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                ci                        ii4E~~~~~1:AGI-iE:5 AND  SFHORIES                          c
                Ii          TECI--iNICAL A~PND DEINMEMO)RANDUM  NO. f34---60

                      [I   ~ ~      ~      ~      ~~~~~~        COASTAL ZONTE                         II
                                                          INFOR.MATION CENTER                       c

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        11            Nat  oi oa   Oceanic:  arid  A-tmfospter ic Aim in istra-rtion,                 0
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    4590
    .F56b                                                                                            c
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            ,Indiana~~~~~4

    FEB   3 1991

            Th is work pr-nv i des detrcr Ipt i on anrd doc ument a I ion o F
      a dva ncewfenltr wrade  inI nutler i ca t mode  ing Procedure.'  used  inI                                                              TABLE OF CONTENTS
      r ec omweend i nrigio bat i on o f Coa  t a 1. Conis I,, uc  t i on Con tr -at         0
      L. i nes (Cha ptfer i 61, , F I[or i c it SA-a t utes ) .  Work1 comp leted             t
       ic riC. udes :I . wa od i f I c.a t ion cii   t he E t oirwIIIllce riioL' III4 IE . foar                                     ScinPage
      efficient pr-oce.esiriq on IIIhe Fl[or ida Departwerit of NaturaL                       0Setn
      Resources NRMES data  center IBM 4341  ModeL Group 2 process-or, to
         2insta [tat ion of ref inewnentsA to the storm ,surge programs                                               I.  INTRODUCTION .1............
      -to  increase coord inat ion between on-   esin  .and
      two-dim   ensional L  odets, andl 3.  setect icin  devetcipewent                                               II.    METHODOLOGY OF STORM4 SURGE CALCULATION .            .1.....
      and  inst akLtat ion of a beach-ilune ercisi on wadeL tthat cane lie
      used  in conj unc t iocn  w ith the str [0-,15urg e wodieli ni  p~roceci ire                                          2.1  Introduction.                                                ....................2
      The contents~ of this document,  in pretiminary fore,  were.                                                           2.2  Parameterized Hurricane.                                    ..............2
      presented  to -the pubLi c  in a Department of Natura L Resources. 2.3  Classification by Path Relative to Shoreline.                                                                   ....3
      workshop  heLd Ju L-> 111-12, 19B34.                                                     '2.4  General Overview of Storm Surge Numerical Models

            The present work is rpresented it) partiaL fuLfil[[went cif                            (-  ~and Procedures .                                                            .....i~'':.......16
      contractua L obli gat ions1  of the FederaL  Coasta l Zone                                        r       *2.5  Features and Solution of the Tw-Dmenional Numerical
                                                                                                        C..') Model.                                                                       .......................20
      Management  Prograw  (subject to provisions of the CoastaL                                        -
      Zone Maniageipriet Imiprovem~ent Act of 1972, as attended) subject                C     o     ~                             Governing Differential Equations For Two-Dimensional
      to prov is i cnw of contract  CM-37 ent i tt[c  'Enigirneer incj Supipor t            M    I        C) r-n                  Nuercl  oel2
      Enhanicement 17rogram".  Unider prov is ionis of DNR contract C0037,                          U iieDfeec om fGvrigDfeeta
      -th is wor-k  is a subcontracted rProduct of the Eleaches aoil Shores                         (I          _FnteDfeec   orso   oenngDfeeta
      Res5ource Center, Institute of Science and Fob tic Affa irs,                 I     n     e    Qn are  Islan Repreenationas.24rali
      F toridca State~ ln ivers i ty.  The clocumenit has ibeen adopted  a s                                 "-                   IltandBrirIln   ersnaina   yrui
                                                                                                                                Elements.                                                 ....................28
      Eleaches and] Shores Technical  and De,,i en Memorandium  in                                      (Z BondryCnitin1     ......3
                                    ac~~cordailce xjith  provisions of  Chapter i6D-13, Ftarida     ~Implicit Solution of the Finui-te Differe'nce'Equations. 36
       adiniiiitrative Code.                                                                        C') CJn"                      yai  Wv   e-p4
                                                                                                         u.() C:)
            At the teei  of subiI~~i(ss on-for coniractura t c~orepLi ance,                         r     ~ :2-             2.    etrso   h   n-iesinlNmrclMdl...4
                                   H. aL.itle ws te   cntrct i-iage(an                                       Co()      2 6 F aue fteOeDmninlNmrclMdl...4
      Jam~es HDA  iULiewa thcotatwneradmRriin istratfor                                                      M -
      of the Antatys is/Research  Sect ion, Hat L~ Detian  was Chief of the                  G       vrigDfentaEqtosFrOe-Dienioa
      Biureau of CoastaL Data Acqiuisition, Deborah  E. Flack  Director                              (p                           Goenn  Difrnta   qutos  o   neDmnsoa
           of the Division ofof-leaches and  Shores, anid Dr. ELt~on J.                                      M-                     ueialMdl4
      Gli senidaniner the Executive Di rector of -the F tori da Depqartluent                        1,1 C_       "'               Finite Difference Forms of Governing Differential
      of Natiira L Resources.                                                                        P. M   C>                    Equations.                                                 .....................47
                                                                                                               r-n             Initial and Boundary Conditions For the One-Dimen-
                                                                                                   C.-O_                       sional Model.                                              ...................47
                                                                                                               __>             Explicit Solution of the Finite Difference Equations   47

                                                                -4 ~~~~~~~~~~~~~ ~~~~~~~~~~~"- ~~~~~~~~2.7  Long-Term Simulation                                                           48

                                              Diebiinora E. Ftack,   anreShore                                      Ill.   APPLICATIONS OF STORM SURGE METHODOLOGY WITH SPECIFIC
                                                                 Division of  Beahes arid ShoresILLUSTRATION BY EXAMPLE TO CHARLOTTE COUNTY.                                               ......50

                                              JuLy, '19f.34                                                                3.1  Two-Dimensional Model (Appendix A).                        ........50

                                                                                                                               Verification With Storms of Record.                       ........50
                                                                                                                               Generation of Data Base for Calibration of One-Dimen-
                                                                                                                               sional Model.                                             ...................55

                                                                                                                          3.2  One-Diiaensional Model (Appendix B).                       ........67

                                                                                                                               Calibration With Two-Dimensional Model Results  . . . 67

                                                                                                                                                    ii

                       TABLE OF CONTENTS (Cont'd.)
                                                                                                                                  LIST OF FIGURES
    Section                                                             Page

                                                                                                        Figure                                                                Page
           3.3  Long-Term Simulations  . . . . . . . . . . .....    68

      IV.   EROSION CALCULATION METHODOLOGY . . . . . . . . . .    .   78                                    II-1    General Location of the Study Area                             4

           4.1  Introduction   . . . . . . . . . . . . . . .   . .       78                                 11-2    Directional Distribution of Historical Hurricanes,
           4.2  Equilibrium Beach Profiles . . . . . . . . . .  .        78                                         Crystal River to East Cape, Florida                            5
           4.3  Cross-shore transport Models . . . . . . . . . . . .  87
           4.4  Prediction of Beach and Dune Erosion Due to Severes                                                                                                                6
                Storms by Kriebel's Model  ....... ......   89
                                                          *Storms by Kriebel's Model... ..........89       11II-4    Designation of Alongshore, Landfalling and Exiting
                Profile Schematization . . . . . . . . . . . . . . .  89                                            Hurricanes Depending on Track Directions Relative
                Governing Equations . . .                               89                                          to Shoreline Orientation
                Method of Solution of Finite Difference Equations        92                                         Cumulative Probability Distribution of  urricane
                Application of Method to Computation of Idealized                                           II-5on
                Beach Response . . . . . . . . . . . . . . . . . . .  93
                Application of Method to Long-Term Beach and Dune
                Response Simulations ................                    102                               II-6    Cumulative Probability Distribution of Radius to
                                                                                                                 Maximum Winds for Landfalling and Exiting Hurricanes          10
           4.5  Prediction of Beach and Dune Erosion Due to Severe
                Storms by Simple Model ...............  108                                                II-7    Cumulative Probability Distribution of Radius to
           4.6  Augmentation of the Erosion Predicted by the Model                                                  Maximum Winds for Alongshore Hurricanes                       11
                for Recommending Position of CCCL ......... 110
                                                   ......for Recommending Position of CCCL... ..110       11II-8    Cumulative Probability Distribution of Central Pressure

      V.   WAVE HEIGHT DECAY CALCULATIONS  . . . . . . . . . .  .    115                                            Deficity, Ap, for Landfalling and Alongshore Hurricanes    12

