more than a upland slopes coinciding with periods of perigean spring possible contributing cause in any one accident. The num- tides. A correlation between simultaneously rapidly in- ber of shipmasters' claims to "water level being lower than creasing readings on river gages and tide gages can provide anticipated" mentioned in a footnote in chapter 3 as a rea7 an appropriate short-range warning. son for the respective grounding casualties is, however, too Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 483 sizable to ignore. The overriding factor for consideration is a matter of open conjecture-as in all cases of this type is that, even aside from these numerous direct attributions where possible multiple causes exist. In keeping with any of grounding due to unexpectedly low water, such cir- such partially uncertain evaluation in this work, the only rational answer is that "under such tide and current condi- cumstances do provide a special hazard for deep-draft tions, a greatly increased potential for danger is present, and, and only slowly maneuverable supertankers. The likeli- proportionately increased safety measures should, in conse- hood for accompanying oilspills, with serious damage to quence, be observed." the coastline and the natural environment, cannot be Two outstanding historical cases of ships running aground emphasized too strongly. subject to the circumstance of especially low water associ- A conti guous navigational threat to the same large, atcd with perigean spring tides are contained in appropri- ate New York City newspaper articles for June 3, 1871 and cumbersome ships consequent upon the existence of peri- February 10, 1895 as abstracted below: gean spring tides lies in the much stronger tidal current ". . . On June 3, 1871 . . . the ship Pacific [bound flows which must necessarily accompany such tides. It is an from Glasgowto New York] . . .went aground off South- incontrovertible fact that these unwieldy craft will be sub- hampton, Long Island . . . 1,000 tons of pig iron which ject to increased navigation problems under the afore- was her cargo was' thrown overboard, after which she floated again mentioned conditions, particularly when the vessels are A very close perigee-syzygy alignment (p - S 1 h) 0-c- underway in narrow coastal rivers or channels where the curred on this same date, having a mean epoch of 1871 currents are running even more strongly and there is little June 3, 0130h 75'W.-meridian time. The resulting greatly room for maneuvering. Should sudden course-correcting depressed tidal waters at low-water phase and associated movements be required as the result of confused signals, strong tidal currents were accompanied by a stiff surface improperly identified targets, misinterpreted orders, or wind. In the news article, this wind-because of its more obvious effects-was mistakedly given as the cause of the poor visibility, the danger that this action will not be ac- very low (ebb) tide and strong currents. This supposition complished in time is directly increased. Collisions may totally ignores the facts, later indicated in this same article, result. Actual examples of such tidal influences follow: that both the flood and ebb currents (incoming and out- going) were very intense at their respective times, without REPRESENTATIVE INSTANCES OF SHIP the wind having shifted through 180'. Continuing with the GROUNDINGS IN SHALLOW DEPTHS news article: PRODUCED AT THE LOW-WATER "Yesterday [6/3] . . . a low ebb tide resulted from the PHASE OF PERIGEAN SPRING TIDES gale, and it was impossible for the ferryboats to cross river, in a direct course . . . so strong was the tide in the middle Ship groundings due to sudden encounter with unusually of the stream shallow water depths naturally occurred more frequently in (New York Evening Post, June 7, 1871, p. 4, col. 8) earlier times when vessels-many still under sail-lacked the quick response of engine power and engine-steering control. It was subject to these treacherous tide and tidal current This early navigational deficiency, while not carried over conditions that the Pacific grounded at Southhampton. into present day ship dynamics is, however, in certain re- spects replaced by the ponderousness, large moments of Similarly, during the low-water phase on February 9, inertia, and correspondingly reduced, maneuverability of 1895, tides occurred which the New York Times described modern supertankers and other deep-draft vessels. in a headline (see table 5, key No. 25) as the "lowest tide Among the following representative examples of ship in twenty years." This extremely low tide was produced by groundings, instances have been chosen in which a direct a perigee-syzygy alignment having a mean epoch of 1895 correlation is possible with the phase of the tides at the time February 9 at 1000h e.s.t.-together with a northwest wind. of the grounding. The New York Times further relates: Although strong surface winds and/or impaired visibility may also prevail during the times of ship groundings, these "Sandy Hook, N.J., Feb. 9-The large four-masted steam- meteorological conditions taken together with the extremely ship Patria of the Hamburg-American Packet Steamship low tides present simply complete a triad of mutually con- Company, while proceeding to sea this evening, grounded in tributing causes to such accidents. [If the winds are offshore, the main ship channel, [!] near the southern edge of Pales- they may depress the tides still further; if onshore, they may tine Shoal . . ." raise the tides, but at the same time force an unsteerable (New York Times, February 10, 1895, p. 1, cols. 3, 7) ship shoreward toward the danger area of the astronomically Since high water occurred at 7:47 p.m., e.s.t. at New York lowered tides.] - (Governors Island) on February 9, 1895, this case of In all of the examples cited below, either an astronomi- grounding probably was contributed to more by the strong cally induced extreme low water or strong tidal currents (or currents than by the unusually low tide situation associated both) were present at the time of the disaster. To what de- with perigee-syzygy. gree these factors might have contributed to each accident 484 Strategic Role of Perigean Spring Tides, 1635-1976 Dense fog or heavy precipitation combined with the low- had occurred at 2:58 p.m., and the tide was falling); the water phase of perigean spring tides also can provide a mean epoch of perigee-syzygy was 1930 February 12, 1500h particularly hazardous combination for a ship. Drifting off P.s.t., P -7 S 2011.1 course by virtue of reduced visibility, the vessel may come * I unexpectedly into waters of unusually shallow depth. Among Despite all that has been said in previous pages of this representative examples of ship groundings known definitely work concerning the advantage offered by perigean spring to have occurred during the low-water phase of perigean tides in facilitating the passage of ships over sandbars and spring tides (although other factors may be attributable) through inshore shoals and shallows, a word of caution must are those of : be sounded where modern deep-draft vessels (especially March 13, 1918 those subject to underway "squat") are involved. It must ". - . The steamship Kersaw with 121 passengers and be clearly emphasized from a safety standpoint that the four crew ran aground early yesterday [morning] [3/13] high-water phase of perigean spring tides does not provide . . . the steamship was bound from Boston to Philadelphia, a navigational panacea for easing modem supertankers or and cause of the accident was that the Captain lost his other deep-draft bulkcarriers into ports or harbors around bearings. When aground, the Kersaw was between the inner which reefs and sandbars exist. and outer bars . . ." A typical case in point is illustrated by the grounding of (New York Herald, March 14,1918, p. 2, col. 1) the oil-carrying supertanker Lake Palourde (of 125,831 "Easthampton, L.I., Mar. 13-The Merchant and deadweight tons) just inside Los Angeles (San Pedro) Har- Miner's Liner Kersaw with 117 naval reservists aboard as bor on November 20, 1976. This date marked the beginning well as other, passengers struck a sandbar during a heavy of a period of perigean spring tides, and came just prior to fog last night [actually, very early in the morning] and is 0 a perigee-syzygy alignment having a mean epoch of 1976 still held fast Fortunately, the weather was calm and November 21, 0030h P.S.t. (P-S= - 13 h). practically no sea was running when the accident occurred Quoting from the Los Angeles Herald-Examiner for No- . . . [the vessel] apparently lost her way in the fog . . . the ship had strained her plates badly when she struck the vember 21 (p. 1, col. 1) bar and all idea of pulling her out this [late morning or "A 974-foot long supertanker loaded with 880,000 barrels evening] high tide was abandoned . . . Kersaw lies just of crude oil has run aground just inside the Los Angeles Har- inside the outer bar on the beach . . . Leaks are being fixed bor in San Pedro and immediate action was begun to free the in time for her to float out at next high tide Kersaw vessel and guq.rd against a potentially disastrous oil spill. displaces 2,600 tons and is 224 feet long." The Lake Palourde ... became locked in the sand at dawn (New York Tribune, March 14,1918, p. 14, col. 1) yesterday while fenroute] . . . to port . . ." As noted, grounding occurred "at dawn." Sunrise for this [The predicted lower low water at New London, Conn., on latitude and date occurred about 6:38 a.m, The ship obvi- March 13, 1918 was at 3:35 a.m., e.s.t.; the mean epoch of ously was trying to take advantage of the extra high tide af- perigee-syzygy was 19 18 March 12, 16001, e.s.t., P - S = + 2 h.] forded by the perigee-syzygy alignment. At Los Angeles Outer Harbor, this morning's higher high water was pre- 1930 February 15 dicted to reach its crest of 6.9 ft above the datum of mean ". . . Inbound with 45 passengers and crew of 65, the liner lower low water at 7:23 a.m. on this date. The tidal range Admiral Benson went aground at 6:40 p.m. Saturday [2/15] (from LLW to HHW) on this date was 8.1 ft, which, subject near the mouth of the Columbia River ... Black fog harn- to the action of the perigean spring tides, is 2.7 ft greater pered the movements of the rescue craft and made it ex- than the diurnal range of 5.4 ft (from MLLW to MHHW) at tremely difficult for them to locate the liner. . ." this location. The predicted height of 6.5 ft is also 1.1 ft (Oregon Sunday journal, February 16, 1930, p. 1, col. 8) above the value of mean higher high water at Los Angeles ". . . Cause of the wreck will not be known until official Harbor, based on a 19-year period of observations. investigation . . . thus far it remains a mystery to those on However, as the events attest, even this -appreciable tidal shore and not even plausible conjectures seemed to have been rise at time of perigee springs is often inadequate to accom- advanced ... The mouth of the Columbia River is a wide modate ships of such unusually large draft over shallow and safe entrance, guarded by navigation aids of all ocean bottoms. kinds . . . Lightship southwest of entrance in line with the Tidal currents probably played no major role in the first channel, lights day and night, with lights visible 11 grounding of this vessel, in spite of their usual acceleration at miles . . . this vessel is in good shape . . . it has submarine times of perigee-syzygy. As noted in the National Ocean Sur- signal devices, foghorn, and radio compass equipment . , * vey's Tidal. Current Tables, Pacific Coast of North America Beyond the jetty markings there are whistles, [and] slightly and Asia-1976, p. 203: "In Los Angeles and Long Beach north of North Head, flashing lights, everything marked and sianaled . . . Benson went on in the fog, just why remains Harbors the tidal current is weak. It is reported, however, to be seen that three minute surge waves are responsible for major ship (Oregon Daily Journal, February 17, 1930, p. 1, cols. 7, 8) movements and damage." No surface winds sufficient to [The predicted lower low water at Astoria, Oreg., on Feb- cause strong surges were present at the time of this ruary 15, 1930 was at 9:28 p.m., P.s.t. (higher high water grounding. Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 485 REPRESENTATIVE INSTANCES OF THE time, strong subsurface currents were present and-at the EFFECTS OF STRONG CURRENT FLOW surface-intense overwater winds. [Descriptions of the elab- ASSOCIATED WITH PERIODS OF PER- orate oceanographic engineering measures designed to pro- IGEAN SPRING TIDES tect a proposed nuclear-powered electric generating plant in a planned location 3 mi off Great Bay, N.J.-and simul- A perigee-syzygy alignment having a separation-interval taneously to safeguard the coastal environment-are con- of only - 8h occur-red at 2300 (es.t.) on February 3, 1939. tained in: Public Service Electric and Gas Company, Atlan- Although the winds were not right to cause tidal flooding on tic Generating Station, Units 1 and 2-Preliminary Site this date, the influence of the astronomical alignment in pro- Description Report, vols. 1-2. (Cf., especially, vol. 1, pp. ducing strong tidal currents is indicated by the following ex- 2.2-5, 2.2-6 for storm tide effects.) cerpts from the New York Times of February 4 (p. 20, col. 3): , INFLUENCE OF PERIGEAN SPRING TIDES ". . . The Cunard White Star liner Aquitania, due to UPON THE ECOLOGY OF THE COASTAL dock at 8 a.m., was not made fast until 3: 10 p.m. because of ZONE an extremely strong ebb tide running at 7 miles an hour that In connection with the dynamic effects of perigean spring held her at the pier head and carried away 4 wire hawsers tides, their associated strengthened currents, and the possibil- . . ." [With total objectivity in mind, the already strong, as- ity for the production of -active storm surges when these tronomically induced current might also have been added to, heightened tides are acco p'anied by strong, persistent, on- in a meteorological sense, by preceding heavy rains, possible m runoff from.snowmelt on the mountains, and prevailing shore winds, there must be mentioned the further aspect of northwest winds. Were any of these conditions indeed con- potential ecological damage to the coastal environment. tributory, this is still exactly the kind of situation in which Among appropriate considerations are the upstream in- special precautionary measures should be observed. Seri- trusion of saltwater far beyond the usual boundary of saline ously aggravated circumstances can be created when such mixing, and saltwater penetration into freshwater ponds factors coincide with perigean spring tides and/or the augm or pools consequent upon wind-blown storm surges and mented tidal currents produced during the same period (al- severe tidal flooding. Both of these actions are made physi- though generally not exactly coincident in time with, the cally possible by the, existence of perigean spring tides. maximized tides).] The first-mentioned expansion of the semidiurnal salt- Again, as reported in the New York Times on the follow- water intrusions may modify estuarine circulation and flush- ing day, February 5 (p. 7, col. 2) : ing patterns, result in a temporary but recurring diversion "Passenger liners sailed from North River pier yesterday of freshwater bound downstream, toward coastal estuarine with 4,000 passengers ... The first to leave at 11 a.m. was destinations, and upset the usual chemical, physical, and the French liner De Grasse for the West Indies-followed at biological exchange relationships with the freshwater run- 11: 30 a.m. by the Conte di Savoia, which was supposed to off. The latter storm-surge effects also may be accompanied be on a slackwater. She moved out from a pier at W. 52nd by the destruction of wildlife habitats, nests, and rookeries. St.-the tide got her and she started downstream broadside Actions taken to offset these detrimental changes may, with 5 tugboats to prevent her hitting the end of the next in themselves, be deleterious to the coastal environment. 0 For example, the construction of seawalls, dikes, and break- pier, where the Aquitania was berthed. Three liners sailed at waters to prevent tidal flooding, and barriers to prevent 5 p.m. . . . the Aquitania which lost seven hours in docking salinity intrusion, may, inturn, exert an ecological influence. Friday [2/3] because of the strong ebb tide . . . lost another Many of the ramifications of such manmade changes are dis- six hours yesterday [2/4] and left at 6 p.m. instead of cussed in the publication series: U.S. Department of the noon . . . Interior, Fish and Wildlife Service, National Estuary Study, EXTREME TIDE AND CURRENT IMPACT vols. 1-7, Washington, D.C. 1970. [Cf., especially, vol. 2, ON OFFSHORE PLATFORMS IN SHAL- pp. 1-39; vol. 4, pp. 1-16.] These factors need not, there- LOW OCEAN AREAS fore, be repeated here. References to certain other matters of ecological import which can be specifically affected by The further potential danger to offshore oil rigs im- perigean spring tides are given in paragraph 10 of the sum- planted on the ocean floor with foundations at depths at mary listing following section D, in succeeding pages. which tidal currents are still strong should not be over- looked. Erosion and weakening of the base of support by C. Unproven Geophysical Relationships such strong tidal currents at the same time that the surface With the Phenomenon of Petigee-Syzygy platform is being battered by strong winds and storm surges may cause an oscillating action of the entire structure which, Thirdly, there are certain events of geophysical nature through resonance, may work toward its final collapse. whose seemingly plausible associations with the alignment Whatever the ultimate cause, it should not be ignored that of perigee-syzygy must be better substantiated before any the destruction of an Air Force's radar tower located 80 correlation can be scientifically accepted. As has happened miles off the mid-Atlantic coast on January 14, 1961 oc- curred on the same day as perigean spring tides which in the case of the many suggested nonphysical attributions caused active coastal flooding in New Jersey. At this same to sunspots, one of the most common unscientific actions 486 Strategic Role of Perigean Spring Tides, 1635-1976 perpetrated is to attribute observed phenomena to oppor-@ produced by the alignment of Sun and Moon at ordinary tune physical causes simply because a time-coincidence syzygy-and particularly the additional forces created at between apparent cause and adduced effect exists between perigee-syzygy-which, in known meteorological theory, them. The lay literature all too frequently abounds with could have an effect upon inducing, reinforcing, or sus- such efforts to establish possible causal connections be- taining strong surface wind movements? More particu- tween two factors based upon their coexistence in time, larly, are there any induced meteorological effects result- or apparent repetition in cycles. Such imagined relation- ing from the enhanced gravitational forces at perigee- ships involve a severe contravention of the principles of syzygy and capable of producing the very winds which, scientific method, since almost any two complex and com- acting upon the perigean spring tides coincidentally raised, prehensive sets of data can-subject to sufficient degrees in turn create tidal flooding? of freedom-be made to show some individual correla- In considering these questions, one closely relevant fac- tions, if the right combinations of parameters are chosen. tor which must not be overlooked is the statistical proba- There is neither intention nor desire in the present work bility of a simultaneous combination of the following indiscriminately to amass various possible factors which events, considered as a meteorological circumstance only: might conceivably be affected by increased lunisolar grav- That (1) a sufficiently deep, intense, atmospheric low itational influences. pressure system (2) will be in exactly the right position However, scientific method dictates that an impartial close offshore (3) with wind movement directed onshore and open mind he maintained toward any rationally es- toward a vulnerable lowland portion of the coast; (4) tablished, empirically verifiable factor of causality. It such winds having blown over the water for a sufficient further prescribes that no deductively or inductively de- length oi time to establish a long fetch and (5) having rived, hypothetical causal relationship which is supported attained a sustained maximum velocity precisely within by a reliable body of evidence, be rejected until it fails one of,the few periods of several days in each year in which completely under a sufficient number of analytic tests. perigean spring tides reach their peak (6) coincidently Because such tests for acceptance are bo-th rigorous and with the short interval of a few hours corresponding to one comprehensive, there is insufficient space in the conclud- or both of the daily high water phases of the tides. ing pages of this work to more than list a few such po- At this point in time, there seems to be no known physi- tential relationships under various degrees of scientific cal mechanism relating lunisolar gravitational force and investigation. Although each of these unquestionably re- barometric fluctuations except those same forces which quires further and broader evaluation, all are of a caliber cause the very small tides detectable in the Earth's atmos- of seriousness sufficient to warrant mention in terms of the phere. (See section 3, below.) If some parameter were possible additional test grounds afforded by perigean present relating such external gravitational influences and spring tides. No one case is to be regarded as any more dynamic convergence in the atmosphere-the latter factor than speculative at the present stage of research. being that creating low pressure systems and the associated steep barometric gradients responsible for strong winds- 1. Wholly Conjectural Relationships Between some more positive connection might be assumed. Meteorological Factors and Perigee-Syzygy A considerable amount of research is underway cover- Statistically considered, a more than random number of ing possible relationships between the tidal forces created cases of major tidal flooding exists involving a coincidence at various lunisolar configurations (those consequent upon beiween perigean spring tides and the presence of strong the phase of the Moon) and the observed amount of at- onshore coastal winds which are a necessary contribution to mospheric cloudiness and precipitation [see bibliography, tidal flooding. Among these are frequent instances of such category (33)]. Further statistical correlations with the flooding: (1) spaced one synodic-anomalistic month Moon being simultaneously at perigee' and the lunar node apart; (2) joined in interrelated sets of I and either 6.5 or have been detected. Such research might ultimately also 7,5 periods of 29.5 days (see chapter 6 for explanation) ; lead to a possible association between lunar influence and (3) bridged in exact long-term multiples of these same those offshore stonns, accompanied by winds, which con- periods; and, perhaps most significantly, (4) which have tribute to coastal flooding at times of perigean spring tides. occurred simultaneously on both the east and west coasts From many years of record, an above-average frequency of North America. (See table 1.) These circumstances of cloudiness has been observed at times of full moon. lead logically to the academic question: Is there any pos- Regions of cloudiness are, almost without exception, repre- sible situation resulting from the extra gravitational forces sented by regions of convergence and low atmospheric Tidal,Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 487 pressure, which are also accompanied by'strong winds. ultimate fracture point; and (3) a triggering action im- Any effect of the reduced parallax and increased gravita- posed by the mechanical jostling of other small earth- tional force of the Moon on the Earth's atmosphere at quakes or microseisms. times of perigee-syzygy is, however, opposed by the con- However, the existence of a physical connection be- verse necessity-if any such augmented cloudiness rela- tween earthquakes and lunar syzygy with its coalignment ,tionship holds true-for a statistical increase in clear skies of lunar and solar gravitational forces has been explored at time of apogee, a circumstance which is not discernible by many reliable scientists, and specific instances of cor- among the records. relation with times of perigee-syzygy also have been cited The entire question of some possible meaningful corre- [see the references following section D, below, and in the lation between the full phase of the Moon and precipita- bibliography, category (3 2) ]. It must be emphasized that tion factors, if real, is a challenging one deserving of fur- any possible relationships assignable between earthquakes ther attention and should be rigorously investigated. By and. increased gravitational forces present at ordinary analogy with the qualification previously imposed, neces- syzygy would be enhanced by the Ialignment of perigee and sitating a decrease in cloudiness at apogee, if a connection syzygy. Accordingly, any promising line of investigation between precipitation and full moon does, exist (without should be comprehensively pursued to give adequate con- requiring that the cause be luminosity-related) a match- sideration to the latter cases. ing statistical decrease in precipitation over sublunar The possibility exists that the wide range of lunisolar regions of the Earth should be noted between full moon forces imposed on the Earth throughout the complete and new moon. half -cycle of lunar positions from perigee-syzygy to apogee- 2. Other Possible Geophysical Influences syzygy may result (to whatever small degree) in an al- The known geophysical influences the Moon exerts ternate compression and resilient expansion of the Earth's upon ocean tides through enhanced gravitational forces at ellipsoidal figure. The consequent maximum rate of de- times of perigee-syzygy leads, in turn, to the possibility of: for-mation of the crust at both perigee-syzygy and apogee- (a) increased influences upon tides in the solid Earth as syzygy could well account for the failure of a large number a result of these same circumstances; (b) a small increase of major earthquakes to coincide with times of perigee- in the established lunar-induced component of the Earth's syzyo, Alone. The only requirement under this expansion OY external magnetic field. and contraction hypothesis (if any connection with earth- a. Potential Connections Between Perigee-Syzygy, Earth quakes exists) would be that earthquakes would occur Crustal Movement, and Seismic Activity statistically with greater frequency within those anoma- The first of the preceding two conjectures also raises list ic months which contain perigee-syzygy alignments, the closely related issue whether any role is played by the since in these months the alternate compression and ex- increased gravitational tide-raising forces at times of peri- pansion would be the greatest at perigee and apogee. In gee-syzygy as a triggering mechanism for earthquakes. Ile any dynamic correlation between lunitidal forces and necessary initiation of this action would be provided by earthquakes, greater emphasis also should be placed on earth-tidally induced ancillary stresses on opposite sides vertical rather than horizontal tide-raising forces (see of a geological fault plane, of sufficient magnitude to Geotimes, 19, 30, 1974). cause shearing and sudden differential slippage along the Inertial reaction times for any such gravitationally in- plane-setting off an earthquake. duced movement of the crust to take place, and corre- Aaam, any correlative attempts to establish a causal 0 sponding relaxation times for the slightly deformed Earth connection between seismic events and the coincidence to recover it@ figure must also be considered in any such of pen'gee-syzygy are marked by many possible pitfalls and investigation. This factor of indetenninancy for so many uncertain factors such as: ( I ) the existence of a fault plane whose contiguous faces are already near Ithe rupture types of rock materials again points to the difficulty of -up differential crustal deforma- point as the result of built establishine a meanineful correlation. tions-and along which a jarring dislocation and release Research in this field has gone forward in a progressive of strain would likely have occurred anyway; (2) other manner and, with equal consideration to opposing opin- factors of dynamic control in dislodgement of the fault- ions, numerous representative examples may be cited. surfaces such as changes in lubrication between the oppos- These examples are grouped in a supplemental commen- ing faces, or in rock tensile-strength when strained to the tary at the end of section D. Other citations to the scien-. 