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11l Im," ?r E: m IIi1 ll Iiin II= ' I Tidk' i a II Am ~~~~~~a I I l F LiII?;. L*---j U!1lI1 Il Urli iiiIZ[~' pl ~~~~hI~ - L IIlE., IL IhiLa urn .r MIa !!' - m iiii 1 NOAA TECHNICAL REPORTS National Weather Service Series The National Weather Service (NWS) makes observations and measurements of atmospheric phenomena, develops and distributes forecasts of weather conditions and warnings of adverse weather, and collects and disseminates weather information to meet the needs of the public and specialized users. The NWS develops the national meteorological service system and the improved procedures and techniques for weather and hydrologic measurements and forecasts and for their dissemination. NIVS series of NOAA Technical Reports is a continuation of the former series, ESSA Technical Report Weather Bureau (WB). Reports 1 to 3 are available from the National Technical Information Service, U.S. Department of Commerce, Sills Bldg., 5285 Port Royal Road, Springfield, Va. 22151. Prices vary. Order by accession number (at end of each entry). Beginning with 4, Reports are available from the Superintendent of Docu- ments, U.S. Government Printing Office, Washington, D.C. 20402. ESSA Technical Reports IVB 1 Monthly Mean 100-, 50-, 30-, and 10-Miillibar Charts January 1964 through December 1965 of the IQSY Period. Staff, Upper Air Branch, National Meteorological Center, February 1967 (AD 651 101) WB 2 Weekly Synoptic Analyses, 5-, 2-, and 0.4-MIb Surfaces for 1964 (based on observations of the Meteorological Rocket Network during the IQSY). Staff, Upper Air Branch, National Meteorologi- cal Center, April 1967 (AD 652 696) IB 3 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Mb Surfaces for 1965 (based on observations of the Meteorological Rocket Network during the IQSY). Staff, Uipper Air Branch, National Meteorologi- cal Center, August 1967 (AD 662 053) WB 4 The March-May 1965 Floods in the Upper Mississippi, Missouri, and Red River of the North Basins. J. L. II. Paulhus and E. R. Nelson, Office of Hydrology, August 1967. Price S0.60. WB 5 Climatological Probabilities of Precipitation for the Conterminous United States. Donald L. Jorgensen, Techniques Development Laboratory, December 1967. Price $0.40. WB 6 Climatology of Atlantic Tropical Storms and Hurricanes. M. A. Alaka, Techniques Development Laboratory, Hay 1968. Price $0.20. WB 7 Frequency and Areal Distributions of Tropical Storm Rainfall in the United States Coastal Region on the Gulf of Mexico. Hugo V. Goodyear, Office of Hydrology, July 1968. Price $0.35. WB 8 Critical Fire Weather Patterns in the Conterminous IUnited States. lark J. Schroeder, Weather Bureau, January 1969. Price $0.40. IVB 9 Weekly Synoptic Analyses, 5-, 2-, and 0.4-fMb Surfaces for 1966 (based on meteorological rocket- sonde and high-level rawinsonde observations). Staff, Upper Air Branch, National [Meteorological Center, January 1969. Price $1.50. WB 10 Hemispheric Teleconnections of Hean Circulation Anomalies at 700 Hillibars. James F. O'Connor, National Meteorological Center, February 1969. Price $1.00. WB 11 Monthly Mean 100-, 50-, 30-, and 10-Millibar Charts and Standard Deviation laps, 1966-1967. Staff, Upper Air Branch, National Meteorological Center, April 1969. Price $1.25. N1B 12 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Millibar Surfaces for 1967. Staff, Uipper Air Branch, National Meteorological Center, January 1970. Price $1.50. NOAA Technical Reports NWS 13 The March-April 1969 Snowmelt Floods in the Red River of the North, Uipper Mississippi, and Mis- souri Basins. Joseph L. II. Paulhus, Office of Ilydrology, October 1970. Price $1.25. (COM-71- 50269) NWS 14 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Millibar Surfaces for 1968. Staff, Upper Air Branch, National Meteorological Center, May 1971. Price $1.50. (COM-71-50383) NIWS 15 Some Climatological Characteristics of Hurricanes and Tropical Storms, Gulf and East Coasts of the United States. Francis P. Ilo, Richard W. Schwerdt, and Hlugo V. Goodyear, M!ay 1975. NWS 16 Storm Tide Frequencies on the South Carolina Coast. Vance A. Myers, June 1975. NOAA Technical Report NWS 17 Estimation of Hurricane Storm Surge In Apalachicola Bay, Florida James E. Overland Office of Hydrology Silver Spring, Md. June 1975 Property of CSC Library U. S. DEPARTMENT OF COMMERCE NOAA COASTAL SERVICES CENTER 2234 SOUTH HOBSON AVENUE ChARLESTON, SC 29405-2413 ! UNITED STATES NATIONAL OCEANIC AND National Weather DEPARTMENT OF COMMERCE ATMOSPHERIC ADMINISTRATION Service 2 Rogers C. B. Morton, Secretary Robert M. White, Administrator George P. Cressman. Director ~. CONTENTS Preface ....................... iv Acknowledgments .IV Abstract .............................. 1 1. Introduction ...................1 2. Theoretical considerations ................... 3 2.1 Basic equations ...................... 3 2.2 Surface and bottom boundary conditions ........... 5 2.3 Oceanic boundarv conditions and narrow inlets ....... 7 2.4 Flooding, barriers, and barrier islands .......... 9 3. Numerical considerations .................... 10 3.1 Choice of numerical scheme .................10 3.2 Finite-difference formulation .12 4. Meteorological specification .................. 13 5. Application to Apalachicola Bay and Franklin County ....... 14 5.1 Description of ~the area., a.14 5.2 Hindcasts--astronomical tides and hurricane Agnes . . . 18 5.3 Response of the Apalachicola Bay model to a major hypothetical storm ................... 23 5.4 Response of Apalachicola Bay to an ensemble of climatological storms .28 6. Conclusions and recommendations ................. 32 Appendix A. Stability analysis of implicit bottom friction ..... 34 B. List of symbols .................... 36 C. Documentation of computer program ........... 38 C.1 List of program variables ............. 38 C.2 Program listing .................. 40 References .............................64 TABLE 1. Summary of tidal calibration ..1.. ..... ii F IGURES 1. Specification of coordinate system. ................4 2. Comparison of proposed functional dependences with a surge time-history at the coastline generated by the SPLASH model ...8 3. Location of descretized variables on a Richardson lattice . . . . 11 4. Shallow water dispersion relation for solution on a Richardson lattice, compared to the analytic solution .. ..........11 S. Assumed dependence of wind speed, inflow angle, and atmospheric pressure gradient as a function of distance from the storm center is 6. Geographic loc ations in Franklin County, Fla .. .........16 7. Discretization of Apalachicola Bay, Fla., and location of barriers 17 B. Depth/elevation of grid squares in feet .. ...........17 9. Path of hurricane Agnes, June 14-23, 1972 .. ..........20 10. Observed high-water marks for hurricane Agnes .. ........21 11. Derived high-water envelope for hurricane Agnes continuing the SPLASH wind field across the Bay .. .............22 12. Derived high-water envelope for hurricane Agnes utilizing local wind information .. ....................22 13. Observed and derived time histories of the surge height at Apalachicola for Agnes; observed and assumed SPLASH winds at Apalachicola ......................... 23 14. Instantaneous water heights for a hypothetical storm, 4 hr before landfall .. .....................25 15. Instantaneous water heights for a hypothetical storm at closest approach to Apalachicola .. .............25 16. Instantaneous water heights for a hypothetical storm 3 hr after landfall .. .....................26 17. Composite high-water envelope for a hypothetical storm . . ....26 18. Composite high-water envelope for a hypothetical storm assuming fixed lateral boundaries .. ..............27 19. Reference locations A, B, C, D for figures 20, 21, 22 .. ....29 20. Surge elevations at four locations as a function of increasing hurricane central pressure with other parameters held fixed . 30 21. Surge elevations at four locations as a function of the forward speed of the storm .....................30 22. Surge height variation at four locations as a function of distance of closest approach to Apalachicola. ........31 23. Estimated tide levels at the 0.01 per year probability level . . . 33 iii PREFACE This report documents the formulation of a shallow bay hydrodynamic model and its application to Apalachicola Bay, Florida. The Apalachicola Bay model and the SPLASH model for estimating open coast surge (Jelesnianski 1972) were used as aids in determining total storm tide frequency information for Franklin County, Florida. The frequency analysis is presented in a separate report (Ho and Myers 1975). The present report is part of the study by the Special Studies Branch, Office of Hydrology, National Weather Service, for the Federal Insurance Administration, Department of Housing and Urban Development, under the National Flood Insurance Act of 1968. ACKNOWLEDGMENTS The formulation of the bay model has drawn upon the efforts of a large number of authors, most notably Hansen (1956), Jelesnianski (1967), Reid and Bodine (1968), and Laevastu and Stevens (1969). Their contribution is freely acknowledged. I extend my appreciation to the staff of the Special Studies Branch, all of whom contrib- uted to the present project. I also thank E. Ramey and his staff at the National Ocean Survey for providing much useful information on Apalachicola Bay. iv ESTIMATION OF HURRICANE STORM SURGE IN APALACHICOLA BAY, FLORIDA James E. Overland Office of Hydrology, National Weather Service, NOAA Silver Spring,.Md. ABSTRACT. A vertically integrated two-dimensional numerical hydrodynamic model is developed for simu- lation of hurricane surge in Apalachicola Bay. Stand- ard explicit time differencing is used in conjunction with a single Richardson lattice. Model features include finite amplitude effects, space variable wind velocities, and parameterization of flooding of ter- rain, overtopping of barrier islands and flow through narrow passes. The model utilizes the results of C. P. Jelesnianskis'sSPLASH model computation for open coast surge as input seaward of the Bay and continues the same storm track and wind field as used in the SPLASH computation across the Bay. The Bay model was calibrated for the astronomical tides and verified against hurricane Agnes. The response of Apalachicola Bay, has been determined from numerical computations for a variety of hypo- thetical hurricanes as specified by various storm parameters. Surge heights in the Bay increase with hurricane central pressure depression in a nearly linear fashion as does the open coast surge. An im- portant parameter is the duration that the open coast surge remains high, a function of the forward speed of the storm and, to a lesser extent, the radius of maximum winds. Surge heights in the Bay increased relative to open coast surge values for slow moving storms. For bays of the extent of Apalachicola Bay, basin orientation relative to wind direction, head- lands, and marsh areas can produce significant local variations in surge heights. 1. INTRODUCTION The National Flood Insurance Act of 1968 and the Flood Disaster Protection Act of 1973 provide a National program for insuring residences and small businesses against damage and destruction by floods. As a part of this 2 program it is necessary to provide frequency information for coastal areas on surges caused by hurricanes. For most areas, observed surge data alone is insufficient to determine expected flood levels. An additional source of frequency information is, however, provided by the specification of the hurricane climatology of a given region,(Ho, Schwerdt, and Goodyear 1975). This information, combined with the use of a hydrodynamic surge calculation such as the SPLASH program for open coast surge (Jelesnianski 1972), can be used to estimate the surge response to an ensemble of hypothetical storms (Myers 1970, 1975). This report documents the modification and application of existing bay modeling techniques to the problem of estimating the re- sponse of a bay to hurricanes. An example of its utilization is given for Apalachicola Bay, Florida. The approach to assessing the response of bays to hurricanes must be sub- stantially different from assessing the response in unrestricted water and on the continental shelf. Variations in open water a-re, in general, of the same order as variations in the storm, while surge heights in a bay may vary greatly on the scale of a few miles. Dynamic processes also differ in their relative importance. An indication of the complexity of the time dependent response of continental shelf waters to storms of various tracks is given by Jelesnianski (1974); bathystrophic adjustment and excitation and subsequent propagation of forced and free inertial-gravitational modes are of primary importance. Bays provide walls for the wind to push water against, and their shallow depths introduce nonlinearities associated with bottom friction and finite-amplitude effects. Flooding of low terrain can greatly increase the surface areas of many bays and converging channels can produce dramatic local surge heights. Dynamic coupling of a bay model with a shelf model that would permit direct interaction between them while spanning the diverse space scales and includ- ing relevant physical processes in both domains is beyond the scope of the present project. Instead., the results of a SPLASH computation for the open coast surge adjacent to the bay have been utilized as input with the same storm parameters and track as used in the SPLASH calculation continued over'' the bay. The present bay formulation simulates propagation of peak surge inland from the open coast, overtopping of barrier islands, local wind a~nd pressure effects over the bay, and how there features are modified by basin orientation, bathymetry, bottom friction, and flooding. The results of the bay model confirm that timing of events is indeed critical, as high water in back bays may be the result of primarily the wind setup, landward propagation of open coast surge, or the two may combine or mitigate. It is emphasized that the present formulation should not be considered op- erational for precise surge prediction, but provides a research'tool to assist making quantitative estimates by combining the results of hydrodynamnic simulations for a large number of hypothetical storms. The response of a bay to a particular storm is strongly dependent upon the landfall point and wind distribution within the storm, much more than for the open coast surge. Technical formulation of the model is presented in sections 2, 3, and 4, and application to Apalachicola Bay is presented in section S. A list of symbols is provided in Appendix B. 3 2. THEORETICAL CONSIDERATIONS 2.1 Basic Equations Quantitative derivation is based upon conservation principles for momentum and fluid volume. A hydrostatic, incompressible fluid is assumed. A-stand- ard right-hand x, y, z coordinate system is used with z the vertical coordi- nate, but with y not necessarily northward, as in figure 1. Momentum and continuity equations are specified as follows: au au2 auv auw 1 al > a (1) - + - + 3 + - fv = +xx 'xy xz t + -a-x 'ay az P a fx p ax ay az 0 0 av auv av2 avw a- J a2) -+ -4.