           5.1  Introduction   . . . . . . . . . . . . . . . .   .    115                                  II-9    Cumulative Probability Distribution of Central Pressure
           5.2 Methodology  . . . . . . . . . . . .  . . . . . . ... 115                                            Deficity, Ap, for Exiting Hurricanes                          13

                Wave Height Decay Due to Shoaling Water .  . . . . . 116                                   II-10   Interdependence of Central Pressure Deficity, Ap, and
                Wave Height Decay Due to Vegetation. . . . . . . . .  116                                          Radius to Maximum Winds, R                                     14
                Wave Height Decay Due to Buildings . . . . . . . . . 117
                Combined Effects of Topography, Vegetation and                                             II-11   Cumulative Probability Distribution of Storm Translation
                Buildings  .        . . . . . . . . . .        .  ..   117                                         Speed V , for Landfalling, Alongshore and Exiting
                                                                                                                Hurricaes                                                     15
     VI.   LONG-TERM EROSIONAL CONSIDERATIONS  .       . . . . . . . .  118
                                                                                                        II-12   Cumulative Probability Distribution of Landfalling
           6.1  Introduction . . . . . . . . . . . . . . . . .  .  .  118                                          Distance, YF, for Landfalling and Exiting Hurricanes           17
           6.2  Methodology .  . . . . . . . . . . . . . . . . . . . 118                                   11-13   Cumulative Probability Distribution of Offshore
     VII.  OVERALL VERIFICATIONS OF CCCL METHODOLOGY . . . . . .        120                                         Distance of Passage, L, for Alongshore Hurricanes             18

           7.1  Hurricane Agnes, St. George Island, Franklin County   120                                  11-14   Flow Chart of Methodology                                      19
           7.2  Hurricane Eloise Damage in Walton and Bay Counties    123
                                                                                                        II-15   Grid System Layout for Charlotte County                       21
           REFERENCES  . . . . . . . . . . . . .           .  . . . .  128

          APPENDIX A  . . . . . . . . . . . . .           .  . . . .  130

          APPENDIX B  . . . . . . . . . . . . .           .  . . . .  153

          APPENDIX C  ......... . .          . . . . .   . . . . . . 159
                                 iii                                                 iv

                          LIST OF FIGURES (CONT'D)                                                                                LIST OF FIGURES (CONT'D)

    Figure                                                               Page                               Figure                                                                 Page

     11-16    Bottom Friction Coefficients for Various Bottom                                               III-9     Comparison between Measured and Computed High Water
              Conditions                                                  25                                          Mayport, Florida for Hurricane David of 1979                 63

     11-17    Schematic of Implicit Method of Solving Momentum                                              III-10a   Calibration Relationship between the One-Dimensional
              and Continuity Equations                                    27                                          and the Two-Dimensional Calculations of Peak Surges
                                                                                                                     at the North and Middle Transect Lines of Charlotte
     II-18    Region of Interest in Description of Sub-Grid                                                            County for Landfalling Hurricanes                            69
              Features                                                   29
                                                                                                          III-lOb   Calibration Relationship between the One-Dimensional
     11-19    Profile of the North Transect Line and its One-Dimen-                                                   and the Two-Dimensional Calculations of Peak Surge
              sional Grid Representation                                  43                                          at the South Transect Line of Charlotte County for
                                                                                                                     Landfalling Hurricanes                                       70
     11-20    Profile of the Middle Transect Line and its One-Dimen-
              sional Grid Representation                                  44                                III-lla   Calibration Relationship between the One-Dimensional
                                                                                                                     and the Two-Dimensional Calculations of Peak Surges
     11-21    Profile of the South Transect Line and its One-Dimen-                                                   at the North and Middle Transect Lines of Charlotte
              sional Grid Representation                                  45                                          County for Alongshore Hurricanes                             71

     11-22    Flow Chart for Storm Tide Simulations (After Calibration                                      III-11b   Calibration Relationship between the One-Dimensional
              to Determine (AMP)LF, (AMP)ALOMG and (AMP)EXIT)             49                                          and the Two-Dimensional Calculations of Peak Surges
                                                                                                                    at the South Transect Line of Charlotte County for
    111-1     Comparison between Measured and Computed Storm Tide at                                                  Alongshore Hurricanes                                         72
              Manasota Bridge, Florida for the September 1947
              Hurricane                                                   52                                11I-12a   Calibration Relationship between the One-Dimensional
                                                                                                                    and the Two-Dimensional Calculations of Peak Surges
    111-2     Comparison between Measured and Computed Storm Tide at                                                  at North and Middle Transect Lines of Charlotte County
              Venice, Florida for the September 1947 Hurricane            53                                          for Exiting Hurricanes                                       73

    III-3     Comparison between Measured and Computed Storm Tide at                                        III-12b   Calibration Relationship between the One-Dimensional
              Ft. Myers, Florida for the September 1947 Hurricane         54                                          and the Two-Dimensional Calculations of Peak Surges
                                                                                                                    at the South Transect Line of Charlotte County for
    111-4     Comparison between Measured and Computed Storm Tide at                                                   Exiting Hurricanes                                           74
              St. Marks, Florida for Hurricane Agnes of 1972              57
                                                                                                          111-13    Combined Total Storm Tide Elevation Versus Return
    Il1-5     Comparison between Measured and Computed Storm Tide at                                                   Period for Three Representative Transect Lines in
              St. Marks, Florida for Hurricane Eloise fo 1975             58                                          Charlotte County                                             76

    III-6     Comparison between Measured and Computed Storm Tide at                                         IV-1     Location map of the 502 profiles used in the analysis
              Fernandina Beach, Florida for Hurricane Dora of 1964        60                                          (from Hayden, et al., (10))                                  79

    111-7     Comparison between Measured and Computed Storm Tide at                                         IV-2     Characteristics of dimensionless beach profile
              Mayport, Florida for Hurricane Dora of 1964                 61

    111-8     Comparison between Measured and Computed Storm Tide at                                                             for various m values(from Dean, (11))             80
              Fernandina Beach, Florida for Hurricane David of 1979    62

                                     v                                                                                                      vi

                         LIST OF FIGURES (CONT'D)                                                                                LIST OF FIGURES (CONT'D)

    Figure                                                               Page                               Figure                                                                Page

    IV-3     Equilibrium beach profiles for sand sizes of 0.2mm                                             IV-14    Effect of breaking wave height on berm recession
              and 0.6 mmn A(D = 0.2mm) = O.1m1/3, A(O = 0.6 mm) =                                                     (from Kriebel, (14))                                         97
              0.20ml/3                                                    81
                                                                                                          IV-15    Effect of static storm surge level on berm recession
    IV-4     Histogram of exponent m in equation h = Axm for 502                                                     (from Krieber, (14))                                         98
              United States East Coast and Gulf of Mexico profiles
              (from Dean, (11))                                           82                                IV-16    Effect of sediment size berm recession (from Kriebel,
                                                                                                                    (14))                                                      100
    IV-5     Beach profile factor, A, vs sediment diameter, D, in
              relationship h = Ax2/3 (modified from Moore,(12))           84                                IV-17    Comparison of the effects of 12,24, and 36 hrs. storm
                                                                                                                    surge on volumetric erosion (from Kriebel, (14))           101
    IV-6     Profile P4 from Zenkovich (1967).  A boulder coast in
              Eastern Kamchatka.  Sand diameter:  150mm - 300mm.                                            IV-18    Flow diagram of N-year simulation of hurricane
             Least squares value of A = 0.82m1/3 (from Moore, (12))   85                                             storm surge and resulting beach erosion (from Kriebel,
                                                                                                                    (14))                                                      105
    IV-7     Profile P10 from Zenkovich (1967).  Near the end of a
             spit in Western Balck Sea.  Whole and broken shells.                                          IV-19    Average frequency curve for dune recession, developed
             A = 0.24m1/3 (from Moore, (12))                             85                                          by Monte Carlo simulation, Bay-Walton Counties, Florida
                                                                                                                    (from Kriebel, (14))                                       106
    IV-8     Profile from Zenkovick (1967).  Eastern Kamchatka.
             Mean sand diameter:  0.25 mm.  Least squares value of                                          IV-20    Probability or risk of dune recession of given
             A = 0.07m1/3 (from Moore, (12))                             86                                          magnitude occurring at least once in N-years, Bay-
                                                                                                                    Walton Counties, Florida (from Kriebel, (14))              107
    IV-9     Model simulation of a 0. 5 meter sea level rise and
             beach profile response with a relatively mild sloping                                         IV-21    Features of simplified beach erosion model                   109
             beach (from Moore, (12))                                    88
                                                                                                          IV-22    Results of applying erosion model to Range R-1,
    IV-10    Effect of varying the sediment transport rate                                                           Martin County (Hutchinson Island), 100 year storm
             coefficient on cumulative erosion during the simulation                                                 tide, average erosion                                       111
             of Saville's (1957) laboratory investigation of beach
              rofile evolution for a 0.2mm sand size (from Moore,                                           IV-23    Results of applying erosion model to Range R-89,
             (12))                                                       90                                          Martin County (Jupiter Island), 100 years storm tide,
                                                                                                                   average erosion                                            112
    IV-11 Model representation of beach profile, showing depth
             and transport relation to grid definitions (from Kriebel,                                      IV-24    Calibration of Simplified Erosion Model By Comparison
             (14))                                                       91                                          with Erosion Occurring at Various Elevation Due to
                                                                                                                   Hurricane Eloise                                           113
    IV-12    Characteristic form of berm recession versus time for
             increased static water level (from Kriebel, (14))           94                                VI-1      General erosion conditions in Florida (Bruun, Chiu,
                                                                                                                   Gerritsen and Morgan, (20))                                119
    IV-13    Comparison of asymptotic berm recession from model (-)
             and as calculated by Eq. (IV.12) (..)                       96                                 VI-la    Beach profile at Range R-105 on St. George Island.
                                                                                                                   A location of severe overwash and damaged roadway
                                                                                                                   due to Hurricane Agnes, 1972 (see Figure VII.lb for
                                                                                                                   extension of this profile)                                 121