488 Strategic Role of Perigean Spring Tides, 1635-1976 tific literature on this topic are given in the bibliography, By contrast on March 8, 1993, the Moon will reach categories (26)-(29) and (32).' one of its closest possible approaches to the Earth (7r @ 6 11 One final comment is germane in this connection. A 30.011). It will then possess a very large A(o-coefficient, rather controversial work was published in 1974 .2 This and the Sun will be at 8 = - 4.8' (close to the plane of the related to the possibility that a "superconjunction" of all Moon, (8 = 0.4') at a time of maximum proxigee-syzygy. of the planets of the solar system in 1982 might cause The mean epoch of the event (P - S = - 2') occurs at devastating earthquakes along the great. San Andreas 0400h (e.s.t.). Astronomically induced ocean tides, at fault rift in California between 1980 and 1984. The least, will certainly be very high and susceptible to wind- earthquake catastrophe would come about, it is stated, by supported flooding conditions along lowland coastlines a triggering action induced by the mutual alignment of of the Earth within several days on either side of this date. the planets. The gravitational effects of this alignment are b. Geomagnetic Fluctuations of Tidal Nature assumed to proceed through a complex series of natural Geomagnetic variations of measurable degree are events, involving tidal disturbance and the production of related to the constantly changing gravitational effects huge sunspots in the solar photosphere, the generation of associated with the actual and the apparent revolutions additional corpuscular streams of high-energy particles, a of the Moon and Sun around the Earth-as well as the saturation of the Earth's upper atmosphere thereby, exci- Earth's rotation with respect to these objects. Such fluc- tation of the motion of large air masses and turbulence, the imposition of an extremely minute .but quick-acting tuations are relatively long-period ones compared with deceleration of the Earth's rotation, a resulting defor-ma- the short-period variations which produce magnetic tion of the crust, and the production of the earthquakes. transients. Although this hypothesis is conceived upon tides raised in (1) Atmospheric Tides as the Basis for Geomag- the Sun by this gravitational alignment, the Moon is at netic Variations all times the principal tide-raising body in connection with just as the Moon and Sun produce tides in the oceans earth tides. Despite the great mass of Jupiter, at even its of the Earth, tides are created in the Earth's atmosphere least distance from the Earth it is still some 1,500 times as a, function of the changing positions and proximities of these bodies with respect to the Earth. Such atmospheric farther away than the Moon. Since the tide-raising force on the Earth varies inversely as the cube of the distance of tides, and the influences they exert in expanding or con- the attracting body, the tide-raising force of Jupiter is less tracting the electrical conducting portions of the iono- than 0.00001 that of the Moon. Likewise, Venus, the sphere, make themselves felt through detectable variations closest planet to the Earth, exerts a tide-raising force only in the observed intensity of the external geomagnetic field. about 0.0001 that of the Moon. These variations comprise periodic functions similar to those produced within the oceanic tides. The Moon's Astronomically considered, no instance of maximum gravitational influence results in a clear-cut semidiumal proxigee-syzygy alignment-nor even a case of proxigee- effect, as well as a lunar declination effect which is super- syzygy (as both configurations are defined in chapter 7 imposed upon it. A semimonthly lunar variation evident occurs during the period 1980 to 1984. in magnetometer records also corresponds to the semi- monthly ocean tidal height variations associated with c A pertinent newspaper summation of conflicting scientific opin- spring and neap tides. A part of the Sun's gravitational ions with regard to a possible lunar triggering action in connection influence in producing atmospheric tides is masked by its with the Seattle earthquake of April 13, 1949, was contained on the expansional heating effects and by the ionization phe- front page of the Los Angeles Examiner for April 15, 1949. The effect was supposed by some seismologists to accompany a lunar eclipse nomena which its ultraviolet radiation produces. occurring on April 12, without mention of the closer approach of These several lunar and solar effects on the total exter- the Moon to the Earth caused by the associated perigee-syzygy align- nal magnetic field of the Earth, and the variations they ment. This alignment (P-S= -20h, =6111 1.1") had a mean epoch of 1949 April 12, 1000h (P.s.t.). Perhaps more 'significantly, produce through tidal action, are described in detail in terms of a possible alternate, minute compression and expansion of below. the Earth's crust suggested in the text above as taking place during (2) The Solar Diurnal and Semidiurnal the succession of a close perigee, a remote apogee, and a second close perigee, the earthquake occurred one anomalistic month after a very Variations close alignment (P-8=2', @-. =61'28.2") having a mean epoch of During each 24-hour period, various components of 1949 March 14, 1200h (P.s.t.). At the subsequent and intervening the Earth's magnetic field exhibit patterns of magnetic apogee-syzygy, the Moon's apogee distance was correspondingly influence associated with the overhead ionospheric cur- greater, followed by a close perigee approach again at the April 12 perigee-syzygy alignment. rents. However, all magnetic observing stations are not Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 489 similarly affected-a definite latitude dependence being The disturbing influences on the ionosphere in general exhibited. The observed changes in intensity of the ter- tend to follow the Sun, but are affected by latitudinal restrial magnetic field-although not following an iden- influences and other causes, including the elasticity of tical pattem---ostensibly, through what might be called the atmosphere. Thus, especially at high latitudes, the an "induction process," are related to barometric fluctu- magnetic effects may vary considerably, and either a max- ations in atmospheric tides. The latter phenomenon imum or a minimum may be observed at 11 a.m. involves a small observed rise and fall in atmospheric (b) Lunar Variation pressure at the ground surface caused by corresponding A much smaller, though similar magnetic variation, adjustments in the pressure of the air in the high atmos- amounting to less than 1 /1 Oth the solar influence, is pro- phere above the observing. station. These particular tidal duced by the tidal action of the Moon upon the upper fluctuations in the upper atmosphere, although produced, atmospheric layers, and is observable with the changing in their main influence by causes other than gravity, nev- phases of the Moon. The corresponding atmospheric tidal ertheless act in a manner similar to tides in the ocean influence at the Equator and sea level, in the same terms waters. Minute but detectable incremental adjustments in as the preceding comparisons, results in a fluctuation of' sea-level atmospheric pressure are created, on the average, about 0.08 millibar (0.06 millimeter of mercury) in baro- each 24 hours, with secondary maxima and minima at metric pressure at each 12'25.5m interval (a period equal 12-hour intervals in between. to one-half that between two successive transits of the Although the Moon's gravitational influence plays the Moon across the local meridian of any place, on the predominant role in the production of the Earths oceanic average). tides, the cornbination of solar heating and expansion of As an academic matter, the reinforcing geomagnetic the atmosphere makes the Sun of greater influence in pro- influences of Moon and Sun should be greater in their ducing atmospheric tides. Both the- 24-hour and 12 *hour maximum tide-raising tendency at perigee-syzygy, if these tidally induced maxima in atmospheric pressure observed effects are also combined with, rather than negated by, arc attributable to this solar influence. the radiational effects of the Sun. A harmonic analysis of barograph data recorded at sea D. Geomagnetic Illustration of the Increase level around the world indicates that, in the 12-hour solar in Velocity of Tidal Currents at Times of cycle between the primary and secondary tidal maxima, barometric pressures may increase, due to atmospheric Perigee-Syzygy tides, as much as 1.3 millibars (0.98 millimeter of mer- A sl )ightly different verification of the increase of gravi- cury) at the Equator. this variation is independent of tational force on the Earth's tidal waters resulting from either the presence or the nature of local topography, but the alignment of the Moon with the Sun at perigee-syzygy the magnitude of the increase in barometric pressure is made possible by the use of geophysical measurements. caused by atmospheric tides decreases directly with in- These involve the fact that the seawater itself (acting as creasing latitude. The 24-hour component in barometric a conductor of electricity) can generate its own electrical pressure, averaging approximately 0.7 millibar (0.52 mil- current flow when caused to pass through the Earth's lines limeter of mercury) is considerably more dependent upon of geomagnetic force. altitude and geographic effects. The minute electrical potential gradient thus estab- (3) Corresponding Geomagnetic Variations lished can be accurately measured between two electrodes (a) Solar Variation floating on the surface of the water and moored to the Suggestively similar maxima are locally observed in ocean floor. The small increment in electrical voltage buiJt the intensity of the Earth's magnetic field, although actu- up as the flow of water between the electrodes increases ally no midnight peak and no midday peak are observed will be a determinable function of the water velocity. at many latitudes. It is theorized that distortions of the (This same relationship comprises the working principle ionosphere resulting from these tidal atmospheric pressure of the von Arx electromagnetic current meter. See Wil- changes produce fluctuations both in the electric current liam S. von Arx, An Introduction to Physical Oceanog- flow in the ionosphere and in the associated external mag- raphy, Reading, Mass., 1962, pp. 260-279.) netic field. In the case of tidal currents, these velocities will, in At the Equator, the observed magnetic fluctuations turn, increase in proportion to the tide and current gen- roughly parallel the barometric fluctuations-a common erating forces of the Moon and Sun-forces significantly maximum being recorded at about 11 a.m., lQcal time. amplified at the times of perigee-syzygy. 490 Strategic Role of Perigean Spring Tides, 1635-1976 Since the effect of perigee-syzygy on the Earth's external 2. Engineering Protection Against Storm Surges and magnetic field is real but minuscule, the resulting varia- Tidal Flooding tion in electrical potential (of the magnitude observed) is' Aspects of protection against the ravages of storm surges due to the increase in water velocity subject to the rein- have been discussed in such articles as: C. A. Evans, et al., forcing gravitational action of the Moon and Sun at "DuPont Tide and Storm Warning Service," American syzygy-together with the proximity of the Moon to the Meteorological- Society Proceedings, Ist National Conference Earth at perigee. [The mean epoch of perigee-syzygy is on Applied Meteorology, Hartford, Conn., October 28-29, 1957, Boston, Mass., pp. A-8 to A-1 8 (1958) ; P. C. Hyzer, 1918 September 20, 2100' (G.c.t.), in the actual circum- "Hurricane Tidal Flood Protection, Narragansett Bay Area, stance illustrated in figure 166, which is redrawn from an Rhode Island and Massachusetts," Shore and Beach, 3, 16- article by F. B. Young, H. Gerrard, and W. Jevons, "On 19 (1965) ; George M. Mayfield, "Surveying and Mapping Electrical Disturbances Due to Tides and Waves," Philo- Aspects, Storm Tide Protection," Surveying and Mapping, sophical Magazine and journal of Science (London, 92, 1-10 (1966) ; and Basil W. Wilson, "Design Sea and Edinburgh, and Dublin), vol. XL (6th series, July-De- Wind Conditions for Offshore Structures," Proceedings, Offshore Exploration Conference (OECON) Long Beach, cember 1920), pp. 149-159, fig. 5.1 Calif., 1966, M. J. Richardson, Inc., Palos Verdes Estates, The very definite reduction.in positive amplitude of Calif., pp. 663-708 (1966). successive curve crests from near the time of perigee-syzygy 3. Possible Coincidence of Tsunamis and Perigean Spring on September 20 (accompanied by perigean spring tides) Tides to lunar quadrature (neap tides) on September 27 is The especially severe threat to Pacific coastal regions in clearly revealed in this diagram. These individual curve the possible coincidence of perigean spring tides and crests correspond to the instants of greatest tidal current earthquake-produced seismic sea waves or tsunamis is in- flow near the times of low water in each successive day. eluded in a report by Charles Petrauskas, et al., in Frequen- Complementing figure 153b, this diagram provides a real- cies of Crest Heights for Random Combinations of Astro- istic illustration of the increase in the velocity of tidal cur- nomical Tides and Tsunamis Recorded at Crescent City, rents-just as the former shows the increase in the rate Calif', University of California, College of Engineering of tide rise subject to the influence of perigee-syzygy. Laboratory, Technical Report No. HEL. 16-18, Berkeley, Calif. (1971) 70 pp. (See also fig. 167, relating to a similar SUPPLEMENTARY COMMENTS, SPECIFIC LIT- event on the east coast.) - ERATURE CITATIONS, AND CASE EXAMPLES 4. Concepts of Earthquake. Triggering IN CONNECTION WITH THE INFLUENCES A tide-enhancing astronomical alignment of perigee- OF PERIGEE-SYZYGY ALIGNMENTS AND syzygy, with a separation-interval of only - 14h, occurred at PERIGEAN SPRING TIDES 0000h (P.s.t.) on November 21, 1976. With a higher high I water of 7.1 ft occurring at 0805 on November 21, the 1. Storm Surge Models and Tidal Flooding resulting maximum daily range of the perigean spring tide In addition to the wide range of papers on storm surges predicted for Los Angeles (Outer Harbor) on November 21 and their damage to the coastline listed in category (18) of was 8.6 ft, or 3.2 ft in excess of the diurnal range (differ- the bibliography, numerous specific studies have been con- ence in height between mean higher high water and mean 0 lower low water) which is 5.4 ft. at this station. ducted and, in some cases, hypothetical models of the asso- ciated hydraulic actions have been established, covering At 0955 on November 22, an earthquake of magnitude various local harbors or estuaries. Illustrative of the reports 3.8 on the Richter scale occurred below'the sea floor some on such projects are: Robert L. Miller, et al., "Preliminary 24 miles west of Los Angeles, Calif. The epicenter was Study of Tidal Erosion in Great Harbor at Woods Hole, situated 7 miles south of Malibu, among a maze of offshore Mass.," U.S. National Technical Information Service, Gov- faults in Santa Monica Bay which are related to the San ernment Reports Announcements (abstract only), 72, 89 Andreas fault. (1972) ; Harry L. Bixby, Jr., Storms Causing Harbor and ' This was succeeded at 0320 (P.s.t.) on November 26 by Shoreline Damage Through Winds and Waves Near Mon- another earthquake of magnitude 6.3, with epicenter in the terey, Calif., (master's thesis), Naval Postgraduate School, Gorda Basin, north of Ferndale, Calif., at a point near to Monterey, Calif. (1962) 186 pp.; B. W. Wilson, et al., that at which the principally offshore Mendocino fracture Feasibility Study for a Surge-Action Model of Monterey zone intersects the San Andreas fault. Maximum perigean Harbor, Calif., Science Engineering Associates, San Ma- spring tides were predicted for nearby Eureka, Calif., at rino, Calif., Contract Report No. 2-136 for U.S. Army 1204 (P.s.t.) on November 22, with the maximum daily Engineer Waterways Experiment Station, Corps of Engi- range of 7.8 ft on November 25 (subject to the continuing neers, Vicksburg, Miss. (1965) 199 pp.; and Abraham S. influence of the perigee-syzygy alignment) being still 1.1 ft Kussman, "The Storm Surge Problem in New York City, above the [mean] diurnal range of 6.7 ft at this location. The Transactions of -the New York Academy of Sciences, series time of higher high water at Eureka on November 25 was 11, vol. 19, No. 8, pp. 751-763 (1957). predicted -for 1429 (P.s.t.). No severe weather systems or Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 491 MOORED ELEPTRODES MI ANDM2200 YARDS APART CD 20- SEA VERY ROUGH SEA MODERATE SEA CALM 3 4.Omv 2.4mv 0 10 2.4mv 16.Omv 18.4mv > 14.8mv 0 - -1 L L i -JOL12W 3 6 H 9 12 L 6 H 9 12W 3 6 H9 12 3 6 9 12 L NOON NOON L H NOON 21-9-18 W W W 22-9-18 W W W 23-9-18 W cn 20 - SEA CALM SEA MODERATE SEA CALM 0 10 e--*, 0, 4 m @Vo m > > @88m@v @Omv@ 0- -10-12 3 6 9 12 3 6 9 12 3 6 9 12 3 6 9 12 NOON L H L H NOON L H L H NOON 23-9-18 W W W W 24-9-18 W W W W 25-9-18 C0 10- SEA CALM SEA CALM SEA CALM Omv Omv Omv Omv 4.OMV -1.6mv 0> 0 Z-9mv-1 @64mv@ @U @6, 0 m @v @L - 4.8m - I f I I I I I I I I I I I I I I I -10- 12 3 6 9 12 3 6 9 12 3 6 9 12 3 6 9 12 H NOON L H L H NOON L H L H NOON W25-9-18 W W W W 26-9-18 W W W W 27-9-18 SEA CALM SEA SLIGHT 10- H H 0 - W -1.6mv 2.4m.v -0.8mv W > 0 -10 12 3 6 9 12 3 6 9 12 3 6 9 12 3 6 9 12 NOON L H L NOON L H L NOON H 27-9-18 W W W 28-9-18 W W W 29-9-18W Resistance of Circuit 235 ohms. -Deflectionst indicate M2+ve with resp6ct to Mi. FIGuRE 166-- (Discussed in text.) @2.@4mv 4. @OM @2.4@MV@ V@l 8 @4mv .8MV 16.0@mv 492 Strategic Role of Perigean Spring Tides, 1635-1976 The Now York Times Shock Dislodged Needle. levard, west of the Flushing Bridge, were Tues., Nov. 19, 1929 under several feet of water when the tide Page 20, Cols. 2, 3 "One of the shocks was so violent that was at its maximum height and at Sands the needle was dislodged from its posi- Boathouse, near the Flushing Bridge, a tion," Father Lynch declared. "I do not flotilla of dories was put into service to think this quake was greater than the one remove people from the inundated areas QUAKE FELT HERE* that was felt in the New England States and in New York about three years ago." Checking up with the man in charge of The Coast Guards at Sandy Hook sta- the seismograph at St. Louis University, tion said that an unusually heavy tide TIDE FLOODS SHORES which is located about 1,712 miles from began running at 8 A. M. and heavy seas the supposed centre of the shock, Father came up ... Lynch reached the conclusion last night Seismograph Needle Breaks at that the disturbance was caused by a ... They agreed that it was an extremely fault in the ocean or in the Gulf of 'St. high tide even for "full moon tide." Fordham-Father Lynch Sees L@wrence. Fault in Sea as the Cause. 'We cannot place the centre definitely until we have taken a more accurate ALL WARNED FROM PELEE. High Water Sweeps Bridge Away check-up," he declared. "I believe the dis- turbance today was the end of the fault Flares From Martinique Volcano and ... New York City and vicinity distinctly that occurred in the St. Lawrence Valley, felt the tremor that followed the earth- somewhere near the Saguenay River, three Rumblings Cause Fear of Eruption. quake off the coast of Nova Scotia yester- years ago, but I cannot say definitely FORT DE FRANCE, Martinique, Nov. day afternoon. High tides preceded and whether it is the end of the fault until 18 (AP).