- +-5-Y+ 3z + fu I ap + 1 [ y X z ] (2) Poa aP :[x yy yz ] L +p + g fu= - p az (3) 0 au av aw (4) -a + y + =0 (4) with p0 density, p pressure, g acceleration of gravity, and f the Coriolis parameter. The component velocities, u, v, and w, represent deterministic variables that have'been smoothed to filter small-scale turbulent features. The total velocity at an instant in time consists of this deterministic velocity, u, plus a random turbulent velocity, u', whose value is distributed according to a probability density function. Horizontal turbulent stresses are defined by the small-scale structure such that: tz - po < u'w' >E etc. (5) where < >E is the smoothing operator, defined so that the average of the fluctuations, <u'>E equals zero. Following Hansen (1956) and Leendertse (1967), a total depth, H, horizontal volume transport per unit width, Qx' and vertically averaged velocity, U, are introduced: H = n- d (6) with n the surface elevation and d the depth with respect to z = 0 , Q-d u dz, (7) u=-W. (8) 4 f f 7 *Au (z) =U [l+ () (9) and applying the kinemiatic condition at the surface and bottom, horizontal transport equations are derived in the following form: p p /QX Da UQX) a (a VQ) = C D + PD)) T ( xz xz (10) an + Qx + y ~~at ax ay .fx = -gH yy o . + +y = 0 (12) with the velocity distribution functions defined by _ 1 Uf (l+ n a ) dz, etc. (15) uv H d u These distribution functions approach 1.0 for small deviations of the velocity from the vertical mean. The term n* is defined by nI* = Pa/pOg with Pa the atmospheric pressure. The superscripts S and B indicate surface and bottom stress, respectively. Only the external contribution to the pressure field has been considered and lateral stress components are not explicitly included. The field acceleration terms in eq (10) and (11) are notably important in two situations. They can be important in pollution dispersion calculations, as they are responsible for generating eddies through nonlinear interaction. They are also important where a fluid parcel may be rapidly accelerated, such as a flow impinging on a narrow opening. These terms will not be ex- plicitly included in the interior of the bay; however, they are considered ,at low barriers and narrow entrance channels, which are treated as special cases, as outlined in sections 2.3 and 2.4. The restriction to shallow bays implies that the water depth is much less than Ekman depth so that surface and bottom stress is rapidly diffused through the water column. The effect of the Coriolis terms in the vertically integrated equations will not be further considered. 2.2 Surface and Bottom Boundary Conditions Stress from the wind at the free surface is related to the wind velocity by means of a drag coefficient Cd = P *C W2 (14) where pa is the air density and Wa is the wind velocity at a given elevation, assumed to be 10 meters above the surface. The drag coefficient represents the bulk parameterization of very localized processes. The very large scat- ter in direct measurements is to be expected and even what bulk parameters, if any, determine its variation remains unclear. The problem is compounded as there is very little drag coefficient data for high wind speeds. Wilson (1960), Roll (1965), and Wu (1969) have tabulated drag coefficient data from a wide variety of sources and methodologies. There is indication that a division is possible into "light" and "strong" winds around 30 knots with mean values of about 1.3 x 10-3 for light winds and 2.4 x 10-3 for strong winds. "Strong" winds imply less than 60 knots. For hurricane con- ditions Miller (1964) has computed drag coefficients from observations of ageostrophic atmospheric transports. While noting the large uncertainties in this approach, Miller suggests a weak increase with wind speed at very high wind speeds. We take some faith in the fact that many of the drag esti- mates were made in enclosed or semi-enclosed basins. The present formulation divides the drag coefficient into three regions, a constant value of 1.2 x 10-3 below 15 knots, a linear increase to 2.1 x 10-3 at 30 knots and a weak linear increase to 2.65 x 10-3 at 90 knots. The SPLASH program assumes a constant drag coefficient of 2.4 x 10-3. The ratio 6 of the density of air to water has been taken as 1.25 x 10-3. The flux of rain water falling directly on the surface of the bay and stream runoff has not been included. It is quite possible, however, that for some basins, particularly narrow estuaries, if intense rains have occurred over the contributing watersheds well in advance of the hurricane, flood waters propagating down tributaries may arrive during the rising stages of the storm surge and thus alter the basin response. Bottom stress (which in the present formulation implicitly includes all momentum loss to turbulent processes) is related to both the characteristics of the bottom and to features within the flow field. In a vertically inte- grated formulation the dependence must be parameterized in terms of the ex- plicit model variables: T = T (Bottom, Qx' Qy' H, TS(15) For shallow flow, bottom stress has been related to a quadratic power law g IQg Q B* 0 C2 H2 (16) H with a Chezy coefficient, CH , specifying the type of bottom. As with the drag coefficient, bottom roughness coefficients parameterize the bulk effect of small-scale phenomena, thus the wide scatter in their estimation. Esti- mates are given by Chow (1959), Dronkers (1964), and Bruun (1967). Experi- ence has also been obtained from modeling of tides in many areas. Reid and Bodine (1968) deduced a friction value corresponding to a Chezy coefficient of 62 m�/s (113 ft�/s) from calibration for Galveston Bay, a bay that con- tains large areas with depths less than 12 feet similar to Apalachicola Bay. Based upon these estimates the model provisionally specified three terrain- dependent Chezy coefficients for very shallow bays, 61 m�/s (110 ftls/s) for areas normally below mlw, 44 m�/s (80 ft�/s) on the tidal flats, and 14 m�/s (25 ft�/s) for vegetated inland areas subject to flooding. In the tuning process (Chapter 5.2) it was found that a small increase in bottom friction provided a slight improvement in overall verification. A final deep water value of 55 m'/s (100 ft'/s) was 'adopted for the study. Equation (16) does not explicitly include the effect of wind stress on bottom stress. Reid (1956) has derived a generalized formulation of bottom stress for quasi-steady turbulent open channel flow which takes the influence of surface stress into account. Reid states that "in general, the effect of the wind stress is such that, for a given current, the effective resistance to flow is reduced for a following wind and increased for an opposing wind." His results show the correction to the bottom stress as a percentage of the surface stress to be a weak function of mean velocity and wind stress. How- ever, over a wide variety of conditions this correction is less than 0.10 of the surface wind stress. This ratio is consistent with the few direct 7 measurements of bottom stress available. As a first-order correction for the effect of wind on bottom stress, the following adjustment is made to the bottom stress: B B* T = B - 0.06Ts (17) 2.3 Ocean Boundary Conditions and Narrow Inlets Mathematical formulation of a bay model requires specification of driving forces and initial and boundary values. Specification of boundary values at an oceanic interface is available after the event from measurements such as tide gages, but for planning or forecasting purposes boundary input must be specified otherwise. Two approaches to providing boundary input are to ex- tend the model seaward and thus also resolve continental shelf processes or to couple a shelf model to the bay model. In the latter case an artificial boundary is immersed into the fluid near the mouth of the bay that is charged with representing the interaction between the bay and the adjacent sea. An ideal artificial boundary would allow transient wave phenomena to propagate out of, as well as into, the bay, provide periodic forcing such as the tides, and allow for wind drift. In this report the simplest type of coupling is considered in which the results of a SPLASH computation for open coast surge are used to specify water elevations seaward of the barrier islands and on the outside of inlets and passes. It is noted, however, that the SPLASH model does not account for the presence of entrances and broken features and does not include feedback from the bay model. Explicit specification of the oceanic sea level is use- ful, to the extent that on the scale of model resolution the presence of entrances has only a minor influence on the development of surge along the open coast and amplitudes of long waves exiting through a channel are dimin- ished by dispersion in two dimensions. The SPLASH program specifies water elevations every 8 statute miles along the coast. Linear interpolation of these values was necessary for input at the finer resolution of the bay model. For storms whose paths are approxi- mately normal to the coastline, it can be assumed that the peak surge arrives at nearly the same time for the stretch of coast adjacent to the bay and that the time history can be normalized at each location along the coast by /T-T lnfl n = rj (x) sech2 0.33 landfall) ~(18) qopen coast nmax(x) sechT 0.53 T T2/3 where T2/3 is a width parameter defined by the duration that the water level remains above (2/3) nmx. Figure 2 shows the fit of eq (18) and an error function dependence against a hydrograph generated by the SPLASH program for a storm landfalling normal to the coast. For more complicated storm trajec- tories the results of a SPLASH II computation (Jelesnianski 1974) can be utilized, specifying the SPLASH-generated time histories of surge heights at the coastline. 18 -- ERROR - ----SECH 2 16- ............ SPLASH 14 - 12 u53'10-' * .._ 6 a,- % a~~~~~~,,' 4- 12- I 0 CD 8- ;/o -200 -150 -100 -50 0 50 100 150 200 TIME (minutes) Figure 2.--Comparison of proposed functional dependences with a surge time-history at the coastline generated by the SPLASH model. For application in the Gulf of Mexico, dynamics of tidal oscillations are not included. Narrow entrance channels on the order of a few tenths of a mile in width which open into extensive bays are regions of high velocities and complicated flow patterns. The flow can experience accelerations both parallel and normal to the axis of the entrance. Transport through narrow passes is esti- mated from Qp = C AU (19) with U the vertically averaged velocity near the axis of the channel, A(t) P the geometric cross-sectional area, and C a contraction coefficient that excludes zones of eddying adjacent to lateral boundaries in the calculation of transport through the pass. The velocity is calculated from a momentum equation: a Du(i + c k) 32a Up k + + Xz (20) at 2 ax CH where Ck is the parameterization of momentum loss to turbulence and lateral acceleration. For large height differences between basins on either side of a pass, velocities through the constriction are limited by bottom friction and the field acceleration term. For this case Chow (1959, p. 479) indicates a Ck of order 0.25 to 0.8. Equations (19) and (20) are utilized at narrow passes using the water eleva- tions adjacent to the pass as input. From consideration of the geometry of the narrow entrances to Apalachicola Bay, the value of Ck was set at 0.35 and Cc is set at 0.90 (Chow 1959). 