                                  vii                                                                                                      viii

                          LIST OF FIGURES (CONT'D)

                                                                                                                                        LIST OF TABLES
    Figure                                                                 Page

                                                                                                              Table                                                                     Page
    VII-lb   Continuation of profile across St. George Island,
              Range R-105, showing location of damaged road, due to                                            111-1      Input Parameters for Calibration Hurricane
              Hurricane Agnes, 1972                                        122                                             (Hurricane of September 1947)                                   51

    VII-2    Landfall location of Hurricane Eloise, September 23,                                              111-2      Input Parameters for Calibration Hurricanes
              1975 and some resulting tide and uprush characteristics                                                     (Hurricane Agnes of June 1972)                                   56
              (from Chiu, (16))                                           124
                                                                                                              I1I-3     Hurricane Eloise of September 1975                              56
    VII-3    Relation of erosional characteristics and pre-Eloise                                              111-3      Hurricane Eloise of September 1975                               56
              vegetation line to set-back line, Bay County, Florida                                            111-4       Input Parameters for Calibration Hurricanes
              (from Chiu, (16))                                            125                                            (Hurricane Dora of September 1964)                               59

    VII-4    Relation or erosional characteristics and pre-Eloise                                              111-5      Hurricane David of September 1975                                59
              vegetation line to set-back line, Walton County,
              Florida (from Chiu, (16))                                    125                                  111-6     Parameters Defining 11 Landfalling Storms Used
                                                                                                                         In Calibrating The One-Dimensional Model With
    VII-5    Damage to structures in relation to location of                                                              The Two-Dimensional Model And The Results                        64
              set-back control line (based on study of 540
              structures in Bay County after Hurricane Eloise,                                                  111-7      Parameters Defining 11 Alongshore Storms Used
              by Shows, (21))                                              126                                             In Calibrating The One-Dimensional Model With
                                                                                                                         The Two-Dimensional Model And The Results                       65

                                                                                                              111-8     Parameters Defining 11 Exiting Storms Used
                                                                                                                         In Calibrating The One-Dimensional Model With
                                                                                                                         The Two-Dimensional Model And The Results                       66

                                                                                                              III-9     Values of 1-D/2-D Peak Storm Surge Correlation
                                                                                                                         Coefficients For Counties Completed to Date                     75

                                                                                                              111-10    Combined Total Storm Tide Values for Various
                                                                                                                         Return Periods                                                  77

                                                                ~~~~~~~~~~~~~~~~~~~~~~ix~~~~~x
                                     ix

                                        METHODOLOGY                                                 be described elsewhere.
                                             ON
                     "COASTAL CONSTRUCTION CONTROL LINE ESTABLISHMENT"

    I.  INTRODUCTION                                                                                       As noted previously, because storm surge data are quite sparce (especially

         The coastal engineering phenomena leading to the rationale for the Coastal                   long-term storm surge data) and because most tide gages and high water marks

    Construction Control Line (CCCL) are:                                                             collected are in locations which are not representative of open coast conditions,

                       Shoreline Erosional Trend                                                     it is necessary to use numerical models with long-term historical hurricane

                       Shoreline Fluctuations (Both Seasonal and Storms) and,                        characteristics which are relatively insensitive geographically, although there

                       Storm Surges and Associated Waves.                                            are, for example, trends in the hurricane parameters.

         The general objective of the CCCL program is to define the zone of impact
                                                                                                   2.2 Parameterized Hurricane
    of a one hundred year storm event along the sandy outer coastline segments of
                                                                                                       Each hurricane is unique in its structure, shape, size, translational char-
    the State of Florida.  This program is implemented on a county-by-county basis.
                                                                                                  acteristics, etc. However, it is generally agreed that when considering many
    The DNR permitting program applies seaward of the CCCL with the two-fold purpose
                                                                                                  hurricanes, it is valid to employ the concept of an idealized or parameterized
    of ensuring:  (1) the protection of the adjacent shoreline, and  (2) the integrity
                                                                                                  hurricane. In this approach, a hurricane is represented by five parameters:
    of structures.
                                                                                                                      op = the central (lowest) barometric pressure relative
         Due to the sparcity of specific data which would identify directly the
                                                                                                                           to the ambient pressure usually reported in inches
    appropriate location for the CCCL, a series of numerical models and calculation
                                                                                                                           of mercury (in. Hg) or millibars of mercury, ap
    procedures is employed and combined with historical hurricane and erosion data to
                                                                                                                           is a measure of the intensity of the hurricane,
    establish the recommended CCCL position.
                                                                                                                      R = radius to the band of maximum winds, usually

    II.  METHODOLOGY                                                                                                            reported in nautical miles.   R is a measure of

         The establishment of the recommended location of the CCCL requires calculation                                         the size of the hurricane,

    of the 100 year storm surge and accompanying waves and shoreline erosion.  These                                      VF = forward translational speed of the hurricane,

    models and their implementation are based on the best data generally available                                              usually reported in knots,

    and on data collected specifically for the purpose of the program.  In particular                                      a  = forward translational direction, defined as the

    an extensive set of nearshore and beach profiles is taken at intervals of approxi-                                          direction from which a hurricane originates,

    mately 1,000 ft with all profiles extending out to the limit of wading and every                                       L  = landfall location or some other parameter positioning

    third profile extending out to approximately the thirty foot contour.  The field                                            the hurricane at some time during the hurricane's

    data are valuable input to the computer models; however, the field program will                                             close proximity to the area of primary concern.

                                             1                                                                                                  2

     2.3 Classification by Path Relative to Shoreline

         iHurricanes causing appreciable storm tides in the vicinity of a county

    shoreline are classified as either "landfalling", "alongshore" or "exiting"

    storms, depending on their paths relative to the shoreline orientation. Reason-

    ably good data are available describing the characteristics of such storms, from

    approximately 1900 to 1978. For purposes of establishing the statistical character-

    istics, the frequency and direction data contained in References (1) and (2) are

    merged for a segment of the coast usually extending from 100 n.mi. to 150 n.mi.

    up and down coast, i.e., a total length of 200-300 n.mi.

        The hurricane direction is defined here as the azimuth of hurricane trans-                            ,. v

    lation direction at the time of landfall, or, if an alongshore storm, when in                                                                           A

    close proximity to the site.  m

        The designation of a storm as "landfalling", "exiting", or "alongshore" is

    somewhat  arbitrary as storms travel over a continuous range of directions and

    there is not a particular direction relative to the shoreline for which the storm
                                                                                                                                      0
    tide-generating characteristics change markedly.  Moreover, one directional dis-

    tribution is applied for all three types of storms.  Figure II-1 presents an ex-

    ample of the directional distribution for Charlotte County, FL, and Figure 11-2

    shows the location of Charlotte County.  It is important to note that the manner                                                                  Chorlotte C

    in which the track of a hurricane is characterized for the purposes of this study

    is different for landfalling, exiting and alongshore hurricanes.  For landfalling

    and exiting hurricanes, the track is specified by a location of landfall (or                                                                           -

    exit) and direction, whereas for the alongshore storms, the track is specified by

    an offshore distance and a track direction. Figure 11-3 presents a definition

    sketch of the three types of hurricanes.