-The government of Martinique followed the shock, sending a high surf we have located the centre within a mile today warned all persons to evacuate the pounding up the beaches all along the or so." zone at the foot of Mont P616e owing to northern shore of Long Island Sound, The authorities in the American Museum the-increasing activity of the volcano. For along the north shore of Queens and on of Natural History said they believed the the first time since the activity began the coast of Northern New Jersey. Queens shock was one of the most violent recorded flares of light were constantly noticed dur- communities suffered considerable damage on their seismograph within the past ing the night from Saturday to Sunday. as a result of the flood tides. twelve years. According to their figures it They seemed to come through a split in Father Joseph Lynch, who has charge began at 3:31 P. M. and lasted one hour. the upper part of the volcano's cone on of the seismograph at Fordham University, They estimated that the centre of the dis- the slope toward St. Pierre, which was said it was quite possible that the extreme- turbance was approximately 465 miles destroyed with great loss of life in 1902. ly high tides and the disturbance in the from New York, while Father Lynch said The split was almost vertical and about ocean were related he estimated its distance from New York 240 feet high. The flashes of light were at 880, miles . . . acompanied by underground rumblings, . . . Father Lynch said that the seismo- which were undoubtedly of volcanic origin graph at Fordham registered the first A sand barge owned by the Hugh shock of the quake at 3:31 P. M. The McGeeney Company, Inc., of Manhattan ... tremors continued for several hours after was caught, by the swift-rising tide and was that, with particularly severe disturbances swept against a bulkhead at the Long 1929 NOV. 17 recorded at 3:35:7 and 3:37.37. Three Island Railroad drawbridge in Flushing 22h e.s.t. (4-54) minutes later another sharp shock was Creel, . . . shown by the needle . . . Gasoline stations along Northern Bou- 54 FIGURE 167. strong onshore winds prevailed during this period to pro- based upon -an increased amplification and reduction of the vide any further tidal amplification. earth-tide raising forces caused by the near-coincidence of The November 22 earthquake followed by almost exactly perigee-syzygy and apogee-syzygy, respectively. A similar one anornalistic month (27.528d compared with 27.555d) relationship has been identified in the production of moon- the first of a series of 12 minor earthquakes which occurred quakes at both perigee and apogee. [See G. Latham, et al., in north Orange County, Calif. (near Fullerton) beginning Science, 174, 687-692 (1971).] Other positive correlations at 2115 (P.s.t.) on October 24, and persisting intermittently have been detected between such periods of gravitational until early on October 26. The largest was of magnitude 2.0. maxima and both earthquake swarms and aftershocks. [See This series of small earthquakes occurred some 2-3 days Geophysical Research Letters, 2, 506-509 (1975).] after a close perigee-syzygy alignment whose mean epoch Conversely, in an article by L. Knopff on "Earth Tides was 1976 October 23 0100h (P.S.t.), P_S@+8h. as a Triggering Mechanism for Earthquakes," Bulletin Seis- A series of some 60 minor earthquakes also had occurred mological Society of America, 54, 1865 (1964), and another in the area of Brawley, Calif., on November 4 (i.e., within by J. S. Simpson having the same title in Earth and Plane- two days of apogee-syzygy, having a mean epoch of 1976 tary Science Letters (Amsterdam, The Netherlands), 2, 473 November 6 11001, P.m.). The dual perigee-apogee occur- (1976), these authors refute any major triggering of earth- rence of these multiple earthquake events, however meager quakes by the lunar gravitationl influences producing in ternis of the total number and variety of earthquakes, oceanic and earth tides. gives interesting grounds for speculation as to the possibility, Another conceivable mechanism for earthquake trigger- previously suggested, of a contractional-expansional cycle ing exists in the concept of tidal loading, which itself is a Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 493 function of enhanced gravitational tide-raising forces. This physical Research Letters, 2, 506-9 (1975) ; and Bulletin of permits a similar question to be raised: Were all four of the the Seismological Society of America, 64, 2005-6 (1974). multiple earthquake events above cited, having epicenters F. W. Klein in a comprehensive article in Geophysical offshore or close onshore, but additional rart 'h tremors journal, Royal Astronomical Society, 45, 245-295 (1976) among the many resulting.from California's very active tabulates the results of a computerized analysis to show a fault zones-or are there contributing ocean tide-loading significant positive correlation between the.occurrence of factors which further enhance the earthquake potential of earthquake swarms in the Imperial Valley of California these and other seismic-prone areas peripheral to the Pacific? and astronomically induced earth tides. He identifies both (See also the recorded Atlantic coast effects in fig. 168.) ocean loading and shear enhancement as probable trigger- In his paper "Triggering of the Alaskan Earthquake of ing mechanisms. March 28, 1964, and Major Aftershocks by Low Ocean The present state of knowledge in this elusive field of in- Tide Loads," Nature, 210, 893 (1964), Eduard Berg attrib- vestigation involving the search for a possible correlation utes the triggering action in the case of this 1964 earthquake between changing distances and aspects of the Moon and to tidal loading. earthquakes would, with any degree of consistency, only As early as 1929 in a contribution titled "Tilting Motion allow for the following general precepts: (1) the existence of the Earth['s] Crust Caused by Tidal Loading," Bulletin of a possible correlation between either of the positions of of the Earthquake Research Institute (Tokyo, Japan), 6, lunar syzygy and the production of microseisms; (2) the 85 (1929), R. Takahasi points out that, near the shore, a absence, at present, of any definitive correlation between crustal deformation caused by the tidal load produced by the occurrences of lunar syzygy or perigee-syzygy and seismic high ocean waters can amount to nearly 50 times the events of intermediate to large magnitudes on the Richter deformations associated with tides in the solid Earth. He scale-although some . acceptable correlations have been cites a specific example where the maximum of such crustal found with earthquakes of magnitude > 5, occurring at deformations occurred accompanying an ordinary spring depths < 30 kin, with fault motion (slip-dip) at least 30 tide on August 15-17, 1928. However, the possible triggering percent in the vertical [Geo times, 19, 30 (19 74) ]; (3) among of earthquakes by such deformations in the crust caused by those seismic events in which an acceptable correlation with tidal loading is still a matter of open speculation, together syzygy or perigee-syzygy has been established, all are of shal- with the question of shear enhancement along fault planes low-focus origin, but those in which fault motion (strike- induced by the effects of earth tides. slip) is parallel to the Earth's surface are. generally excluded. E. Groten and J. Brennecke in a. paper on "Global Inter- actions Between Earth and Sea Tides," Journal of Geo- 5. Tidal Loading physical Research, 78, 8519-26 (1973) point up the need The effects of vertical movement of the crust produced for further knowledue relating to both the lateral attraction by tidal loading are summarized in a report by A. Waale- and vertical loading influences upon earth tides caused by wijn, "Hydrostatic Measurement of Vertical Movement of unusually high ocean tides. the Coast Dependent on the Tides," in: Contributions to G. P. Tanrazyan in an article "Tide-Forming Forces and IAG Special Study Group 2.22 by the Permanent Service Earthquakes," Icarus, 7, 59-65 (1967) substantiates a for Mean Sea Level, J. R. Rossiter, ed., presented at the strong positive correlation between the lunar alignment at 1970 Coastal Geodesy Symposium held in Munich, Ger- perigee-syzygy and earthquakes observed in the U.S.S.R. He many, pp. 239-247 (1970). also extends an earthquake-tidal force relationship to deep- focus and suboceanic-floor earthquakes in his article "On 6. Earth Tides the Seismic Activity in the Area of the North-western Pa- A significant surnmary of the varying values of earth cific Ocean Margin," Akademiya Nauk SSSR, Izvestiya, tides has been presented in an article by J. T. Kuo, et al., Seriya Geofizicheskaya (Moscow, U.S.S.R.) (1958) pp. 664- "Transcontinental Tidal Gravity Profile Across the U.S.," 668. Numerous papers have been published establishing a re- Science, 168, 968-971 (1970). This survey also reveals the lationship between lunar phase relationships, earth tides, futility of attempting to apply the theoretically derived data and earthquake microseisms. Typical examples are in: jour- of corange and cotidal charts to determine the indirect nal of Geophysical Research, 81, 2543-55 (1967) ; Geo- effects produced by ocean tides upon tides in the solid Earth. The New York Times swept the New England'coast Wednesday Microselsms, as explained by Lewis Don Tues., March 10, 1931 and Thursday, leaving a trail of damage teet, instructor in seismology, who is in Page 1, Col. 2 and ruin in and around Boston, the Har- charge of the station, are microscopic vard seismograph station today came for- shakings or rhythmic motions of the ward with additional documentary evi- ground which continue for hours and, as Earth Shivers Are LWed dence of the destructive forces at work in this case, for days. They have puzzled To the Wo rid- Wide Storms coincidental with the flood tide, but defy- seismologists for many years . . . ing scientific explanation. The seismograms of the two days of the Special to The New York Time& storm and yesterday give a record which even a layman can readily distinguish CAMBRIDGE, Mass., March 8-on the from normal oscillations and from the 1931 Mar. 4 heels of the storm and record tide which characteristic records of earthquakes. 5.5 e.s.t. (0) D-57 FIGURE 168. 494 Strategic Role of Perigean Spring Tides, 1635-1976 7. Crustal Tilt relationship was the detection of large-amplitude internal The further importance of tidally induced crustal tilt in waves in the Great Channel between Great Nicobar Island the case of precise geodetic leveling measurement is obvious. and Sumatra during the Indian Ocean Expedition of the The effects on both gravity measurements and land tilt pro- U.S. Coast and Geodetic Survey ship Pioneer in 1964. The duced by a large mass of tidal water which piles up in an internal waves were first discovered on June 12 (G.c.t.), embayment or landlocked estuary have been well demon- within 2 days of an alignment of perigee-syzygy having a strated in such investigations as "The Response of the Earth mean epoch of June 10 0300h (G.c.t.) and a separation be- to Loading by the Ocean Tides Around Nova Scotia," by tween components of - 2 hours. The presence of the in- A. Lambert, Geophysical journal, Royal Astronomical So- ternal waves was manifest at the sea surface by a phenome- ciety, 19, 449-77 (1970). non resembling tide rips. [See bibliography, category (11), Perry, R. B., and Schirnke, G. R. (1965).] 8. Deflection of the Vertical In a direct followup to this earlier sighted occurrence, a The deflection of the vertical as the result of high ocean letter dated March 4, 1977, from the chief scientist of the tides and its importance to geodesy have been discussed in Exxon Production Research Co., pursuing offshore drill- such articles as that-by G. W. Lennon, "The Deviation of ship operations in the Andaman Sea, indicated "with fair the Vertical at Bidston in Response to the Attraction of assurance that internal wave activity in the Andaman Sea Ocean Tides," The Geophysical Journal of the Royal'Astro- corresponds very well with spring tide activity . . . the max- nomical Society, 6, 64-84 (1962). imal internal wave activity occurring within a four-day period centered around the spring tides." Occasional internal 0 9. Geomagnetic Effects wave activity noted during other times of the month "is Examples of the influence of lunar tides upon geomagne- much reduced from that occurring near the,spring tides." tism and aeronomy are instanced by: E. S. Batten, Com- 12, Turbidity Currents parison of Tidal Theory with Lower Thermospheric Wind Observations, Rand Corporation Papers No. P-4655 (May The possibility that strong underwater currents produced 1971) 16 pp., and Tidal Winds in the Mesosphere and Iono- at the times of perigean spring tides might also be associated sphere, (Ph. D. Thesis), University of California, Los An- with subsurface turbidity currents is raised by the report geles, Calif. (1970) 137 pp.; P. Amayene, "Simultaneous of a NOAA two-man submarine diving operation at the Neutral Wind and Temperature Oscillations Near Tidal head of Oceanographer Canyon off the east coast of North Periods in the F-Region Over St. Santin," Journal of At- America on July 17, 1974. A perigee-syzygy alignment oc- mospheric and Terrestrial Physics (Oxford, England), 35, curred on July 19, 1974, with the mean epoch of perigee- 1499-1505 (1973) ; Jagdish Chandra Gupta, "Special Anal- syzygy at 1000" (e.s.t.). The report reads, in part, as follows. ysis of Geomagnetic Variations to Study the Tidal and the "Dive 14. Head of Oceanographer Canyon . . . head- Storm Modulation Effects," Planetary and Space Science ing 180' . . 7/17/74 . . . Gamma Dive #441. (Oxford, England), 20, 1613-1625 (1972) ; R. D. Harris 0846 . . . on bottom 565' . . . Savoy silt with a few and R. Taur, "Influence of the Tidal Wind System in the erratic boulders . . . started down slope between the two Frequency of Sporadic E Occurrence," Radio Science, major tributaries . . . At 600' we started picking up a Washington, D.C., 7, 405-410 (1972); and Windele; et al., slight westerly current (possibly coming out of the N.E. "Sea Tidally Induced Variations of the Earth's Magnetic head), . . . This current became stronger with time and Field (Leakage of Current from the Atlantic)," Nature, depth . . . Visibility was 30-40' . . . Temperature 49.5' 230,296,317-318 (1971). F. at 600' . . . Continuing down to 700' the current be- 10. Ecological Aspects came quite strong . . . water temperature at 700' was 51'! . . . Suddenly we were enveloped in a cloud of sediment Important environmental influences of exceptionally high . . . Visibility <21 . . . The sub started moving sideways tides are described in such papeis as that by N. M. Ridge- (to the west) quite rapidly ([velocity] at least 2 knots- way, "Directions of Drift of Surface Oil with Wind and hard to estimate, but the bottom was going by very fast Tides," New Zealand Journal of Marine and Freshwater . . . observer thought 4 or 5 knots) . . . I got the sub .Research, 6, 178-184 (1972) ; B. Johns, "Mass Transport turned around and started upslope. (to the north) while in Rotatory Tidal Currents," Pure and Applied Geophysics, still drifting rapidly to the west . . . the bottom here was 60, 107-116 (1965) ; and J. Sherman Bleakney, "Ecological silty with many pebbles and 3-5" ripples (orientation un- Implications of Annual Variations in Tidal Extremes, Ecol- known) . . . upon reaching the 650' level we suddenly ogy, 53, 933-938 (1972). came into still clear water . . . visibility 30' . . . no cur- 11. Internal Waves rent . . . turning around I could see the turbid area be- low us. All very strange and exciting . . . the whole thing Recurrent evidences have shown up in the scientific lit- erature relating the phenomenon of internal waves to the took only 5 (?) minutes.... syzygy position of the Moon-with the most significant 13. Fish Migration correlation appearing to exist in connection with the extra In an earlier technical paper by Otto Pettersson on "The strong subsurface currents running in narrow straits or chan- Connection Between Hydrographical and Meteorological nels at times of perigee-syzygy. A typical instance of this Phenomena," Quarterly Journal of the Royal Meteoroi6gi- Tidal Flooding Potential; Perigee-Syzygy in Relationship to Other Geophysical Phenomena 495 cal Society, 38, 173-191 (1912), the author discusses cer- The Challenge of Geophysical Dis- tain tidal and tidal-current phenomena in connection with climatology. He relates the undercurrent of the Skagerak covery: An Advocacy of Interdisci- and Kattegat to the declination of the Moon and its chang- ing distance from the Earth (thus indicating a deep-water plinary Cooperation tidal movement of the tropical and parallactic type). These deep-water movements are, in turn, associated with the It is obvious from the preceding sections and chapters migration of herring shoals into the Kattegat in winter. that many complex geophysical and biophysical problems Oscillatory movements occurring in the deep waters pro- exist that are dependent upon both regular variations and duce large, long-period submarine waves of differing densi- ties and possessing a distinct correlation with the phase and irregular extremes in gravitational force, and which, ulti- position of the Moon. The subsurface waves produced in mately, only the application of a multidisciplinary scien- this phenomenon are termed "the Moon waves of the Gull- tific approach can solve. mar fjord." The peaking of these waves (i.e., attainment of Such cooperative effort as that which motivated the their shallowest depths beneath the sea.' surface) near the joint National Academy of Sciences-Government agency- times of syzygy is clearly shown in the article. academic institution-private research corporation studies 14. Biological Rhythms of the Great Alaskan Earthquake of 1964 [and which was Technical discussions of many aspects of biological set down for the record in the prefaces to the 3-volume rhythms as they relate to tides are contained in John D. ESSA (NOAA) publication series on that earthquake] Balmer, et al., An Introduction to Biological Rhythms, New has been demonstrated as both feasible and productive. York (1976) 392 pp. In this work, the various contributors describe (chapter I) the responses to tidal rhythms by In the predominantly empirical, case-study approach fiddler, penultirnate-hour, and green shore crabs, as well as of several chapters of the present volume, the large sand hoppers and even unicelled diatoms. They also subse- amount of data tabulated giving special attention to de- quently evaluate the evidence for external timing of bio- tails of time and position has been included with a direct logical clocks, certain geophysically dependent rhythms, and purpose in mind-that of providing a suitable base for the observed propensities among various life forms toward coordinated use in other related disciplines of science. lunar periodisms. This plan of presentation is occasioned by a strong feel- 15. Breakup of River Ice ing that the innovative approaches resulting from overlap A classic and interesting example of the effect of perigean and feedback between various related sciences can best spring tides in breaking up river ice is contained in a record serve to reveal and confirm exact new causal connections of natural events which occurred in the colonial period of not previously known-or at least to crystallize knowl-. America. In an article on "Some Old-Fashioned Winters in edge in many of the propositions and concepts earlier Boston," Fitz-Henry Smith, Jr.d notes (p. 275) an episode enumerated in theoretical form only. that occur-red in the winter of 1766: "The harbor remained frozen from Sunday, Jan. 5 [N.S.] As has been several times remarked in connection with until the following Saturday [Jan. 11] when an extraordinary various suggested relationships throughout the immedi- thaw and south wind dissipated the ice." He further states ately preceding pages, available theories are presented that "Tudor e commented that it was 'very remarkable for which are often not yet fully supported by substantiating the Harbor to frees [sic] up so strong and be so clear again data. Further confirmatory evidence is definitely needed in 6 Days'." to establish such supposed relationships on a firm basis Table 16 shows that syzygy (new moon) occurred on and, at the same time, to determine and verify the exact 1766 January 10 at 2000h (750 W.-meridian time) and method of operation of the forces involved. In direct am- perigee at 1400' on the same date, giving the mean epoch plification of the latter statement in terms of the case of of perigee-syzygy as 1766 January 10, 1700h (75' W.- its misinterpretation, this work will be concluded on a meridian time) preceding by just a day [together with the purely academic note. effects of phase- and parallax-age] that on which the ice Theories .are inventions rather than discoveries. Some- breakup occurred. The perigean spring tides and their associated strong currents undoubtedly provided an active what anomalously, therefore, from a pure research point contributing cause to dissipation of the ice. of view, they may sometimes serve to limit progress to a certain degree rather than to accelerate it-since, after a 'Fitz-Henry Smith, Jr., "Some Old-Fashioned Winters in Boston, theory is created, valuable time is often consumed in striv- with Particular Reference to Times When the Harbor Froze," vol. ing to make data conform to it as a purely mechanistic 65, Proceedings of the Massachusetts Historical Society, Boston, artifice, instead of this same time being devoted to investi- 1940. William Tudor, ed., Deacon Tudor's Diary, Boston, 1896. gation of the cause of the impelling action itself. 496 Strategic Role of Perigean Spring Tides, 1635-1976 Thus, as a hypothetical example in the field of gravi- swer the question why rays of certain colors of light travel tation presently under discussion, in the days before Sir faster than rays of other colors through a medium of the Isaac Newton a physical law might conceivably have been same optical density, nor why rays of short wavelength deduced to explain how an object gets from a point A to carry with them more energy than long waves. As yet un- a point B under free-fall without bothering to explain answered also are the reasons why a moving or rotating how the motivating force originated, or even how the electron possesses an electrical field, and why a particle moving object got underway. Yet, the newly derived law of mass exerts a gravitational force. Confronted by such of motion under free-fall, if self-sufficient, would be fully basic questions as these, the depth of our knowledge and accepted as describing this motion and its effect in getting understanding of the forces, fields, and physical phenom- an object from point A to point B. To satisfy the physical ena of the universe remains grossly inadequate. cause of this action, the assumption might simply have Perhaps one zof the great benefits which may come out been made that some arbitrary force of attraction exists of interdisciplinary research in the geophysical sciences between A and B. This assumption would be deemed ade- is a reappraisal of our whole scientific thinking-over- quate to fulfill the immediate need. coming any Aristotelian-like, conditioned sense of satis- But science, fortunately, does not work in this "closed- faction with classic theories. With the continuously door" environment, satisfied to ignore the cause of any growing trend in basic research may come a realization force or action until the need arises. to ascertain the that there may be other new and as yet totally undiscov- cause. Although over 300 years have elapsed since Newton ered laws, principles, or factors of physical causation at first propounded his descriptive law of gravitation. and work-or fundamental modifications required in our ex- numerous generations of scientists have sought, unsuc- isting scientific laws-even including those of gravitation cessfully, physically to define the interacting force, the and geomagnetism. search still o-oes on in laboratories and researchinstitutions As an example, with respect to gravitation, there is to find a clue to the exact nature of this force. presently no way of knowing whether the gravitational Nor is this the only gap in fundamental 'geophysical force field averaged for thelentire universe might not actu- knowledge. Examples from other fields are equally famil- ally be effective in permeating and altering the local iar. Even assuming the validity of the theories propounded gravity field of the Earth-assuming that this universal, for describing various types of motions, the scientist is still smoothed force field might be of such a small magnitude at a loss today in endeavoring to define the basic forces that its differential effects could not be detected across the which, as single examples: (I) started electrons revolving relatively short distance comprising the diameter of the Earth. The extension of the available baseline to outer around the nuclei of atoms; (2) initiated ring currents in space through the use of artificial satellites, and the con- the body of the Earth to produce an electromagnetic duct of experiments in deep space to evaluate more pre- field; or (3) caused the Sun to rotate on its axis and the cisely the gravitational constant-which provides a Planets to revolve around it. common denominator for gravitational action through In the realm of other intangible physical entities, such the known universe--should provide important strides as electromagnetic radiation, neither can he directly an- forward in this connection. Appendix The Basic Theory of the Tides ing, surfing, and a considerable variety of. related water sports activities. Introduction The Astronomical Tide-Producing Forces: The word "tides" is a generic term used to define the General Considerations alternating rise and fall in sea level with respect to the At the surface of the Earth, the Earth's force of gravi- land, produced by the gravitational attraction of the Moon tational attraction acts in a direction inward toward its and Sun. To a much smaller extent, tides also occur in center of mass, and thus holds the ocean waters confined large lakes, in the atmosphere, and within the solid crust to this surface. However, the gravitational forces of Moon of the Earth, acted upon by these same gravitational and Sun also act externally upon the Earth's ocean waters. forces of the Moon and Sun. Additional nonastronomical These external forces are exerted as tide-producing, or factors such as configuration of the coastline, local depth so-called "tractive" forces. Their effects are superimposed of the water, ocean-floor topography, and other hydro- upon the Earth's gravitational force and act to draw the graphic and meteorological influences may play an im- 6cean waters to positions on the Earth's surface directly portant role in altering the range, interval between high beneath these respective celestial bodies (i.e., toward the and low water, and times of arrival of the tides. "sublunar" and, "subsolar" points). The most familiar evidence of the tides along our shores High tides are produced in the ocean waters by the is the observed recurrence of high and low water-usually, "heaping" action resulting from the horizontal flow of but not always, twice daily. The term tide correctly refers water toward two regions on the Earth representing the only to such a relatively short-period, astronomically in- positions of maximum attraction of the combined lunar duced vertical change in the height of the sea surface and solar gravitational forces. Low tides are created, by a (exclusive of wind-actuated waves and swell) ; the ex- compensating maximum withdrawal of water from regions pression tidal current relates to accompanying periodic around the Earth midway between these two tidal humps. horizontal movements of the ocean water, both near the The alternation of high and low tides is caused by the coast and offshore (but as distinct from the continuous, daily (or diurnal) rotation of the solid body of the Earth stream-flow type of ocean current). with respect to these two tidal humps and two tidal de- Knowledge of the times, heights, and extent of inflow pressions. The changing arrival times of any two succes- and outflow of tidal waters is of importance in a wide sive high or low tides at any one location is the result range of practical applications such as the following: of numerous factors later to be discussed. Navigation through intracoastal waterways and within estuaries, bays, and harbors; work on harbor engineer- Origin of the Tide-Raising Forces ing projects, such as the construction of bridges, docks, To all outward appearances, the Moon 'revolves around breakwaters, and deep-water channels; the establishment the Earth, but in actuality, the Moon and the Earth re- of standard chart datums for hydrography and for de- volve together around their common center of mass, or marcating the seaward extension of shoreline property gravity. The two astronomical bodies are held together boundaries; the determination of a base line or "legal by gravitational attraction, but are simultaneously kept coastline" for fixing offshore territorial limits, both on the apart by an equal and opposite centrifugal force produced sea surface and on the submerged lands of the Continental by their individual revolutions around the center-of-mass Shelf; provision of information necessary for underwater of the Earth-Moon system. This balance of forces in demolition activities and other military eng, ineering uses; orbital revolution applies to the centers-of-mass of the and the furnishing of data indispensable to fishing, boat- individual bodies only. At the Earth's surface, an imbal- 202-509 0 - 78 - 34 497 498 Straic,`* Role of Perigean Spring Tides, 1635-1976 ance between these two forces results in the fact that there the restraining hand. All points in or on the surface of exists, on the hemisphere of the Earth turned toward the the Earth acting as a coherent body acquire this com- Moon, a net (or differential) tide-producing force which ponent of centrifugal force, just as all points on an object acts in the direction of the Moon's gravitational attrac- whirled around the head tend to fly outward under the tion, or toward the center of the Moon. On the side of the action of centrifugal force. And, since the center-of-mass Earth directly opposite the Moon, the net tide-producMig of the Earth is always on the opposite side of this common force is in the direction of the greater centrifugal forte, or center of revolution from the position of the Moon, the aw ay from the Moon. centrifugal force produced at any point in or on the Earth Similar differential forces exist as the result of the revo- will always be directed away from the Moon. This fact is lution of the center-of-mass of the Earth around the cen- indicated by the common direction of the arrows (repre- ter-of-mass of the Earth-Sun system. senting the centrifugal force Fc) at points A, C, and B in figure 1, and the thin arrows at these same points in Detailed Explanation of the Differential figure 2. Tide-Producing Forces It is important to note that the centrifugal -force pro- The tide-raising forces at the Earth's surface thus result duced by the daily rotation of the Earth on its axis must from a combination of basic forces: (1) the force of be- completely disregarded in tidal theory. This element gravitation exerted by the Moon (and Sun) upon the plays no part in the establishment of the differential tide- Earth; and (2) centrifugal forces produced by the revolu- producing forces. tions of the Earth and Moon (and Earth and Sun) around It may be graphically demonstrated that, for such a their common centers-of-gravity (mass). The effects of case of revolution without accompanying rotation as above those forces acting in the Earth-Moon system will here be enumerated, any point on the Earth will describe a circle discussed, with the recognition that a similar force com- around the Earth's center-of-mass which will have the plex exists in the Earth-Sun system. same radius as the radius of revolution of the center-of- With respect to this center-of-mass of the Earth-Moon mass of the Earth around the barycenter. Thus, in figure system (known as the barycenter) the above two forces 1, the magnitude of the centrifugal force produced by the always remain in balance (i.e., equal and opposite). In revolution of the Earth and Moon around their common consequence, the Moon revolves in a closed orbit around center-of-mass (G) is the same at point A or B or at any the Earth, without either escaping from, or falling into other point on or beneath the Earth's surface. Any of the Earth-and the Earth likewise does not collide with these values is also equal to the centrifugal force produced the Moon. However, at local points on, above, or within at the Earth's center-of-mass (C) by its revolution around the Earth, these two forces are not in equilibrium, and the barycenter. This fact is indicated in figure 2 by the oceanic, atmospheric, and earth tides are the result. equal lengths of the thin arrows (representing the cen- The center of revolution of this motion of the Earth trifugal force Fc) at points A, C, and B, respectively. and Moon around their common center-of-mass lies at a 2. The Effect of Gravitational Force point approximately 1,718 krn (1,068 mi) beneath the Earth's surface, on the side toward the Moon, and along While the effect of this centrifugal force is constant for a line connecting the individual centers-of-mass of the all positions on the Earth, the effect of an external gravita- Earth and Moon. (See G, figure 1.) The center-of-mass tional force produced by another astronomical body may of the Earth describes an orbit (Ei, E2, E3 . .) around be different at different positions on the Earth because the the center-of-mass of the Earth-Moon system (G) just magnitude of the gravitational force exerted varies with as the center-of-mass of the Moon describes its own. the distance of the attracting body. According to Newton's .monthly orbit (MI, M2, M3 around this same point. Universal Law of Gravitation, the force, value decreases as the second power of the distance from the attracting 1. The Effect of Centrifugal Force body. As a special case, the tide-raising force varies in- It is this little-known aspect of the Moon's orbital mo- versely as the third power of the distance of the center-of- tion which is responsible for one of the two force com- mass of the attracting body from the surface of the Earth. ponents creating the tides. As the Earth and Moon Thus, in the theory of tides, a variable influence is intro- gravitate around this common center-oi-mass, the cen- duced based upon the different distances of various posi- trifugal force produced is always directed away from the tions on the Earth's surface from the Moon's center-of- center of revolution in the same manner that an object mass. The relative gravitational attraction (Fg) exerted whirled on a string around one's head exerts a tug upon by the Moon at various positions on the Earth is indicated Appendix 499 The solid and dashed circles represent near-equatorial cross-sections through the earth, containing the plane of M3 the moon's orbit around the barycenter (G). Points El, E2, E3, and Mi, M2- M3. are corresponding positions of the centers of mass of the earth and moon, respectively. El M2 cl G Earth E2 E3 (C) Fc B Fc Moon M, FiGuRE I.-The monthly revolution of the Earth and Moon around the Barycenter of the Earth-Moon System. This revo- lution is responsible for a centrifugal force component (Fe) necessary to the production of the tides. in figure 2 by arrows heavier than those representing the curnstance is that the tidc-producing, force (Ft) at the centrifugal force components. Earth's center is zero. 3. The Net or Differential Tide-Raising Forces: At point A in figure 2, approximately 6,378 km (3,963 Direct and Opposite Tides mi) nearer to the Moon than is point C, the force produced It has been emphasized above that the centrifugal force by the Moon's gravitational pull is considerably larger under consideration results from the revolution of the cen- than the gravitational force at C due to the Moon (the ter-of-mass of the Earth around thecenter-of-mass of the Earth's own gravity is, of course, zero at point C). The Earth-Moon system, and that this centrifugal force is the smaller lunar gravitational force at C just balances the same anywhere on the Earth. Since the individual centers- centrifugal force at C. Since the centrifugal force at A is of-mass of the Earth and Moon remain in equilibrium at equal to that at C, the greater gravitational force at A constant distances from the barycenter, the centrifugal must also be larger than the centrifugal force there, The force acting upon the center of the Earth (C) as the result net tide-producing force at A obtained by taking the dif- of their common revolutions must be equal and opposite ference between the gravitational and centrifugal forces to the gravitational force exerted by the Moon on the is in favor of the gravitational component--or outward center of the Earth. This fact is indicated at point C in toward the Moon. The tide-raising force at point A is figure 2 by the thin and heavy arTows of equal length, indicated in figure 2 by the double-shafted arrow extend- pointing in opposite directions. The net result of this cir- ing vertically from the Earth's surface toward the Moon. 500 Strategic Role of Perigean Spring Tides, 1635-1976 A north-s6uth cross-section through the Type of Force Designation earth's center in the plane of the moon's hour angle; the dashed ellipse represents. a profile Fc =centrifugal force due to earth's revolution Thin through the spheroid composing the tidal force around the barycenter arrow envelope; the solid ellipse shows the resulting Fg =gravitational force due to the moon Heavy effect on the earth's waters. arrow Ft =the resultant tide-raising force due Double to the moon shafted arrow Fg Fc )li A C B Fg f Fc 0. Fc F'= 0 9 Moon F t t Ft Relative Magnitude Earth At of the Forces Present A Fg > Fc > Ft v 11 v c Fg = Fc > 0 v 11 A B Fg < Fc > Ft Fie-URE 2-The combination of forces of lunar origin producing the tides. (A similar complex of forces exists in the Earth-Sun system.) The resulting tide produced on the side of the Earth Earth-gravity, although always present, plays no -direct toward the Moon is known as the direct tide. part in the tide-producing action. The tide-raising force At point B, on the opposite side of the Earth from the exerted at a point on the Earth's surface by the Moon at Moon and about 6,378 km farther away from the Moon its average distance from the Earth (384,318 km or than is point C, the Moon's gravitational force is consid- 238,855 mi) is only about one 9-millionth part of the erably less than at C. At point C, the centrifugal force is force of Earth-gravity exerted toward its center (6,378 in balance with a gravitational force which is greater than krn from the surface). The tide-raising force of the Moon, at B. The centrifugal force at B is.the same as that at C. is, therefore, entirely insufficient to "lift" the waters of the Since gravitational force is less at B than at C, it follows Earth physically against this far greater pull of the Earth's that the centrifugal force exerted at B must be greater than gravity. Instead, the tides are produced by that component the gravitational force exerted by the Moon at B. The of the tide-raising force of the Moon which acts to draw resultant tide-producing force at this point is, therefore, the waters of the Earth horizontally over its surface toward directed away from the Earth's center and opposite to the the sublunar and antipodal points. Since the horizontal position of the Moon. This force is indicated by the dou- component is not opposed in any way to gravity and can, ble-shafted arrow at point B. The tide produced in this therefore, act to draw particles of water freely over the location, halfway around the Earth from the sublunar Earth's surface, it becomes the effective force in generat- point, coincidentally with the direct tide, is known as the ing tides. opposite tide. At any point on the Earth's surface, the tidal force 4. The Tractive Force produced by the Moon's gravitational attraction may be It is significant that the influence of the Moon's gravita- separated or "resolved" into two components of force- tional attraction superimposes its effects upon, but does the one in the vertical, or perpendicular to the Earth's not overcome, the effects of the Earth's own gravity. surface-the other horizontal or tangent to the EartYs Appendix 501 surface. This second component, known as the tractive variable in distance and relative orientation with respect ("drawing") component of force is the actual mechanism to the Earth, and if there were no other accelerating or for producing tides. The force is zero at points on the retarding influences affecting the motions of the waters of Earth's surface directly beneath and on the opposite side the Earth. Such, in actuality, is far from the situation of the Earth from the Moon (since, in these positions, the which exists. lunar gravitational force is exerted in the vertical-i.e., First, the tidal force envelope produced. by the Moon's opposed to, and in the direction of Earth-gravity, respec- gravitational attraction is accompanied by a tidal force tively). Any water accumulated in these locations by trac- envelope of considerably smaller amplitude produced by tive flow from other points on the Earth's surface tends to the Sun. The tidal force exerted by the Sun is a composite remain in a stable configuration, or tidal "bulge." of the Sun's gravitational attraction and a centrifugal Thus, there exists an active tendency for water to be force component created by the -revolution of the Earth's drawn from other points on the Earth's surface toward the center-of-mass around the center-of-mass ofthe Earth-Sun sublunar point (A, in fig. 2) and its antipodal point (B, system, in an exactly analogous manner to the Earth- in fig. 2) and to be heaped at these points in two tidal Moon relationship. The position of this force envelope bulges. Within a band around the Earth at all points 90' shifts with the relative orbital position of the Earth in from the sublunar point, the horizontal or tractive force respect to the Sun. Because of the great difference between of the Moon's gravitation is also zero, since the entire the average distances of the Moon (384,400 kin or tide-producing force is directed vertically inward. There 239,000 mi) and Sun (149,500,000 kin or 92,900,000 is, therefore, a tendency for the formation of a stable mi) from the Earth, the tide-raising force of the Moon depression here. The words "tend to" and "tendency for" is approximately 2V4 times that of the Sun. employed in several usages above in connection with tide- Second, there exists a wide range of astronomical vari- producing forces are deliberately chosen since, as will be ables in the production of the tides caused by the changing seen below, the actual representation of the tidal forces distances of the Moon from the Earth, the Earth from the at work is that of an idealized "force envelope" within Sun, the angle which the Moon in its orbit makes with the which the rise and fall of the tides are influenced by many Earth's Equator, the superposition of the Sun's tidal en- factors. velope of forces upon that caused by the Moon, the vari- 5. The Tidal Force Envelope able phase relationships of the Moon,, etc. Some of the principal types of tides resulting from these purely astro- If the ocean waters were completely to respond to the nomical influences are described below. directions and magnitudes of these tractive forces at vari- ous points on the surface of the Earth, a mathematical Variations in the Range of the Tides: Tidal figure would be formed having the shape of an oblate Inequalities spheroid. The longest (major) axis of the spheroid extends As will be shown in figure 6, the difference in height, toward and directly away from the Moon, and the short- in meters or feet, between consecutive high and low tides er (minor) axes are centered, and mutually orthogonal to, the major axis. The two tidal humps and two tidal depres- occurring at a given place is known as the range. The sions are represented in this force envelope by the direc- range of tides at any one location is subject to many variable factors. Those influences of astronomical origin tions of the major axis and rotated minor axis of the will first be described. spheroid, respectively. From a purely theoretical point of view, the daily rotation of the solid Earth with respect to 1. Lunar Phase Effects: Spring and Neap Tides these two tidal humps and two depressions may be con- It has been noted above that the gravitational forces of ceived to be the cause of the tides. both the Moon and Sun act upon the waters of the Earth. As the Earth rotates once in each 24 hours, one would It is also obvious that, because of the Moon's changing ideally expect to find a high tide followed by a low tide at position with respect to the Earth and Sun (figure 3) the same place 6 hours later; then a second high tide after during its monthly cycle of phases (29.53 days), the gravi- 12 hours, a second low tide 18 hours later, and finally a tational attraction of Moon and Sun may variously act return to high water at the expiration of 24 hours. Such along a common line or at changing angles relative to would nearly be the case if a smooth, continent-free Earth each other. were covered to a uniform depth with water, if the tidal When the Moon is at new phase and full phase (both force envelope of the Moon alone were being considered, positions being called syzygy) the gravitational attractions if the positions of the Moon and Sun were fixed and in- of Moon and Sun act to reinforce each other. Since the 502 Strategic Role of Perigean Spring Tides, 1635-1976 First Quarter Looking down on the north pole of the earth's figure (central solid circle). The two solid ellipses represent the C tidal force envelopes produced by the moon in the positions of syzygy (new or full moon) and quadrature (first or third quarter). respectively; the dashed ellipse shows the smaller tidal force envelope produced by the sun. _ap Tides Spring Spring To Sun Full Moon Tides Tides New Moon Neap Tides C Third Quarter The gravitational attractions (and resultant tidal force envelopes) produced by the moon and sun reinforce each other at times of new and full moon to increase the range of the tides, and counteract each other at first and third quarters to reduce the tidal range. FIGURE 3.-The phase inequality'; spring and neap tides. resultant or combined tidal force is also increased, the out the month by about 49,900 km (31,000 mi). The observed high tides are higher and low tides are lower Moon's gravitational attraction for the Earth's water will than average. This means that the tidal range is greater change in inverse proportion to the third power of the dis- at all locations which display a consecutive high and low tance between Earth and Moon, in accordance with the water. Such greater-than-average tides resulting at the previously mentioned extension of Newton's Law of Grav- syzygy positions of the Moon are known as spring tides- itation. Once each month, when the Moon is closest to the a term which merely implies a "welling up" of the water Earth (perigee), the tide-generating forces will be higher and bears no relationship to the season of the year. than usual, thus producing above-average ranges in the At first- and third-quarter phases (quadratures) of the tides. Approximately 2 weeks later, when the Moon (at Moon, the gravitational attractions of the Moon and Sun apogee) is farthest from the Earth, the lunar tide-raising upon the waters of the Earth are exerted at right angles force will be smaller, and the tidal ranges will be less than to each other. Each force tends in part fo counteract the average. Similarly, in the Sun-Earth system, when the Earth is closest to the Sun (perihelion), about January 2 other. In the tidal force envelope representing these com- of each year, the tidal ranges will be enhanced, and when bined forces, both the maximum and minimum force the Earth is farthest from the Sun (aphelion), around values arereduced. High tides are lower and low tides July 2, the tidal ranges will be reduced. are higher than average. Such tides of diminished range When perigee, perihelion, and either the new or full are called neap tides, from a Greek word meaning moon occur at approximately the same time, considerably cc scanty." increased tidal ranges result. When apogee, aphelion, and 2. Parallax Effects (Moon and Sun) the first- or third-quarter moon coincide at approximately Since the Moon follows an elliptical path (figure 4), the the same time, considerably reduced tidal ranges will distance between the Earth and Moon will vary through- normally occur. Appendix 503 Common projection of the earth's orbital plane around the sun (the ecliptic) and the moon's orbital plane around the earth. S = Sun El = Earth at perihelion (Jan. 2) E2 = Earth at aphelion (July 2) M, = Moon at perigee M2 =Moon at apogee Aphelion (July 2) Moon's Orbit Perigee Al Apogee E 94.5 000 91.5 @k El 'Al, 2 million miles S million miles M2 Perihelion (Jan. 2) Earth's Orbit FIGURE 4.-The lunar parallax and solar parallax inequalities. Both the Moon and the Earth revolve',in elliptical orbits and the distances from their centers of attraction vary. Increased gravitational influences and tide-raising forces are produced when the Moon is at a position of perigee, its closest approach to the Earth (once each month) or the Earth is at its perihelion, its closest approach to the Sun (once each year). This diagram also shows the possible coincidence of perigee with perihelion to produce tides of augmented range. 1 3. Lunar Declination Effects: The Diurnal In- and low tides are then also nearly equally spaced in time, equality and occur uniformly twice daily. (See top diagram in The plane of the Moon's orbit is inclined only about 5' fig. 6.) This is known as the semidiurnal type of tides. to the plane of the Earth's orbit (the ecliptic) and thus the Factors Influencing the Local Heights and Moon in its monthly revolution around the Earth remains Times of Arrival of the Tides within 28.5' of the Earth's Equator, north and south of It is noteworthy in figure 6 that any one cycle of the which the Sun moves once each half year to produce the seasons. In a similar fashion, the Moon in making a revo-, tides is characterized by a definite time regularity as well lution around the Earth once each month, passes from a as the recurrence of the cyclical pattern. However, con- position of maximum angular distance north of the Equa- tinuing observations at coastal stations will reveal-in tor to a position of maximum angular distance south of addition to the previously explained vaxiations in the the Equator during each half month. (Angular distance heights of successive tides of the same phase-noticeable perpendicularly north or south of the celestial equator is differences in their successive times of occurrence. The termed declination.) Twice each month, the Moon crosses aspects of regularity in the tidal curves are introduced by the Equator. In figure 5, this situation is shown by the the harmonic motions of the Earth and Moon. The varia- dashed outline of the Moon. The corresponding tidal force tions noted both in the observed heights of the tides and in envelope due to the Moon is depicted, in profile, by the their times of occurrence are the result of many factors, dashed ellipse. some of which have been discussed in the preceding sec- Since the points A and A' lie along the major axis of tion. Other influences will now be considered. this ellipse, the height of the high tide represented at A The Earth rotates on its axis (from one meridian transit is the same as that which occurs as this point rotates to of the "mean sun" until the next) in 24 hours. But as the position A' some 12 hours later. When the Moon is over Earth rotates beneath the envelope of tidal forces pro- the Equator--or at certain other force-equalizing declina- duced by the Moon, another astronomical factor causes tions-the two high tides and two low tides on a given day the time between two successive upper transits of the are similar in height at any location. Successive high tides Moon across the local meridian of the place (a period 504 Strategic Role of Perigean Spring Tides, 1635-1976 0 A no rth-south cross-section through the Moon earth's center; the ellipse represents a meridian (at high declination) section through the tidal force envelope pro cluced by the moon. C' (Diurnal Tide) ----------- C (Mixed Tide) 8----------------------- -1 (Semidiurnal Tide A Equator A' Equatorial Type) hi;Zon (directly over the equator) Ea rth FIGuRE 5-The Moon's declination effect (change in angle with respect to the Equator) and the diurnal inequality. The effects of the diurnal inequality in introducing semidiurnal, mixed, and diurnal harmonic constituents in' the tides are also shown. (Compare with fig. 6.) known as the lunar or "tidal" day) to exceed the 24 hours this phenomenon can cause a displacement of force com- of the Earth's rotation period-the mean solar day. ponents and acceleration in tidal arrival times (known as The Moon revolves in its orbit around the Earth with priming of the tides) resulting in the occurrence of high an angular velocity of approximately 12.2' per day, in tides before the Moon itself reaches the local meridian of the same direction in which the Earth is rotating on its the place. Between first-quarter phase and full moon, and axis with an angular velocity of 360' per day. In each between third-quarter phase and new moon, an opposite day, therefore, a point on the rotating Earth must com- displacement of force components and a delaying action plete a rotation of 360' plus 12.2', or 372.2', in order to (known as lagging of the tides) can occur, as the result of "catch up" with the Moon. Since 15' is equal to one hour which the arrival of high tides may take place several of time, this extra amount of rotation equal to 12.2' each hours after the Moon has reached the meridian. day would require an extra period of time equal to These are the two principal astronomical causes for 12.2'/ 15 0 X 60m/, or 48.8 minutes-if the Moon revolved variation in the times of arrival of the tides. In addition in a circular orbit, and its speed of revolution did not vary. to these astronomically induced variations, the tides are On the average it requires about 50.415 minutes addi- subject to other accelerating and retarding influence$ of tional each day for a sublunar point on the rotating Earth hydraulic, hydrodynamic, hydrographic, and topographic to regain this position directly along the major axis of the origin-and may further be.modified by meteorological Moon's tidal force envelope, where the tide-raising influ- conditions. ence is a maximum. In consequence, the recurrence of a The first factor of consequence in this regard arises from tide of the same phase and similar height (see middle the fact that the crests and troughs of the large-scale, diagram of figure 6) would take place at an interval of gravity-type, traveling wave formations comprising the 24 hours 50 minutes after the preceding occurrence, if this tides strive to sweep continuously around the Earth, fol- single astronomical factor known as lunar retardation lowing the-position of the Moon (and Sun). were considered. This average period of 24 hours 50 min- In the open ocean, the actual rise (see middle diagram, utes has been established as the tidal day, but its wide figure 6) of the tidally induced wave crest is only one to variations form an important aspect of the present a few feet. It is only when the tidal crests and troughs monograph. move mto shallow water, against land masses, and into A second astronomical factor influencing the time of confining channels, that noticeable variations in the height arrival of tides of a given phase at any location results from of the water level can be detected. the interaction between the tidal force envelopes of the Possessing the physical properties of a fluid, the ocean Mum .......... N .......... @A Moon and Sun. Between new moon and first-quarter waters follow all of the hydraulic laws 'of fluids. This phase, and between full moon and third-quarter phase, means that since the ocean waters possess inertia and a Appendix 505 Distribution of Tidal Phases Tidal Day Tidal Period Tidal Period .3 2 1 11 0 Da um -2 E -3 .2 SEMIDIURNAL TIDE Tidal Day Tidal Period V) 3 Higher Lower 2 NH '@"h --High ater ig Tidal Water 0 1 Rise 0 0 Datum Tidal (v Range Tidal > - 1 Range I 0 -0 Higher -2 Low Water Tidal Amplitude 4! -3 =1/2 Range -4 Lower Low Water MIXED TIDE CO Tidal Day Tidal Period 2 Datum -2 DIURNAL TIDE FIGURE 6-The Principal types of tides. 