2.4 Flooding, Barriers, and Barrier Islands Flooding is of primary importance. Concern is not only with possible reduc tion of surge heights in the bay through flooding but also the extent of flooding possible while the surge in the bay remains high. The model has a resolution on the order of 1 mile, and the effect of flooding of an area con- taining brush, trees, ponding areas, small channels, streets, buildings, etc., is parameterized as the average effect on the scale of this grid size. One can specify the average elevation, bottom friction, and parameterization of the physical processes of flooding. One mechanism for parameterizing flooding is given by Sielecki and Wurtele (1970) which represents flow up gradually sloping boundaries. Another ap- proach was used by Reid and Bodine (1968) in which the land elevation is re- garded as uniform over each grisd square. If the elevation of the water is less than the land elevation at the junction of a flooded square and a dry square, zero water transport is taken. % = 0. (21) However, if the water level is greater than the adjacent dry land the rate of flooding per unit width is considered to be given by QN Co D v~g D (22) where Db is the depth of water above the level of the land and C is a flooding coefficient. While the approach of Sielecki and Wurtele has an aesthetic appeal and could be of importance in open coast surge runup, for uneven terrain and marsh areas in bays Reid's approach is considered a better parameterization of flooding and is used in the present formulation with a CO of 0.7. The accuracy of the value of C and the form of eq (22) is not considered critical, as eq (22) is applied for one time step and then the flooded square is considered part of the bay. If the water level in the bay drops so that water remains ponded inland, it is assumed to drain at the rate given by eq (22). Very narrow geographic features can be treated as walls between adjacent grid squares. Causeways and dune ridge systems are treated in this manner. If the barrier is higher than the adjacent water levels, zero flow is speci- fied. If the elevation on one side is in excess of the barrier height, eq (22) is assumed. If the barrier becomes submerged, transport toward the low head side is computed by QN =Cs Db T/g'H - H i T (23) =I 2 with Cs a discharge coefficient taken as 0.7 and Db is the average depth, (n + n )/2 -Zb, with Zb the height of the barrier. 1 2 3. NUMERICAL CONSIDERATIONS 3.1 Choice of Numerical Scheme The primary variables are discretized on the well-known single Richardson lattice as shown in figure 3. Transport points lie midway between height points so that no averaging of spatial derivatives is required. For conveni- ence, transport points at QX (i - �, j) and QY (i, j - �) are assigned to box (i, j). The single Richardson lattice has the additional advantage of being able to collapse to a one-dimensional channel. Its main deficiency is, of course, that transport components are not defined at the same location, neces- sitating averaging in friction terms and Coriolis terms, if utilized. Discre- tization produces an error in wave propagation as wavelengths approach the grid dimensions. The dispersion relation for the linearized shallow water equations is aE = */gH k. (24) with a the frequency and k the wave number. The group velocity is non-zero unless H vanishes. The Richardson lattice gives the following relation ar = 2gV- sin (kAx) (25) ~R Ax ( 2 ) ' The shortest resolvable wave has wavelength 2AX with corresponding wave number k = w/AX; all waves lie between O<kAx<w. A plot of the dispersion relations (24) and (25) is shown in figure 4, scaling Ax//g'A as 1.0 arbitrary time units. For short waves the phase speed and group velocity are reduced com- pared with the analytical solution. Simple explicit time differencing is used: a (t + 1/2) t (t + 1t) - (t(26) 3t AT where (t) {QX(t+�), QY (t + �), n(t)}-. 11 yij+2 y +lj+2 1ij+1 iij~iH. j Zji (jl)&x Q ijl ijl Qx j 1 +lj+la QYij+1mQi+ii+ 1j iji i H LyfiQY +1I iAXL IJ i+lj iax (i+1)ax Figure 3.--Location of descretized variables on a Richardson lattice. 3.0 - 2.5 - DIFFERENTIAL EQUATION . 2.0 - z LU U- W 1.5 -DIFFERENCE EQUATION rr E~~~~~~~~~X 2 1.0 - 0.5 - 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 KAX/TT Figure 4.--Shallow water dispersion relation for solution on a Richardson lattice, compared to the analytic solution. 12 Transport variables are defined only at a level one-half time step ahead of water elevations, so that while eq (26) has the appearance of a "leap frog" formulation, it is equivalent to the forward scheme of Sielecki (1968), and does not experience separation of the solution at alternate time levels. Stability is governed by the Courant-Friedrich-Lewy condition (Platzman 1972), AT < (27) * /2gH - The scheme is computationally neutral, neither amplifying or damping wave modes. This is a desirable trait for surge computations, but it also implies that short wavelength noise is not dissipated. 3.2 Finite-Difference Formulation The finite-difference formulation for the momentum equations is as follows: T+i T T+. QX.. - QX.. F iQI = -g ij i + AT ii Ax +X T+i o, gQ QXi + 1.06 Pa Cd IWI gQQ i ,A Po d C2 ;,(28) H with Hi th 0.5 [H . . + Hi..ij]T+( T Q /QXii + A (QYij + QYi,j+l + QYi ,j + QYi-l,j+1)2 and yT;ij .Tqy iii- AT -. AX AX T+� 1 gQ QY.. 0 ' = -gij T p d y C 2 12_2 0H ij with H..--J 0.5 Hij + H. .l]T+� (29) T - / Qy~j + ~ (Q~ij + QXij+1 + QXi+l.+jI)2 The wind speed IWI is given by (W2 + Wy)� where W and W are component wind x.y x y velocities. The continuity equation is given by T+� - T-� T T T T nij nT QX i+l,j - ,QXij QYi,j+l ij (30) AT AX, AX In utilizing the transport formulation, interpolation of depth is not re- quired in the continuity equation; this is preferred, as elevation changes are very sensitive to small errors in the horizontal divergence. It has been shown that inclusion of an explicit friction term may reduce the permissible time step for stable computations (Holsters 1962); here, an implicit friction formulation is used. A stability analysis including im- plicit friction is presented in Appendix A. No smoothing of the primary variables, QY, QY, n, has been used with the present formulation. Formulation at narrow passes is as follows: UT+l_ T (Il+Ck)i = Up p + _ T+U T AT 2AX CT r P P H g~ ~~~ [T+-3p1]d aC WWT T1 P1 T+ (1.06) aCd jIT4� [7 H (31) = C.cb H U (32) where b is the ratio of pass width to grid length. 4. METEOROLOGICAL SPECIFICATION Ho, et al. (1975) have classified hurricane occurrences in terms of five independent variables, P0, the central pressure (an index of intensity of the storm), R, the radius to maximum winds (an index of storm size), F, the forward speed of the storm, 0, the direction of entry to the coast, and L, the landfall point of the storm center. In the SPLASH model, P0, R, and an assumed wind speed variation with radial distance from the center are used as input to the steady-state momentum equations to derive a self-consistent meteorological input to the open coast surge model. The same storm parameters as utilized in the SPLASH run to obtain open coast surge values are used as input to the bay model. The wind speed, inflow angle and atmospheric pressure gradient are given as a function of the radial distance from the center of the storm, r. 14 The wind speed profile is the same as specified in SPLASH model 2Rr W max Ws(r) = RZ + rZ W max, obtained from the SPLASH run, is the maximum wind speed if the storm was stationary and is a function of central pressure and radius of maximum wind. For use with the bay model the variations of the pressure gradient and inflow angle with radius are assumed rather than derived but are in qualita- tive agreement with derived SPLASH profiles. This assumption is expedient and reflects the fact that the extent of bays is small and the storm is, no doubt, modified during the transition from the sea to land. The inflow angle, 0, is assumed to have a maximum of 22� at 3 R and to approach 17� at large radius with the following dependence: = 0-2856[]exp [R] r <4.4R (34) = 0.2967 r >4.4R The atmospheric pressure gradient has the following dependence with a maxi- mum at 0.5 R (Myers 1954): a R Br (PN P) exp (35) with PN the pressure at some great distance from the center of the storm. Equation (35) represents a minor correction when applied over a bay and has usually been neglected in previous studies. Profiles of wind speed, inflow angle, and pressure gradient are plotted in figure 5. The storm is moved across the grid with a given forward speed with the local wind velocities corrected for forward speed in the same manner as in the SPLASH storm + =iW (r) + RrF (36) =s( R2 + r2 with W the composite wind velocity at a given location. 5. APPLICATION TO APALACHICOLA BAY AND FRANKLIN COUNTY 5.1 Description of the Area and Schematization Franklin County is located in Northwest Florida on the northern edge of the Gulf of Mexico. The lateral extent is from Ochlockonee Point on Apalachee 15 100 I INFLOW ANGLE (34) 80 - LU \ ATMOSPHERIC 20|ESSU / E GRADIENT (35) 20 , ~,, I I I I I ; I 0 R 2R 3R 4R 5R 6R RADIAL DISTANCE FROM CENTER OF STORM Figure 5.--Assumed dependence of wind speed, inflow angle, and atmospheric pressure gradient as a function of distance from the storm center scaled on the radius to maximum winds, R. Numbers in parentheses refer to equation numbers. Bay to Indian Pass near Cape San Blas (fig. 6). The major geographic fea- tures are a 35-mile barrier island system, the 4-mile wide Saint George Sound, which opens into Apalachicola Bay, and the East Bay area, which is comprised of several bayous and low marsh areas. Saint George Sound has wide access to the Gulf through Duer Channel and East Pass. Major population centers are Apalachicola and Carrabelle, Fla., both located on minor rivers. Apalachicola Bay is discretized with a horizontal resolution of 1 nautical mile as shown in figure 7. The shaded regions indicate areas normally above mean sea level. Dune ridges and causeways are specified by a heavier line with their average elevation given in feet. Reference datum is 1 foot below mean sea level; this level approximates the mean low water elevation through- out the region. Average elevation/depth of a grid square is given in figure 8. The letter S indicates location of sea points where 'the external water level is specified. Squares indicated with the letter X show the extent of computation landward. Possible flooding into these squares is computed with the volume of water considered lost from the system. Two narrow inlets are included, West Pass at location (6, 7) and Indian Pass at (2, 13) with widths of 0.30 nautical mile and 0.075 nautical mile, respectively. Water depths, land elevations, and terrain type were obtained from National Ocean Survey charts and Geological Survey 7�-minute quadrangles, supplemented by recent aerial photographs supplied by the National Ocean Survey. I OCt4LOCK0NEE PT. ) FRANKLIN COUNTY, FLORIDA CARRABELLE IDASWAMP Vj7;r PORT ST. JOE / S..', 9' j45' .r~:F~~. /APALACHI OLA ------ APALACHICOLA 'S; ~ BY' -I - - o\P~~~~ ~~ -- 4., ".3~~~~~~~~ 290 30' I t g1 -1-9 29~ 30' 'I I~~z 'S J 0 5 10 15 ----- 60 - ---- WATER DEPTH IN FEET SCALE NAUTICAL MILES Figure 6.--Geographic locations in Franklin County, Fla. 14 13- 12 //9,R//''19P 8101 / // ~ ~/, ?/"IS I~ 'Z ~ /" S~ a /~ 3 j /- .1 ~1O // ISIMI5V ''V 7/1 (VI6 --9 N/ / ~ 1 /1~ /1P1?.11 4 is0 .. o 2 15 8 6 7 12 16 24j27420 18 18 18 i56;:q 11 :15: 25 2512 B 7 7 8 252518 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 32 34 35 36 37 38 39 40 41 42 43 44 45 Figure 7.--Discretization of Apalachicola Bay, Fla. Figure also-.shows location of barriers with elevations in feet (MLW). is~~x x x x X x x x x x x x x X X x X X K K X XXX 14 X-).10 10 10 10 10 10 0 4 4 4"4 4 44 4 10 10 0 12 12 12 2 12 IS 1.3 0 -4 -2 2-2 -2,16 5115 4 4 6 21,4 4 4 4 4r 9 7 8 0 n1 44 2 2 2 7 2 4 7 5 10 10 X ii 0 2 i0~f'0*c 5 -~ 15 iv 12 2 1 2 2 3 331 X X X X X XK X X 10 0 13 132 ' -s5 -S -33. I IF, 1?NO:I , k2,6.iro 2 4 147 7 7 7 67 14 14 14 14 X S .4-4.475-38 4~~~~~~~~~~~~~~5i~~~ -~~~~.4 1519191510 151418181916 P2152121 XXX XXX XXX X~~~~~~~~~~~~~~~~s 1 3I I 1 I 0 1 2 2 J 7 -.18 -10 -4 -9 -7 -7 -7 -2 -7 -7 -0 -5i.2.2120 20 20 20 20 2915 18 2010 _7~-510 21 ~,30 2030 30 30 30 30 30 30 30 6 0 ~~~~-3 -10 -4 -8 -9 -0 -0 -0 -7 -8 -7 -,7 -3 -8 -00 -9 -.8 -9 -7 -9 -10 -7 -10 -12 -19 -0 L10 -3 -3 _-4 -4 -4 -4 -10 -0 '18 10 IS 18 30 5 0 ~~~ ~ai0 -10 -in -10 -10 -10 -9 -9 -9 -10 --8 -8 -8 -10 -0 _9 -9 -10 -13 -14 -15 -17 -20 -iS 9 -11 -13 -18 -18 -18 -13 -15 -13 -3 -2 -18C -10 -2,.30 4 0 94 RIR3.-8 -1i -12 -10 -0 -0 -a -.5 -9 -4 -9 -9 -10 -7 -11 -13 -13 -17 -20 -20 -Ij -17 -20 -20 -18 -15 :10 -20 -17 -15 -15 -11 -13 -14 -15 -9 30 2~---Z.:28-6. 1-1"I _5 k :_ ,a 1O' - -10 47:- 3 10 -209-20 -i9-1S -20 -20 -20 -20 -10 k30 s 0.- 0 a 0 0 0 0 0 0 0 0 0 0 0 i 00002 1 23 45 78 Ia9 10 11 12 1314 15 16 17 18 19 20 21 2223224 25 202728929230 31 32332342052037 382394041 42 42 44 45 Figure 8.--Depth/elevation of grid squares in feet. 'IS" indicates location -of sea points, and X points indicate landward extent of the computation. - 18 5.2 Hindcasts--Astronomical Tides and Hurricane Agnes In estimating what might happen, it is helpful to know how well we do by hindcasting what has already occurred. For Apalachicola Bay a limited amount of astronomical tide data is avail- able, and in 1972 Hurricane Agnes passed to the west of the Bay, providing a set of high-water marks throughout the Bay plus a single tide-gage record of the time history at Apalachicola. Franklin County is in the region of transition between predominantly diurnal tides at Pensacola and predominantly semi-diurnal tides at Saint Marks and Cedar Keys. The tides at Apalachicola are influenced both by the main entrances and the small passes to the west, with the tide occurring earlier relative to the East Pass than if the small passes wiere closed. As hourly values of water elevations at the passes were unavailable, the averaged tidal data obtained from the National Ocean Survey tide tables pro- vided a first check on the overall model formulation. The tidal height and relative phase lag for high water was specified at East Pass and West Pass and the heights and phase lag computed at selected locations throughout the Bay assuming a semi-diurnal periodicity. The results for four values of the Chezy friction coefficient, 50, 100, 110, and 160 ft2/s, are summarized in Table 1. The large coefficient, 160 ft'/s, underestimated the damping of Table l.