        For purposes of this study, landfalling and exiting hurricanes are considered

    to be of possible significance if they made landfall within a 250 nautical mile                                 Figure II-I.  General Location of the Study Area

    segment of the coast comprising the study area. Generally, this segment is

             3o2 Chalotte Cto                                                                                                          shoreline

                                                               100�

         potr  Ce IId it that  00
    from whlc h jrrlcsane
    *r19h sort1.

     Figure 11-2. Directional Distribution of illstorical Hurricanes,
                    Crystal River to East Cape, Florida                                                  Figure 11-3.  A Definition Sketch of Three Types of Hurricanes

                                  5                                                                                                    G

    centered approximately near  the mid-point of the county of interest.  Usually an

    offshore limit of alongshore storms is on the order of 50 to 100 nautical mildes.

    Figure 11-4 shows the sectors of propagation paths for landfalling, exiting and

    alongshore hurricanes for Charlotte County.

         For purposes of computer use, the cumulative probability distribution is
                                                                                                                                                           m
    developed from Figure 11-2 and is presented in Figure 11-5.

         In the following discussion of the remaining parameters defining the idealized                                        shoreline-
                                                                                                                           orlenltion-"-
    hurricane, Charlotte County will be used as an illustrative example.  Figure 11-6

    presents the cumulative probability distribution of radius to maximum winds for

    landfalling and exiting hurricanes, and Figure 11-7 presents the same for along-

    shore hurricanes.                                                                                                       alongshore
                                                                                                                        hureoones
         The cumulative probability distribution of central pressure deficit for

    landfalling and alongshore hurricanes is presented in Figure 11-8 and Figure 11-9

    presents the same information for exiting hurricanes.                                                                                         hure                     1 49

         Examination of historical hurricane data has demonstrated that for land-

    falling storms the distributions for radius to maximum winds and central pressure

    deficit are not independent.  The correlation is such that the hurricanes with the                                 lon lli

    more extreme central pressures tend to be smaller.  Figure 11-10 presents the                                      hurricane

    interdependence ranges of R and Ap for a wider segment of the coast comprising the

    area of interest.  For purposes of computer application, the joint cumulative

    probability distribution of R is modified to conform to the limited range shown                                   '

    on Figure II-10 for any specific ap selected within the range of -0.9 to -2.6

    in. Hg.                                                                                                                                           alongshore
                                                                                                                                                 hurricanes

          The cumulative probability distribution of the forward speed of translation

     for landfalling, exiting and alongshore hurricanes is presented in Figure 11-11.
                                                                                                               Figure 11-4.  Designation of Alongshore, Landfalling and Exiting
                                                                                                                             Hurricanes Depending on Track Directions Relative
                                                                                                                             to Shoreline Orientation

                                               7                                                                                                8

                                                                                                                    CHARLOTTE CO.
           .o00                                                    (260, 1.00)                                         LANDFALLING  a EXITING STORMS
                                                        ,"(240. 0.94)                                    1.00                                                  (40,1.00)

    o
           0.75 -     exiting      alongshore   landfalling                                          c
     s~torms                          storms  storms                         -    a
                                                                                                    o,75
                                 :  *        ~I       .    (220, 0.60)

          0.50-                                                                                     m a

                                         lSO, 0.40)                                                       00                            ,  2Q  50)

                                                                                                    0 0.025  , /

                    0.25                                                         -                                                          0,
                                            "   z                                               o"        a~~~~~~000.25

          v                1 0.00 50
            0*050         100          150          200          250          300

                                                                                                     0o (5 0.00)
                                                                                                        0            tO          20            30           40-.
                  Direction from which hurricane originates with respect to
                  North, oN (degrees)                                                                                    Radius to maximum winds,R(n.m.)

                                                                                           Figure 11-6. Cumulative Probability Distribution of Radius to
                                                                                                        Maximum Winds for Landfalling and Exiting Hurricanes
    Figure 11-5.  Cumulative Probability Distribution of Hurricane
                 Track Direction

                                                                                                                           10
                                9

                             CHARLOTTE CO.

                          ALONGSHORE STORMS
                                                                                                                                    CHARLOTTE CO.

                                                           (D0  [38.5,1.00)                                              LANDFALLING  a ALONGSHORE STORMS
                                                                                                       1.    1.00                                                           (-2.6,1.00)

    C*
    o     0.75                                                                                                                                                         07 5

                                                                                                      0.75                                                   /(-L9 .75)

          0.50

    .-c
                                                             10   20 30 4

    D      0.25
    r0                                                                                                   Q hn 0 0.25                         0
    0       0�.0700.0
                                                                                              Io_

              0            10           20          30            40                                c
                                                                                               �....u-_ 0    OpVr0.8 000)
                        Radius to Maximum Winds, R (n.m.)                                                   0          -05           -1.0         -1.5          -2.0        -2.5          -.0

                                                                                                                             Central Pressure Deficit, A P(in. Hg.)

     Figure 11-7.  Cumulative Probability Distribution of Radius to                            Figure I1-8.  Cumulative Probability Distribution of Central Pressure Deficity, Ap.
                    Maximum Winds for Alongshore Hurricanes                                                   for Landfalling and Alongshore Hurricanes

                                      11

                             CHARLOTTE CO.
                            EXITING  STORMS                                                    60'
                                                       /-t63 LO).                                                      Io.,)

                                                                                               50_                            \\

    c                                                                                                                                    0-  _
    "10                                                                                                                                  0

             c   025                                                                                                                         0    �

             0n~                                                                                40                     I

               o0                                                                                                     P                       o -2.0
                                                                                                0 1
                         Central Pressure Deficit  L P (inHg.)                                    0                    -to                 -2.0                -3.0                  -40
                                                                                                                       center pressure deficit  P Ih.Hg.)

    Figure 11-9. Cumulative Probability Distribution of Central
                   Pressure Deficity, Ap, for Exiting Hurricanes                                 Figure 11-lO.  Interdependence of Central Pressure Deficity. Np. and Radius
                               Pressure Deficity, AP. f                                                          to  Maximum Winds,   R
            cvCnta Jrssr  Deii                        Pi~g)o-o.

                                    -I0/ -                         Z.

                                                                                        For the landfalling and exiting hurricanes, the track position is determined

                                                                                   by y coordinate, YF' representing the landfall or exit point (Figure 11-3).

                                                                                   Figure 11-12 presents the actual landfalling position defined by YF and the

                                                                                   associated cumulative probability distribution. Figure II-13 presents the cumu-

                                                                                   lative probability distribution of offshore distance of passage, L, for along-

                               CHARLOTTE  CO.                                           shore hurricanes.
                   LANDFALLING, ALONGSHORE, EXITING
                                   LSAFA   TOR M AL MS   ETIGTo generate a parameter (say R) in accordance with the statistical distribution,
                                   STORMS
                                                               I.O(18C\.o)  ~a random number is generated between 0 and 1 and the associated R value interpolated
                                                        (18.0,1.o0
                        'a,3~~~~~~~~~~~~~~ /                                                ~from the cumulative probability distribution.  Since the cumulative probability

    0d)                                                    /distribution (cdf) is the integral of the probability density function (pdf), the
    aj)
                              0.75O~~~~~~~~~~ /:~ ~slope of the cdf is proportional to the probability of occurrence and thus the
            0.75 j
    3,C70)                                                                                 method above yields the correct population of the parameter (in this case, R).

    E                                                                                       2.4  General Overview of Storm Surge Numerical Models and Procedures
    o
         0.50                                                                                   In the establishment of the return period vs storm surge relationship, two

    �                                       /                                              numerical models were employed to obtain the best combination of accuracy, detail

    ->,/                                                                                    and economy.  The first model employed is a two-dimensional (2-D) variable grid

    D>       025                                                                            numerical model and may extend over a shoreline length of 100-200 n.mi.  The
    -oc
    0 C
                                                                                    purpose of the 2-D model is two-fold:  (1) to verify and develop confidence in

                          Ent~~~~~~~ /                                                  ~~~~~~~~the 2-D model by comparing predicted storm surges with those caused by storms of

        0                     (1(6, 05)                                                    record, and  (2) to provide a data base of storm tides for calibration of the
                0           5            10           15           20                     faster and more economical one-dimensional (1-D) model.  As inferred, the 2-D

                            Tronslation SpeedVF(knots)                                  model is much more expensive to run than the 1-D model.  The ratio of run times

                                                                                    is approximately 200:1 to 400:1.