506 Strategic Role of Perigean Spring Tides, 1635-1976 definite, small internal viscosity, both properties prevent Prediction of the Tides their absolutely free flow, and somewhat retard the over- all movement of the tides. In the preceding discussions of the tide-generating Secondly, the ocean waters follow the principles of forces, the theoretical equilibrium tide produced, and fac- traveling waves in a fluid. As the depth of the water tors causing variations, it has been emphasized that the shallows, the speed of forward movement of a traveling tides actually observed differ appreciably from the ideal- wave is retarded, as deduced from dynamic considera- ized, equilibrium tide. Nevertheless, because the tides are tions. In shoaling situations, therefore, the advance of produced essentially by astronomical forces of harmonic tidal waters is slowed. nature, a definite relationship exists between the tide- Thirdly, a certain relatively small amount of friction generating forces and the observed tides, and a factor of exists between the water and the ocean floor over which predictability is possible. it moves ain slightly slowing the-movement of the Because of the numerous uncertain and, in some cases, tides, particularly as they move inshore. Further internal completely unknown factors of local control mentioned friction (or viscosity) exists between tidally induced cur- above, it is not feasible to predict tides purely from a rents and contiguous currents in the ocean-especially knowledge of the positions and movements of the Moon where they are flowing in opposite directions. and Sun obtained from astronomical tables. A partially The presence of land masses imposes a barrier to prog- empirical approach based upon actual observations of ress of the tidal waters. Where continents interpose, tidal tides in many areas over an extended period of time is movements are confined to separate, nearly closed oceanic necessary. To achieve maximum accuracy in predictions, basins and the sweep of the tides around the world is not a series of tidal observations at any one location ranging continuous. over at least a full 18.6-year tidal cycle is required. Within Topography on the ocean floor can also provide a re- this period, all significant astronomical modifications of straint to the forward movement of tidal waters-or may tides will occur. create sources of local-basin response to the tides. Restric- Responsibility for computing and tabulating-for any tions to the advance of tidal waters imposed both by day in the year-the times, heights, and ranges of the shoaling depths and the sidewalls, of the channel as these tides-as well as the movement of tidal currents in various waters enter confined bays, estuaries, and harbors can parts of the world is vested in appropriate governmental further considerably alter the speed of their onshore agencies which devote both theoretical and practical effort passage. to this task. The resulting predictions are based in large In such partially confined bodies of water, so-called part upon actual observations of tidal heights made Ciresonance effects" between the free-period'of oscillation throughout a network of selected observing stations. of the traveling, tidally induced wave and that of the The National Ocean Survey, a component of the Na- confining basin may cause a surging rise of the water in tional Oceanic and Atmospheric Administration of the a phenomenon basically similar to the action of water U.S. Department of Commerce, maintains for this pur- caused to "slosh" over the sides of a washbasin by re- pose a continuous control network of approximately 140 peatedly tilting the basin and matching the wave crests tide gages at fixed stations as illustrated in figure 7. These reflected from opposite sides of the basin. are located along the coasts and within the major embay- All of the above, and other less important influences, rhents of the United States, its possessions, and United can combine to create a considerable variety in the ob- Nations Trust Territories under its jurisdiction. Tempo- served range and phase sequence of the tides-as well as rary secondary stations are also occupied in order to variations in the times of their arrival at any location. increase the effective coverage of the control network. Tital data are recorded on chart rolls (figure 8), on Of a more local and sporadic nature, important meteor- punched tape (figure 9), and are translated onto punched ological contributions to the tides known as "storm cards or magnetic tape (figure 10) for electronic com- surges," caused by a continuous strong flow of winds either puter processing, tabular printout, and analysis. onshore or offshore, may superimpose their effects upon Predictions of the times and heights of high and low those of tidal action to cause either heightened or dimin- water are published by the National Ocean Survey for a ished tides, or active coastal flooding. High pressure at- large number of stations in the United States and its mospheric systems may also depress the tides, and deep possessions as well as in foreign countries and United low pressure systems may cause them to increase in height. Nations Trust Territories. These predictions are published Appendix 507 each year (approximately 6 months or more in advance) Coast of North America; and (2) Pacific Coast of North in four volumes. The titles are: Tide Tables-High and America. and Asia. Low Water Predictions (1) East Coast of North and Although for many years tidal data were calculated by South America, Including Greenland; (2) Europe and the use of a special harmonic-constant tide-predicting West Coast of Africa, Including the Mediterranean Sea; machine developed within the National Ocean Survey, the (3) West Coast of North and South America, Including daily predictions published in these tide tables and tidal the Hawaiian Islands; and (4) Central and Western current tables are now handled through high-speed auto- Pacific Ocean, and Indian Ocean. matic data-processing equipment, especially programmed Predictions of tidal currents are published annually in to handle the mathematical evaluation of tidal two volumes, titled: Tidal Current Tables (1) Atlantic information. :-MEMO @"V 744 W, wZ4 7 0 '51111@@ o low Pill, .1 FrGuRE 7-The NOS tide station on Padre Island, near Port Isabel, Tex. Ift, @_z 508 Strategic Role of Perigean Spring Tides, 1635-1976 Ask ANIL 17 VI FIGURE 8.-A pressure-recording tide-gage system consisting of: (A) a gas bubbler (background) which senses the tide level by variation of hydrostatic pressure with changing height of the water above the remote, submerged orifice of the tide gage, and (B) a chart recorder or marigraph (center) which traces the water height against time. The resulting marigram trace is run through a marigrarn scanner, which yields a printout tabulation of hourly tidal heights. Appendix 509 Ail "V, k" FIGURE 9-Tidal heights sensed by the float in a tide well are punched on a paper tape in a standard digital (binary-coded decimal) form by the instrument in the center foreground. 202-509 0 - 78 - 35 510 Strategic Role of Perigean Spring Tides, 1635-1976 V ftiew mono* W. 6- mom swam own*"& aim o FIGURE 10-By means of the converter unit (center) the tidal data already punched on tape (right) are transferred onto punched cards (left) which are then fed into an electronic computer for printout, tabulation, and subsequent analysis. Reference Sources and Notes Part I CHAPTER I 1. William Bradford, Of Plymouth Plantation, 1620-1647, the complete text, with notes and introduction by Samuel Eliot Morison, new ed., New York, 1952, pp. 279-80. 2. Nathaniel Morton, Xew-Englands memoriall: or, A Brief relation of the most memorable and remarkable passages of the provi- dence of God, manifested to the planters of New-England in America; with special reference to the first Colony thereof, called New-Plimouth. Cambridge, Mass., 1669, pp. 102-3. 3. John Winthrop, The History of New Englandfrom 1630 to 1649 . . . From his original manuscripts With notes . . . by James Savage. A new edition (2 vols.) . . . Boston, Mass., 1833, vol. 1, pp. 195-8. Also: Winthrop's journal, "History of New England," 1630-1649, edited by James Kendall Hosmer, 2 vols., New York, 1908 [entry for August 16, 1635]. Sidney Perley, Historic Storms of New England, Salem, Mass., 189 1, pp. 3-10. Edward Rowe Snow, Great Storms and Famous Shipwrecks of the New England Coast, Boston, Mass., 1943, pp. 34-6. 4. Gordon E. Dunn and Banner 1. Miller, Atlantic Hurricanes (rev. ed.) Baton Rouge, La., 1964, p. 308; also pp. 308-362. 5. David M. Ludlum, Early American Hurricanes, 1492-1870, Boston, Mass., 1963, pp. 10-13. Also: Dunn and Miller, op. cit., pp. 204, 272-3. 6. Edward Rowe Snow, op. cit., pp. 59-60. [Ouoting a letter titled "Tide and Storm of Uncommon Circumstances," from the Reverend Cotton Mather in Boston to Dr. John Woodward of the Royal Society in London.] 7. Boston Xews-Letter (New England weekly) of February 21-28, 1723 (O.S.), p. 2, col. 2. [See also under this date in table 5.] 8. The Boston Gazette and Country gournal of December 11, 1786 (N.S.), No. 1690, p. 3, col. 1. [See also under this date in table 5.] 9. Edward Rowe Snow, op. cit., pp. 81-6. Also: Sidney Perley, op. cit., pp. 124-8. David M. Ludlum, Ear4y American Winters 1, 1601-1820, Boston, Mass., 1966, pp. 70-1- 10. The New Hampshire Gazette, Portsmouth, N'H., March 30, 1830, p. 2, col. 2. Also: Sidney Pcrley, op. cit., pp. 249-51. 11. Sidney Perley, op- cit., pp. 302-10. 12. Edward Rowe Snow, op. cit., pp. 128-38. 13. U.S. Weather Bureau [now the National Weather Service, NOAA], Monthty Weather Review, vol. 38, No. I (January 1916), Washington, D.C., p. 4. 14. Ivan Ray Tannehill, Hurricanes (9th ed.) Princeton, N.J., 1956, pp. 141-263, 283-295E. CHAPTER 2 1. Howard I. Chappelle, The History of the American Sailing Aravy, The Ships and Their Development, New York, 1949, p. 74. Louis F. Middlebrook, History of Maritime Connecticut During the American Revolution, 1775-1783, Salem, Mass., 1923, vol. 1, p. 204. M. V. Brewington, "The Designs of Our First Frigates,",in The American Neptune, vol. VIII, No. I (January 1948), p. 20. 2. William James Morgan, ed., Naval Documents of the American Revolution, Washington, D.C., vol. 6, 1972, p. 654. Louis F. Middlebrook, op. cit., vol. II, p. 265. M. V. Brewington, op. cit., p. 24. Pennsylvania Evening Post, September 7, 1776. 3. M. V. Brewington, op. cit., pp. 15,,20. 4. Charles J. Hoadly, ed., The Public Records of the Colony of Connecticut, vol. XIII, May 1768 to May 1772, Hartford, Conn., 1885. [Map opposite p. 503: a reduced heliotype copy of a tracing of Capt. Parker's Chart of Saybrook Barr, prepared by Charles Burdette, 1885. The original map is in the possession of the Connecticut Historical Society.] 5. Lawrence J. Wroth, Abel Buell of Connecticut, Middletown, Conn., 1958, p. 62. 6. Thomas R. Harlow, "Connecticut Engravers, 1774-1820," in quarterly Bulletin of the Connecticut Historical Society, vol. 36, No. 4 (October 1971), p. 101. 7. Refer to the first paragraph of the resolution ordered by the Governor and Council of Safety of the State of Connecticut in response to an authorization by the Congress of the United States, as quoted in the present text (reference No. 16). 8. Compare the activities of John Deshon (member of the Eastern Navy Board) in this regard, as quoted from the Colonial Records of Connecticut in the present text (reference No. 14); see also the extract from a letter written by William Vernon, a member of the same Navy Board, on March 25, 1778, quoted in Gardner W. Allen, A Naval History of the American Revolution (reprint of 1913 ed.) 2 vols., New York, 1962, vol. I, p. 307. 511 512 Strategic Role of Perigean Spring Tides, 1635-1976 9. Gardner W. Allen, op. cit., vol. 1, p. 362. William Bell Clark, ed., Naval Documents of the American Revolution, Washington, D.C., vol. 2, 1966, p. 498. 10. Entry for the date August 11, 1779, in the diary of Samuel Tully of Saybrook Point, Conn., excerpted in History of Middlesex County, Connecticut, with Biographical Sketches of Its Prominent Men, New York, 1884, p. 468. Also, Gardner W. Allen, op. cit., vol. II, p. 498. 11. Letter to the author from Thomas A. Stevens, historian of the Connecticut River, dated January 30, 1975. [The following information was added in press, w ith the issuance of volume 7 of Naval Documents of the American Revolution. William James Morgan, editor, Naval History Division, Department of the Navy, Washington, D.C., 1976.] Precise contemporary documentation of the Revolutionary War period newly available in this volume confirms several stated opinions with regard to: (1) the date of the Trumbull's passage down the, Connecticut River; (2) the necessity of an extraordinarily high tide to permit the Trumbull to clear the rivermouth bar; and (3) other tactical circumstances associated with the British attack on the Colonies which could well have prevented the T?umbull's use of intervening perigean spring tides between November 1776 and August 1779 to good advantage. John Cotton, shipbuilder of the Trumbull (launched near Middletown, Conn.) wrote to Barnabas Deane, the Continental Navy's designated authority for supervision of ship construction (himself resident at Wethersfield, Conn.) under the date November 18, 1776. In this letter, the former asks for disposition of shipbuilding stores not used, and concludes with a statement of the ship's imminent readiness to make the trip down the Connecticut River: "Sir/ Middletown Novbr 18th 1776- When Capn. [Dudley] Saltonstall went away to Wethersfield I had forgott that you had pork Stored with Tewels Butt Desired him to a Quaint you that that pork left with Cooper was taken away, I shall take outt of Tewels Store two Barrels and putt on Board the Ship- I would be Glad. if you Could hire and Send Down a Vessell to Take our Matters from the Ship yd Before we Go a way with the Ship as I Dont Like to Leave them there for fear of a Loss in Some Things that is Much Wanted Especialy Pitch-Nothing further, the Ship Will be Ready to Goe Down Tomorrow Or Next Day Yr[&c.] John Cotton." [Morgan, op. cit., p. 197] In a footnote to a second communication sent on the following day, Cotton notes that the ship has not left yet, and indicates a dependence on high tides in the tidewater river. [Full moon and spring tides would have occurred around the date November 23, which is within the proposed week for "going down" to which Cotton refers. A close perigee-syzygy alignment (P-S @ -5h) already had occurred on September 27, 1776, with a mean epoch of 8:30 a.m., 75'W.-meridian time.] "Sir/ Middletown Novbr 19th 1776 1 Wrote to Aquaint you that I have Taken to blls of Your Pork for the Ship Which was in Tewels Store Capn [Dudley] Saltonstall Desires that I would have You Send Down Some Coffee and Sugar and Chocolate if you have Any for the Ships Stores Round to New london What Other he wants I shall Endeavor to Gett here, and the above if they are to be Gott here if they Are they [are] Extravagant the prices Being high, as people are So Exceeding high in their prices they Know well Nott to ask if you have any Spare Bags I Could wish you Would Send Down % Dozen as the Ship Wants them and the Capn Mentioned itt To Me I am Sir With Regards [&c.] John Cotton" N B The Ship Must Goe away this Week if the Tides Rises yrs J-C." [Morgan, op. cit., p. 2091 In a letter from Barnabas Deane to John Hancock datelined "Wethersfield 25th Jany 1777" Deane wrote to the chair- man of the Continental Marine Committee as follows: 19sir The Trumbull Frigate under my Direction Proceeded down Connecticut River the Last of Novr and when She had got within a few miles of the Rivers mouth Two of the Enemys Frigates Appear'd of[f] the River & kept that Station untill the River Froze, I Advisd with Govr Trumbull & his Opinion was, to Lay the Frigate up in Some Safe Creek which I did about Twenty miles from the Rivers mouth-Capt Manly Call'd on me with a Letter from Govr Trumbull (a Copy of which you have on the Other Side) And Agreeable to,his Advice I have Supply'd Capt Manly with the Trumbulls Cannon which I hope will be Agreeable to the Honble Congress; Govr Trumbull has Engaged that the First Cannon made After the Furnace in this State begins Again to Cast Shall be for to Replacethose Supply'd Capt Manly with I am Respectfully [ &c. Bar- Deane" [Morgan, op. cit., p. 1036] Reference Sources and Notes 513 It is significant in terms of the draft of the Trumbull at the time she cleared Saybrook Bar that the ship's cannon were still lacking on September 7, 1779, a month after the vessel left the river mouth. [Cf., Charles 0. Paullin, ed. Out-Letters to the Continental Marine Committee and Board of Admiralty, August 1776-September 1780, New York, 1924, vol. 2, pp. 106-115.] The Trumbull therefore was not encumbered with this extra load of armament on crossing the bar. A further meaningful letter was transmitted from Nathaniel Shaw, Jr., Continental agent at New London, Conn., to Robert Morris, Chairman of the Secret Committee of the Continental Congress in Philadelphia, datelined "New'London Feb 4 1777." This contains the following confirmatory information regarding the situation of unusually high tide required to permit clearance of Saybrook Bar by the frigate Trumbull: I have and shall Continue to supply Capi [Dudley] Saltonstall with what money he may want to get his ship out, at pre-sent she is in Connecticut River and am fearful we shall meet with Difficulty in getting her out as she draws so much water, it must be a very extraordinary tide to get her over the Barr, and in case she lies any time on the barr, as the British Ships are Continually passing they may take that opportunity to Destroy her, however you may depend that the greatest prudence will be observed-the Sale of the prize Ship Clarendon taken by the Cabot is not compleated soon as it can be effected shall send the Accot [Morgan, op. cit., p. 11031 12. Henry P. Johnson, ed., The Record of Connecticut Men in the Military and Naval Service During the War of the Revolution, 1775-1783, Hartford, Conn., 1889, pp. 598-9. 13. Charles Oscar Paullin, The Navy of the American Revolution, Cleveland, Ohio, 1906, p. 526. 14. Charles J. Hoadly, ed., The Public Records of the State of Connecticut, vol. 1, October 1776 to February 1778, Hartford, Conn., 1894, p. 113. 15. Ibid., pp. 517-18. 16. Ibid., pp. 567-8. 17. Ibid., p. 569. - 18. Charles J. Hoadly, op. cit., vol. 11, May 1778 to April 1780, Hartford, Conn., 1895, p. 499. 19. William James Morgan, ed., op. cit., vol. 6, 1972, pp. 322, 350, 360, 706, 759, 763, 892, 949, 1178, 1218-19, and especially p. 1220. 20. Ibid., p. 323. History of Middlesex County, Conn., loc. cit. 21. Samuel Adams Drake, Nooks and Corners of the New England Coast, New York, 1875, pp. 447-8. 22. Gardner W. Allen, op. cit., vol. II, p. 498. 23. Henry Steele Commager and Richard B. Morris, cds., The Spirit of 'Seventy-Six-The Story of the American Revolution as Told by Participants, New York, 1967, p. 956. 24. Charles J. Hoadly, op. cit., vol. XV, p. 206. 25. Ibid., pp. 238-9. 26. John Hamilton Moore, The New Practical Navigator, Being an Epitome of Navigation 12th ed., London, 1796, p. 133. 27. Howard 1. Chappelle, loc. cit. Cf., also: M. V. Brewington, op. cit., pp. 15, 20. 28. Gardner W. Allen, op. cit., vol. II, p. 494 29. Frank Moore, compiler, and John Anthony Scott, ed., The Diary of the American Revolution, 1775@4781, New York, 1967, p. 412. 30. Loc. cit. 31. Letter from A. W. H. Pearsall, Historian, National Maritime Museum, Greenwich, England, to the author, dated November 4, 1974. 32. U.S. Navy Department, Official Records of the Union and Confederate Navies in the War of the Rebellion, series 1, vol. 12, Washington, D.C., 1901, pp. 259-261. Virgil Carrington James, The Civil War at Sea, 3 vols., New York, 1960, vol. 1, pp. 266-73. 33. Report of Assistant C. 0. Boutelle, aboard U.S. Coast Survey Steamer Vixen at Port Royal Bay, S.C., November 8, 1861, in Appendix No. 31 of the annual Report (f the Superintendent of the Coast Surveyfor 1861, Washington, D.C., 1862, p. 267. 34. Virgil Carrington James, op. cit., vol. 1, p. 274. 35. Ibid., pp. 274-5. 36. Verified by Ships' Histories Branch, Naval History Division, U.S. Navy Department, Washington, D.C. 37. U.S. Navy Department, op. cit., series 11, vol. 1, Washington, D.C., 1921,p. 234. 38. Annual Report of the Superintendent of the Coast Surveyfor 1847, Washington, D.C., 1847, p. 37; also Appendix No. 13, p. 77. 39. Ibid., in Appendix No. 13, pp. 76-7. 40. Ben Dixon McNeill, The Hatterasman, Winston-Salem, N.C., 1958, pp. 136, 282. 41. Virgil Carrington James, op. cit., vol. 1, pp. 197-8. 42. Gary S. Dunbar, Historical Geography of the North Carolina Outer Banks (Louisiana State University, coastal studies series No. 3), Baton Rouge, La., 1958, pp. 28, 139. 1 43. Frank M. Bennet, The Stewn Navy of the United States, Pittsburgh, Pa., 1896, p. 242. 514 Strategic Role of Perigean Spring Tides, 1635- 1976 CHAPTER 3 1. Hubert Shirley Smith, The World's Great Bridges, Ist. ed., New York, 1953, pp. 79-80.@ 2. David B. Steinman and Sara R. Watson, Bridges and Their Builders (reprint of 1941 ed.), New York, 1957, pp. 255-6. [Note: In connection with the perigean spring tide incident involving the Firth of Forth Bridge mentioned in the text of the present work, an explanatory detail is desirable. An obvious discrepancy occurs between the date of this happening ("New Year's Day of 1884") specified in the above-cited reference source and the date (May 26, 1884) given as that of the first actual constructional work, including caisson launching and implanting, in the immediately preceding paragraph of this same source. This inconsistency must also be considered against the confirmatory mention of an unusually high and low tide on the day of the accident-and the date (October 19, 1885) of subsequent surfacing of the caisson for the northwest comer of the Queensferry pier after ith plunge to the bottom. Together, these evidences clearly indicate that the printed date for the accident should read "New Year's Day of 1885" instead of 1884.1 3. Ibid., p. 152. 4. F. D. Bickel. "Demolition of Ripple Rock," in The Military Engineer, vol. 51, No. 341 (May-June 1959), pp. 173-7. Jim Gibbs, Disaster Log of Ships, New York, 1971, pp. 105-114. [For April 7, 1958 in this article read April 5, 1958, and for Maude Island and Maude Inlet, read Maud Island and Maud Inlet, respectively.] Business Week, "Tunneling Under Sea to Blast Channel Clear," March 29, 1958, pp. 78-80; "The Big Bang at Ripple Rock," April 19, 1958, p. 42. 5. Will F. Thompson and Julia Bell Thompson, "The Spawning of the Grunion," State of California Fish and Game Commission, Fish Bulletin No. 3, Sacramento, Calif., July 15, 1919, pp. 1-29. CHAPTER 4 1. Johann Kepler, Astronomia Nova seu de Motu Stellae Martis, in,7oannis Kepleri Astronomi Opera Omnia, edited by Dr. Christian Frisch, vol. II, Frankfurt, Germany, 1859, p. 313. 