--Summary of tidal calibration Lower East Pass Carrabelle Cat Point Apalachicola Anchorage West Pass High High High High High High Water Water Water Water Water Water (ft) Lag (ft) Lag (ft) (ft) Lat (ft) Lag (hr) (hr) (hr) (hr) (hr) (hr) MSL MSL MSL MSL MSL MSL Observed 1.3 0.1 1.3 0.6 1.1 1.3 0.9 2.0 0.8 1.7 0.7 1.6 Friction Coef. 50 ft%/s 1.25 1.0 0.85 2.2 0.65 3.2 0.60 2.7 Friction Coef. 100 ft1/s 1.30 0.6 1.10 1.4 0.90 2.2 0.80 1.9 110 fts 1.30 0.6 1.15 1.4 0.95 2.1 0.80 1.9 Friction Coef. 160 ft'1/s 1.35 0.4 1.25 1.0 1.05 1.7 0.85 1.5 the heights in the Bay relative to East Pass, while strong friction, 50 ft2/s, greatly retarded the propagation of the tide in Saint George Sound and under- estimated the heights in the Bay. 19 Hurricane Agnes passed to the west of Franklin County on June 19, 1972 (fig. 9). The track was almost due north while in the Gulf of Mexico, curv- ing to the north-northeast before landfalling near Panama City on the west side of Cape San Blas. Agnes was a relatively weak storm in the Gulf with a minimum pressure of 978 mb. An unfavorable environment led to its weaken- ing before landfall (Simpson and Hebert 1973). Military reconnaissance indi- cated maximum sustained winds of 65 knots prior to landfall, while Apalachi- cola reported a maximum hourly wind speed of 34 knots and a fastest mile of 48 knots. Low-lying coastal villages between Carrabelle and Apalachicola suffered great damage. The estimated damage for Franklin County due to high tides was over $1 million (DeAngelis and Hodge 1972). Agnes is most noted, however, for reintensification of the storm center while over land with the attendant rainfall and floods over the Northeast United States. The total number of deaths attributed to Agnes was estimated at 124, and the total United States damage at $3,097 million (Simpson and Hebert 1973). Figure 10 shows the location and magnitude (feet, MSL) of observed hig watermarks in Franklin County for Agnes as supplied by the National Ocean Survey along with corrected values which remove the effects of the astronomi- cal tide given in brackets. The highest values occur at Carrabelle. The elevation drops slightly westward along Saint George Sound with a large drop across the causeway near Cat Point to the high-water mark on the barrier island opposite Apalachicola. The water elevations increase again in East Bay to the north of Apalachicola. A SPIASH computation for the outer coast surge height was made specifying the input meteorology for the storm while still at sea. Values consisted of a pressure drop of 35 mb and a radius of maximum winds of 21 nautical miles with the storm traveling north at 11.0 knots. The derived maximum wind speed corresponding to a stationary storm was computed to be 63 knots. Heights of 7 to 8 feet external to Apalachicola Bay were in agreement with the high watermarks on the outer coast. Two runs on the bay model were made to simulate hurricane Agnes. The first case continued the wind field consistent with the SPLASH computation over the basin with the storm containing higher wind velocities than were observed at Apalachicola. The second case utilized a wind field obtained from the hourly winds at Apalachicola. In the latter case, the winds were uniform in speed and direction over the grid, changing in time. The computed high-water envelope utilizing the SPLASH wind field is shown in figure 11, and the envelope using the local winds in figure 12. Lightly shaded squares indicate areas that became flooded during some part of the computation and dashed barrier lines indicate overtopping from the Gulf. Both runs show the qualitative trends of the observed high-water marks. In figure 13 the upper curves portray the observed hourly surge height at Apa- lachicola and the computed heights using the SPLASH and local winds. In the lower section the local and SPLASH winds at Apalachicola are also shown as a function of time. The use of the SPLASH wind field overestimated the onshore winds associated with the rear of the storm, resulting in higher than ob- served surge in East Bay. The observed wind field tended to underestimate the height variations in the Bay, perhaps in response to the smaller drag N A / (I! ,?-:7 U~~~ELMIRA rZ ( - ~~~~~~~~~-6 NEW YORK PITTSBURGHb AO Track ~~~~~HARRISQURG -WASHINGTOND.C.,W Agnes ~ - ROANOKE XNROK CAPE-W ATLAN OLND WOSTONA 10 S ACKS~~A OSVITINLT110S AL~ Figure 9.---Path of hurrican~~~eAgnesJneD42,92 (De~~~~~~~~~~~~ Q::0 ATgi and0 HdEST72 I~~~~~~~~~~~~~~~~~~~~8.4 FRANKLIN COUNTY, FLORIDA V- 417 CARRABELLE (8.5) INDIAN 8.3 I d SWAMP (8-29\5~ PORT 6.4 / ST.JO E (6.3)J so~~~~~O C~4"0 290 45' APALACHICoL--- ~~ IDGE (7(5-3 ST. ViNC 50UN0 (535.4 APALACHICOLA 4.6 Sr� ~i~u~-~i Bav (4.5): = o "L4~~~~d 7.5~~~(7.4) :J op - V./ 19850 000 840 45' 840 30' -r290 30' - -!-29' 30' + 290 30' XICO GLJLL0 M HIGH-WATER MARK (FT - MSL) 0 5 10 15 -----60-----WATER DEPTH IN FEET SCALE NAUTICAL MILES Figure IO.--Observed high-water marks for hurricane Agnes (ft, MSL). .12 .. -' " f", '-, --S~~~~i~ia '-1 ! ...8. M. ... M.... 6_ 7.5 ' ,"9 . - I 8- I'- 7. - 1 1 1 1 1 I I 1 2 3 4 5 6 7 8 9 1011121314 15 16171819 2021 2 23 24 25 26 27 28 29 303132 33 34 35 36 37 38 39 40 41 42 43 44 45 Figure ll.--Derived high-water envelope (ft) for hurricane Agnes continuing the SPLASH wind field across the Bay. Lightly shaded regions indicate flooded terrain. 14 3 12 _ 5 A 9 t @ sa 9.S;, -g 4 2 I 2 WON" 6 7.5 ,. .R / u !-8. . .-- �.2 i-- "ci__- . 2 7.5! rmm 79 1 111 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Figure 12.--Derived high-water envelope for hurricane Agnes utilizing local wind information. 23 - '-� 'OBSERVED 6 __- COMPUTED WITH SPLASH WINDS �~COMPUTED WITH OBSERVED WINDS 5- 4- 3 4- I- 2- *%% � - ' v' b, OBSERVED WINDS SPLASH WINDS 22 24 02 04 06 08 10 12 14 16 18 20 22 24 JULY 18 JULY 19 DATE - TIME Figure 13.--(Top) Observed and derived time histories of the surge height at Apalachicola for Agnes. (Bottom) Observed and assumed SPLASH winds at Apalachicola. coefficient assumed for lower wind speeds or to the Apalachicola winds not being representative over the, entire region. The delayed maximum in the observed surge is evident in the SPLASH wind derived profile and in the latter case coincides with propagation of surge in from the east end of Saint George Sound and onshore winds. It is a long progression from specifying several generalized storm parame- ters for Agnes to obtaining a surge height at Apalachicola. Observed hourly values at the Pass entrances would have shortened the number of links and thus might have increased the agreement with data, particularly the time history. However, the intent was a check upon the entire procedure. Even with the highly generalized input, the overall results are encouraging, par- ticularly in the estimation of the reduction in surge height from Carrabelle to Cat Point and Cat Point to Apalachicola as seen by comparing figures 11 and 12 with the high-water marks in figure 10. 5.3 Response of the Apalachicola Bay Model to a Major Hypothetical Storm This section discusses the results of the model for simulation of a major storm. The storm is specified by a pressure drop of 52 mb, a radius of 24 maximum winds of 23 nautical miles, a forward speed of 13 knots with a maxi- mum stationary storm wind speed of 77 knots. The storm travels perpendicular to the coastline with the center of the storm passing 28 nautical miles to the west of Apalachicola. While this storm is considerably less intense than a Camille (1969) type storm, it represents an unfavorable storm track for Apalachicola Bay. Figures 14, 15, and 16 portray the instantaneous water heights in the Bay at 4 hours before the storm passes close to Apalachicola, while the storm passes, and 3 hours later. Wind arrows are included at Car- rabelle and Apalachicola with one bar representing 10 knots. Flooded regions are again specified by lighter shading. Before the storm hits (fig. 14) strong east winds blow down Saint George Sound and across Apalachicola Bay with wind setup in Saint Vincent Sound and on the west side of the Bay. The setup, however, does not build substan- tially until the water level external to the Bay begins to rise and negate the flow through the passes driven by the inside-outside height difference. Water is blown out of East Bay. This figure also portrays the effect of the initial rise of the open coast surge propagating into Saint George Sound. Figure 15 shows the water elevations an hour after the open coast surge has peaked at 11.7 feet near East Pass. Water heights in Apalachicola Bay and East Bay are rapidly increasing as the surge propagates down Saint George Sound. Maximum winds over Apalachicola. Bay have produced a strong height gradient towards the north side of the Bay. Overtopping of sections of the barrier island is occurring, but the strong onshore winds maintain the strong inside-outside height difference across the barrier island opposite Apalachi- cola. After landfall (fig. 16) the open coast surge is decreasing, draining the Bay while the strong winds in the rear of the storm drive the water up against the higher topography in East Bay. The composite high-water envelope for this storm is shown in figure 17. It is evident that the maximum elevations are dependent upon the timing of the wind direction and magnitude and propagation of the open coast surge with the occurrence of maximum surge greatly separated in time for different parts of the region. As a further check on the model formulation, the effect of low-elevation *flooding was investigated. Figure 18 shows the high-water envelope gener- ated by rerunning the same storm but assuming that the lateral boundaries of the basin are held fixed so that the surface area does not increase with increasing water elevation. Most areas are not overly sensitive to this assumption except East Bay. In this region heights are 2 feet higher than in the case including flooding. This is the result of neglecting the large extent of low swamp area north of East Bay. 13 12 10 53.0 2t,, If I . 3 2 I I I 1 I I II i- =I I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 38 37 38 39 40 41 42 4344 5 Figure 14.--Instantaneous water heights for a hypothetical storm, 4 hr before landfall. Wind velocities are given for Apalachicola and Carrabelle. 14 ~ 13 10 xJ. 7A* -5mw MqmRC 1 2 34 6 7 8 9 10 11 12 13 14 15 16 17 15 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 40 41 42 43 44 4 Figure IS.--.Instantaneous water heights for a hypothetical storm at closest approach to Apalachicola. 13\ 7 I M~...II' Y/ I _ -2.O-- 1 2 3 4 5 6 7 8 5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 326 21 28 2030 31 3233334 35 36 37 38 39 40 41 42 434445 Figure 16.--Instantaneous water heights for a hypothetical storm 3 hr after landfall. 14 M'% 0 .d\MMMM NM// 13 MM V / /I 11 N&K�/ t R W MM/M'// 4t 9 - .~ 1 II il 1 23 4 56 78 9 10 111213 14 1516 1718 19 20 21 22 23 24 22627 28 2930 31 3233 343536 37 3839 404142 4344 45 Figure 17. --Composite high-water envelope for hypothetical storm. 13- v 7r' .. &~~~11 'a -W9 V M 4 08 I2 2 110 I 1 II I I~~~~~~-----!I 2 11-o7~~ ,,_,-1.-f~/34, 1 2 3 4 5 6 7 6 9 10 11 12 13 14 15 16 17 16 19 20 21 22 23 24 26 26 27 28 29 30 31 32 33 34 30 36 37 38 39 40 41 42 42 44 45 Figure 18.--Composite high-water envelope for hypothetical stotm assuming fixed lateral boundaries. 28 5.4 Response of Apalachicola Bay-to an Ensemble of Climato logical Storms While in sections 5.2 and 5.3 the height values at a given location for a particular storm are subject to the absolute error in estimafi6n 'bf the model coefficients as well as how close the model storm simulates the actual hurri- cane, analysis of the sensitivity of the model to systematic variations in storm parameters while maintaining the same model assumptions should be in~- dicative of the general response of the Bay. To this end a series of major storms were investigated, with results analyzed for various locations through- out the Bay. The results are summarized here for four geographic locations A, B, C, D as shown in figure 19. Point A indicates the variation of the open coast v~alue derived from the SPLASaf'run used as input for tl~e bay model. Saint- George Sound showed similar variation as point A with the height value at Carrabelle slightly greater than for the open coast with heights decreasing toward Cat Point. Points B and C show the response inside Apalachicola Bay. Point C is considered representative of the vicinity of Apalachicola. Heights generally increas~ed across the Bay and continued to increase into Saint Vincent Sound. Point D is representative of the East Bay region. Maxi- mum water levels in this region were mostly associated with southwest winds in the rear of storms, coinciding with high surge in Apalachicola Bay. Heights east of point D generally increased until they intersected topography, while in the region to the west of point D and north of Apalachicola, maximum heights generally decreased over the large areas of low terrain. Figures 20 and 21 show the variation of surge height with variations in central pressure and forward speed, respectively, for a storm with a maximum wind radius of 23 nautical miles traveling perpendicular to the coastline with the center of the storm passing 28 nautical miles to the west of Apala- chicola. Fov variation in central pressure all storms had a forward speed of 13 knots and for variation of forward speed all storms had a central pressure depression of 62 mb. The response of surge height in the Bay to increasing storm intensity is nearly linear with pressure, as is the open-coast surge, with the inside- outside height difference increasing slightly with storm intensity. A major feature of figure 20 is the response of East Bay. For low open coast surge wind effects over the East Bay become relatively more important, and as the surge increases above 7 feet large areas become subject to flooding, reducing the surge heights relative to other locations. For a fixed storm size, curve A in figure 21 shows the increase in open coast surge height as the speed of the storm increases. The remaining curves are indicative of two opposing influences in the interior to the Bay. As forward speed decreases, the open coast surge and thus the heights near the entrances decrease. However, with slower speeds, the wind duration and time for filling the basin and back bays are increased. The net effect is that the open coast surge height and storm duration tend to cancel in Apalachicola Bay, producing an almost flat response with forward speed. East Bay is more sensitive than Apalachicola Bay to the duration of high water. In general, )FRANKLIN COUNTY, FLORIDA. KOEP. INDIAN ~~~~~~~~CARRABEE ST. JOE -84' 30 APALACHICOLA p5~~~85 ,0 84' 4 5 " 8 4 30- 29- 30' -:-29 - '0 + 29-30 ' 5 0 10 15 ----- 60 ----- WATER DEPTH IN FEET~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 WAERETHNFE SCALE NAUTICAL MILES Figure 19.