     Figure 1-11.  Cumulative Probability Distribution of Storm Translation                     The flow chart presented in Figure 11-14 describes the general methodology
                    Speed VF, for Landfalling, Alongshore and Exiting Hurrica             and relationship of the two numerical models to the overall computational process.

                                15
                                                                                                                             16

             1.00O,

                                                                                                                                              CHARLOTTE CO.
             c 0.5                                             /         ____                                                           ALONGSHORE STORMS

    .aC:.     50                                                                                           0 750.-,

    o                                                                                                                   I

                               18025
    LL-

                       I125  -100   -50   -                                                                                                                              o 10    r
       "0                                                            .~

                                                              c17~~~~~~~~~~~~0(o~o                                                2    0   40  o                                  70   0

                                                                                                               The following sections describe each of the two numerical models, with

                                                                                                          illustrative examples from Charlotte County.

                                                                                                          2.5 Features and Solution of the Two-Dimensional Numerical Model

    Develop 2-0 variable             Calibrate 2-0 variable           Choose'hurricane char-
    grid model                       grid model against                acteristicS in a d                          As noted previously, this is a variable grid two-dimensional   del for the
                                   recorded storm tides              ance with historical offshore and coastal areas which affects the generation of storm tide for the
                                                                    data for the study area
                                                                                                          particular county of interest. For Charlotte County, the grids of the model

                                                                                                          are arranged in such a way that

                                                                                                               1)  The finest grids cover the coastal areas of Charlotte County to yield

      ~ Deelo  1-  moel adruRu11cssec   oladaingextn                                                          detailed information for the study.  Fine grids are also used in locations where
    the same cases for land-               and alongshore hurricanes with 2-0 variable
    falling, exiting and                   grid model                                                         calibration of the model results against measured storm tides is going to
    alongshore hurricanes
                                                                                                          take place.

                                                                                                               2) The coarsest grids cover the north, south and seaward model boundary

                                                                                                          areas where detailed information is not needed.

    H Correlate results              Simulate storm                    Rank storm tides                            3) A number of grids varying gradually in size are used for'the transition
    of 2-0 to I-D                    tides-joint                       and calculate
                                    probability                      return periods                          from the coarsest to the finest grids.
                                    analysis
                                                                                                               This arrangement of the varying grid system of the two-dimensional model

                                                                                                          gives good efficiency of computing time utilization.

                                                                                                               The size of the finest grid is 1,000 ft. x 5,000 ft. and the coarsest

                                                                                                          50,000 ft. x 35.500 ft.  The two-dimensional model covers an area of 188.3 n.mi.

              Figure 11-14.  Flow Chart of Methodology                                                        X 167.0 n.mi.  with the eastern side in approximate orientation with the
                                                                                                          shoreline of Charlotte County.  Figure 11-15 shows the grid system layout.

                                                                                                               The two-dimensional hurricane model is an implicit finite difference system

                                                                                                          in which the three governing differential equations are the two vertically

                                                                                                          averaged equations of momentum and the equation of continuity. The solution to

                                                                                                          the equations is carried out by a fractional time step procedure.  The advantage

                                                                                                          of this fractional time step procedure is that it is time and space centered to

                                                                                                           first order. The finite difference equations appropriate for implicit solution
                                                   19

                                                                                                                                                    20

                             CHARLOTTE COUNTY                                                              are solved by the "double sweeo"method, and will be described later in this section.

                                 18:.3 n.J.    .                                                          The surface (wind) and bottom (friction) shear stresses, the barometric pressure,

                                                                             _1  He 7 uirormdy           the Coriolis effect, the components of slope of the water surface and the boundary
                                                                             -V.ring grid.
                                                                         (   V O   -15.0 n.n-            conditions are all incorporated into the solution processes.
                                                                            -  t4.icac s~rv

                                                                    7 In r.         . ufonyInlets and barrier islands which are too small to be resolved by the
                                                                             f.,drving grids
                                                                    i(;7--     .7 ...                      normal grid sizes are represented in the model by a special treatment.  The
                                                                i Ah  Pi     3~~ constant
                                                                (~]         ~~~~grids - 10.n..=;.
                                                                                    Sll ~~grids .         boundary conditions specified on the two-dimensional model are that the water
                                                                             tow~ .,niforlt
                                                                             "'V.7rg grids                surface displacement on the boundaries where water is present are equal to
                                                                             -12.7 -1.aa'.
                                                                        ., .4.1 .       .s                 the barometric head, due to atmospheric pressure variations.  The normal
                                                        ________ ____   ___ _______ (5   uniformly
                                                                                      .ausfryir:  ~       discharge at these boundaries is that necessary to satisfy the volume requirement
     ::CR1 1T-ISE�CT I� .....................- . . . -_.--------- ----___---------__--bn                                        -     -

    .sZD~R.�I�O  ....................... SNAgld~.  ..=_______,.-co by the rising and falling water surface encompassed by the boundaries.  Although
    TsSRZ  RISECT LINE.----------------   - -                               -------- .-u c--

                                                              <   + t  -  X  12 uniforasg 9this is an approximation. if the boundaries are sufficiently distant from

                                                                   xL_   '? - eon14st.nt gris              the site of interest, any extraneous effects of this approximation should be
                                                      ) ~~~~~~~~~~. 1 r. ....Gl .... . n.m1.
                                                                   Z,..    N                               small.  The second type of boundary condition is the no-flow requirement which

                                        +r~                             ~~~                              ~ ~ 4,~~~ ~~~~~~ y  ~ensures that the flows are zero normal to grid lines where land elevations

                                                                             18 uniformly
                                                                             ./r1lng grids                exist that are higher than the adjacent water elevations.  At times when the
                                                                             -51.2 n.n;.
                                                                        I.8   -51~1.2 n.ni~. ~             elevation of a rising water surface exceeds the land elevation of an adjacent

                                                                                                          grid block, that block is flooded by a simple algorithm and vice versa for

                                                                                                          the "deflooding" from grid blocks at times that the falling water surface
                                                                   ______   S constant  grids
                                                                             " }   _ c~s  *    ;4-1 n m-leaves a block exposed.  The effects of vegetation on bottom and surface friction
                                                                             7 uniformlg
                                                                             -,SA.FE  grids nmfactors are accounted for in an approximate manner.

                  6 constant grids            -                 ..ifor ng
                       "7.4 -a..                   14 const   -! rying grids
                  ______2==~ ~4    -grids-2.3 n.I.                   1  . u.s.;.                             Governing Differential Equations For Two-Dimensional Numerical Model
                                  40 uniform         11 un2forle J  J11 . nscant
                                  s.riqv.ryng grids grids    n...                                                The governing differential equations for the two-dimensional model are the
                                  grids-10.2 n.-.3. n.mi..

                                                                                                          two vertically averaged equations of momentum and the equation of continuity,

                                                                                                          given by:
               Figure 11-15.  Grid System Layout for Charlotte County

                                                21
                                                                                                                                                    22

                    aqx   qx aq    q  aqx       an D        TW    lb                                            f       = DarcyWeisbach  friction coefficient
                     a    x +    + Da= 9                 O    x          x    q   (11.1)
    M*�omrentum                                                                                                  B      = Coriolis parameter = 2n sin p
        ...Sutions + q q                                    T+  Tb                                              A      = angular speed of earth rotation = 7.27 x 10-s rad/sec

                    at    0 ax   D                         ay   ay P  aPX                                               = latitude of site of interest

    Continuity      an    aqx    q  (11.3)
    Couation       31 Iat +    -ax    ay                                                                The surface and bottom shear stress components are related to the wind

    in whlich                                                                                      speed W and discharge components by

                qx I
                        = volumetric transport components per unit width in                                               =

                 qy       the  {Y}  directions                                                                   W
                 t      =time

                 D      = total water depth (h+n) including the still water depth,                            |  x           fqIq  =    2X   + q 2                              (1.5)
                           hS and the storm surge,                                                               bD2 8y               q

                        = storm surge above mean water level
                                                                                                in which K is an air-sea friction coefficient developed by Van  orn (3);
                 x      = horizontal coordinate, directed offshore
                                                                                                 and depends on the wind speed as follows:
                 y      = horizontal coordinate direction according to the

                           left-hand coordinate system                                                                      1.110    for W Wcr                                   (.6)

                 g      = gravitational constant                                                                            1.  x 10Wr)2   for W>.
                 p      = mass density of water                                                                                 x      +        x

                 p      = barometric pressure
                                                                                                 where Wcr = 23.6 ft/sec.

                 ( Twx i                                                                           The quantity, f, is the Darcy-Weisbach bottom friction coefficient and varies
                 |X :     wind shear stress components in the  {Y   directions                     with depth, bottom roughness and vegetation, if present.  For pufposes of
                                                                                                 this study, f was developed by Christensen and Walton ( 4) of the University of

                                                                                                 Florida and is presented in Figure 11-16.