2. Francis S. Benjamin, Jr. and G. J. Toomer, eds., Cam@anus of Novara [Campano Novarese] and Medieval Planetary Theory: Theorica planetarum, Madison, Wis., 197 1, pp. 44-5, 175-7, 1 B1, 377. 3. Royal Society Letter Book, C. 1, No. 4, "A Letter of Mr. Joseph Childrey to the Right Reverend Seth Lord [Bishop of Sarum] concerning some Animadversions upon the Reverend Dr. John Wallis's Hypothesis about the Flux and Reflux of the Sea, publish't No. 16 of these Tracts"; letter dated March 31, 1669/1770, Philosophical Transactions of the Royal Society, vol. 5, No. 64 (October 1670), pp. 2061-8. Also: Joshua Childrey, Syzygiasticon Instauratum. Or, An Ephemeris of the Places and Aspects of the Planets, as they respect the Sun as Center of their Orbes, Calculatedfor the rear of the Incarnation of God, 1653, London, 1653. 4. Florian Cajori, ed., Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World. Translated from the Latin by Andrew Motte in 1729 [from the 3d ed. of Newton's Philo@ophiae naturalisprincipia mathematica, etc. of 1726]. The translations revised, and supplied with an historical and explanatory appendix by Florian Cajori (2d printing) Berkeley, Calif., 1946, p. 479. 5. The Mathematical Principles of Natural Philosophy, by Sir Isaac Newton, translated into English by Andrew Motte, etc., care- fully revised and corrected by W. Davis, in three volumes, vol. III, London, 1803, pp. 241, 243. Also: Sir Isaac Newton's Principia (original Latin edition) reprinted for Sir William Thomson and Hugh Blackburn, Glasgow, 1861, pp. 465, 467. 6. Encyclopaedia Britannica, or a Dictionary of. Arts and Sciences Compiled Upon a New Plan, etc., by a Society of Gentlemen in Scotland in three volumes, vol. I, Edinburgh, Scotland, 1771, p. 474. 7. John Hamilton Moore, The New Practical Navigator, etc., being an Epitome of Navigation, 12th edition, London, 1796, p. 133. 8. John Hamilton Moore, loc. cit. 9. D. L. Hutchinson, "The Saxby Gale," in Transactions of the Canadian Institute, vol. IX (1911 ), Toronto, 1913, p. 256. 10. David M. Ludlow, Early American Hurricanes, 1492-1870, Boston, 1963, pp. 108-111. I L D. L. Hutchinson, op. cit., pp. 253-5. 12. Ibid., p. 259. 13. William Ferrell, "Report of Meteorological Effects on Tides," in the annual Report of the Superintendent of the Coast Survey for 1871, Appendix No. 6, Washington, D.C., 1874, p. 98. [Note: The sketch No. 38 referred to in the passage here quoted directly from the text of the article is a typographical error in the original publication and should read "Sketch No. 34."] 14. Horace Lamb, Hydrodynamics, Ist American printing of British 6th ed. (1932), New York, 1945, pp. 353-355. 15. William Thomson Kelvin and Peter G. Tait, Treatise on Natural Philosophy, 2 vols., Cambridge, England, 1923, article 60 [reprinted as Principles of Mechanics and Dynamics, New York, 1962]. 16. George B. Airy, Treatise "On Tides and Waves," in Encyclopaedia of Astronomy, London, 1848, vol. 5, p. 362, article 459 [re- -printed from Encyclopaedia Metropolitana, London, 1845, vol. 5, p. 362]. 17. Hermann L. F. von Helmholtz, Lehre von den Tonemfindungen, 2d ed., Braunschwerg, Germany, 1870, p. 622. Reference Sources and Notes 515 Part H CHAPTER 3 1. Paul Schureman, Manual of Harmonic Analysis and Prediction of Tides. National Ocean Survey (formerly U.S. Coast and Geodetic Survey) Special Publication No. 98, rev. (1940) ed., reprinted 1958 with corrections; 2d printing 1971. U.S. Government Printing Office, Washington, D.C., 1971, pp. 170-171. 2. Hugh Godfray, An Elementary Treatise on the Lunar Theory (3d ed., revised) Macmillan and Co., New York, 1871, p. 64. The historical development of the theories of lunar evection, variation, and other solar-induced perturbational terms since the time of Newton can be traced through the following sources: (a) Sir Isaac Newton, Mathematical Principles of Natural Philosophy and His System of the World, translated (from Latin) into English by Andrew Motte in 1729 (from the 3d ed. of 1726); the translations revised, and supplied with an historical and explanatory appendix by Florian Cajori. University of California Press, Berkeley, Calif. (2d printing), 1946. Book 1: The Motions of Bodies, Proposition LXVI, Theorem XXVI, pp. 173-182; also Book III: The System of the World, Proposition XXII, Theorem XVIII, pp. 433-434. (b) Roger Long, Astronomy, in Five Books, Cambridge, England, 1764. Book 4, volume II, chapter 4: The Irregularities of the Moon's Motion Caused by the Attraction of the Sun, pp. 620-629, sections 1441-1458. (c) Ferdinand R. Hassler, A Popular Exposition of the System of the Universe, G. & C. Carvill, New York, 1828. Part III, chapter III, pp. 88-94. (d) John Gurnmere, An Elementary Treatise on Astronomy, in Two Parts, revised by E. Otis Kendall (4th ed.) E.C. &J. Biddle, Philadelphia, Pa., 1851. Chapter XXII, pp. 209-214, sections 404-407. (e) Ernest W. Brown, An Introductory Treatise on the Lunar Theory, Cambridge University Press, London, England, 1896 (reprinted by Dover Publications, New York, 1960), pp. 124-130. (f) Carnegie Institution of Washington (Publication No. 9), The Collected Mathe matical Works of George William Hill, in four volumes, Carnegie Institution of Washington, Washington, D.C. 1905-1907. Volume I, memoir No. 29-On the Part of the Motion of the Lunar Perigee Which Is a Function of the Mean Motions of the Sun and Moon, pp. 243-270; volume 1, memoir No. 32-Researches in the Lunar Theory, chapter 11: Determination of the Inequalities Which Depend Only on the Ratio of the Mean Motions of the Sun and Moon, pp. 305-335; volume IV, memoir No. 31-The Secular Variation of the Motion of the Moon's Perigee, p. 105; volume IV, memoir No. 55-LiteraI Expression for the Motion of the Moon's Perigee, pp. 41-50. (g) Forest Ray Moulton, An Introduction to Celestial Mechanics (2d rev. ed.), The Macmillan Co., New York, 1914. Chapter IX, section 1: Effects of the Components of the Disturbing Force, pp. 325-332, and section 11, The Lunar Theory, pp. 347-360. (h) Dirk Brouwer and Gerald M. Clemence, Methods of Celestial Mechanics, Academic Press, New York, 196 1. Chapter XI I, Lunar Theory, pp. 324-328, and pp. 360-366. CHAPTER 4 1. Rollin A. Harris, Manual of Tides, compiled from various technical appendixes to the annual Reports of the Superintendent of the U.S. Coast and Geodetic Survey, 1894-1907. U.S. Government Printing Office, Washington, D.C., 1895-1908. The pertinent reference appears in Appendix No. 9 of the annual report for 1897, Washington, D.C., 1898, part II, chapter IV, p. 525, equation 288. 2. Forest Ray Moulton, An Introduction to Celestial Mechanics (2d rev. ed.) The Macmillan Co., New York, 1914, p. 327. 3. U.S. Naval Observatory, Improved Lunar Ephemeris, 1952-1959, U.S. Government Printing Office, Washington, D.C., 1954, p. 317. The approximate equation given here contains only five of a series of 181 terms, the rest having very small coefficients. 4. This 1931 March 4 instance of an extremely small separation-interval between perigee and syzygy (P - S = + 6 min.) ranks among the closest such alignments in the 400-year period 1600-1999. Its positive effects upon tidal flooding potential are amply demonstrated in the multiple descriptions of coastal inundation which accompanied the strong perigean spring tides produced (see Key No. D-57) as noted in tables I and 5 and in chapter 7 of the text. The extended astronomical influence of this wry close agreement between the positions of perigee and syzygy is further emphasized by a chain of five interrelated tidal flooding. events in the space of 23 consecutive months. These events are separated by periods of 2, 1, 7.5, and I anornalistic months, respectively (see table 1). Each interval between floodings is indicative of the mathematically commensurable relationships which govern successive perigee-syzygy alignments and their associated perigean spring tides. 5. Edgar W. Woolard and Gerald M. Clemence, Spherical Astronomy, Academic Press, New York, 1966, p. 161. 6. An exact coincidence between the ascending node of the lunar orbit and the vernal equinox would require that the Moon be crossing the ecliptic (i.e., the apparent celestial latitude of the Moon,,3(C =0*, and increasing from - to +) at the same time that the Sun is crossing the celestial equator from south to north (i.e., the apparent declination of the Sun, BO = 00). Although such an exact agreement is very rare, the attainment of the above conditions within a few days of each other is sufficient to produce the extreme lunar declinations noted in the text. See The American Ephemeris and Nautical Almanac for the year 1950, U.S. Government Printing Office, Washington, D.C., 1948, p. 4, pp. 60, 104, and pp. 134, 142. 516 Strategic Role of Perigean Spring Tides, 1635-1976 CHAPTER 5 1. Otto Pettersson, "The Connection Between Hydrographical and Meteorological Phenomena," Quarterly -7ournal of the Royal Meteorological Society, vol. XXXVIII, No. 163, July 1912, pp. 173-191 (especially pp. 190ff.). 2. Hans Pettersson, "Long Periodical Variations of the Tide-Generating Force," Conseil Permanent International pour FEx- ploration de ]a Mer, Publications de Circonstance No. 65, Copenhagen, Denmark, July 1913, pp. 3-23 (especially pp. 7ff.). 3. R. C. H. Russell and Commander D. H. Macmillan, Waves and Tides, (Ist reprint ed.) Greenwood Press, Westport, Conn., 1970, p. 207. 4. Clyde Stacey, "Earth Motions," The Encyclopedia of Atmospheric Sciences and Astrogeology, vol. 11, 1967, p. 337, Col. 2. 5. U.S. Naval Observatory, Improved Lunar Ephemeris, 1952-59, U.S. Government Printing Office, Washington, D.C., 1954, pp. 286, 292; Explanatory Supplement to The Astronomical Ephemeris and The.American Ephemeris and Nautical Almanac, Her Majesty's Stationery Office, London, England, 1969, pp. 44, 107; Supplement to the A.E. 1968, U.S. Naval Observatory, Washington, D.C., 1966 (reprinted with footnote revisions, 1973), pp. 16s-18s. 6. H. F. Fl,legel and T. C. Van Flandern, "A Machine Algorithm for Processing Calendar Dates," Communications of the Association for Computing Machinery, vol. XI, No. tO, Oct. 1968, p. 657. CHAPTER 6 1. Cf., Hugh Godfray, An Elementary Treatise on the Lunar Theory, New York, Macmillan and Co., 1871, pp. 73-74. CHAPTER 7 1. George F. McEwen, "Destructive High Waves Along the Southern California Coast," Shore and Beach, vol. III, No. 2, April 1935, pp. 61-64 (especially p. 63). See also: Morrough P. O'Brien, "The Coast of California as a Beach Erosion Laboratory," Shore and Beach, vol. IV, No. 3, July 1936, pp. 74-79 (especially p. 74). 2. Dorothy Franklin, West Coast Disaster, Columbus Day, 1962, Gann Publishing Co., Portland, Oreg. (no publication or copy- right date). CHAPTER 8 1. Glenn W. Brier, "Diurnal and Semidiurnal Atmospheric Tides in Relation to Precipitation Variations," Monthly Weather Review, vol. 93, No. 2, February 1965, pp. 93-100. 2. John R. Gribben and Stephen H. Plagemann, The gupiter Effect, Walker and Co., New York, 1974; reprinted, 1975, revised, 1976, Vintage Books, New York. For technical reviews of the proposed theory, see: American Scientist, vol. 62, pp. 721-722, 1974; Annals of Science, vol. 32, pp. 601-603, 1975; Icarus, vol. 26, pp. 257-267, 270, 1975; Physics 7"oday, April 1975, pp. 74-75; and Science, vol. 186, pp. 728- 729, 1974. Bibliography on Tides A selected list of reference sources, arranged by category, as follows: (1) CLASSIC WORKS AND TREATISES ON THE TIDES (See also category 8.) (2) TEXTBOOKS AND SURVEY WORKS ON PHYSICAL AND DYNAMICAL OCEANOGRAPHY (3) REFERENCE AND GENERAL SUMMARY ARTICLES ON THE TIDES (4) DESCRIPTIVE WORKS AND POPULAR PRESENTATIONS ON THE TIDES (5) THE EARTH-MOON SYSTEM; CLASSIC THREE-BODY PROBLEM; LUNAR THEORY AND PERTURBA- TIONS; EARTH TIDAL INFLUENCES ON THE MOON'S ORBIT (See also category 25.) (6) GRAVITATIONAL FIELDS Of' THE EARTH, MOON, AND SUN; TIDE-GENERATING FORCES AND THE GRAVITATIONAL POTENTIAL (See also category 7.) (7) TIDAL THEORY AND TIDAL DYNAMICS (See also categories 12,13,14, 15,16.) (8) HARMONIC ANALYSIS OF TIDES: TIDAL CONSTANTS AND CONSTITUENTS (9) NUMERICAL INTEGRATION, MODELS, AND SOLUTIONS OF SPECIAL TIDAL PROBLEMS (10) DEEP-SEA TIDES (See also category 24.) (11) INTERNAL TIDAL WAVES; SURFACE MANIFESTATION AS TIDE RIPS (12) TIDES IN A ZONAL OCEAN (13) TIDES IN SEAS AND BASINS, AND IN BAYS, HARBORS, AND GULFS; RESONANCE FACTORS (14) TIDES IN SHALLOW WATERS AND ESTUARIES; FRICTIONAL EFFECTS; TIDAL MIXING (15) SHORT-PERIOD TIDES: CLASSIFICATION, THEORY, AND CHARACTERISTICS (16) LONG-PERIOD TIDES AND WAVES; SECULAR TIDAL INFLUENCES (17) SPECIAL STUDIES OF TIDAL PHENOMENA BY TYPES AND REGIONS (OBSERVATIONS AND ANALYSES) (18) METEOROLOGICALLY INDUCED WAVES AND SWELL EFFECTS ON HIGH TIDES; WIND COUPLING AND WIND STRESS; STORM SURGES (19) TIDAL HYDRAULICS; COASTAL PROCESSES (See also category 24.) (20) SEASONAL EFFECTS ON TIDES AND SEA LEVtL (21) TIDE GAGES AND OTHER TIDE-RECORDING INSTRUMENTATION; RADAR DETECTION OF EXTREME TIDAL HEIGHTS; FREQUENCY ANALYSIS OF THE HIGHEST TIDES OF RECORD (22) LONG- AND SHORT-PERIOD FLUCTUATIONS IN MEAN SEA LEVEL; INFLUENCES ON GEODETIC SURVEYS (23) TIDAL PREDICTIONS, COMPUTATIONS, AND TABLES; ANALYSIS OF OBSERVATIONS, INCLUDING DIGITAL COMPUTER PROCESSING (See also category 8.) (24) TIDE AND TIDAL,CURRENT RESPONSES ON THE OCEAN FLOOR; DEEP-SEA CURRENTS (25) TIDAL FRICTION ON THE ROTATING EARTH; ENERGY TRANSFER AND DISSIPATION; VARIATION IN THE LENGTH OF THE DAY (26) EARTH TIDES: TIDAL VARIATION IN THE FORCE OF GRAVITY (27) TIDAL LOADING; ELASTIC STRAIN; DEFORMATION; TILT; AND DEFLECTION OF THE VERTICAL (28) EARTH TIDES: GROUND-WATER RESPONSES IN WELLS AND RESERVOIRS (29) EARTH TIDES: DETERMINED FROM ANALYSIS OF ORBITAL PERTURBATIONS OF ARTIFICIAL SATELLITES (30) HYDRODYNAMICS; FIGURES OF THE EARTH AND MOON (31) TIDE EFFECTS ON THE ORBITS OF ARTIFICIAL SATELLITES (32) CORRELATION OF EARTHQUAKES WITH EARTH TIDES AND OTHER LUNISOLAR INFLUENCES; TIDAL INTERRELATIONS WITH MOONQUAKES, (33) ATMOSPHERIC TIDES; POSSIBLE LUNITIDAL CORRELATIONS WITH ATMOSPHERIC PRECIPITATION (34) TIDAL CURRENTS: OBSERVATION, MEASUREMENT, AND PREDICTION TABLES (35) SALINITY EFFECTS OF TIDAL AND CURRENT MOVEMENTS (36) WATER TEMPERATURE VARIATIONS RESULTING FROM TIDAL AND CURRENT MOVEMENTS; DEN- SITY STRATIFICATION AND ENTRAINMENT (37) ELECTROMAGNETIC EFFECTS ASSOCIATED WITH VELOCITY OF TIDAL CURRENTS (38) PRACTICAL EFFECTS OF TIDES AND CURRENTS (39) TIDAL POWER (40) HISTORY OF. TIDAL AND TIDE-RELATED ASTRONOMICAL OBSERVATIONS, MEASUREMENTS, THEORIES, AND PREDICTIONS (41) LUNAR INFLUENCES IN GEOMAGNETISM (CORRELARY TO INCREASED TIDAL EFFECTS) (42) BIBLIOGRAPHIES, SOURCE BOOKS, GLOSSARIES, AND STATE-OF-THE-ART LITERATURE RELATIVE TO TIDES AND TIDAL CURRENTS 517 518 Strategic Role of Perigean Spring Tides, 1635-1976 (1.) CLASSIC WORKS AND TREATISES ON THE TIDES Whewell, W., 1836: Researches on the tides; Fifth series: On the (See also category 8.) solar inequality and the diurnal inequality of the tides at Liver- Darwin, George H., 1879: On the bodily tides of viscous and serm- pool. Royal Society of London, Philosophical Transactions, Series elastic spheroids, and on the ocean tides upon a yielding nucleus. A, 135, 131-147. Royal Society of London, Philosophical Transactions, part 1, -, .1837: Researches on the tides; Seventh series: On the 1-35. diurnal inequality of the height of the tides, especially at Ply- ,1879: On the precession of a viscous spheroid, and on the mouth and Singapore; and on the mean level of the sea. Royal remote history of the Earth. Royal Society of London, Philo- Society of London, Philosophical Transactions, series A, 136, 75- sophical Transactions, part 11, 447-538. 85. 1880: Problems connected with the tides of a viscous -, 1838: Researches on the tides; Ninth series: On the de- termination of the laws of the tides from short series of observa- spheroid. Royal Society of London, Philosophical Transactions, part 11, 539-593. tions. Royal Society of London, Philosophical Transactions, series -, 1880: On the secular changes in the elements of the orbit A, 137, 231-247. of a satellite revolving about a tidally distorted planet. Royal So- -, 1839: Researches on the tides; Tenth series: On the laws ciety of London, Philosophical Transactions, part 11, 713-891. of the low water at the Port of Plymouth and on the permanency ,1881: On the tidal friction of a planet attended by several of mean water. Royal Society of London, Philosophical Trans- satellites, and on the evolution of the solar system. Royal Society actions, series A, 138, 151-161. of London, Philosophical Transactions, part 11, 491-535. 1882: On the stresses caused in the interior of the Earth by (See also part I, chapter 4, of the present work.) the weight of continents and mountains. Royal Society of Lon- don, Philosophical Transactions, part 1, 187-230. (2) TEXTBOOKS AND SURVEY WORKS ON PHYSICAL -, 1962: The Tides _(reprint ed.) Freeman, San Francisco, AND DYNAMICAL OCEANOGRAPHY 342 pp. Aix, Wil -liam S. von, 1962: An Introduction to Physical Ocean- Ferrel, William, 1874: "Tidal researches," reprinted Appendix from ography. Addison-Wesley, Reading, Mass., 422 pp. the annual Report of the Superintendent of the U.S. Coast Survey Defant, Albert, 1961: Physical Oceanography. In 2 vols., Pergamon, for 1874, U.S. Government Printing Office, Washington, D.C. Oxford, 1327 pp. 268 pp. Dietrich, Gunter, 1963: General Oceanography. Wiley-Interscience, Harris, Rollin A., 1898: Manual of Tides, part 1, Introduction and New York, 588 pp. Historical Treatment of the Subject, as Appendix No. 8, pp. 319- Gross, M. Grant, 1972: Oceanography: A View of Earth. Prentice- 469; part II, Tidal Observation, Equilibrium Theory and the Hall, Englewood Cliffs, N.J., 560 pp. Harmonic Analysis, as Appendix No. 9, pp. 471-575, plus aux- Neumann, Gerhard and Pierson, Willard J., Jr., 1966: Principles iliary tables for the reduction and prediction of tides. pp. 577- of Physical Oceanography. Prentice-Hall, Englewood Cliffs, N.J., 699, in the annual Report of the Superintendent of the U.S. 545 pp. Coast and Geodetic Survey for 1897. U.S. Government Printing Neumann, Gerhard, 1968: Ocean Currents. Elsevier, Amsterdam, Office, Washington, D.C. The Netherlands, 352 pp. -, 1895: Manual of Tides, part III, Some Connections be- Officer, Charles B., 1976: Physical Oceanography of Estuaries and tween Harmonic and Nonharmonic Quantities, including Appli- Associated Coastal Waters. Wiley-Interscience, New York, 465 cations to the Reduction and Prediction of Tides, as Appendix PP. No. 7, pp. 125-187, plus auxiliary tables for the reduction and Phillips, Owen M., 1966: The Dynamics of the Upper Ocean. prediction of tides, pp. 189-262, in the annual Report of the Cambridge University Press, London, 261 pp. Superintendent of the U.S. Coast and Geodetic Survey for 1894. Proudman, Joseph, 1953: Dynamical Oceanography. Wiley, New U.S.Government Printing Office, Washington, D.C. York, 409 pp. -, 1901: Manual of Tides, part IV-A, Outlines of Tidal Sverdrup, Harald U., Johnson, Martin W., and Fleming, Richard Theory, as Appendix 7, pp. 535-693, in the annual Report of the H., 1959: The Oceans: Their Physics, Chemistry and General Superintendent of the U.S. Coast and Geodetic Survey for 1900. Biology. Prentice-Hall, Engl@wood Cliffs, N.J., 1087 pp. U.S. Government Printing Office, Washington, D.C. Turekian, Karl, 1976: Oceans. Prentice-Hall, Englewood Cliffs, -, 1904: Manual of Tides, part IV-B, Cotidal Lines for the N.J., 160 pp. World, as Appendix 5, pp. 315-400, in the annual Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1904, (3) REFERENCE AND GENERAL SUMMARY ARTICLES U.S. Government Printing Office, Washington, D.C. ON THE TIDES -, 1908: Manual of Tides, part V, Currents, Shallow-Water Doodson, A. T., 1958: "Oceanic tides," in: Advances in Geophys Tides, Meteorological Tides, and Miscellaneous Matters, as Ap- ics, vol. 5. Academic Press, New York, 118-153. pendix 6, pp. 231-545, in the annual Report of the Superintendent Groves, Gordon W., 1971: "Tides,'; in: McGraw-Hill Encyclopedia of the U.S. Coast and Geodetic Survey for 1907, U.S. Govern- of Science and Technology, vol. 13, McGraw-Hill, New York, ment Printing Office, Washington, D.C. 650-657. Levy, Maurice, 1898: Lefons sur la thdorie des maries (Studies on Hansen, Walter, 1962: "Tides," in: The Sea, vol. 1. Wiley-Inter- the theory of the tides). Gauthier-VilIars et Fils, Paris, France, science, New York, 764-780. 298 pp. Henderschott, M.C. and Munk, W., 1970: Tides. Annual Review of Fluid Mechanics, 2, 205-224. Whewell, W., 1834: On the empirical laws of the tides in the Port of Henderschott, M. C., 1973: Ocean tides. Eos (American Geophys- London: 'Some reflexions on the theory. Royal Society of London, ical Union Transactions), 54, 76-86. Philosophical Transactions, series A, 133, 15-45. National Academy of Sciences, 1932: "Tides and tidal currents," -, 1836: Researches on the tides; Fourth series: On the empir- in: Physics of the Earth-Oceanography, vol. 5, ch. 7. Na- ical laws of the tides in the Port of Liverpool. Royal Society of tional Research Council Bulletin No. 85, Washington, D.C., London, Philosophical Transactions, series A, 135, 1-15. 581 pp. Bibliography on Tides 519 Rossiter, J. R., 1963: "Tides," in: Oceanography and Marine Brown, Ernest W., 1960: An Introductory Treatise on the Lunar Biology: An Annual Review, 1, 11-25. Theory. Reprint of original 1896 ed. published by Cambridge 1 1967: "Tides," in: International Dictionary of Geophysics. University Press. Dover, New York, 292 pp. Pergamon, Oxford, vol. 2, 1539-1543. - (with the assistance of Hedrick, Henry B.), 1919: Tables of , 1967: "Tides in oceans," in: International Dictionary of the Motion of the Moon, in 3 vols. and 6 sections. Yale Univer- Geophysics. Pergamon, Oxford, vol. 2, 1547-1549. sity Press, New Haven, Conn. Rouch, Jules Alfred Pierre, 1961: Les maries (The Tides). Paris -, 1926: Complement to the Tables of the Motion of the Payot, Paris, France, 230 pp. Moon. 'Transactions of the Astronomical Observatory of Yale Rudaux, Lucien and de Vaucouleurs, G., 1967: "The tides," in: University, vol. 3, pt. 5, The Observatory, New Haven, Conn. Larousse Encyclopedia of Astronomy. Prometheus Press, New Ferrel, William, 1871: On the Moon's mass as deduced from a dis- York, 169-174. cussion of the tides of Boston Harbor. Appendix No. 20 in the Swanson, R. L., 1976: Tides. Marine EcoSystems Analysis (MESA) annual Report of the Superintendent of the U.S. Coast Survey Program, MESA New York Bight Atlas Monograph 4. New for 1870. U.S. Government Printing Office, 1873, Washington, York Sea Grant Institute, Albany, N.Y., 34 pp. D.C., pp. 190-199. U.S. Navy Hydrographic Office (now the U.S. Naval Oceano- Gerstenkorn, Horst, 1967: On the controversy over the effect of graphic Office), 1966: "Tides and tidal currents," in Nathanial tidal friction upon the history of the Earth-Moon System. Icarus, Bowditch's American Practical Navigator, ch. XXXI. U.S. Navy 7, 160-167. Department Hydrographic (Oceanographic) Office, Publication -, 1969: The earliest past of the Earth-Moon System. Icarus, No. 9, 1966 Corrected Print. U.S. Government Printing 'Office, 11,189-207. Washington, D.C., 1524 pp. Godfray, Hugh, 1871: An Elementary Treatise on the Lunar Wood, Fergus J., 1950- : "Tides," in: Collier's Encyclopedia. Theory, 3d ed., rev. Macmillan and Co., New York, 123 PP. P. F. Collier, New York, vol. 22,'308-312. Goldreich, P., 1966: History of the lunar orbit. Review of Geo- 1957-67: "Tides," in: Encyclopedia Americana. Ameri- physics and Space Physics, 4, 411-439. cana Corp., New York, vol. 26, 611-619. Groves, G. W., 1962: "Dynamics of the Earth-Moon system," in: , 1979: "Tides," and "Proxigean Spring Tides," in: Ency- Physics and Astronomy of the Moon, edited by Zden6k Kopal. clopedia of Beaches and Coastal Environments. Western Wash- Academic Press, New York, 338 pp. ington State College, Bellingham, Wash. Jeffreys, H., 1930: The resonance theory of the origin of the Moon. Zetler, Bernard D., 1968- : "Tides", in: Encyclopedi a Ameri- Royal Astronomical Society, Monthly Notices, 91, 169-173. cana. Americana Corp., New York, vol. 26, 731-735. Kaula, W. M., 1971: Dynamical aspects of lunar origin. Review of Geophysics and Space Physics, 9, 217-238. (4) DESCRIPTIVE WORKS AND POPULAR PRESENTA- Koziel, K., 1967: Difference in the Moon's moments of inertia. TIONS ON THE TIDES Royal Society of London, Proceedings, series A, 296, 248-253. Conoon, C. R., 1971: Principal features of tidal phenomena. Mari- Lambeck, Kurt, 1975: Effects of tidal dissipation in the oceans on ners Weather Log, 15, 337-340. the Moon's orbit and the Earth's rotation. journal of Geophysical Cummings, W. C., 1969: Tides: The longest waves in the ocean. Research, 80, 2917-2925. Oceans Magazine, 1, 50-51. Lambert, Walter D., 1927: The variation of latitude and the fluctu- MacMillan, D. H., 1966: The Tides. C. R. Books, London, 240 pp. ations in the motion of the Moon. Journal of the Washington Marmer, Harry Aaron, 1926: The Tide. D. Appleton and Com- Academy of Sciences, 17, 133-139. pany, New York, 282 pp. Michael, W. H., Jr., 1970: Moments of inertia of the Moon. The Russell, R. C. H. and Macmillan, D. ff., 1970: Waves and Tides Moon: An International Journal of Lunar Studies (Dordrecht, (Ist reprinting). Greenwood Press, Westport, Conn., 348 pp. The Netherlands), 1, 484-485. Sager, GUnther, 1959: Gezeiten und Schi�ahrt (Tides and Navi- Michael, W. H., Jr., Blackshear, W. T., and Gapcynski, J. P., 1969: gation). Fachbuchverlag, Leipzig, East Germany, 172 pp. Dynamics of satellites, 1969. Proceedings of the Prague 12th Smith, Frederick George Walton, 1968: Tidal vagaries. Sea Fron- Plenary of COSPAR and l0th International Space Science Sym- tiers, 14, 263-271. posium, May 11-24, 1969, edited by Bruno Morando (Prague, 1969: Ebb and flow. Sea Frontiers, 15, 86-89. Czechoslovakia), 42-56. 