--Reference locations A, B, C, D for figures 20, 21, 22. 30 18 I 16- A 14- X 6 XX 2- 20 30 40 50 60 70 80 CENTRAL PRESSURE DEPRESSION (mb) Figure 20.--Surge elevations at four locations as a function of increasing hurricane central pressure with other parame- ters held fixed. 16 - CD xx X M X8X 6- 4 a X=x x 2- 20 30 40 - 0 60 70 80 CENTRAL PRESSURE DEPRESSION (mb) Figure 20.--Surge elevations at four locations as a function of increasing hurricane central pressure with other parame- ters held fixed. _ 4 - 2- 4 6 8 10 12 14 16 18 20 22 24 26 FORWARD SPEED (knots) Figure 21.--Surge elevations at four locations as a function of the forward speed of the storm. 31 as forward speed increases, the outside-inside height difference continually increases. Figure 22 summarizes the response of the same four locations to an increase of the distance from the storm center to the Bay. The same storm was used at all locations, having a 62-mb drop, a forward speed of 13 knots traveling 18 I I I I I I I I 16- x ~~~~~X 14- A X 12 - X LU ~ ~~~ B CD ~X x ~~~~~~~~~~~~x En X X 6X- 4 - X 2 - 0 I I I I I I I I -70 -60 -50 -40 -30 -20 -10 0 10 20 STORM TRACK LOCATION (NAUTICAL MILES EAST OF APALACHICOLA) Figure 22. --Surge height variation at four locations as a function of distance of closest approach to Apalachicola. normal to the coastline, and a radius of maximum winds of 26 nautical miles. The surge heights for storms passing to the west of the Bay exhibited the same general trends as the open coast surge gradient outside the Bay; wind speed and direction are qualitatively similar for these storms. When a storm passes over the Bay, the open coast surge outside the west end of the Bay is reduced and the winds over Apalachicola Bay have an offshore component before landfall, both factors reducing the surge height at Apalachicola and in Saint Vincent Sound. East Bay experiences maximum surge corresponding to maximum southwest winds. The bay model formulation specifies a unique surge height at each location for a given storm. Sensitivities at points A, B, C, and D to storm parame- ters of the type suggested in figures 20, 21, and 22 and for other points throughout Franklin County have been utilized as an aid in assessing tide height potential from the hurricane climatology of the region. The results of this work are in a separate report (Ho and Myers 1975). The basic approach is to sum over the combination of storm parameters, each with its own probability of occurence per year, that contribute to giving a certain surge elevation at a particular location. The results of this methodology are 32 summarized by figure 23, which depicts the estimated tidal elevations at the 0.01 per year probability level for Franklin County. 6. CONCLUSIONS AND RECOMMENDATIONS The primary objective to recommend expected tide height frequencies, es- pecially at the 0.01 per year probability level, is summarized by figure 23. The pzresent model can be considered the simplest two-dimensional formulation that is capable of resolving the major influences in the Bay. Possible direc- tions for further refinement are specification of meteorological input that accounts for transition over land and a more sophisticated treatment of the bay-ocean interface, particularly in situations in which the interaction with the astronomical tides must be- considered. The hydrodynamics of these en- trances'. with their associated high velocities, strains the assumptions viable in both the bay and on the adjacent shelf. However, as tools, the best improvement to bay models of this type is their continued consistent application and refinement in different locations ~and situations. This provides improv'ed insight into the physical phenomena, interpretation of the mathematical and parametric formulation, and experience in application necessary for providing improved estimates. FRANKLIN COUNTY, FLORIDA INDIAN ~~~~~~~~CARRABELLE PORT ST. JOE / S ~~~~~~~~~~~~~~~~840 30' - ~~ APALACHICOLA 1. SS BA Y~~�A -~ ~~~~~~9 0 29'' 3 0' 29E - 5 0 5 1 0 5'r * - --- 6 0 - - - WAE-ET NFE SCAL N UICA MIE Figure 23.-.-Estim~~~~~~~ate ielvl (t S)a h 0.1 prya rbblt ee.Vle'ers compo~~~s i ae lvtosdrvdfo nesml of hoheia strm.~ 34, APPENDIX A: STABILITY ANALYSIS OF IMPLICIT BOTTOM FRICTION Express the momentum equation in the following form: T+l T AX T+-T+ Qj.~r T j T r [ njl/2 nj-1/2] +fr QT = (37) where Cr is the Courant'number C A aT v gH (38) r AX and f is the friction term fr ATavg. (39) The continuity equation is T+l/2 T-l/2 AT T nj+l/2 - nj+l/2 +'X [Q+l Q ] = (40) Assume a truncated Fourier solution nQ }= {Q} exp (ijkAX + iTaAT), i -- (41) Upon substitution of (41) into (37) and (40), Q* [(1 + fr) eiaT -_ 1] + AX Cr2n*e(iuAT)/2 [e(ikAX)/2 AX)/2 0 (42) and * iFAT 1] + Q* AT e(ioAT)/2 [e(ikAX)/2 -(ikAX)/2] 0. (43) iaAT Setting X = e and combining gives: ( ) -1 )kA (44) 1) [(1 + fr) X - 1] + 4Cr2 sin2 = (44) with roots B + TBz- (1 + fr), 1,2 f (45) 35 where R = I + r 2 C 2 Sinrn2 kAX (46) f The-requiremrent j)XI < 1 is satisfied by 1 *+ T BIo Cr T /g (I + . (471 - 36 APPENDIX B: LIST OF SYMBOLS Symbol Definitions - A Cross sectional area of entrance b Ratio of pass width to grid length Cc Entrance flow contraction coefficient Cd Drag coefficient CH Chezy bottom friction coefficient H Ck Entrance momentum loss coefficient CO Flooding coefficient C Barrier coefficient s d Land elevation/depth relative to MLW Db Depth of water over a barrier E Ensemble averaging operator f Coriolis parameter F Forward speed of hurricane g Acceleration of gravity H Local water depth I X grid point location J Y grid point location k Wave number L Hurricane landfall point MLW Mean low water MSL Mean sea level p Pressure P Atmospheric Pressure a P Central pressure in hurricane O~p Total volume transport through a narrow entrance %n Qx or Qy Qx X component of horizontal transport per unit width 'y Y component of horizontal transport per unit width r radial distance from center of storm R Radius to maximum winds in hurricane T Time 37 Symbol Definitions T2/3 Time open coast surge remains above 2/3 its maximum value u X component of? velocity u' Component of turbulent velocity fluctuation U Vertically integrated velocity, X component U Vertically integrated velocity near axis of a narrow channel p v y component of velocity V Vertically integrated velocity y component w Vertical component of velocity W Composite wind velocity Wa Wind speed , Wmax Maximum wind speed for stationary storm Wx X component of wind velocity Wy Y component of wind veloci.6 zb Barrier height ai Vertical dependence function of horizontal velocity (9) aij Velocity distribution function (13) AX Grid length AT Time step Water elevation relative to datum n* Equivalent height of atmospheric pressure nmax Maximum open coast surge at a given location e Direction of entry of hurricane relative to coastline 7r 3.1416 Pa Density of air Po Density of water aE Frequency-analytical solution OR Frequency-Richardson lattice Tij Stress component TS Surface stress TB Bottom stress tB* Bottom stress with TSo-. Inflow angle. Discretized vector variable composed of x and y volume transport components and water surface displacement 38 APPENDIX C: DOCUMENTATION OF COMPUTER PROGRAM This section provides a listing of the model program and sample output which was run on the CDC 6600 at the NOAA computer facility at-Suitland, Md. Compilation time is 8 seconds, and 24 hours of simulation required 83 seconds of CPU time with a CM requirement of 62K octal. A list of variable definitions is given in Section C.1. All input except bathymetry is internal to the program. Storm input consists of forward speed, FRDS; radius to maximum winds, RM; central pressure deficit, PD; maxi- mum stationary storm wind speed, VR; landfall location, LNDFL; path- orienta- tion, ALPHA; maximum open coast surge amplitude, A; and surge duration parameter, T23. The program listing is provided for completeness; it has not been opti- mized nor specifically programed for operational use or modification. Any changes such as application to other bays should be made with care. C.1 List of Program Variables "IV" specifies intermediate variables. Dimensions are given in comments in the listing. Variables Definitions Variables Definitions A Amplitude of open coast CH2 Chezy coefficient--tidal surge flats AH IV CH3 Chezy coefficient--land ALPHA Angle--Storm path and CH4 IV J-Axis CK Momentum loss coefficient AR IV for narrow passes ARG IV CO Flooding constant ARGMAX IV CPHI IV AWPASS Depth of West Pass CS Barrier constant AXPASS Depth of Indian Pass CTHETA IV CALPHA IV C2 IV CC Contraction coefficient D Land elevation--MLW for narrow passes DT Time step CD Drag coefficient DTD IV CHEZY IV ~~~~CHEZY IV ~DWPASS Mean Depth--West Pass CH1 Chezy coefficient--deep DX Grid length water 39 Variables Definitions Variables Definitions DXPASS Mean Depth--Indian Pass RAIN Rainfall ETA Water elevation RM Radius maximum wind ETAMAX Maximum surge SALPHA IV F IV SPHI IV FLUX IV SSSG IV FLUXX IV STHETA IV FLUXY IV T Time FORCE IV TEXIT IV FR IV TIME IV FRDS Storm speed TMLDF Time before landfall FX IV TMN MSL-MLW difference G Acceleration of gravity TSTA IV GAGE Storage for gages TSTB IV GPAD IV TSTC IV H Water depths TSTD IV HMAX Maximum water depth TSTOP Termination time I, J, K Counters T23 Time during which A IMAX Maximum grid point is greater than 0.66A IMAX Maximum grid point V Wind speed IM1 IV ~INDEX Counter VR Maximum wind speed INDEX Counter VY IV JM1 IV VX IV JMAX Maximum grid point VX IV WDIS IV LGAGE IV LNDFL Landfall location W Height barrier normal ~~LNDFL Landfall locationto coast NTLDF IV WX IV OMEGA IV WPASS Velocity through West Pass PD Central pressure X I component of distance depression from storm center PG IV WY IV PGX IV XPASS Velocity through Indian PGY IV Pass PHI Inflow angle Y J component of distance ~~QX X-transport ~~~from storm center QX X-transport Z Height of barrier parallel QY Y-transport to coast ~~R Distance from s~torm coasenter R Distance from storm center 40 C.2 Program Listing PROGRAM APLCH CDC 6600 FTN V3.0-324 OPT=2 01110175 12.03.03. PAGE PROGRAM APLCH( INPUT.OUTPUT) DIMENSION OX(-46,15),OY(46 115) ETA(46,15).H(46,15),D(46,15). IF(46,15) 2ZC46,15),WI(46.15),ETAMAXC46,15) 2lWY(4'6,*15),wIX(46. 15) 5 3.PGX(46.15),PGY(46,15),CHEZY(46,15) 7. GAGE(900.*7) CCC MODEL COMPUTES IN ENGLISH UNITS CCCC LOAD DATA DATA INAX.JMAXC/46.15/ 10 INl=IMA)(-1 JMl=JMAX-1 DATA G,CO.CS.CHI.CH2.CH3I32.2,0.70.0.70,100.,80.,ZS.I SSSG=SORT(G) TMN=0.9 15 DX=6076. MMAX=40. DTD=G2MMAX OTD=SORT(DTO) DT=DXI (1 .414214*DTD) ZO CCCBATHYMETRY DO 2 I1=IMAX READ Z2ZZ.(DCIJ).J:1.JMAX) 2 CONTINUE 2222 FORMAT(15F3.0) 25 CCCC PASS PARAMETERS"i CC:0O*9 CK:0O*35 CH4=:G/CHi**Z ONPASS=38. 30 DXPASS=15. K--O 105 CONTINUE K--K+I cc STORM PARAMETERS 35 CCC FORKARO SPEED STMPH, RM NAUTICAL MILES YR STNPH CCC PRESSURE DROP IN MB CCC CCC LNOFL IN NAUTICAL MILES ALONG X AXIS CCC THLDF IS MRS BEFORE LANDFALL CCC SURGE PAR--- IS A*ZO GT HMAX51 T23 IS FUNCTION OF RH AND FRDS 40 CCC ANGLE MEASURED LEFT FROM NORMAL FRDS=15. RII:=22 .15 TZ3=3.Z LNDFL=-21 45 PD=52. A=11.7 VR38S.9 TNLDFz16. RAIIIZO. s0 ALPHA=O. CCC PRINT PARAMETERS PRINT 4,(C(I.,J),J:1.JMAX),I=1,IMAX) 4 FORMAT(1HI,1OX.*TCPOGRAPHY*I(I0X.15FS.0)) PRINT 5.DXDT,CH1.CI42.CH3,CO.CS.Ck. 55 IFRDS.VR.RM.LNDFLP0,TZ3,AALPI4A 41 PROGRAM APLCH CDC 6600 FTN V3.O-324 OPT=Z 01/10/75 1Z.03.03. PAGE Z 5 FORMAT(SX.iPARAMETERS---UNITS ARE IN FOOT-SECONDSm/I0X,*SFACE IGRID TIME STEP FRICTION-DEEP.FLATS.IIOODS FLOODING CONSTANTS ACCI.CS ENTRANCE COEF CktI 2lOX,3C6X.F?.2)./I.ZOX.* STORN'PARAMETERSe.. 60 3ZX.* FSPEED(NPH) MXVELOCITY(NPH) RADIUS MH IIND(NM) LANDFALLCNM) 4PRESS(MB) T23(HRS) AMP(FT) ALPHA(RAD)*/ 55X.3(F6.1.9X).17.9X.4(F?.3,6X)) CCCCCSCALE VARIABLES RN=RN*6076. 65 FRDS:1 .466666?*FRDS VR=1 .4666667*VR CALPHA=COSCALPI4A) SALPHA=SIN(ALPHA) NTLOF=FRDSaCALPHAt3600. 'TNLDFIDX 70 TSTOP=1 .5*3600. 