                        = bottom shear stress components in the         directions                  nite Difference Forms of Governing Differential Equations
                  y                                                                                      The finite difference representations of Equations (11.1), (11.2) and (11.3)

                                            23                                                                                              24
                                            23

                                                                                                                                                             qx  6qx
                                                                                                are expressed as follows with the convective terms (i.e., -  TX- , etc.) onmitted

                                                                                                in preparation for an implicit type of solution.  The solution to the equations

                                                                                                will be carried out in a fractional time step procedure.  This procedure is

                                                                                                schematized in Figure 11-17.  The advantage of this fractional time step procedure

                                                                                                is that it is time and space centered to first order.

                                                                                                     The finite difference equations for the first portion of the fractional

                                       1   1   1                                                time step that are appropriate for the implicit method of solution are:
                                      LEGEND
                                       GULF AREA                                                          n+�        n+l        n+     e                                           (11.7)
                                       MANGRoVE AREA Ai  i  + i                                                            i    i         i
                    lo0-  -- -   -    GRASS AREA                                                                      1
                                       FORESTED AREA

                                                                  \/0                                Ai qnx+lj     B  nij + Ci qi,   ' D(11.8)
                                                               08J___  __ __ - -_1_X1~1,~j                              lj         iXj

                                                          /\                                   where Eq. (11.7) represents the momentum equation in the x-direction and Eq. (11.8)

                         \0                       /                                             represents the continuity equation; these two equations are to be solved simutaneously.
                                   -- _     _7- _ _   _   _          dD- v-
                            \                2'         A.-*--                                  The second set of simultaneous equations which is solved subsequent to the solution

                                                                                                of the first set is

                                                     _ + A* qn+l    + 8*                                                      no                                                     +C qy1  = '*A  (11.10)

         0
          o                       6                      lo                      15
                                       DEPTII (leet)

    Figure 11-16. Bottom Friction Coefficients for Various Bottom Conditions.

                                                                                                                                            26

                                                                                               Inlet and Barrier Island Representation as Hydraulic Elements

                                                                                                    Inlets and barrier islands represent features which are too small to be

                                                                                               resolved by the normal grid sizes (= miles) of the numerical model.  Thus, these

                                                                                               features are termed "sub-grid" features and must be represented by a special

                   n+�                                                                           treatment.
                  nn+
            '1
                                                                                                    The domain of interest here is the two adjacent half grid blocks with a

                                                    Eq. (7)                                      sub-grid feature imbedded in the grid line common to the grid blocks, see

               n+�i  n                         ni-�  ,   n+1                                      Figure 11-18.  The grid line can be oriented in either the x or y-direction and
              qx  ' q y                       qx
                                                                                               here is indicated generically as in the i-direction with the direction of flow

                  Eq. (8)                            Eq. (10)                                     occurring in the s-direction. The sub-grid feature can consist of the following
                                                     nn+                                         combinations:

                                                                                                                  a)  a barrier of a prescribed height, and frictional

                                                     Eq. (9)                                                             characteristics, extending over the full length,
                                                                                                                       DL of grid line,

        Time level                   Time level                     Time level
                                                                                                                   b)  a barrier of prescribed height, width, WB, and
           n                           n+�                             n+I
                                                                                                                       frictional characteristics. The remaining width,

                                                                                                                       (DL - WB), of the grid line is considered too

                                                                                                                       high for flow to occur over the top,

       Notes:  (1)  Vertical links denote equations which are solved
                    simultanteously.                                                                                  c)  a barrier of prescribed height, width and

               (2)  Values adjacent to the horizontal bars indicate                                                        frictional characteristics with an inlet of
                     the time level of the different variables entering
                     into the computations.                                                                                designated width, WI, depth and frictional
                                                                                                                       characteristics occupying a portion of the

                                                                                                                       grid line length.

    Figure 11-17. Schematic of Implicit Method of Solving Momentum and
                  Continuity Equations

                                        27
                                                                                                                                          28

                                                                                                       The computer program allows flow to occur over the barrier if the

                                                                                               average water elevation as determined from the two adjacent grid blocks exceeds

                                                                                               the barrier elevation. In addition the appropriate flow occurs through the inlet,

                                                                                               if present.

                                                                     tGEND                                 The section below describes the methodology for representing the

                                                                   Barrier of                     barrier/inlet features and of incorporating this representation into the
                                                                i Infinite Elevation
               DS                        DS                                                               numerical formulation.

                                                        I|~~ X          Barrier of
                                           --- -  -   XX      -   ~-   -IE}S Elevation                Methodology
      .....~~~~~~~ Elevation
                           .%X xx
                           \< xx

                                                                EI 4   /Inlet                               Consider the following simplified form of the monentum equation

                                           IZZ ~~~~~~~ v .~~~ , 4  1expanded in the s direction (direction of flow).

          Center  of (i-l>
                   1   ~~~Grid  $  X       (i.j) Grid                                                                      af 1qqs5q
            {'Grid -  g (h  +   n)   an                                                                                                                         2

                                    B/2 aqs .                                                                                                  n 8(h+ n)

                                                                                               in which qs is the average discharge per unit width in the s-direction and

                                                                                               h + n  represents the total water depth.  The application of Eq.(II-ll) is relatively

                                                                                               straight forward to a normal grid block in which there are no sub-grid features.

                                                                                               This results in the following finite difference form.

    Figure 11-18.  Region of Interest in Description                                                                           n                         -               1 1
                  of Sub-Grid Features.                                                                                    qngh+n)  I                          2

                                           29
                                                                                                                                     30

                                                                                                                         2                      2       2
                                                                                                                       f1Q1 DS     + (K n+KeX) IQI   fB  B DsB
    in which                                                                                                           L   8g(h+n)   W2 2(h+n)I W"I    g2(hn)B WB

                              8 (hn)                                                                                        2g(hrn)B Ih

            In order to utilize the existing framework for solution of the finite                  or

    difference equations, Equations (II-12)and (-13) are modified slightly to                                         B_    __                                                     (11-17)

                    qn+l +Ir   q                      n_ n(                                        in which
                                                                                                               a I              +

                                                                                                                    8     3         2Wg  (h+) WI 2

    factors F; and F.                                                                               and a similar expression applies to s      Eq.(II-15)can now be expressed as

            The only invariant in the flow in the s-direction is the total discharge.
                                                                                                              sat- F1W(h+n) GS
    Thus we first integrate Eq.(II-ll)over the I-direction to obtain Q, then integrate                              at

    over the s-direction between the centers of the i-  and i grid cells.  The                      wheref Ds

    resu~lt of the first integration is                                                                                    8(h+ ) W

                     -Q.   - W ( +                     n)l-. Z                   (11-15)    a n -i                  G  -a W (h+n)  Inlet Only Present and Active
                     - s    gW (h +     anEi)                                                      Sub-GridI s
                         at             as T8(h+n) 2                                               Contri-         GCB   c BWB(h+n)B  Barrier Only Present and Active
                                                                                                bution                                                                           (11-20)
    in which W represents the local width at some locations, i.e. W-W(s).  The                                               G                            Both Barrier and

    last term which represents the flow resistance involves a sum since the flow                                        I[                                and Active

    properties a; various locations along the grid line differ.  In order to express                                              a]       L      I

    this flow term as a funciton of QJQJ, we consider that the flow over the grid line                               To carry out the integration of Eq.(II-19)in the i-direction, it

    will be friction-dominated, i.e., equations the head loss across the grid line                   is necessary to know the approximon of an  with s.  Inspection of
                                                                                                is necessary to know the approximate distributn  �

    and introducing  entrance and exit loss terms.                                                  Eq. (II-19)reveals that

                                        31                                                                                               32
                                                   = Sub-Grid~~~~~~~~~~~~~~~~~~3

                                                                                                                     D     K       -              QfQDEcs As
                               I                                                        at                                                                        I                         IDS~--gr ue(~)   (II-25)
                    as       n                                                     (11-21)                                a                         QQG  As                              (11-25)
                         ws  (h+n)n
                                                                                                    in which the sub-grid term entering into the two summations should be considered
    where
                                 1,1 if inertia-dominant                                             as effective values and will be expressed in detailed form later.  Reducing
                        m,n -
                                 2,3 if friction-dominant                                            Eq. (II-25) to the form of Eq.(II-11)by dividing by (D1 � DS), and inserting the