1969: Man and tides. Sea Frontiers, 15, 142-151. Moulton, Forest Ray, 1914: An Introduction to Celestial Mechan- 1973:, The Seas in Motion. T. Y. Crowell, New York, ics (2d rev. ed.), chs. VIII, IX. Macmillan, New York, 277- 248 pp. 365. Stewart, John Q., 1945: Coasts, Waves, and Weather, chapters Oesterwinter, C. and Cohen, C. J., 1972: New orbital elements for 13-14. Ginn and Co., New York, pp. 183-2 10. Moon and planets. Celestial Mechanics, 5, 317@395- Tricker, R. A. R., 1964: Bores, Breakers, Waves and Wakes. Mills O'Keefe, J. A., 1969: Origin of the Moon. journal of Geophysical and Boon, London, 250 pp. Research, 74, 2758-2767. Voit, S. S., 1956: What Are the Tides? Izdatel'stvo Akademiya -, 1972: Inclination of the Moon's orbit: The early history. Nauk SSSR (Moscow, USSR), 102 pp. Irish Astronomical journal, 10, 241-250. Oppolzer, Theodor Ritter von, 1962: Canon der Finsternisse (5) THE EARTH-MOON SYSTEM; CLASSIC THREE-BODY (Canon of Eclipses), translation of original 188.7 ed. by Owen PROBLEM; LUNAR THEORY AND PERTURBA- Gingerich. Dover, New York, 376 pp. TIONS; EARTH TIDAL INFLUENCES ON THE Rubincam, David Parry, 1975: Tidal friction and the early history MOON'S ORBIT (See also category 25.) of the Moon's orbit. Journal of Geophysical Research, 80, 1537- Alfven, H., 1963: The early history of the Moon and Earth. Icarus, 1548. 1, 357-363. Schindler, Gerhard, 1959: Die Vollmondatten der letzten 110 Jahre Brouwer, Dirk and Clemence, Gerald M., 1961: Methods of Celes- (Full moon data -for the last 100 years). Meteorologische tial Mechanics, ch. XII. Academic Press, New York, 308-375. Rundschau, 12, 132-133. 520 Strategic Role of Perigean Spring Tides, 1635-1976 Schubart, J., 1961: Der Umlauf von Knoten und Perigaum des (7) TIDAL THEORY AND TIDAL DYNAMICS (See also cate- Mondes (The revolution of the nodes and the perigee of the gories 12,13,14,15,16) Moon). Die Sterne (Leipzig, East Germany), 37, 7-9. Bouasse, Henri, P. M., 1924: Houle, rides, seiches, et maries Singer, S. F., 1968: The origin of the Moon and geophysical conse- (Swells, Ripples, Seiches and Tides). Librairie Delagrave, Paris, quences. Geophysical journal, 15, 205-226. France, 516 pp. Van Flandern, T. L., 1970: The secular acceleration of the Moon. Eckart, C., 1952: "The propagation of gravity waves from deep to Astronomical Journal, 75, 657-658. shallow water," in: Gravity Waves, National Bureau of Stand- (6) GRAVITATIONAL FIELDS OF THE EARTH, MOON, ards Circular 521, Washington, D.C., 165-174. AND SUN; TIDE-GENERATING FORCES AND THE -, 1962: "The equations of motion of sea water," in: The Sea, GRAVITATIONAL POTENTIAL (See also category 7.) vol. 1, edited by M. N. Hill. Interscience, New York, 31-40. Akim, E. L., 1966: Determination of the gravitational field of the 1 1963: Some transformations of the hydrodynamic equations. Moon by the motion of AMS Luna 10. Akademiya Nauk SSSR, Physics of Fluids, 6, 1037-1041. Doklady (Moscow-Leningrad, USSR), 171, 799-802. Godin, Gabrie 1, 1972: The Analysis of Tides. University of Toronto Cartwright, D. E. and Tayler, R. J., 1971: New computations of Press, Toronto, Canada, 264 pp. o the tide-generating potential. Royal Astronomical Society, Geo- Haubrich, R. and Munk, W. H., 1959: The pole tide. Journal of physical journal, 23, 45-74. Geophysical Research, 64, 2373-2388. Cook, A. H., 1961: Resonant orbits of artificial satellites and longi- Longman, I. M., 1939: Formulas for computing the tidal accelera- tude terms in the Earth's external gravitational potential. Royal tions due to the Moon and Sun. Journal of Geophysical Research, Astronomical Society, Geophysical journal, 4, 53-72. 64, 2351-2360. Doodson, A. 1., 19 2 1: Harmonic development of the tide-generating Michelson, Irving, 1965: Resolution of tidal high water anomaly. potential. Royal Society of London, Proceedings, series A, 100, Pure and Applied Geophysics (Basel, Switzerland), 61, 149-151, 305-329. Mosetti, F. and Manca, B., 1972: Some methods of tidal analysis. Garland, G. D., 1965: The Earth's Shape and Gravity. Pergamon, International Hydrographic Review (Monaco), 49, 107-120. London, 175 pp. Munk, W. H., 1962: "Long ocean waves," in: The Sea, vol. 1, Heiskanen, W. A. and Vening Meinesz, F. A., 1958: The Earth and edited by M. N. Hill. Interscience, New York, 647-663. its Gravity Field. McGraw-Hill, New York, 470 pp. Munk, W. H. and Bullard, E. C., 1963: Patching the long-wave Kaula, W. M., 1959: Statistical and harmonic analysis of gravity. spectrum across the tides. journal of Geophysical Research, 68, Journal of Geophysical Research, 64, 2401-2421. 3627-304. , 1967: Geophysical implications of satellite determination Munk, W. H. and Hasselman, K., 1964: "Super resolution of of the Earth's gravitational field. Space Science Review, 7, 769- tides," in: Studies on Oceanography, Tokyo Geophysical Insti- /794. tute, University of Tokyo, Japan, 339-344. -, 1969: The gravitational field of the Moon. Science, 166, Proudman, J., 1923: A theorem in tidal dynamics. Philosophical 1581-1588. Magazine, 49, 570-579. Koch, K. R. and Morrison, F., 1970: A simple layer model of the (8) HARMONIC ANALYSIS OF TIDES: TIDAL CON- geopotential from a combination of satellite and gravity data. STANTS AND CONSTITUENTS Journal of Geophysical Research, 75, 1483-1492. Koch, K. R., 1971: Errors of quadrature connected with the sim- British Admiralty, 1959: The Admiralty Semi-Graphic Method of ple layer model of the geopotential. NOAA Technical Memoran- Harmonic Tidal Analysis. Admiralty Tidal Handbook No. 1 dum NOS 11, National Ocean Survey, National Oceanic and (H.D.505). Hydrographic Department, Admiralty, London, Atmospheric Administration, U.S. Department of Commerce, 74 pp. Washington, D.C., 1-10. Darwin, G. H., 1883: Report of a committee for the harmonic Longman, 1. M., 1959: Formulas for computing the tidal accelera- analysis of tidal observation. British Association for the Advance- tions due to the Sun. Journal of Geophysical Research, 64, 2351- ment of Science, Reports, 48-118. 2355. Doodson, A. T., 1921: The harmonic development of the tide gen- MacMillan, W. D., 19,58: The Theory of the Potential. Dover, New erating potential. Royal Society of London, Proceedings, series A, York, 343, 405. 100, 303-329. Melchior, P., 1971: Precession-nutation and tidal potential. Celes- Doodson, A. T. and Warburg, H. D. (Admiralty, Hydrography De- tial Mechanics, 4,1190-212. partment), 1941: Admiralty Manual of Tides. His Majesty's Munk, W. H. and MacDonald, G.'J. F., 1960: Continentality and Stationery Office, London, 270 pp. gravitational field of the Earth. Journal of Geophysical Research, Hough, S. S., 1897: On the application of harmonic analysis to the 65, 2169-2172. dynamical theory of the tides. Royal Society of London, Philo- O'Keefe, J. A., 1960: "Determination of the Earth's gravitational sophical Transactions, series A, 189, 201. field," in: Space Research, vol. 1, edited by H. Kallmann. North- -, 1899: On the application of harmonic analysis to the dy- Holland, Amsterdam, The Netherlands, 448-457. namical theory of tides. 11. On the general integration of Lap- Pollack, Henry N., 1973: Longman tidal formulas: Resolution of lace's tidal equations. Royal Society of London, Philosophical horizontal components. Journal of Geophysical Research, 78, Transactions, series A, 191, 139-185. 2598-2600. Pekeris, C. L. and A@-@ad, Y., 1969: Solution of Laplace's equations Suess, Steven T., 1970: Some effects of gravitational tides on a for the M. tide in the world oceans. Royal Society of London, model Earth's core. Journal of Geophysical Research, 75, 6650- Philosophical Transactions, series A, 265, 413-436. 6661. Rossiter, J. R., 1967: "Harmonic constituents of tides," in: Inter- Vinti, J. P., 1971: Representation of the Earth's gravitational po- national Dictionary of Geophysics. Pergamon, Oxford, vol. 2, tential. Celestial Mechanics, 4, 348-367. 1545-1547. 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B., 1949: The tide in the David Taylor Model Basin. 1950. American Geophysical Union, Transactions, 37, 278-286. American Geophysical Union, Transactions, 30, 357-368. Summers, H. J. and Emery, K. 0., 1963: Internal waves of tidal period off southern California. Journal of Geophysical Research, (10) DEEP-SEA TIDES (See also category 24.) 68, 827-839. Cartwright, D. E., 1969: Deep-sea tides. Science journal, 5, Uda, M., 1938: Researches on "siome" or current rip in the seas 60-67. and oceans. Geophysical Magazine (Tokyo, Japan), 17, 307-372. Cartwright, D., Munk, W., and Zetler, B., 1969: Pelagic tidal meas- (12) TIDES IN A ZONAL OCEAN urements. Eos (American Geophysical Union, Transactions), 50 472-477. Doodson, A. T., 1935: Tides in oceans bounded by meridians. Heaps, N. S., 1969: Some notes on tidal theory and its possible II: Ocean bounded by complete meridian. Diurnal tides. Royal relevance to a program of deep-sea tidal measurement. 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Academic Press, New York, 445 pp. Bight. NOAA Technical Report ERL 321-MESA 2, Boulder, Muller, P. M. and Stephenson, F. R., 1975: "The acceleration Colo., 78 pp. of the Earth and Moon from early astronomical observations," -, 1976: Evaluation of Proposed Sewage Sludge Dumpsite in: Growth Rhythms and History of the Earth's Rotation, edited Areas in the New York Bight. NOAA Technical Memorandum by S. K. Runcorn and G. D. Rosenberg. Wiley-Interscience, ERL MESA-1 1, Boulder, Colo., 212 pp. New York, 560 pp. Bibliography on Tides 529 Newton, R. R., 1970: Ancient astronomical observations and the (42) BIBLIOGRAPHIES, SOURCE BOOKS, GLOSSARIES, accelerations of the Earth and Moon. Johns Hopkins Press, Balti- AND STATE-OF-THE-ART LITERATURE RELATIVE more, 749 pp. TO TIDES AND TIDAL CURRENTS Rossiter, J. R., 1972: The history of tidal predictions in the American Meteorological Society, 1965: Meteorological and Geo- United Kingdom before the twentieth century. 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K., 1963: The influence of the Moon on geomagnetic Science, 29, 19-40. disturbances. Journal of Geophysical Research, 68, 1909-1913. Baker, B. B., Jr., Deebel, W. R., and Geisenderfer, R. D., 1966: -, 1963: Lunar and planetary influences on geomagnetic dis- Glossary of Oceanographic Terms, 2d ed. (S.P.-35). Department turbances. journal of Geophysical Research, 68, 4099-4104. of the Navy, U.S. Naval Oceanographic Office and U.S. Govern- Cochrane, N. A. and Srivastava, S. P., 1974: Tidal influence on ment Printing Office, Washington, D.C., 240 pp. electric and magnetic fields recorded at coastal sites in Nova Bretschneider, C. L. and Pick, G. S., 1966: A Bibliography on Storm Scotia, Canada. Journal of Atmospheric and Terrestrial Physics, Surges and Related Subjects, Sponsored by Office of Naval Re. 36, 49-39. search (unclassified). Clearinghouse for Federal Scientific and Jackson, J. S., 1971: Diurnal variation of the geomagnetic field, Technical Information (now National Technical Information 2. The lunar variation. Journal of Geophysical Research, 76, Service), Springfield, Va., 48 pp. 6909-6914. Pore, N. A., 1970: Summary of Selected Reference Material on Michel, F. C., Dessler, A. J., and Walters, G. K., 1964: A search the Oceanographic Phenomena of Tides, Storm Surges, Waves, for correlation @etween K, and the lunar phase. journal of and Breakers. Weather Bureau Technical Memorandum WBTM Geophysical Research, 69, 4177-4181. TDL 30, Environmental Science Services Administration (now Rassabach, M. E., Dessler, A. J., and Cameron, A. G. W., 1966: the National Oceanic and Atmospheric Administration), Silver The lunar period, the solar period, and Kp. Journal of Geophysical Spring, Md., 103 pp. Research, 71, 4141-4146. Schureman, Paul, 1975: Tide and Current Glossary. Revised by Stolov, Harold L. and Cameron, A. G. W., 1964: Variations of Steacey D. Hicks, (Formerly U.S. Coast and Geodetic Survey Special Publication No. 228), U.S. Government Printing Office, geomagnetic activity with lunar phase. Journal of Geophysical Washington, D.C., 25 pp. Research, 69, 4975-4982. Wiegel, Robert L., 1953: Waves, Tides, Currents and Beaches: Stolov, H. L., 1965: Further investigations of a variation of geo- Glossary of Terms and List of Standard Symbols. Council on magnetic activity with lunar phase. Journal of Geophysical Re- Wave Research, The Engineering Foundation, University of search, 70, 4921-4926. California, Berkeley, Calif., 113 pp. Index Tage Page Accelerate currents at perigee-syzygy -------------- 95, Carbon dioxide variations in seawater ------------- 100 98,105,106,485,489 Catch-up motions: duration of tide-raising forces- 269, 271 Aeronomy: tidal winds ------------------------- 494 Celestial equator ------------------------------- 121 Age of parallax inequality ----------------------- 298 Celestial latitude ------------------------------ 123 Age of phase inequality ------------------------- 297 Celestial longitude ---------------------------- 7, 123 Almucantars --------------------------------- 123 lunar motion in ----------------------------- 192 Angle of eccentricity ------- -------------------- 127. Celestial meridian -------------------------- 122, 123 Annual equation -------------------- 165,270,292,435 Center-of-mass: Earth-Moon system ------------- 498 Annual variation ------------------------------ 159 Centrifugal force: Anomalistic month ------------- 130, 275, 288, 318, 436 Earth-Moon system -------------------------- 498 gain in length perigee-syzygy ------------------ 288 in lunar orbit ------------------------------- 498 length variations ---------------------- 287, 288, 290. Charleston Harbor, S.C., effects of perigean spring mean value --------------------------------- 287 tides on Second Battle of ------------------ 70-78 relation to synodic month ------------------- 284-290 Coastal processes: Anomalistic tides ------------- I ----------------- 115 foreshore undercutting ---------------------- 84, 424 Apparent motion -------------------- L --------- 125 historical aspects of -------------------------- 85 Aphelion ------------------------------------ 130 perigean spring tides in relation to -------------- 84 Apogee ---------------- --------------------- 130 Computational sources ------------------------- 13 figure of lunar obit at ------------------------- 208 Conjunction --------------------------------- 7 Apogee-syzygy: Coplanar lunisolar alignment ---- 199-208, 218, 313, 435 lunar parallax ----- ------------------------ 207 Coplanar lunisolar declinations ---- 198, 201-202, 218, 435 new moon at -------------------------------- 216 Crustal tilt ----------------------------------- 494 Apse ---------------------------------------- 142 Daily lunar retardation ---------------------- 137, 271 Astronomical positions: methods of defining ------- 121 Data source selection --------------------------- 327 Astronomical tidal forces ----------------------- 497 Declination ---------------------------------- 121 Atmospheric tides --------------------------- 488, 489 maximization in 18.6-year nodical cycle ---------- 189 geornagnetic fluctations caused by ------------ 488, 489 Deflection of the vertical ------------------------ 494 Augmented tide-raising forces -------- 11, 203, 218, 313 Delta omega-syzygy coefficient -------- 435, 436, 440, 475 Autumnal equinox -------------------------- 122, 190 Differential tide-producing forces ---------------- 498 Azimuth ------------------------------------ 123 Direct tides ----------------------------------- 500 Baguio -------------------------------------- 25 Diurnal inequality ------------------ 152, 198, 475, 503 Barycenter: nullified ----------------------------------- 204 Earth-Moon system -------------------------- 498 -Docking, effect of perigean spring tides on --------- 96 Earth-Sun system --------------------------- 501 Draconitic month ----------------------------- 126 Beach flooding -------------------------------- 102 Duration of tide-raising forces ------------ 192, 271, 306 Biological rhythms ----------------------------- 495 Earth astronomical motions ---- ---------------- 124 Bridge construction-influence of perigean spring Earth-Moon system: tides: center of mass ------------------------------ 498 explosive decompression of caissons ------------ 94 centrifugal force ---------------------------- 498 Firth of Forth caisson ------------------------ 94 Earth's rotation: hydrostatic pressure changes caused by tides ------ 94 catch-up on Moon at perigee-syzygy ------------ 270 effects of accelerated currents ------------------ 96 catch-up on Moon's orbital motions ---------- 126, 272 Calendar styles: conversion --------------------- I diurnal --------------------------------- 124, 198 Camel (buoyancy device) ---------------------- 60, 70 Earth tides ----------------------------------- 492, 493 531 532 Index Earthquake triggering potential: Page Page at apogee-syzygy ----------------------------- 487 Fetch --------------------------------------- 6,437 at perigee-syzygy ----------------------------- 487 First point of Aries ----------------------------- 122 East Coast (North America) : Fish migration: tidal currents ------------------- 495 Connecticut River hydrographic data ----------- 69 Flattening of Earth's poles ---------------------- 148 Connecticut River, navigation problems --------- 70 Flood tide currents ---------------------------- 96 Connecticut River, perigee-syzygy high water ----- 69 Flounder-behavior in accelerated currents -------- 102 Connecticut River, phase and parallax ages ------ 69 Full moon: Connecticut River, tidal response -------------- 69 parallax near apogee-syzygy ------------------- 215 Connecticut River, tide heights ---------------- 69 parallax near perigee-syzygy ------------------- 214 Connecticut River, water depth over sandbars ---- 65, 70 increased cloudiness at perigee ----------------- 486 Connecticut River, water depths ---------------- 60, 64 Gaussian gravitational constant ------------------ 187 Connecticut River, 1771 chart ----------------- 60 Geocentric distance: North Carolina, Bodie's Island inundated -------- 85 at time of perigean. spring tides ------------ 25-285 481 North Carolina, Hatteras Inlet, Civil War ------ 87, 89 Earth from Sun ----------------------------- 144 North Carolina, Hatteras Inlet formation -------- 85-88 Moon from Earth ---------------------------- 143 North Carolina, Pamlico Sound ---------------- 85, 86 relation to geocentric horizontal parallax -------- 142 Nova Scotia, Saxby Tide ---------------------- 112 Geocentric parallax --------------------- 134, 148, 224 South Carolina, Charleston Harbor ------------ 70-74 Geoid --------------------------------------- 124 South Carolina, Port Royal Entrance ---- 79, 80, 83, 84 Geomagnetic fluctuations due to atmospheric tides-- 488 South Carolina, Port Royal Sound, Civil War---- 78 Geomagnetism: lunar tides --------------------- 494 Ebb Currents ---------------------------- 96, 98, 485 Geophysical investigations: tidal effects -----I---- 107, 485 duration of --------------------------------- 96 Gravitational force: Earth-Moon system ---------- 498 Eccentricity -------------- 127, 173, 176, 179, 21.6, 217 Gravitational force potential --------------------- 187 Bcho-sounding ------------------------------- 97 Greenwich hour angle -------------------------- 122 Eclipses ------------------------------------- 7 Greenwich mean astronomical time --------------- 13 Ecliptic ----------------------- 1, 2, 7, 198, 199, 202 Greenwich mean time ---------------- I---------- 13 Ecliptic system -------------------------------- 7, 122 Grunion: I coordinate transformation to equatorial system-- 124 avoidance of peak of perigean spring tides ---- 101, 102 Ecology: biological clock ------------------------------ 101 extreme high and low tides, effect on ------ 98, 485, 494 Gulf Coast: smaller tidal ranges ------- 96, 300, 406, 408 Ellipse -------------------------------------- 127 Harmonic analysis: methods -------------- 294-296, 475 Elliptic terms: lunar orbit ---------------------- 175 High water springs: mean range ----------------- 297 Elliptic variation (inequality) ----------------- 159, 179 Highest astronomical tide ------------------------ 31 Entrainment --------------------------------- 99 Horizon ------------------------------------- 123 Ephemeris time ------------ ------------------ 13 Horizon system -------------------------------- 123 Epoch of osculation ---------------------------- 216 coordinate transformation to equatorial system --- 124 Epoch: tidal constituent ------------------------ 297 Hour angle subsystem ------------------------ 122,134 Equatorial horizontal parallax Hour angles ------------------- 7-------------- 122 ------------------- 174 Equatorial system ------------------------------ 121 Hour circles ---------------------------------- 122 coordinate transformation to ecliptic system ------ 124 Hurricanes -------------------------------- 3,6,481 coordinate transformation to horizon system ------ 124 examples ---------------------------------- 25 Equinoctial colure ----------------------------- 122 frequency ---------------------------------- 321 Equinoctial tides ------------------------------ 150 intensity classification ------------------------ 25 Erosion ------------------------ 31, 36, 84, 424, 481 nomenclature ------------------------------- 28 Estuarine environment ------------------- 99, 482, 485 Hydrological runoff ---------------------------- 102 Estuarine pollution -------------------------- 100, 483 blocked by tides ------------------------ 31, 35, 482 flushing by tides ---------------------------- 98, 102 Interdisciplinary cooperation -------------------- 495 Euryhaline organisms --------------------------- 99 Internal waves: lunar syzygy -------------------- 494 Evaporation basins ----------------------------- 99 "Inverted barometer" effect ---------------- 6, 408, 420 Evection term: lunar parallax ------------------- IM Julian Day ----------------------------------- 229 Exogee -------------------------------------- 316 Kepler's laws of planetary motion --------- 127, 129, 130 Extreme low water ----------------- 31, 33, 34, 93, 426 Lagging of the tides ------------------------- 303, 504 Extreme proxigean spring tide's ------------------- 316 Latus rectum ----------------------- I---------- 217 Index 533 Page Lunar orbital relationships@Continued Page Line of apsides -------------------------------- 142 apparent daily motion ------------------------ 197 forward motion ----------------------------- 179 centrifugal force component ------------------- 498 Low tides extreme: declination angle ---------------------------- 272 adverse effects ------------------------------ 105 eccentricities ------------------- 155, 169, 205, 272 beneficial effects ----------------------------- 105 eccentricity at perigee-syzygy ----------- 174, 179, 217 caisson blowouts --------------------------- 94, 105 effect of maximum declination on motion in right deep-draft vessel strandings ------------- 95, 105, 483 ascension ---------------------------- 192, 268 exposure of seafloor -------------------------- 105 elliptic inequality ---------------------------- 175 extreme at perigee-syzygy --------- 31, 33, 34, 93, 426 evection ------------------------------ 5, 216, 272 fixed marine structure repair ------------------ 105 figure ------------------------------ 127, 128, 207 gangplank adjustment ---------------------- 95, 105 figure at apogee-quadrature ------------------- 207 moored vessel groundings -------------------- 105 figure at quadrature ------------------------- 208 offloading belt adjustment ----I------------------ 105 figure at syzygy ------------------------------ 208 offshore -winds accompanying -------------- 6, 12, 105 figure, interpretation of ----------------------- 205 Lower branch of meridian ---------------------- 122 figure, variations in -------------------------- 214 Lower transit --------------------------------- 122 geocentric inclination ---------------------- 196, 272 Lunar apsides cycle ------------------------- 292, 293 in right ascension ----------------- 132-135, 196-226 Lunar ascending node: vernal equinox coinci- in true anomaly ----------------------------- 266 dence -------------------------- 190, 193, 196 increased daily motion in longitude ------------- 196 Lunar augmentation ------------------------- 147, 202 long-term perturbation effects ----------------- 272 Lunar day --------------- 137, 139, 269, 271, 272, 504 maximum inclination to ecliptic ---------------- 123 duration ---------------------------------- 7 maximum motion in right ascension ------------ 196 relation to solar day -------------------------- 271 mean daily motion --------------------------- 127 variations in length -------------------------- 272 mean eccentricity ---------------------------- 173 Lunar declination ----------------------- ---- 218, 503 mean inclination to ecliptic ------------------- 123 effect on motion in right ascension -------------- 193 osculation, epoch of -------------------------- 216 regional effects on tides ----------------------- 148 parallax increase ---------------------------- 197 relation to right ascension --------------------- 149 perigee-qua'd 'rature -------------------------- 175 Lunar descending node: vernal equinox coincidence- 190 perturbation equations ----------------------- 217 Lunar eclipses --------------------------- 1, 2, 7, 198 proxigee-syzygy ----------------------------- 218 Lunar evection -------------------- 153, 154, 175, 302 radius of curvature -------------------- 158, 205, 207 analysis of equation for ----------------------- 173 relative motion in declination ------------------- 192 effect of solar gravitation --------------------- 214 relative motion inright ascension --------------- 192 perigee-syzygy, at ---------------------------- 