'TNIOF TEXIT=3600. *TNLDF T23=O.5*TZ3l3600. ONEGA=0.66IT23 P0:0 .033455 'PD 75 CCCCINITIALIZE ARRAYS T=O. INDC-Xz0 ARGMAX--0. LGAGE=0 s0 WPASS=0. XPASS=0. DO I IzI.IWA DO I J=I.JMAX OXCI .J):OYCI .J)=0. 85 PGY(I.J)=O. PGXCI.J)=0. WX(IJ):IIY(I,J)=O. ETAMAX(I .J)=-0.00001 ETACI .J)=TMN 90 HCI.J)ZTPIN-D(I.J) IF(D(I.J).GT.TNN) ETA(I.J)=DCI.J)-O.00001 CHEZYC I J)=CH1/SSSG IF(D(I.J).GT.-Z.5) CHEZY(IJ)=CHZ/SSSG IF(DCI.J).GT.O.'5) CHEZY(I.,J)=CH31SSSG 95 CCC SET BARRIERS IF(J.EO.JMAX) ZCI.J)=D(IJ) IF(I.EQ.2) MCIJ)=D(I.J) 100 IF(I.EQ.INAX) WC.J):100. 1 CONTINUE DO 6 I=ZINAX DO 6 J=2.JNA IFC(OI.J).GT.23 5.OR.DdI.J).LT.ZZ.5) GO TO 6 105 IF(DCI-lJ).LT.ZZ.5) II(1.J=)(DC-1.J) IF( COI J-1) LT22.5 ) Z(IJ)*DCI.J-1) IF(D(I-t.J).LT.2Z.5.OR. D(IJ-1).LT.2Z.5) ETA(I.J)=0.93 6 CONTINUE ZC17,A) = 16. 110 Z(14.9)=16. 42 PROGRAM APLCH CDC 6600 FTN V3.0-324 OPT=Z 01110175 12.03.03. PAGE 3 Z(35.3) : 18. Z(34.3) : 18. 115 Z(33.3) : 25. Z(32.3) : 25. 2(31.3) =8. 2(27.3)27. 120 Z(26.3):8. 2(25.3) : 12. 2(24.3) =25. Z(23.3) : 25. 2(22.3) � 15. 1252(1)11 2(18.3) : 18. 2(17.3) : 18. 130 Z(16.3):18. Z(15.3) :20. 2(14.3) :24. Z(13.3) :24. 2(12.3) :16. 135 2(11.3) :12. 2(10.3):?. ZC 9.3) :6. Z( 8.3) S.3 Z(7.3):1S. 140 2~~~(6,4)=1S. Z( 5.8) :W1. Z3. 10):13. Z(2.12):12. 145 11(36.3) : 15. M30. 3) :7. 11(28.3):?. N(7.3):15. 11(6. 4):15. 150 11(6.5)=7. 11(4.9)215. W(11(2 2 12. CCC LOOP FDA INTEGRATION 100 CONTINUE T:T*DT 160 INDEX:INDEX.1 CCCC NEW ETA DO 20 1=2.I111 DO 20 J:3.JN1 IF(0(I.J).GT.Z2.5) GO TO 20 165 FLUIXX=OX(I.1.J)-OX(I.J) 43 PROGRAM APLCH CDC 6600 FTN V3.0-324 OPT=Z 01/10/75 12.03.03. PAGE 4 FLUXY=QY(IJ+I)-GY(IJ) FLUX=FLUXXIDX+FLUXY/DX-RA IN ETA(I.J)=ETA(IJ)-DT*FLUX 20 CONTINUE 170 AR=OMEGA. (T-TEXIT) AR=A*(1 .0-TANH(AR)**2) DO 22 I1=1IMAX GRAD=1 .0 IF(I.GT.30) GRAD=1.0-0.06*(I-30)115 175 IF(I.LT.20) GRAD=0.90*0.005tl ARG=TMN+GRAD-AR ETACI.I) =ARG ETA(I.Z)=ARG DO 22 J=Z.JMAX( 180 IF( D(I.J).GT.800.) ETA(I.J)=ARG 22 CONTINUE C OUTPUT tt*tattt** IF(MOD(INDEX.100).ECO.) GO TO 900 901 CONTINUE 185 IF(MOD(INDEX.4).NE.0) GO TO 951 TIME=T/3600. LGAGE=LGAGE* I GAGE(LGAGE,I1)=TIME GAGE (LGAGE .2) :ETA (29. 4) 190 GAGE(LGAGE,3)=ETAC31,6) GAGE(LGAGE,4)=ETA(I&.6) GAGE(LGAGE.S)=ETA(13,3) GAGE(LGAGE,6)=ETA( 8.4) GAGE(LGAGE,7)=ETAC 6.7) 195 951 CONTINUE CCC NEWl DEPTHS DO 94 I:2.IMI DO 94 J=Z.JMI IF( D(I.J).GT.22.5) GO TO 94 Z00 H(I.J)=ETA(I.J)-D(IJ) IF(H(I.J).LT.0.) GO TO 94 IF(ETAiI.J).GT.ETAMAX(I.J)) ETAMIAXCI.J)=ETA(I .J) 94 CONTINUE CCCCC WIND FIELD COMPUTATION 205 IF(MOD(INDEX.4).NE.3) GO TO 49 DO 41 J=3,JPII DO 41 ]=Z.1MI IF(H(I.J ).LT.0.99) GO TO 42 Y=(J+N LDF) 'DX-CALPHA*FROStT 210 Xz(I-LNDFL)vDX-SALPHA*FRDS*(T-TEXIT) IF(R.LT.10 ) R=10. R=SORT(R) Zis CTHETA=X/R STHETA=Y/R cc INFLOW ANGLE Of ZZOEGREES CCCC AT LARGE R PHI IS 17DEGREES PHI=RIRN 220 IF(PHI.GT.4.4) GO TO 44 44 PROGRAM APLCH CDC 6600 FTN V3.O-324 OPT=Z 01110175 12.03.03. PAGE 5 PHI=0.Z8564*PHI i,3*EXP(-PHI) 44 IF(PHI.GT.4.4) PHI=0.Z9670597 CPH I:COSC PH 1) SPHI=SIN(PHI) 225 PG=PD*RMtEXP(-RMIR)/Rst2 PG: PGDX PGX(I ,J),PG*XIR PGV( I .J)PG*YIR NDIS=R*RNIWdDIS 230 VX=-WDOIS*(2.0*VR*(STHETA*CPHI*CTHETAtSPHI)-FRDStSALPHA) VY=WDIS*(2.0*VR*(CTHETA#CPHI-STHETAtSPHI)*FRDSoCALPHA) v=VX* .2+Vy*tZ V=SORT(V) CD:1 .62 CD:CDs 0.000001 MX(IJ)=CDRV*VX MYC I.J)=CD*V*VY 240 GO TO 43 42 CONTINUE NXCI.J)=O. 43 CONTINUE 245 41 CONTINUE 49 CONTINUE CCC FRICTION FACTOR FOR OY DO 61 J=3,Jn1 DO 61 I=ZIMI 250 IFCD(I.J).GT.2Z.5) GO TO 61 FCI. J ):O.2 -5FC I.J) )Nmz* 61 CONTINUE CC OX DETERMINATION 255 D O 50 I=Z.INI 00 50 J=3.JMI CCC FLOODING ROUTINE FOR OX IF(W(IJ).GT. 0.) GO TO 55 CCCC BOTH AREAS DRY 260 IFCH(I.J).LT.0..AD.H(I:I J).LT.0.)DX(I.J)=0. IFCH(I.J).LT.0..AND.HCI-1.J)AT.0.) GO TO 59 CCCC NORMAL CASE TST9=ETA(I-1,J)-D(I.J) TSTC=ETA( I J)-D(I-1I.J) 265 IF(H(I.J).GT.O..AND.H(I-1,J).GT'.D..AND.TSTO.GT.0..AND.TsTC.GT.0.) 1 GO TO 57 CCC ADVANCING OR RECEEDING TIDE IF(H(I,J).LT.0.) GO TO 501 IFCH(I-IJ).LT.O.) GO TO 503 270 OX(I,J)=CO*H(I-1.J~tSdRT(G*H(1-1.j)> IF(TSTC.GT.0.) OX(I.J)z-CO*H(IJ)*SQRTCGOH(I.J)) GO TO 59 501 CONTINUE IF(TSTB.LT.0.) OX(IJ)90. 275 IF(TSTS.LT.0.) GO TO 59 45 PROGRAM APLCH CDC 6600 FTN V3.0-324 OPT=Z 01/10175 12.03.03. PAGE 6 IF(TSTB.GT.H(I-IJ)) TSTB=H(I-1,J) OX(I .J)=CO*TSTB-SQRT(GtTSTB) GO TO 59 503 CONTINUE 280 IF(TSTC.LT.0.) OX(I.J)=O. IF(TSTC.LT.D.) GO TO 59 IF(TSTC.GT.H(IJ)) TSTC=H(I.J) OX( I,*J)=-COsTSTClS0RT(GwTSTC) GO TO 59 285 55 CONTINUE CCC BARRIER TEST TSTC=ETA(I.J)-W(IJ) TST8=ETA(I-IJ)-Id(I J) IF(TSTB.LT.0..ANO.TSTC.LT. 0.)OX(IJ):0. 290 IF(TSTB.LT.0. .ANO.TSTC.LT. 0.) GO TO 59 IF(TSTB.GT.0. .AND.TSTC.GT.0.) GO TO 555 IF(TSTB.GT.O.) QX(I.J)=COTST8*SORT(G*TSTB) IF(TSTC.GT.O.) OX(I.J)=-CO*TSTC*SCRT(G*TSTC) GO TO 59 295 555 CONTINUE TSTA=ETA(I.J)-ETA(I-1,J) TSTD=ARS(TSTA) TSTB=(TSTB+TSTC) /2. OX( I,J)=CS*TSTB*SORT(G*TSTD) 300 IF(TSTA.GT.O.) OX(I.J)=-OX(I."J) GO To 59 57 CONTINUE CCCC NORMAL CASE IF(H(I.J).LT.O.99) WX(I.J)=O. 305 IF(H(I-1.J).LT.O.99) UXCIJ0=O. AH=AHIZ. CZ=CHEZY(I.J) *CHEZY(CI-l. J) FORCE=ETA(I .J)-ETA( I-I .J)+PGX(il.J) 310 FORCE=-GsAH*FORCElDX+WX(I,J) FORCE=DT*FORCE FR=(0.25*FR)**2 FX=CX(I.J)*,2 315 FX=S0RT(FR+FX)/(C2aAHx*-Z) FX:1 .+DT'FX OX(IJ)=OX(I .J)+FORCE OX(I.J)=GX(I.J)IFX 59 CONTINUE 320 50 CONTINUE CCC OY DETERMINATION 00 60 J=3.JMAX DO 60 1=2.1M11 CCCC FLOODING ROUTINE OY 325 IF(Z(IJ).GT.O.) GO TO 65 CCC BOTH AREAS DRY IF(H(I,J).LT.0. .AND.H(I,J-1).LT.O.) DY(I.J)=O. IF(H(IJ).LT.O..AND.H(IJ-1).LT.O.) GO TO 69 TSTB=ETA(IJ-I)-D(IJ) 330 TSTC=ETA(IJ)-D(I.J-1) 46 PROGRAII APLCH CDC 6600 FYI V3.0-324 OPTM'2 01110175 12.03.03. PAGE 7 CCC NORNAL CASE IF(HCI.J).GT.O..AND.HII.J-1).GT.D..A�D.TSTU.GT.O..AlD.TSTC.GY.O.) 1 GO TO 67 EEC ADVANCING OR RECEEDIUG TIDE 335 IFC(Mi.).L.T.O.) GO TO 601 IF(H(I.J-1).LT.0.) GO TO 603 GYCI J)=CO*HCI.J-l)sSIIAT(G*H(I.J-M) GO TO 69 340 601 CON7 NINe IMCSTI.LT.S.) OT(I.J):0. IFCTSTO.I.T.O.) GO TO 69 IF(STU.GT H(J-1)) TSTI:H(I.J-1) GY( N J)-COrnTST5'SORT(G'TSTI) 345 GO T669 603 CONTINUE IF(TSTC.LT.0 ) OYCI J):g* IF(TSTC.LT:0:) GO Tb 69 IF(TSTC.GT.H(I J)) TSTCzHCI J) 350 GY(I J):-COm7StCsSORT(GsTST) GO Tb 69 65 CONTINUE CCC PRANEN TEST TSTI:ETA(N.J-I)-Z( IJ) 355 TSTCcETA(IJ)-ZCN.J) IR(TSTI.LT.0- AhO.TSTC LTA. 0 OY(I.J)xC. MFTSTU.LT.0- AND.TSYETC:.O.) GO TO 49 IFCSTI.G7.0.-AND.TSTC.GT.0.) GO TO 455 IF(TSTC.GY.0.) 0YC IJ)m-COsTSTC*S0RT(GoTSTC) 360 NFCTSTB.GT.0.) QYCI .J)*COtTSltIWT(6,TSTlP GO TO 69 655 CONITNUE TSTAmETA( I J)-ETACI NJ-i) TST0D:AB(T�TA) 365 TSTI:(TST�#TS7CWZ. OY( N J1zCS*TSTU'S0RTCG'tITD) IF(TiTA.GT.O.') OY0i.J)-OY(I.J GO TO 69 67 CONTINUE 370 CCCC NORRAL CASE IF(H(I.J-1).LT.O.99) Ny(I.J)=0. IF(H(N.)LI.9)M(.)S WAN-MIJ 375 C22CHEY( Jj)'CHEZW( I.J-J) FORCE:TACI.J1-ETA(I.J-E..PGYcIXJ F RE-GmAM.*FORCElDX#MY(N J) FX:OY(.Jtaz FX:SRTFXF(IN.JW()CCZ'AH..Z) 380 FX:1..DOFX OY(NJ)mQV(N .J)oDT'FORCE Qycl J)zOY(I.J)IFX 69 colf i nM 60 COINYI NM 345 CCC SOUIOARY FLUX DETERUINATION 47 PROGRAI9 APLCH 'CDC 6600 FTN V3.0-324 OPT=Z 01110175 12.03.03. PAGE 8 AWIPASS=DMPASS#0.5-(ETA(5, 7)+ETA(6,7)) FORCE=ETA(6. 7)-ETA(5. 7)+PGX(6., 7) FORCE=-G*FORCEIDX*MX(6 * 7) IAMPASS F ORCE:0 * F OR CE 390 FX=ABS(IJPASS) FX=I.O*DTPFX*(O.S*(1 .+CK)IOX#CH4/AMPASS) WPASS=IIPASS#FORCE IWPASS=HPASSI FX OX(6, ?)=CC*0.30-AWIPASS*MPASS 395 AXPASS=DXPASS+0.5*(ETA(1.13),ETA(Z.13)) FORCE=ETA(2. 13)-ETAC 1 .13)*PGXCZ. 13) FORCE=-G*FORCEIDX,&IX(2, 13)IAXPASS FORCE=OTa FORCE FX=ABS(XPASS) 400 FX=I.O+DT*FX*(O.S*(I.*CK)IDX#CH41AXPASS) XPASS=XPASS*FORCE XPASS=XPASSIFX OX(2. 13)=CC-.0.5tAXPASS*XPASS IF(T.LT.TSTOP) GO TO 100 405 GO TO 101 C OUTPUT t..a* 900 CONTINUE TINE=T/3600. 00 920 IZZ,1N1 410 D O 920 JclJNAX F(I.J):ETA(I.J) IF(H(I.J).LT.0.15) F(I.J)=88.8 920 CONTINUE PRINT 1040.TIME.C(F(IJ).Jx1,JNAX),I:Z,1N1) 415 1040 FORHAT1 IHI1.1OXTINE IN HRS.*.F10.Z.1,(2X.FS.1,1OX.14F5.I)) GO TO 901 101 CONTINUE DO 910 I:Z,IM1 GRAD:1 .0 420 IF(I.GT.30) GRAD=1.0-0.06*(1-30)115 IF(I.LT.20) GRAD=0.9040.005oI DO 910 J=2,JMAX IF(D(I.J).GT.99.) STA MAXC(I.J)=TMN.GRAD&A 910 CONTINUE 425 PRINT 03(OIJ.JZJA)1.I1 1043 FORMAT(1H1.t TOPOGRAPHY VALUES ABOVE MLW 1' (I/12X.14F5.1)) PRINT 1045,((ETANAX(I IJ).J:Z.JMAX),I=2.IN1) 1045 FORMATIiHI,* MAXIMUMUM HATER LEVEL PRODUCED BY THIS STORM 430 1*,(//ZX,14FS.I)) 00 103 I=ZIM1 00 103 J=Z.JNAX F(I.J)=ETANAX(I.J)-D(l.J) IF(F(I J).LT.O.) F(I,J>=0.0 435 IFCD(I:J).LT.0.) F(1.J):SE.3 103 CONTINUE PRINT 1043,C(F(I.J).J=2.JNAX),l=2,IM1) 1048 FORMAT(1H1.t FLOODING DEPTH 888.8 INDICATES BELON MI.No 1 112IX 14FS.1)) 440 PRINT 1049,(GAGE(1,1),GAGE(I.Z).GAGE(I.3),GAGE(1,4).GAGE(1,5), 48 PROGRAM APLCH COC 6600 flU V3.0-3Z4 OPT=2 01110/75 12.03.03. PAGE 9 lGAGE0, 04,AGE01.7). W-.LGAGE) 1049 FORMAT(IlH1. TIME DOG ID CARSELE CAT PT APLCLA L IANCHR N PASS .F.C7CZX.PI.2))) STOP 445 END 49 TOPOGRAPHY 999. 999. 999. 999. 999. 999. 999. 999. 999. 999. 999. 999. 999. 10. 10. 999. 999. 999. 999. 999. 999. 999. 999. 999. 999. 999. 8. -4. 10. 10. 999. 999. 999. 999. 999. 999. 999. 999. 999. 13. 1Z. 10..-Z. 10. 10. 999. 999. 999. 999. 999. 999. 999. 999. 15. 13. 10. O. -Z. 10. 10. 999. 999. 999. 999. 999. 999. 999. 6. 7. Z. 4. -Z. -Z. 15. 10. 999. 999. 999. 9. Z. -3. -18. 3. Z. 3. O. -5. 15. 10. 4. 999. 999. 9. 5. -10. -10. -10. -6. Z. Z. -5. -6. 15. 10. 4. 999. 999. 2. -5. -10. -4. -4. -5. -5. -5. -5. O. 15. 8. 4. 999. 999. 2. -8. -10. -8. -8. -6. -5. -5. -3. 15. 4. 4. 4. 999. 999. 2. -11. -10. -9. -7. -6. -4. -3. 15. 15. 4. 4. 4. 999. 999. 2. -12. -10. -9. -7. -7. -4. 15. 15. 10. 6. 4. 4. 999. 999. 8. -10. -10. -8. -7. -6. -Z. 15. 8. Z. Z. 4. 4. 999. 999. 15. -8. -9. -8. -7. -3. 15. 12. 1. Z. 4. 4. 4. 999. 999. 15. -8. -8. -7. -7. -5. O. O. 1. 4. 4. 4. 4. 99. 999. 1Z. -8.-9. -8. -7. -6. -3. 1. Z. 4. 4. 4. 4. 999. 999. 10. -5. -10. -7. -5. -5. -4. 1. Z. Z. 4. 4. 4. 999. -7. -5. -5. -3. O. 1. Z. 4. 10. 13. 999. 10. -9. ,Z ~ -3. 999. 11 -1 -5. -Z. O. Z. 5 10. 1) 999. 5.-4 ..... 999. 999. -7. -9. -8. -8. ZO. 10. -3. -3. 3. 7. 9. 9. 13. 999. 999. -7. -9. -10. -10. ZO. 15. 4. -Z. -I. Z. 7. 12. 15. 999. 999. O. -10. -8. -9. ZO. 19. 8. -Z. 4. 4. 8. 12. 15. 999. 999. -1. -7. -8. -&. ZO. 19. 13. O. 3. 7. 9. 12. 15. 999. 999. -S. -11. -9. -9. ZO. 10. 10. Z. ]. 6. 9. 12. 17. 999. 999. -5. -13. -10. -?. ZO. 10. 7. 4. 3. 10. 10. 12. 17. 999. 999. -Z. -13. -13. -9. ZO. 15. 14. 14. 10. 10. 10. 15. 18 999. 999. ). -17. -14. -10. ZO. 14. 10. ?. Z). 23. Z). 23. Z) 999. 999. 5. -20. -15. -7. l&. 15. 10. 7. 23. Z). 23. 23. 23 -ZO. -20. -9. -20. -17. -10. 18. 18. 10. ?. 23. 23. Z]. 23. 2) -ZO. -ZO. -10. -17. -20. -12. 20. 19. 10. 7. Z). Z). 23. 23. 2] 999. 999. ?. -17. -15. -10. 10. 15. 6. 6. 23. 23. 23. 23. 2] 999. 999. -1. -20. O. O. 1. 1. 6. 7. 23. Z). 23. 23. 23. 999. 999. -1. -ZO. -11. -10.- Z$. 2. 3. 14. 23. 23. 23. 23. 23. 999. 999. 8. -18. -13. -3. 18. 15. ). 14. 23. 23. Z). Z). 23. 999. 999. 10. -18. -18. -3. 21. 21. 4. 14. 23. 23. 23. 23. Z). 999. 999. 10. -10. -18. -4. 30. 21. 4. 14. 23. Z). 23. 23. 23. -20. -20. -ZO. -ZO. -18. -4. 30. 23. 23. 23. 23. 23. 23. 23. 23. -20. -20. -20. -17. -13. -4. 30. 23. 23. 23. 23. 23. 23. 23. 23. -20. -20. -18. -15. -15. -4. 30. 23. 23. 23. 23. 23. 23. 23. 23. -ZO. -20. -18. -15. -13. -10. 30. 23. 23. 23. 23. 23. 23. 23. 23. -20. -20. -20. -11. -3. -5. 30. 23. 23. 23. 23. 23. 23. 23. 23. -ZO. -20. -20. -13. -2. 18. 30. 23. 23. 23. 23. 23. 23. 23. 23. -ZO. -20. -ZO. -14. -10. 18. 30. 23. 23. 23. 23. 23. 23. 23. 23. -20. -20. -ZO. -15. -10. 18. 30. 23. 23. 23. 23. 23. 23. 23. 23. -ZO. -20. -10. -9. -2. 18. 30. 23. 23. 23. 23. 23. 23. 23. 23. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75. 75r 75. 75. 75. 75. 75. PARAfiETERS---UNITS ARE IN FOOT-SECONDS SPACE GRID TlfiE STEP FRICTION-DEEPFLATSgOODS FLOODING CONSTANTS COCS ENTRANCE COEF �K 6076.00 119.71 100.00 80.00 Z$.00 .70 .70 .~5 STORfi PARAfiETERS FSPEEO(fiPH) fiXVELOCITY(fiPH) RADIUS fi WINO(Nfi) LANDFALL(Nfi) PRESS(fiB) TZ3(HRS) AHP(FT) ALPHA(RAD) 15.0 88.9 22.9 -21 $2.000 ).ZOO 11.700 0.000 so TIME IN HRS. 3.33 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.1 88.8 88.8 88.8 88.8 88.8 88.a 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 I.0 88.8 88.8 88.8 1.2 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.1 1.0 1.1 88.8 88.8 1.1 1.0 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.i 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 1.0 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .8 .8 .8 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .8 .8 .8 .8 .8 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .8 .8 .8 .7 .7 .7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.1 1.0 88.8 .6 .6 .6 .6 88.8 88.8 88.8 88.8 88.8 88.8 1.1I 1.0 1.1 1.1 88.8 88.8 .5 .5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.0 1.0 '1.0 88.8 88.8 88.8 .4 .4 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 88.8 88.8 88.8 .2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.0 1.0 1.0 88.8 88.8 88.8 .3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.'8 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 88.8. 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 TIME IN HRS. 6.65 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.,8 88.8 88.8 88.8 1.5 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 818.8 88.8 88.8 88.8 88.8 88.8 1.4 1.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 88.8 88.8 88.8 1.4 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 88.8 88.8 1.3 1.2 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.1 1.2 12Z 1.2 1.1 1.1 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 1.0 1.0 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 1.0 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .8 .8 .8 .8 .8 .8 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .8 .8 .8 .8 .8 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .8 .7 .7 .7 .7 .7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .8 .7 .7 .6 .5 .5 .5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.2 1.1 88.8 .3 .4 .4 .4 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 88.8 88.8 .2 .2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 I12 1.2 1.2 88.8 88.8 88.8 -.0 .0 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.1 1.1 1.1 88.8 88.8 88.8 -.