                                                                                                    expression for K
    For purposes here, we will consider that

                         K    122                                                  (1I-22)                                   -        E    An.   As DS As
                    as          2w2                                                                           -F m                                        - DLDS
                           (h+))  -       qqGs As                                                                                                                                        11-26)

    in which K represents a constant to be determined by equating the result from

    integrating Eq. (11-22) with the total (known) An between the centers of the                                                                1Ls                                       ( 27)
                                                                                                                     at     g(h+ n) A                W
    two adjacent grid cells.  For the grid-line where both inlets and barriers are                                      at              As  7DL(h+n)W  (hi-n)- DS

    present, the right hand-side of Eq. (11-22) will be represented by the respective
                                                                                                    Thus, by comparison with Eq.(II-14) we see that the expressions for F1 and F2 are
    widths of inlets and barriers. The result is then

                                 Da1         Ds2             WI                                                        F        1          [_             Ds2         WI

                        n   K   (h+n2      (I)            (h+)2W      (h+)    J                                              DL(h+)      >      )1                  i(h+n)1

                                   (hC~)3"3_1                               g(h+n I  'h+22B  W:)B
                                +  22]        W,)(11-23)  +                                                                           I  +          ](11-28)

                    K pi

                                                                                                                     F;2  1.0 +    [I + G2 + (GI  GB or Gi)]  qlDT                    (11-29)
    which defines p as the bracketed term in Eq. (11-23)-  Eq. (II-19)can now be

    intetraged over the total length of the domain of interest to yield
                                                                                                   This completes the description of the treatment of the sub-grid features.

                   DS  -- g  Ws (h+n) a            ) as  - QQzsGiAs               (11-24)

    which can be simplified to

                                                                                                                                            34
                                            33

    Boundary Conditions
                           ~~~~~~~~~~~~Boundary Conditions  ~effects (represented by the pressure and wind stress components) on each cell

         To complete formulation of the problem, boundary conditions must be                       are calculated and the finite-difference equations (Eqs. (II-7), (II-8), (11-9)

    specified at the boundaries of the grid presented in Figure II-15. On the "open"               and (II-10) employed.  The results are updated values of n, qx and qy for each cell.

    (water) boundaries, the water surface is specified to be that associated with
                                                                                                Implicit Solution of the Finite Difference Equations
    the barometric pressure, i.e.
                                                                                                    The solution for each time step progresses by first solving Eqs. (11-7) and

                            p (     P. .I-0                                                       (11-8) simultaneously for each j grid line sweeping over all values of i.  This
                               P 9,3                                              (iI-30)
                      jpg                                                                         establishes the values of nn'1 and q    for the entire (i,j) field.  The pro-

    in which p  denotes the far field barometric pressure.  In addition, on the                    cedure is then repeated for Eqs. (11-9) and (11-10) in which this pair of equations
    open boundary grid cells, it is specified that only discharge components                       is solved simultaneously for       and  y   for the entire (i.) field.  This
                                                                                               is solved simultaneously for nn~  and q~yrteetr  0J il.Ti

    perpendicular to the boundaries occur and that these discharges on the exterior                latter pair of equations is expressed sequentially for each value of i, then solved

    boundaries of the grid system are those required to satisfy the continuity                     for all values of J, for that particular i grid line.  The expressions for the
                           ~~~~~~~~~~~equation (Eq. 11-8).               ~various coefficients are presented as follows:
    equation (Eq. II-8).
         On the "closed" boundaries, i.e., at the shoreline where land elevations

    are higher than the adjacent water elevations, a no-flow boundary condition is                              A  = g(hn)
                                                                                                                        Ax
    specified perpendicular to that boundary.  However, "flooding" and "deflooding"                                      fq n  at

    of grid blocks adjacent to the boundaries can occur.  Flooding occurs when the               Bi     :   iJ

    water level is greater by a specified small amount than  the ground elevation

    of an adjacent grid block.  When this condition exists, the grid block is activated                         C  =A

    by a simple allocation of this excess elevation on the newly activated block and                            D   .       + a    a                                 nX
                                                                                                                  xi~J       a        x-               -OTl
    in subsequent time steps the grid block is incorporated into the normal calculation                                1,                p    ax       P         yq

    scheme.  Deflooding occurs when the water level on a grid block drops below a                               At
                                                                                                            A1 4ax
    specified level leaving a very small depth on that block.  The block is "deactivated"

    and the excess water placed on the adjacent grid.                                                          B. = 1.0
                                                                                                                   at
         The solution is started from an intial condition of zero water surface                                C=       t

    displacement and zero discharge components.  The hurricane system is translated

    along a specified path at a designated speed.  At each time step, the hurricane

                                             35
                                                                                                                                       36

           i      1 At   /  nil    n  \         a       nq
                  ,I   4At   n        n         At                                              With the coefficients specified as detailed In Section 11.1.5.2, the method
                             (~~~ ~                  \1+3 i                               of solving the sets of simultaneous equations will be described.  The method is

      nn       F          +q       +q           + q;       1                              termed the "double sweep" method in which the first sweep involves "conditioning"
                     qyi~j  [           i-1,j+1     i~i+1J                               two sets of auxiliary coefficents (Eil Fit E, F').  The second sweep determines

      n           /n\2           (n       x2                                              the values of n and q and, in the process, incorporates the required boundary
     qyil.j   "    qx1~)    + (qyi. )                                                     conditions.  The procedure will be illustrated for Equations (11-7) and (11-8) and

                                                                                        it is noted that the same exact procedure is applicable to solving Equations (11-9)
    A -q(h+n) At
     j       2   Ax                                                                       and (11-10).  The procedure commences by establishing two auxiliary equations with
              flq;,jjAt                                                                   four variables (Ei. F1, EL, F*) which are initially unknown,
           - 2
               8(h+ri)

    Cj =-A                                                                                                    n+�       qn+l
                                    j~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i   x.-I
        C. = -A                                                                                                    =E1 qi.+ F1                                                  (II-31a)
       qn              [      (+) A        t    - n             (h-i-) At nn                                            E   n+I n+I
                 Iqy                                             0 L  2Ax  A  Ji -1                         q p* n                              F                               (11,31b)

             Tw               1                                                                      Eqs. (11-31) and (I1-32) are substituted in Eqs. (I1-7) and (I1-8) and the
              +          ")                                                                    -results simplified to yield

    -n       1    q          nn                   g                                                           n+I          C        n-i-A                                       (11-32aF
       -q   4     x        x%          x                                                                      Xq  A     AE-+B.   'i-11i   A.E-+B.
     i'i         9i,j        i xlj-1  j9"+l,j    xilj-                                                                    iii

                                                                                                                      C*    ~          Di-A-jF+
                 '-'V          + )2                                                                                     1 1  1    i~j n )2  n+1,  E   q n+j     AE-i            (II-32b)
            'Ixix                  ly In                                                                        j      Atit+R#   x          E~I+B

                                                                                             Comparison of Eqs (11-31) and (11-32) establishes the values of the unknown
    A*- At
     j   2z4Y                                                                             coefficients (E, F, E*, F*) in terms of the known coefficients (A,B,.    A*B*....

    t= 1.0
     j                                                                                    The expressions are
     Cl   -At                                                                                                        C~j            Dt-AtF,
                                                                                                         1    -Aide- Fc     .A I  I                                         (11-33)
         +            At   n         qn     a      t    qn+I    -  n+1                   I   I                                           1
                 ij    6ax  X9+1.       13 /           \   i+lJ      xij  /                                           C                  1.-A F
                                                                                                            Et_~ =  1    ~  ii                                              (134
                                                                                                          I-1      A E +B+       i-I   A.E++B8

                                  37                                                                                                 38

         To illustrate the manner in which boundary condition information is in-

    corporated into the procedure, suppose that water surface level, n, is specified                   Dynamic Wave Set-Up
                                                                                                          When waves break, a shoreward directed force in addition to the wind stress,
    at i = IMAX and that q  is specified as zero at i = 25.  The first sweep commences                        hen waves break  a shoreward directed force in addition to the wind stress,
                            ~~~~~~by noting (from Eq.~ (11-31a)                ~is exerted on the water in the surf zone.  This causes an additional rise in water
    by noting (from Eq. (Il-31a)
                                                                                                     level termed "wave set-up". This effect has been studied extensively in the
                        EIMAX = �.                                                     (1-35) 0laboratory (Saville (5). Bowen et.al., (6 )), and tide gage measurements during

                           : -_n+~
                        FIMAX   nIMAX,j                                                                severe storms have confirmed its importance in nature.  Most of the information