174 seasonal influences --------------------------- 219 Lunar evection effects -------------- 162, 163, 170, 175 semimajor axis ----------------------- 128, 173, 218 diurnal tidal analysis ----------- ------------ 172 solar gravitational effects --------------------- 214 fortnightly tide analysis ----------------------- 172 solar perturbation component at apogee --------- 207 semidiurnal tide analysis ---------------------- 172 solar-produced eccentricities ------------------ 209 Lunar months, lengths: Sun at apsides ------------------------------ 175 anomalistic -------------------------------- 131 syzygy-apse orientation ------------------------ 197 draconitic ---------------------------------- 126 tangential forces ---------------------------- 173 sidereal ------------------------------------ 126 topocentric inclination --------------------- 193, 196 variation increases eccentricity ----------------- 219 sinodic ------------------------------------ 126 velocity and perturbations --------------------- 173 tropical ----------------------------------- 126 velocity at large parallax --------------------- 192 Lunar motion: in celestial longitude-- 146, 192, 309, 310 velocity at perigee --------------------------- 216 Lunar orbital - relationships: velocity at small parallax ---------------------- 192 alternate solar acceleration and deceleration of velocity decrease at perihelion ----------------- 271 Moon in orbit --------------------------- 156 velocity in anornalistic month ----------------- 192 alternate solar acceleration and deceleration of velocity variations -------------------- 157, 158, 192 Moon with respect to Earth --------------- 157 Lunar nodes: coincidence with equinoxes --------- 199 angular velocity ------------------ 214, 309, 310, 504 Lunar nodical cycle ------------------------- 189, 291 apogee-quadrature ------------------------ 175, 207 declination maximization --------------------- 189 534 Index Page Page Lunar parallactic inequality -------------- 159, 435, 502 Mean longitude: sinusoidal variation with true longi- summary analysis ---------------------------- 176 tude ---------------------------------- .184 Lunar parallax: Mean lunar day ------------------------- 138,272,273 absolute maximum --------------- 159, 203, 219, 220 derivation of length and mean solar days --------- 272 absolute minimum ------------------------- 159, 219 Mean vs. true motions --------------------- 1643 176, 177 angle to linear distance conversion ------------- 212 Mean parallax -------------------------------- 212 apogee value of ----------------------------- 212 Mean sidereal month --------------------------- 138 apogee-syzygy value of ------------------------ 207 Mean sidereal time ---------------------------- 125 decrease toward apogee-quadrature '4 ------------ 208 Mean solar day ------------------------------- 125 effect of solar gravitation --------------------- 214 Mean solar time -------- 7-------------------- 13, 125 evection effects on --------------------------- 219 Mean Sun ----------------------------------- 125 maximum winter values ---------------------- 218 Mean tidal day ----------------------------- 138, 273 perigee-apogee comparison -------------------- 210 Metonic cycles -------------------------------- 296 perigee-quadrature value of ------------------- 208 Minor axis ----------------------------------- 127 perigee-syzygy value of ------- 174, 205, 210, 211, 213 Mixed tides ---------------------------------- 298 solar perigee (perihelion) value of ----------- 199,218 diurnal inequality --------------------------- 474 syzygy value of ---------------------------- 175, 208 variation effects on -------------------------- 219 Moon: Lunar parallax age: local variation in tide arrival --- 273 angular velocity at apogee-quadrature ---------- 143 Lunar perigee: motion of --------------------- 177-184 angular velocity at apogee-syzygy -------------- 143 Lunar period: modified by lunar apsides cycle ------ 292 angular velocity at perigee-quadrature ---------- 143 Lunar phase age: local variation in tide arrival ----- 273 angular velocity at perigee-syzygy -------------- 143 apparent motion in right ascension ------------- 140 Lunar reduction -------------------------------- - 159 celestial latitude, limits of --------------------- 123 Lunar retardation ---------------------- 137, 272, 504 conditions for closest approach ---------------- 219 Lunar right ascension: daily angular velocities ----------------------- 130 motion decrease in --------------------------- 196 effect of parallax on apparent motion ----------- 133 motion increase in --------------------------- 196 geomagnetic variations ----------------------- 489 velocity in, and catch-up time ------------------ 196 local meridian transit ------------------------ 272 Lunar variation ----------------------------- 155,301 maximum declinations ----------------------- 190 Lunar variation effects: mean anornalistic period of revolution ---------- 131 analysis of equations for ---------------------- 173 mean daily motion -------------------------- 127 diurnal tidal analysis ------------------------- 172 mean daily synodic motion -------------------- 138 fortnightly tidal analysis ---------------------- 173 mean diurnal geocentric motion --------------- 134- perturbative ---------------- 156, 160, 162, 165, 175 mean diurnal topocentric motion -------------- 134 semidiurnal tidal analysis --------------------- 172 mean sidereal rate of revolution ---------------- 130 Lunisolar declinational constituent --------------- 298 motion calculated in geocentric coordinates ------ 133 motion calculated in topocentric coordinates ----- 133 Lunitidal intervals ----------------------------- 139 motion in declination ------------------------ 132 Major axis ----------------------------------- 127 relative angular speed of revolution ------------- 127 Marconi's tower ------------------------------- 93 revolution around Earth ---------------------- 125 Marine ecobiology ----------------------------- 100 true parallax ------------------------------- 175 Marine engineering ---------------------------- 96 National Ocean Survey: tide gages -------------- 506 Marine technology ----------------------------- 93 Navigation: Marine temperature variations ------------------ 100 perigean spring tides, effects on --------------- 96, 483 Maritime technology --------------------------- 93 tides in shallow harbors, effects on -------------- 68 Marshlands ---------------------------------- 99 Neap tides ------------------------------------ 501 Maximum perigean spring tide ------------------ 313 New Moon: Maximum perigee springs ----------------------- 203 parallax near apogee-syzygy ------------------- 216 Mean anomaly: lunar parallax ------------------ 175 parallax near perigee-syzygy ------------------- 216 Mean daily lunar retardation ------------------ 138,272 Newton's Universal Law of Gravitation ----------- 498 Mean distance -------------------------------- 127 Nodal alignment ------------------------------ 218 Mean high-water lunitidal interval --------------- 297 Nodes -------------------------------------- 7 Index 535 Page Page Nodical month -------------------------------- 126 Perigee ---------------------------------- 5, 128, 130 Obliquit@ of ecliptic --------------------------- 190 equation for motion of ------------------------ 180 Offshore platforms: tidal and current impact ------ 485 full moon accompanying -------- L------------- 214 Offshore winds ---------------- 3, 6, 12, 105, 408, 420 increased duration --------------------------- 176 Onshore winds ------ 3, 6, 78, 79, 96, 97, 218, 302, 326, 481 mean and true motions of ------------------ 179, 182 Opposite tides --------------------------------- 500 mean daily motion of ------------------------- 177 Opposition ---------------------------------- 7 mean progression of ------------------- 178, 179, 289 Ordinary spring tides ------------------- 301, 311, 31-8 new moon accompanying --------------------- 216 Parallactic inequality ------------------------ 142, 143 retrograde motion of ---------------------- 179, 435 Parallax me -------------------------- 6, 11, 68, 297 true motions of ----------------------- 177, 179, 184 Perigean neap tides: conditions ------------------ 31 Perigee-quadrature: figure of lunar orbit at -------- 209 Perigean spring tides ----------------------- 5, 7, 317 Perigee-syzygy --------------------------------- 2,4,7 adverse effects ------------------------------ 103 coincidence with perihelion ------------------- 271 amplitude control factors --------------------- 153 conjectural meteorological relationships --------- 486 astronomical factors ------------------------- 169 cycles of alternation -------------------------- 285 buoyancy increase and mast clearance ----------- 103 extreme high and low water effects ------------- 486 buoyancy increase and small craft ------------- 103 extreme lunar declination ------------------- 195, 196 classification ----------------------------- 312-317 figure of lunar orbit -------------------------- 210 @coastal ecology ---------------------------- 482, 485 lunar angular velocity ------------------------ 131 coastal erosion -------------------------- 31, 36, 84 lunar declination ---------------------------- 196 coincidence with hurricanes --------------- 25-28, 481 lunar motion in right ascension ---------------- 196 concealment of navigational hazards ---------- L_ 103 lunar node and equinox coincidence ------------ 194 deep-water layer isolialine undulations ----------- 104 lunar node at equinoxes ---------------------- 193 deflection of the vertical ---------------------- 104 lunar parallax value ------------------------- 174 dive times and decompression ---------------- 94, 104 mean period ------------------------------ I-_ 318 earliest references to ----------------------- 1105 111 node-apse-perihelion coincidence -------------- 219 ecological effects ----------------------- 98-102, 482 periodic relationships --------- 177, 189, 285, 318@326 environmental effects ---------------- ----- 102, 482 relation to cloud conditions, study of ------------ 486 height variations ---------------------------- 214 seismic activity, potential relation to ------------ 486 historical impact ----------------------------- 59 separation-interval --------- 203,266,286,2875289,290 historical survey ----------------------------- 109 tidal current effects -------------------------- 482 hydrological runoff impaired -------------- 31, 35, 482 unproven geophysical relationships ------------- 485 international terminology ----------- ---------- 203 31-year cycle -------------------------------- 321 lunar proxigee, effects on --------------------- 169 lunisolar augmentation of --------------------- 169 Perihelion --------------------------------- 1275 130 maximization conditions ----------- 11, 2035'218, 313 winter solstice ------------------------------ 271 meteorological reinforcement of ---------------- 326 Phase age -------------------------------- 6, 68, 297 negating conditions -------------- 3, 6, 1055 408, 420 Pi factor ----------------------------------- 438, 439 new inlets and channels breached --------------- 104 Plimsoll marks: saltwater intrusions -------------- 102 ocean environment studies -------------------- 104 Potential tidal flooding: astronomical-meteorological offshore winds, and -------------- 3, 65 105, 408, 420 index ------------------------------- 7- 437 onshore winds, and -------------------------- 2 Precipitation: potential lunar syzygy relationship-- 486, 487 onshore wind lacking (calm) ------------------ 196 Principal declinational constituent --------------- 298 origin of concepts ---------------------------- log Progression of lunar apsides --------------------- 184 perigee-syzygy separation-interval --------------- 266 Proxigean. spring tides ----------------- 5, 203, 313, 316 periodicity ----------------- 177, 189, 285, 318-326 future occurrences --------------------------- 480 physical oceanography studi 'es ----------------- 104 Proigee -------------------------------- 55 116, 316 pollutant flushing enhanced ---7------ 97, 98, 102, 104 Proxigee-syzygy: pollution runoff ----------------------------- 103 lunar angular velocity ------------------------ 176 practical influences -------------------------- 103 lunar orbital velocity ------------------------- - 131 systematic quantitative designation ----------- 312-317 Pseudo-perigean spring tides --------- 8@ 695@ 71, 317, 481 winter storms, and --------------------- ----- 320 Quadrature: ordinary ------------------------- 208 18th century knowledge ---------------------- 68 Radius vector -------------------------- 142, 158, 217 536 In dex Page Sun-Continued Page Recreational beaches, tidal flooding of ------------ 102 gravitational force --------------------------- 214 Reference tide stations ------------------------- J69 mass -------------------------------------- 214 Right ascension ------------------------------- 7 maximum declination ------------------------ 132 Salinity: mean anomaly ------------------------------ 166 corrosion ----------------------------------- 99 Synodic month ------ 126,138,177,272,284,288,290,318 green algae --------------------------------- 99 conditions for duration ----------------------- 275 irrigation --------------- ------------------ 100 influence of perigee-syzygy ---- ----------------- 275 Salt flats -------------------------------------- 99 relation to anomalistic month --------------- 284-290 Saltwater intrusions: Syzygean spring tides: onshore winds ------------- 28 high buoyancy ------------------------------ 102 Syzygy -------------------------------------- 501 prevention of ice formation ----------------- 102, 498 Tangential forces ------------------------------ 173 Saltwater wedges ------------------------------ 99 Saxby tide --------------------------------- 112, 113 Temperature variations: effect on marine ecobi- Scotland: Firth of Forth bridge ------------------ 94 ology ---------------------------------- 100 SCUBA diving operations --------------------- 94, 104 Tidal acceleration ----------------------------- 296 Sediment transport ---------------------------- 85 Tidal amplification: Semidiurnal. tides ----------------------- 298, 448, 503 lunar parallactic inequality ------------------- 269 Separation-interval ---------------------------- 266 lunisolar declinations ------------------------- 270 Ship groundings: low water phase- 95, 96, 482, 483, 484, 485 Tidal amplitudes: Sidereal day: average value -------------------- 125 semidiurnal lunar constituents ----------------- 297 Sidereal month ----------------------------- 126, 138 semidiurnal solar constituents ----------------- 297 Solar day ------------------------------------ 271 Tidal analysis ---------------------------------- 68 Solar declination effect on lunar orbital velocity ---- 271 Tidal bulge ----------------------------------- 497 Solar diurnal variation ----------------------- 488,489 Equator ----------------------------------- 198 Solar eclipses ----------------------- 2,7,198,199,202 maximum peak ------------------------------ 198 effect on lunar parallaxes -------------------- 199 Tidal currents --------------------------------- 497 Solar parallactic inequality ----------- 131,288,435,502 adverse effects ------------------------------- 105 Solar perigee --------------------------- 143,199,218 atmospheric tide reinforcement ---------------- 106 motion of line of apsides --------------------- 270 basins with interconnecting channels ------------ 106 Solar semidiurnal variation ------------------- 488, 489 beneficial effects ----------------------------- 106 Solstitial tidal peaks --------------------------- 132 collisions ----------------------------------- 105 Solstitial tides -------------------------------- 149 deepwater diving ---------------------------- 105 electrical potential ------------------------- 106,489 Spring tides ---------------------------------- 5,501 1erosion intensified_@ ----- /------------------- 106 onshore winds ------------------------------ 481 hydrography alteration ----------------------- 105 syzygy -------------------------------------- 502 ice flow drift accelerated ---------------------- 105 Stars: individual motions ----------------------- 125 marine engineering hazards ------------------- 105 Station differences ----------------------------- 69 navigational hazards ------------------- 105,483,485 Stenolialine organisms --------------------------- 99 pollutant diffusion accelerated ----------- 97,104,105 Stern chase motions: sheet ice formation, deterrent to --------------- 106 lunar acceleration at perigee effect on ---------- 269 thermolialine balance in estuaries -------- ------ 106 lunisolar declination angles effect on ------------ 269 tide rip effect ------------------------------- 105 Storm surges ----------------------------- 15,490,506 Tidal day ------------------------------ 139,302,504 Sun: changing parallax effects --------------------- 150 angular velocity in right ascension -------------- 270 conditions for lengthening -------------------- 291 apparent annual motion ---------------------- 199 declinational influences ----------------- 150,290,291 apparent daily motions ----------- ----------- 199 duration ----------------------- 7,132,150,191,271 daily angular velocities ----------------------- 131 duration as indicator of flooding potential ------ 440 daily motions at aphelion and perihelion -------- 131 duration at maximum lunar declination --------- 270 daily motions at equinoxes -------------------- 131 duration at perihelion ------------------------ 270 daily motions at solstices ---------------------- 131 duration decreased -------------------------- 196 declinational effects on solar motion ------ 132,148,198 duration increased --------------------- 196,197,269 geomagnetic variations ----------------------- 489 duration influences --------------------------- 273 Index 537 Tidal day-Continued Page rage duration maximum -------------------------- 274 Tidal loading: earthquakes -------------------- 492,493 lunar orbital velocity increase ----------------- 274 Tidal prediction ----------------------------- 14, 506 lunar orbit inclination ------------------------ 196 lunar augmentation -------------------------- 147 lunar velocity in right ascension ---------------- 196 Tidal priming -------------------------------- 302 relation to lunar day ------------------------- 440 Tidal priming and lag: analysis ----------------- 306 solar declinational effects ------------------- 148,150 Tidal range ------------------------ 82,84,95,96,298 systematic variations in duration ------------- 273,440 at aphelion --------------------------------- 502 at perihelion -------------------------------- 502 Tidal depression ------------------------------- 497 increase at pengee-syzygy --------------------- 6 Tidal flood engineering ------------------------ 490 lunar declination ---------------------------- Tidal flooding: lunar phase -------------------------------- 501 astronomical . conditions ---------------------- 11,25 physical retardation ------------------------- 504 conditions --------------------------------- 10 variations --------------------------------- 501 damage ----------------------------------- 408 Tidal retardation: effectiveness of advisories --------------------- 406 climatological factors ------------------------ 273 examples ---------------------------------- 15 hydrological factors -------------------------- 273 hypothesis tested ----------------------------- 197 Tidal types --------------------- 298,448,474,475,505 inaccurate documentation -------------------- 12 Tide amplitude ------------------------------- 59 local conditions ----------------------------- 437 Tide growth: rates ----------------------------- 290 lunar declination ---------------------------- 196 Tide-raising forces ----------------------------- 6 off- vs. on-shore winds ----------------------- 12 apogee ------------------------------------ 502 onshore winds ----- :------------------------- 291 augmentation of ---------------------- 147,198,202 protective barriers --------------------------- 409 compensating influences ---------------------- 204 recurring short-range potential ---------------- 117 counterproductive influences ---------------- 185,204 research hiatus ------------------------------ 117 declination effects ------------------------- 186-191 wind function ------------------------------- 117 duration ------------------------- 176, 192, 271, 306 1927 events -------------------- ------------- 474 harmonic constituents ------------------------ 296 1931 event -------------------------------- 331,474 intensification factors ------------------------ 197 1933 event --------------------------------- 474 limiting conditions --------------------------- 199 1939 event --------------------------------- 374 lunar declination equations ------------------- 187 1959 event --------------------------------- 383 lunar parallax effect ------- L --------------- 1933 502 1962 event --- ---------------------- 117, 386, 445 lunisolar declinations ------------------------ 271 1974 event advisory ------------------------ 405,406 magnitude and duration --------------------- 137 1976 event --------------------------------- 424 maximum ---------------- 11,199,202,203,218,313 1978 events --------------------------- 429,430,43t Moon vs. Sun ----------------------------- 204,501 Tidal flooding potential: parallax effects ------------------------------ 502 numerical index of astronomical factors --------- 434 perigee ------------------------------------ 502 tide rise rate ------------------------------- 448 semidiumal solar constituent ------------------ 502 Tidal force envelope -------------------- 303, 306, 501 time related factors -------------------------- 296 produced by Moon -------------------------- 501 Tide-raising potential ------------------------ 197, 498 produced by Sun ---------------------------- 501 augmentation of --------------------------- 197, 433 Tidal height: duration of augmented forces -------------- 296, 306 equations ---------------------------------- 169 seasonal factors ----------------------------- 198 predicted ---------------------------------- 440 Tidelands ----------------------------------- 99 related to lunar positions --------------------- 273 Tide-reducing forces --------------------------- 204 seasonal factors ----------------------------- 151 Tide rips ------------------------------------- 105 semidiurnal component ----------------------- 173 Tide tables ----------------------------- 14, 449-452 Tidal lag ------------------------------------ 303 Tides: Tidal literature: atmospheric systems ------------------------- 506 18th century -------------------------------- III accelerating factors -------------------------- 504 early 19th century ----------------------------- 112 arrival time -------------------------------- 503 late 19th century ---------------------------- 114 basic theory --------------------------------- 497 20th century -------------------------------- 115 causes ------------------------------------- 121 538 Index Tides-Continued Page Pago control factors ------------------------------- 497 True parallax: perigee-syzygy value -------------- 176 lagging of ---------------------------- 302,303,504 True perigee longitude ------------------------- 217 True tidal day: tide curves ---------------------- 303 local height -------------------------------- 503 1 military engineering ------------------------- 497 Trumbull ', American frigate ---------------------- 59-70 navigation --------------------------------- 497 Tsunamis ------------------------------------ 490 offshore territorial limits ----- I --- 497 Turbidity currents --------------------------- 105,494 -- ---------- priming of ---------------------------- 302,303,504 Typhoons ------------------------------------ 25 resonance effects ---------------------------- 506 Ultimate-maximum proxigean spring tides --------- 313 retarding factors ---------------------------- 502 Universal time -------------------------------- 13 shoreline property boundaries, importance for ---- 497 Upper branch of meridian ---------------------- 122 standard chart datums ----------------------- 497 Upper transit --------------------------------- 122 strong wind effects -------------------------- 506 Vernal equinox -------------- 4-------------- 122,190 types of ---------------------- 298,448,474,475,505 Vertical circles -------------------------------- 123 unique local timing response ------------- ----- 69 Wales: 1849 floods ---------------------------- 96 water sports, effect on ------------------------ 497 Water pollution ------------------------------- 99 Topocentric parallax -------------------------- 148 Weather maps --------------------------- 14,328,329 Tractive forces -------------------------------- 500 West Coast (North America) : Tropic tides ---------------------------------- 149 British Columbia, Ripple Rock ---------------- 97,98 Tropical cyclones ------------------------------ 25 Tropical depressions --------------------------- 25 California --------------------------------- 408 Tropical month ------------------------------- 126 Wind damage --------------------------------- 481 True anomaly ---- --------- I---------------- 184,217 Wind symbols, synoptic map ------------------ 330,331 True longitude: sinusoidal variation with mean "Windows" of tidal flooding -------------------- 4-74 longitude ------------------------------ 184 Zenith -------------------------- ------------ 123 U.S. GOVERNMENT PRINTING OFFICE 1978-0-202-509 4Q- All, 17- WOW M71 "Al tgl AL MW Zeta kl4_11M 64 Portion oll' barrier beach @oulh o,fAfeCoX BaY, near Southanipw?, Long JS/an(',,\'.Y., breached bi lzdallfloodln4@ oll-Alarch 6-7, Pk;2. 11118111110 @-'3 6668 1410Z: 7 18 A