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.1 1.1 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.1 1.1 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.1 1.1 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88'.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.'8188.8 .9 .9 .9 .9 .9 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .8 88.8 88.8 88.8 88.8 88'.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 52 * TIME IN HRS. 9.98 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.2 1.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.0 1.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.7 1.6 88.8,88.8 88.8 2.0 1.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.7 1.6 1.6 1.7 88.8 88.8 1.7 1.7 88.8 88.8 88.8 88.8 88.8 88.8 1.6 1.5 1.5 1.5 1.5 1.6 1.6 1.5 1.4 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.4 1.4 1.3 1.3 1.3 1.3 1.2 88.8 88.8 88'.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.2 1.1 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.1 1.1 1.0 1.0 1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .9 .9 .9 .9 .9 .7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .8 .8 .8 .8 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .7 .7 .7 .7 .8 .8 .8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8. .6 .6 .6 .6 .7 .8 88.8 88.8 88.8 88.& 88.8 88.8 88.8 88.8 88.8 .5 .5 .5 .5 .4 .5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .6 .5 .5 .3 .0 .2 88.8 88.8 88.8 88.8 38.8 88.8 88.8 88.8 88.8 1.4 1.7 1.5 88.8 -.1 -.2 .0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.6 1.6 1.6 1.7 88.8 88.8 -.7 -.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.5 1.5 1.6 1.6 88.8 88.8 88.8 -.9 -.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.5 1.5 1.6 88.8 88.8 88.8 -1.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.5 1.5 1.5 1.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.4 1.5 1.5 1.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.4 1.4, 1.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.4 1.4 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.3 1.4 88.8 88.8 88.8 88.8 88.8 83.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.3 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.3 1.3 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.2 1.2 88.8 88.8 88.8 88.8 88.8 83.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.1 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 98.8- 88.8 88.8 1.2 1.3 1.2 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.3 1.4 1.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.3 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.3 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.3 1.3 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.3 1.3 1.3 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.3 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.3 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.2 1.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.1 1.1 88.8 88.8 88,8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.3 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.3 88.8 88.8 88.8 88.8 888 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.2 1.2 1.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.1 1.1 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 53 TIME IN HRS. 13.30 8T8S.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 89.8 88.8 88.8 4t.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 8.8.8 88.8 4.0 3.8 88.8 88.8 88-.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.5 3.1 88.8 88.8 88.,8 88.8 88.8 88.8 4.0 4.0 4.2 4.0 2.6 88.8 3.5 3.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 ~3.3 3.5 3.'7 3.8 4.1 2.9 3.0 3.0 88.8 88.8 88.'8 88.8 88.8 2.5 2.5 2.7 2.8 3.0 3.1 3.2 3.0 2.8 2.4 88.8 88.8 88.8 88.8 88.8 88.8 2.0 2.2 2.3 2.5 2.5 2.5 2.5 2.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.6 1.7 1.9 2.0 2.1 2.1 2.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.4 1.5 1.6 1.7 1.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .8 1.0 1.2 1.3 1.4 1.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .5 .7 .9 1.0 1.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .2 .5 .6 .8 1.0 2.0 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .1 .3 .4 .5 .7 1.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .2 .3 .4 .2 .0 .3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .6 .2 .6 .2 -1.0 -.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.6 3.4 3.2 88.8 88.8 -1.6 -.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.1 3.2 3.3 3.5 88.8 88.8 -2.2 -1.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.8 3.1 3.3 3.5 88.8 88.8 88.8 -1.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.6 3.1 3.3 3.5 88.8 88.8 88.8 -1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.2 3.3 '43.4 3.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .88.8 88.8 3.3 3.4 3.6 3.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.2 3.5 3.7 3.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.1 3.7 3.8 4.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.6 3.9 4.0 4.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.0 4.1 4.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 5.0 5.0 4.7 4.3 4.3 4.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 5.0 5.0 4.6 4.3 4.2 4.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.2 4.1 4.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.1 4.2 4.2 3.8 2.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 HA'8 88.8 4.0 4.3 4.5 4.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.4 4.5 4.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.4~ 4.6 4.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.6 4.7 4.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.9 4.9 4.9 4.8 4.8 4.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.9 4.9 4.9 4.9 4.9 5.0 88.8 88.8 88.8 88.8 88%8 88.8 88.8 88.8 88.8 4.9 4.9 4.9 4.9 4.9 5.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.9 4.9 4.9 4.9 4.8 4.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.9 4.9 4.9 4.9 4.8 4.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.8 4.8 4.9 4.9 5.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.8 4.8 4.8 4.9 5.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.8 4.8 4.8 4.8 4.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.8 418 4.7 4.7 4.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 54 TIME U'N HRS. 16.63 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 10.5 11.9 11.7 88.18 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.0 11.6 11.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 10.9 11.0 11.8 11.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 10.7 9.8 8.8 10.8 11.3 11.7 88.8 88.8 88.8 88.8 88.8 88.8 7.4 8.4 9.0O 9.5 9.7 9.9 11.0 11.6 88.8 88.8 88.8 88.8 88.8 88.8 6.3 6.9 7.8 8.7 9.2 9.9 10.2 10.9 11.6 88.8 88.8 88.8 88.8 88.8 7.5 6.1 6.7 7.5 8.4 9.0 9.6 10.3 10.9 11.4 88.8 88.8 88.8 88.8 88.8 6.9 6.0 6.6 7.4 8.1 8.8 9.5 10.2 10.8 88.8 88.8 88.8 88.8 88.8 88.8 6.7 5.8 6.5 7.2 7.9 8.5 9.3 10.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.3 5.6 6.3 7.0 7.7 8.4 9.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 5.5 6.2 6.9 7.5 8.2 9.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 5.4 6.1 6.7 7.3 8.1 88.8 88.8 2.5 2.3 88.8 88.8 88.8 88.8 88.8 88.8 5.3 6.0 6.6 7.1 7.7 6.1 6.9 6.7 4.5 88.8 88.8 88.8 88.8 88.8 88.8 5.4 6.1 6.6 6.9 6.9 6.6 6.8 4.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 5.9 6.4 6.8 6.9 6.1 6.1 6.3 2.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 6.9 6.8 7.5 7.4 4.2 4.6 4.8 2.1 88.8 88.8 88.8 88.8 88.8 88.8 10.1 9.6 10.5 10.6 88.8 2.3 2.7 2.9 2.3 88.8 88.8 88.8 88.8 88.8 88.8 10.2 10.5 11.0 11.4 88.8 88.8 .8 2.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 10.3 10.8 11.3 11.7 88.8 88.8 88.8 -.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 10.5 11.1 11.5 12.0 88.8 88.8 88.8 -1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.1 11.5 11.9 12.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.4 11.8 12.2 12.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.6 12.0 12.4 12.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.7 12.2 12.5 12.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.18 12.3 12.6 12.9 88.8 88.8 88.8 88.8 88.8 88.8 88.3 88.8 88.8 88.8 88.8 12.1 12.4 12.7 13.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.9 11.9 12.1 12.5 12.7 13.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.9 11.9 12.3 12.5 12.7 13.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.9 12.5 12.7 13.0 13.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 12.2 12.5 12.7 12.9 13.0 10.6 7.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 12.3 12.5 12.8 13.1 88.8 7.1 5.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 12.2 12.5 12.7 13.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 12.1 12.4 12.6 12.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 12.0 12.3 12.5 12.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.6 11.6 11.9 12.2 12.4 12.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.5 11.5 11.8 12.1 12.3 12.6 88.8 88.8 88.8 88.8 88.3 88.8 88.8 88.8 88.8 11.5 11.5 11.7 12.0 12.2 12.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.5 11.5 11.7 11.9 12.2 12.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.4 11.4 11.6 11.8 12.1 12.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.4 11.4 11.6 11.8 12.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.3 11.3 11.5 11.7 11.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 11.3 11.3 11.5 11.7 11.9 88.. 88.8 88.8 88.8 88.8 83.8 88.8 88.8 88.8 88.8 11.2 11.2 11.4 11.6 11.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 TIME IN HRS. 19.95 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 7.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 7.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 7.8 8.5 10.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 6.6 7.2 7.8 7.3 8.2 8.7 88.8 88.8 88.8 88.8 88.8 88.8 4.2 4.6 4.8 5.3 6.5 7.2 7.9 8.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.7 5.0 5.3 5.8 6.6 7.5 8.1 8.6 88.8 88.8 88.8 88.8 88.8 3.8 4.6 5.0 5.3 5.7 6.3 6.9 7.5 8.2 8.9 88.8 88.8 88.8 88.8 88.8 4.3 4.9 5.3 5.6 6.1 6.6 7.2 7.8~ 8.4 88.8 88.8 88.8 88.8 88.8 88.8 4.7 5.2 5.5 5.8 6.2 6.7 7.3 7.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 5.0 5.4 5.7 6.0 6.5 6.9 7.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 5.6 5.9 6.3 6.7 7.1 7.6 88.8 88.8 5.0 4.2 88.8 88.8 88.8 88.8 88.8 5.8 6.1 6.4 6.7 7.2 88.8 88.8 7.6 7.6 5.0 88.8 88.8 88.8 88.8 88.8 5.9 6.2 6.6 6.9 7.3 7.5 8.1 8.5 8.5 7.0 4.3 88.8 88.8 88.8 88.8 6.0 6.3 6.7 7.1 7.5 7.9 8.4 8.8 9.0 7.7 4.3 88.8 88.8 88.8 88.8 6.0 6.4 6.7 7.2 7.6 8.0 8.5 9.0 9.3 9.0 4.6 88.8 88.8 88.8 88.8 6.1 6.5 6.8 7.3 7.8 8.2 8.7 9.2 9.6 10.0 88.8 88.8 88.8 88.8 88.8 5.5 5.7 6.3 88.8 8.0 8.5 8.9 9.4 9.9 10.4 88.8 88.8 88.8 88.8 5.0 5.3 5.7 6.0 88.8 88.8 8.6 9.0 9.5 10.1 9.4 88.8 88.8 88.8 88.8 5.0 5.3 5.6 5.9 88.8 88.8 8.8 9.0 9.5 9.9 9.7 88.8 88.8 88.8 88.8 5.0 5.3 5.6 5.9 88.8 88.8 8.8 9.0 9.5 9.6 8.2 88.8 88.8 88.8 88.8 4.6 5.1 5.4 5.7 88.8 88.8 88.8 8.9 9.2 7.7 88.8 88.8 88.8 88.8 88.8 4.5 4.9 5.2 5.5 88.8 88.8 88.8 8.4 6.6 6.3 88.8 88.8 88.8 88.8 88.8 4.5 4.7 5.0 5.3 88.8 88.8 88.8 4.8 3.7 88.8 88.8 88.8 88.8 88.8 88.8 4.4 4.5 4.8 5.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88..8 4.2 4.3 4.5 4.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 4.1 4.3 4.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.6 2.6 3.2 3.9 4.1 4.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.6 2.6 3.2 3.8 4.1 4.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.7 4.1 4.3 88.8 88.8 7.7 6.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.3 3.6 3.9 4.5 6.0 7.2 8.2 7.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.2 3.5 3.6 3.8 88.8 7.4 8.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.4 3.5 3.9 88.8 88.8 8.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.3 3.4 3.7 88.8 88.8 6.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.1 3.3 3.6 88.8 88.8 4.2 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.7 2.9 3.2 3.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.7 2.9 3.1 3.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.7 2.9 3.1 3.4' 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.7 2.8 3.1 3.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.6 2. 8 3.1 3.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.6 2.8 3.1 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.6 2.8 3.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.6 2.8 3.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 2.5 2.6 2.9 3.2 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 .88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 56 TIME IN HRS. 23.28 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.5 88. 888.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.0 3.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.4 3.8 88.8 88.8 88.8 88.8 88.8 88.8 2.6 2.2 2.2 88.8 3.3 3.6 3.4 3.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 2.6 2.6 2.6 2.9 3.1 3.3 3.7 3.9 88.8 88.8 88.8 88.8 88.8 2.8 2.7 2.8 2.9 3.0 3.2 3.4 3.6 3.8 4.1 88.8 88.8 88.8 88.8 88.8 3.0 2.9 3.0 3.1 3.2 3.4 3.6 3.8 4.0 88.8 88.8 88.8 88.8 88.8 88.8 3.0 3.1 3.2 3.3 3.4 3.6 3.7 4.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.0 3.2 3.3 3.4 3.6 3.7 3.9 88.8 88:8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 3.3 3.4 3.6 3.7 3.9 4.1 88.8 88.8 5.5 5.9 4.5 88.8 88.8 88.8 88.8 3.4 3.6 3.7 3.9 4.0 88.8 88.8 5.4 5.9 6.4 4.4 88.8 88.8 88.8 88.8 3.6 3.7 3.8 4.0 4.3 4.8 5.1 5.7 6.3 6.9 4.5 88.8 88.8 88.8 88.8 3.7 3.8 4.0 4.2 4.5 4.9 5.4 6.0 6.6 7.1 4.5 88.8 88.8 88.8 88.8 3.7 3.9 4.0 4.3 4.9 5.2 5.7 6.4 6.9 7.4 4.6 88.8 88.8 88.8 88.8 3.6 3.9 4.0 4.3 5.3 5.6 6.0 6.5 7.2 7.7 88.8 88.8 88.8 86.8 88.8 2.9 2.7 3.2 88.8 5.7- 6.0 6.3 6.7 7.3 8.1 88.8 88.8 88.8 88.8 2.2 2.5 2.6 2.7 88.8 88.8 6.3 6.6 7.0 7.6 88.8 9.4 88.8 88.8 88.8 2.3 2.4 2.5 2.7 88.8 88.8 6.6 7.0 7.3 7.6 8.5 88.8 88.8 88.8 88.8 2.3 2.3 2.4 2.6 88.8 88.8 88.8 7.3 7.6 8.2 9.3 88.8 88.8 88.8 88.8 1.7 2.1 2.2 2.4 88.8 88.8 88.8 7.6 8.0 8.7 9.2 88.8 88.8 88.8 88.8 1.7 1.8 2.0 2.2 88.8 88.8 88.8 7.9 8.4 9.1 9.3 88.8 88.8 88.8 88.8 1.6 1.7 1.8 2.0 88.8 88.8 8.0 8.3 8.7 88.8 88.8 88.8 88.8 88.8 88.8 1.6 1.6 1.7 1.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.5 1.6 1.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.4 1.5 1.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.2 1.4 1.5 1.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.2 1.4 1.5 1.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88..8 88.8 88.8 88.8 1.4 1.5 1.6 88.8 88.8 6.9 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.3 1.4 1.9 4.1 5.5 6.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.1 1.2 1.3 1.3 88.8 5.9 6.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.3 1.4 88.8 88.8 6.7 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.4 88.8 88.8 7.0 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.2 1.2 1.4 88.8 88.8 4.5 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.1 1.2 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.2 1.2 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.2 1.3 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.2 1.3 1.5 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.2 1.3 1.6 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.1 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.2 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.2 1.3 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 1.0 1.0 1.1 1.3 1.4 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 88.8 57 MAXIMUMUM WATER LEVEL PRODUCED BY THIS STORM 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 10.6 11.9 11.8 -.0 11.6 11.6 11.6 11.6 11.6 11.6 11.6 11.6 -.0 -.0 11.3 12.0 12.0 =.0 11.7 11.7 11.7 11.7 11.7 11.7 11.7 -.0 -.0 11.3 11.9 12.4 12.3 -.0 11.7 11.7 11.7 11.7 11.7 11.7 11.3 10.1 10.1 11.4 1Z.Z 12.7 -.0 -.0 11.8 11.8 -.0 7.6 8.4 9.1 9.6 10.1 10.7 11.8 12.5 -.0 -.0 -.0 11.8 -.0 6.7 7.4 8.0 8.7 9.4 10.3 11.1 11.9 12.6 -.0 -.0 -.0 11.9 7.9 6.8 7.5 8.2 8.9 9.6 10.4 11.2 12.0 12.7 -.0 -.0 -.0 12.0 7.0 7.0 7.7 8.3 9.0 9.710.511.312.0 -.0 4.0 -.0 -.0 i2.0 7.1 7.3 7.8 8.4 9.1 9.9 10.6 11.4 -.0 -.0 4.0 4.0 -.0 1Z.1 6.8 7.5 8.0 8.5 9.Z, 9.9 10.7 -.0 -.0 -.0 6.1 4.0 -.0 1Z.1 -.0 7.6 8.1 8.7 9.3 10.0 10.8 -.0 -.0 5.8 6.2 4.5 -.0 12.2 -.0 7.8 8.3 8.8 9.410.0 -.0 -.0 7.7 7.6 7.1 4.4 -.0 12.2 -.0 7.9 8.4 8.9 9.4 9.9 9.1 9.7 9.4 8.7 8.0 4.6 -.0 12.3 -.0 8.0' 8.5 9.0 9.4 9.6 9.5 10.0 9.5 9.1 8.7 4.8 -.0 12.4 10.0 8.2 8.7 9.1 9.5 9.3 9.4 9.6 9.4 9.3 9.4 5.0 -.0 12.4 10.1 8.5 8.9 9.4 9.7 8.7 9.1 9.3 9.6 9.6 10.1 10.1 -.O 1Z.$ 10.4 10.1 11.0 11.1 11.0 8.6 8.9 9.2 9.7 10.0 10.5 10.2 -.0 1Z.5 10.5 10.9 11.3 11.7 -.0 -.0 8.8 9.Z 9.6 10.1 10.4 9.4 -.0 1Z.6 10.6 11.1 11.5 11.9 -.0 -.0 8.8 9.1 9.5 10.0 10.5 -.0 -.0 1Z.6 10.8 11.3 11.7 1Z.1 -.0 -.0 9.0 9.1 9.6 10.0 10.5 -.0 -.0 12.6 11.Z 11.6 1Z.O 1Z.4 -.0 -.0 -.0 9.1 9.4 9.8 9.5 -.0 -.0 12.6 11.$ 11.9 1Z.Z 1Z.5 -.0 -.0 -.0 8.8 9.0 9.6 9.3 -.0 -.0 1Z.611.61Z.O 1Z.41Z.7 -.0 -.0 8.0 8.8 9.Z -.0 -.0 -.0 -.0 161171.1258I . . . . . . . . . . 12.6 11.9 12.4 12.7 12.9 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 12.6 12.4 12.6 12.8 13.1 -.0 -.0 -.0 -.0 -.0' -.0 -.0 -.0 -.0 12.6 12.6 12.7 12.9 13.2 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 ~-.0 12.6 12.8 12.7 13.0 13.2 -.0 -.0 -.0 -.0 '-.0 -.0 -.0 -.0 -.0 12.6 12.7 12.8 12.9 13.2 13.6 -.0 7.7 6.3 -.0 -.0 -.0 -.0 -.0 12.6 12.5 12.8 13.0 13.1 13.0 10.7 9.87 6.3 -.0 -.0 -.0 -.0 -.0 12.5 12.5 12.9 13.1 13.4 13.0 10.2 9.3 7.3 -.0 -.0 -.0 -.0 -.0 12.5 12.5 12.9 13.1 13.4 -.0 9.2 9.3 -.0 -.0 -.0 -.0 -.0 -.0 12.4 12.6 12.9 13.1 13.3 -.0 -.0 7.4 -.0 -.0 -.0 -.0 -.0 -.0 12.4 12.4 12.9 13.0 13.3 -.0 -.0 4.5 -.0 -.0 -.0 -.0 -.0 -'.0 12.3 12.6 12.8 13.0 13.2 -.0 -.0 4.5 -.0 -.0 -.0 -.0 '-.0 -.0 12.3 12.5 12.7 12.9 13.2 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 12.2 12.4 12.6 12.8 13.1 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 12.2 12.4 12.6 12.8 13.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 12.1 12.3 12.5 12.7 12.9 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 12.1 12.3 12.5 12.7 12.9 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 12.0 12.2 12.4 12.6 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 12.0 12.2 12.3 12.5 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 112.9 12.1 12.3 12.5 -.0 -.0 -.0 -.0, -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 -.0 59 FLOODING DEPTH 888.8 INDICATES BELOW MLW 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.6888.8 1.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.3888.8 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.3 11.9888.8 2.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.3 3.1 3.1 1'.4888.8889.8 .0.0 0.0 0.0 0.0 0.0 5.6888.8888.8 6.6 8.1 7.7 11.8888.8 0.0 0.0 0.0 0.0 0.0 1.7888.8888.8888.8888.8 8.3 9.1888.8888.8 0.0 0.0 0.0 0.0 .98.8888.888888888.88812.7 0.0 0.0 0.0 0.0 5088888888888888888888 0.0 .0 0.0 0.0 0.0 5.8888.8888.8888.888 0.0 0.0 .0 .0 0.0 0.0 4.8888.8888.888.8.8888.8888.8888.8 0.0 0.0 0.0 .1 .0 0.0 0.0 0.0888.8888.8888.8888.8888.8888.8 0.0 0,.0 3.8 4.2 .5 0.0 0.0 0.0888.8888.8888.8888.8888.8 0.0 0.0 6.7 5.6 3.1 .4 0.0 0.0 0.0888.8888.8888.8888.8888.8 9.1 9.7 8.4 4.7 4.0 .6 0.0 0.0 0.0888-8888.8898.8888.8888.,,8888.8 9.0 7.5 5.1 4.7 .8 0.0 0.0 .0888.8888.8888.8888.8888.8888.8 8.6 7.4 7.3 5.4 1.0 0.0 0.0 .1888.8888.8888.8888.8888.8888.8 9.3 8.6 7.6 6.1 .1 0.0 0.0 5.4888.8888.8888.8 .0888.8888.8888.8 9.7 8.0 5.5 .2 0.0 0.0888.8888.8888.8888.8 0.0 0.0888.8888.8 6.6 3.1 1.4 ~4 0.0 0.0888.8888.8888.8888.8 0.0 0.0 4.8888.8888.8 8.0 3.5 0.0 0.0 0.0 10.98888.8888.8888.8 0.0 0.0 1.0888.8 5.6 6.0 2.5 0.0 0.0 0.0888.8888.8888.8888.8 0.0 0.0 0.0 9.1 6.4 2.8 .5 0.0 0.0 0.0888.8888.8888.8888.8 0.0 0.0 0.0 6.8 6.0 3.6 .3 0.0 0.0 0.0888.8888.8888.8888.8 0.0 0.0 1.0 4.8 6.2 0.0 0.0 0.0 0.0 60 0.088888.888.88.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.9888.8888.8888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.4888.8888.8888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.888888.888.888.8 0.0 0.0 0.0, 0.0 0.0 0.0 0.0 0.0 0.0 888.8888.8888.8888.8888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.7888.8888.8888.8 3.6 0.0 1.7 .3 0.0 0.0 0.0 0.0 0.0 0.0888.8888.8 13.0 13.1 12.0 9.7 3.8 .3 0.0O 0.0 0.0 0.0 0.0 0.0888.8888.8888.8888.8 0.0 7.-2 6.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.5888.8888.8888.8 0.0 0.0 5.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.6888.8888.8888.8 0.0 0.0 3.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.4888.8888.8888.8 0.0 0.0 .5 0.0 0.0 0.0 0.0 0.0 0.0 888.8888.8888.8888.8888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.8888.8888.8888.8888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.888888.888.888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.8888.8888.8888.8888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.888888.888.888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.888888.888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.888888.888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.888888.888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 888.888888.888.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 61 TIME DOG ID CARBELE CAT PT APICLA L ANCHR W PASS .13 .90 .90 .90 .90 .90 .90 .27 .89 .89 .90 .90 .93 .92 .40 .89 .87 .91 .89 :96 .94 .53 .88 .85 .90 .88 .98 .96 .67 .88 .85 .90 .88 1.01 .97 .80 .88.6 .91 .87 1.03 .98 .93 .88 .86 .92 .88 1.04 .97 1.06 .89 .87 .92 .91 1.01 .96 1.20 .89 .88 .92 .92 .99 .96 1.33 .89 .88 .92 .92 .99 .98 1.46 .89 .88 .92 .92 1.00 .98 1.60 .89 .87 .94 .91 1.03 .98 1.73 .90 .86 .95 .90 1.04 .98 1.86 .90 .86 .95 .89 1.05 1.00 2.00 .90 .88 .96 .89 1.04 1.00 2.13 .90 .89 .97 .99 1.04 1.00 2.26 .90 .89 .97 .90 1.05 1.00 2.39 .91 .89 .97 .90 1.04 1.00 2.53 .91 .38. .98 .89 1.0k. 1.00 2.66 .91 .88 .99 .89 1.04 1.00 2.79 .91 .88 .99 .89 1.04 1.01 2.93 .91 .89 .99 .89 1.05 1.01 3.06 .91 .90 1.01 .88 1.06 1.02 3.19 .91 .90 1.01 .88 1.06 1.02 3.33 .91 .89 1.01 .88 1.07 1.02 3.46 .90 .88 1.02 .88 1.07 1.03 3.59 .90 .86 1.01 .89 1.07 1.03 3.72 .90 .86 1.01 .89 1.07 1.03 3.86 .90 .87 1.03 .88 1.07 1.03 3.99 .90 .88 1.03 .88 1.08 1.04 4.12 .91 .89 1.02 .88 1.09 1.04 4.26 .91 .89 1.02 .88 1.09 1.05 4.39 .91 .88 1.03 .88 1.10 1.05 4.52 .91 .87 1.03 .88 1.10 1.06 4.66 .91 .86 1.03 .88 1.10 1.06 4.79 .91 .87 1.03 .88 1.11 1.06 4.92 .90 .87 1.04 .88 1.11 1.07 5.05 .91 .88 1.04 .88 1.12 1.07 5.19 .91 .88 1.05 .88 1.13 1.08 5.32 .91 .88 1.06 .87 1.13 1.08 ~5.45 .91 .87 1.06 .87 1.14 1.09 5.59 .91 .87 1.07 .87 1.15 1.09 5.72 .91 .87 1.07 .87 1.15 1.10 5.85 .91 .87 1.08 .87 1.16 1.11 5.99 .91 .87 1.08 .87 1.17 1.11 6.12 .92 .87 1.09 .87 1.17 1.12 6.25 .92 .88 1.10 .87 1.18 1.13 6.38 .92 .88 1.10 .87 1.19 1.14 6.52 .92 .88 1.11 .87 1.20 1.15 6.65 .92 .88 1.12 .86 1.21 1.15 6.78 .93 .88, 1.13 .86 1.22 1.16 6.92 .93 .88 1.14 .86 1.23 1.17 7.05 .93 .88 1.15 .86 1.23 1.18 7.18 .94 .89 1.15 .86 1.24 1.20 7.32 .94 .89 1.17 .86 1.26 1.21 7.45 .94 .89 1.18 .86 1.27 1.22 7.58 .95 .90 1.19 .86 1.28 1.23 7.71 .95 .90 1.20 .86 1.29 1.25 7.85 .96 .90 1.21 .86 1.30 1.26 7.98 .96 .91 1.23 .86 1.32 1.28 8.11 .98 .92 1.24 .86 1.33 1.29 8.25 .99 .95 1.25 .86 .1.34 1.31 8.38 1.01 .98 1.27 .86 1.36 1.32 8.51 1.01 .99 1.28 .86 1.37 1.34 8.65 1.02 .98 1.30 .86 1.38 1.36 8.78 1.03 ..96 1.32 .86 1.39 1.38 8.91 1.04 .96 1.34 .85 1.41 1.40 9.05 1.05 .98 1.36 .85 1.42 1.42 9.18 ~1.07 .99 1.38 .85 1.44 1.44 62 9.31 1.09 .99 1.40 .85 1.45 1.46 9.44 1.12 1.01 1.42 .85' 1.47 1.49 9.58 1.13 .98 1.44 - .85 1.49 1.51 9.71 1.17 1.03 1.46 .85 1.51 1.54 9.84 1.17 .98 1.48 .84 1.53 1.57 9.98 1.23 1.05 1.51 .84 1.55 1.60 10.11 1.22 .97 1.53 .84 1.58- 1.64 10.24 1.30 1.01 1.56 .84 1.61 1.68 10.38 1.29 .98 1.59 .85 1.63 1.72 10.51 1.37 1.08 1.62 .84 1.66 1.77 10.64 1.37 1.08 1.66 .84 1.69 1.81 10.77 1.47 1.04 1.69 .84 1.71 1.87 10.91 1.51 1.03 1.73 .85 1.76 1.92 11.04 1.57 1.07 1.77 .85 1.79 1.98 11.17 1.63 1.17 1.82 .86 1.81 2.05 11.31 1.71 1.27 1.86 .86 1.86 2.11 11.44 1.81 1.36 1.91 .87 1.89 2.18 11.57 1.89 1.43 1.97 .88 1.92 2.26 11.71 2.01 1.51 2.03 .89 1.96 2.35 11.84 2.12 1.61 2.09 .90 2.00 2.45 11.97 2.24 1.73 2.16 .92 2.04 2.55 12.10 2.38 1.87 2.23 .93 2.08 2.66 12.24 2.52 2.02 2.31 .95 2.13 2.78 12.37 2.69 2.17 2.39 .97 2.18 2.91 12.50 2.87 2.34 2.48 1.00 2.23' 3.05 12.64 3.06 2.53 2.58 1.03 2.28 3.17 12.77 3.27 2.74 2.69 1.06 2.34 3.33 12.90 3.49 2.97 2.80 1.10 2.40 3.51 13.04 3.73 3.22 2.91 :1.14 2.45 3.71 13.17 3.99 3.48 3.04 1.19 2.50 3.96 13.30 4.27 3.76 3.18 1.23 2.50 4.16 13.43 4.58 4.05 3.32 .1.28 2.66 4.44 13.57 4.91 4.36 3.47 1.36 2.78 4.81 13.70 5.25 '4.73 3.63 .1.43 2.86 5.07 13.83 5.62 5.13 3.81 1.52 2.98 5 24 13.97 6.00 5.55 3.99 1.65 3.12 5.43 14.10 6.41 5.98 4.18 1.79 3.29 5.71 14.23 6.83 6.40 4.39 1.95 3.41 5.96 14.37 7.30 6.87 4.62 2.15 3.40 6.22 14.50 7.78 7.39 4.85 2.36 3.71 6.52 14.63 8.29 7.97 5.09 2.57 3.65 6.72 14.76 8.83 8.52 5.35 2.85 4.27 7.08 14.90 9.34 9.09 5.63 3.12 4.22 7.28 15.03 9.86 9.64 5.93 3.40 4.45 7.62 15.16 10.39 10.30 6.24 3.74 4.61 7.89 15.30 10.84 10.74 6.57 4.05 4.78 8.12 15.43 11.24 11.18 6.93 4.47 4.96 8.31 15.56 11.62 11.62 7.34 4.75 5.16 8.46 15.70 12.01 12.1-5 7.78 5.19 5.24 . 8.62 15.83 12.32 12.50 8.20 5.54 5.38 8.76 15.96 12.55 12.76 8.67 5.98 5.48 8.89 16.09 12.68 12.95 9.10 6.35 5.66 9.03 16.23 12.74 13.07 9.53 6.77 5.78 9.04 16.36 12.71 13.08 9.92 7.20 5.90 9.09 16.49 12.61 13.01 10.27 7.61 5.93 8.98 16.63 12.46 12.89 10.58 8.05 6.11 9.05 16.76 12.24 12.70 10.81 8.38 6.06 8.88 16.89 11.95 12.44 10.98 8.77 6.24 8.92 17.03 11.62 12.13 11.08 9.05 6.26 8.72 17.16 11.23 11.76 11.12 9.37 6.37 8.70 17.29 10.82 11.38 11.10 9.55 6.44 8.49 17.43 10.37 10.95 11.02 9.75 6.48 8.51 17.56 9.91 10.55 10.91 9.82 6.49 8.30 17.69 9.49 10.10 10.74 9.96 6.58 8.17 17.82 9.07 9.72 10.53 9.96 6.52 7.91 17.96 8.56 9.08 10.28 9.99 6.76 7.60 18.09 8.18 8.86 9.99 9.92 6.52 7.52 18.22 7.77 8.39 9.64 9.82 6.66 7.28 18.36 7.39 7.98 9.28 9.72 6.50 7.16 18.49 7.03 7.75 8.87 9.60 6.46 6.98 63 18.62 6.62 7.36 8.48 9.41 6.34 6.92 18.76 6.32 7.03 8.10 9.25 6.26 6.74 18.89 5.92 6.70 7.80 9.00 6.13 6.65 19.02 5.62 6.42 7.49 8.77 6.03 6.38 19.15 5.28 6.08 7.30 8.52 5.79 6.20 19.29 5.01 5.76 7.15 8.25 5.79 5.97 19.42 4.71 5.47 6.96 8.01 5.39 5.73 19.55 4.47 5.25 6.77 7.74 5.32 5.52 19.69 4.21 4.98 6.66 7.63 5.02 5.27 19.82 3.99 4.74 6.45 7.38 4.74 5.04 19.95 3.80 4.52 6.32 7.23 4.64 4.80 20.09 3.62 4.37 6.15 7.03 4.46 4.52 20.22 3.42 4.21 5.99 6.87 4.35 4.35 20.35 3.26 4.03 5.81 6.68 4.27 4.18' 20.48 3.11 3.86 5.65 6.51 4.13 4.04 20.62 2.96 3.70 5.51 6.33 4.07 3.88 20.75 2.82 3.54 5.37 6.18 3.94 3.75 20.88 2.70 3.42 5.22 6.06 3.85 3.60 21.02 2.57 3.28 5.09 5.94 3.73 3.56 21.15 2.45 3.15 4.94 5.82 3.67 3.42 21.28 2.34 3.02 4.82 5.68 3.57 3.32 21.42 2.23 2.90 4.69 5.55 3.43 3.20 21.55 2.13 2.78 4.57 5.42 3.58 3.12 21.68 2.04 2.68 4.44 5.30 3.47 3.00 21.81 1.96 2.59 4.32 5.20 3.27 2.83 21.95 1.88 2.50 4.19 5.04 3.37 2.92 22.08 1.81 2.42 4.07 4.98 3.20 2.77 22.21 1.75 2.34 3.95 4.83 3.25 2,73 22.35 1.69 2.27 3.85 4.72 3.09 2.65 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