                            With the values of E  and F  known,- E*  and F  can  be                   c alrelative to wave set-up has been developed for "regular" waves, that is for a
    With the values of EiMAX and FIMAX known, EiMAX~i and   *         can be calculated
                                            fohnvleof AX I  andIMAX-   computed fromwave train in which each wave is the same as the preceding wave.  Waves in nature,
    from Eq. (11-34), then values of EIMAX_l and FIMAXli computed from Eq. (11-33)
                                                                                                     however, are not regular and tend to occur in groups.  A recent analytical study
    and so on. E* and F'* are set equal to
                                                                                                     by Lo ( 7 ) has shown that for natural wave trains there is a dynamic wave set-up
                        Et= Ft = 0.0                                                   (11-36)
                         1                                 I                                           that is approximately 50% larger than would be predicted by a static treatment.

    in accordance with the boundary condition and Eq. (II-31b).  This completes the                     In order to evaluate this result, model studies were conducted in the large

    first sweep and establishes all the coefficients over the grid line.                                University of Florida wave tank.  It was found that the experimental and analytical

         The second sweep simply consists of applying Eqs. (II-32) from small i to                     results by Lo were in approximate agreement.

    large i (IMAX).  In summary, the "double sweep" procedure as presented here, pro-                          The maximum dynamic wave set-up,  max,  across the surf zone can be shown

    gresses from large i to small i for the first sweep (conditioning the E, F, E*, F*                   to be approximately

    coefficients), and then progresses back from small i to large i for the second                                                     r            HbI

    sweep (determining the n, qx values from the coefficients).                                                         nmax = 0.285  1- 2.82 ( )] Hb                                     (11-37)

         It can be shown that this procedure results in an exact solution of the tri-
                                                                                                      which includes the dynamic factor of 50% and in which T is the wave period and
    diagonal set of simultaneous equations represented by Eqs. (11-31).  As noted
                                                                                                      Hb is the breaking wave height based on the deep water significant wave height, Ho,
    previously, the same procedure is then applied to solve Eqs. (11-9) and (II-10)
                                                            th                                         taken approximately as
    which completes establishing n, qx and qy at the (n+l)th time step.                                                   b k  0.94                                                        (11-38)
                                                                                                                     Hb - 0.94 H�

       It is noted that other combinations of boundary conditions at the t'o ends                        The deep water significant wave height is determined from an extension of a
       of tne grid line could beaccomodated.  Also, internal boundary conditions
                     n+l
       of the type q    = 0 are satisfied by the choice of coefficients: E*  =F*  = �.                   method recommended for hurricane generated waves as summarized in the Shore
                    xi,j
                                                                                                       Protection Manual (8),

                                               39                                                                                                 40

                                   (Hma . R(Ap/100) ( 0.208 VF
                                                                                (11-39)           2.6  Features of the One-Dimensional Numerical Model
                                                     (416
                                                       R                                                 As noted earlier, a simple one-dimensional numerical model was developed

    where R - radius of maximum winds in nautical miles, Ap - central pressure                          and calibrated to allow the statistics to be generated based on simulation

    deficit in inches of mercury, VF . translation speed of hurricane in knots,                         (calculations) of many storms and associated storm tides.

    and UR � maximum sustained wind speed in knots.  For purposes here the local                             The one-dimensional numerical model is described as follows.  A transect
    effective deep water significant wave height is based on the local winds, U,                        line is established along a line which is approximately perpendicular to the

    at the surf zone area of interest and the maximum winds in the hurricane, Umax                      bottom contours.  The characteristics ({p, R, a, VF and track) of the hurricane

    as                                                                                                  are defined and the hurricane is advanced along the track line.  The water sur-
                                   H0 -(H) max                                     (11-40)           face displacement (boundary condition) at the seaward end of the transect line is
                       o             a Umax
                                                                                                 taken as the static response of the water surface to the barometric pressure
    Equations 22, 23, 24 and 25 provide the basis for determining the maximum
                                                                                                 deviation at that point. The locations of the three transect lines for Charlotte
    dynamic wave set-up within the surf zone.  The computed value of n'   was
                                                                       max                        County are shown in Figure 11-15.  Figures 11-19 , 11-20  and 11-21  present
    added to the nearshore storm surge.  It is stressed that *I  represents the
                                                               max                                 the profiles of the three transect lines and their one-dimensional grid represent-
    maximum dynamic wave set-up across the surf zone and that this value varies
                                                                                                 ations.
    with time (since the wind speed varies with time).  The value of nma  was
                                                                       max
    computed at each time step for the shoreward grid, and added to the corresponding                   Governing Differential Equations For One-Dimensional Numerical Model

    surge value resulting from wind stress, barometric pressure and the effect of                            The one-dimensional numerical model is significantly less expensive and
    astronomical tide to yield the combined total storm tide history.                                   simpler to run and is used in the long-term simulation phase, in order to generate

         With this combtined total storm tide history thus determined, it is a                         the required data within budgetary constraints.  The justification for using the

    simple matter to search in the computer to obtain the maximum of the combined                       one-dimensional model is that it can be adequately calibrated with the rather

    total storm tide at the site of interest.                                                           complete two-dimensional model.
                                                                                                       The one-dimensional numerical model is the Bathystropic Storm Tide model by

                                                                                                 Freeman, Baer and Jung (9) and is static in the x-direction model. The governing

                                                                                                 differential equations in the x and y directions are:

                                                                                                             6n   1 ITwx        ]                         1                         (11-41)
                                                                                                             6x   gOD   p     yj   pgx

                                                                                                                          -o Tby                                                    (11-42)
                                                                                                             4t 1(y 4 "by)

                                           41 42

                        Charlotte County -  North Profile                                                               Charlotte County  -  Middle Profile

                                                                                              0

                            ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~200
    Ui_
                           -ioo~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i
                            -300~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~-0

       -'00 3
    L --00

                                                                                        Q_
                         I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~L

                         a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -t~oo
    o                                                                                              w   -'coO

       -Sao
                            -500~~~~~~~~~~~~~~~~~~~~~~~~~-0

       -600   . . . . . ............-o
                            -soo~~~~~~~~~~~~~~~~~~~~~~~~~~~~-o
            0     100000    2    00000 30000 0 ROOOO    500000   600000   700000    800coo   ......   ..........
                                                                                                 0      100000   200000   300000   '100000   500000    00000   700000   eoo3oo
                                     DISTANCE (Feel)
                                                                                                                         DISTANCE (Feel)

       Figure 11-19. Profile of tue North Transect Line and its One-Dimensional               Figure 11-20.  Prolle o1 tile iiicle Transect Llnc and its Oiie-iioensioilal Grid iclrcocntatiou
                    Grid Representation

                                                                                                                        44
                                            43

                                                                                          in which all variables are evaluated along the transect line perpendicular to

                                                                                          shore and passing through the site.

                          Chorlotte County - South Profile

        zoo

    co. -2oo

        -300

       t-oo
     .  00

       -300

       -500 -

            0       100000    200000    3000C0    400000    500000    6000'0    700000   e0oo0C

                                     DISTANCE (Feel)

    Figure 11-21.  Profile of the South Transect Line and its One-Dimensional
                  Grid Representation

                                        45
                                                                                                                                46

    Finite Difference Forms of Governing Differential Equations                                           2.7  Long-Term Simulation
         The finite difference forms of the governing one-dimensional differential                             With the statistical characteristics of historical hurricanes available and

    equations (Eqs. 11-1) and (11-2) are:                                                                 the simple one-dimensional model calibrated as described previously, the long-

                                                                                                       term simulation (500 years, generally) is carried out.  The first phase of the
                        qn+l    1  qn  + A-rtTw                                         (11-43)          simulation comprises the selection of the hurricane characteristics in accordance
                            Yi     Yi q     P - Wyi
                                  w I                n+l    n+l                                         with the historical data.  In each storm, this involves the following (also,
                   nn~~l  n~l      wx      Pi nl-         -i '  i+l
               n+l   n+   ax         i       n+l     i        pill                       (11-44)         see Figures 11-14 and 11-22).
                        ~i~l  ~  +-sq0   1~ pg
                            g. i
                                                                                                      1)  Quantifying ap, R, VF,O and hurricane track in accordance with the historical
    where  probabilities (Section 2.2).
                          f * tlqn I
               BB = 1.0 +      D    i                                                    (11-45)         2)  For these characteristics, a random astronomical tide from the hurricane

                                                                                                            season is generated as a boundary condition to the one-dimensional numerical
    where the variables are as defined previously for the two-dimensional model.                               model and the model is run to determine the storm surge at the site of interest.

                                                                                                           This storm surge is then adjusted in accordance with the factors obtained
    Initial and Boundary Conditions For the One-Dimensional Model
         The one-dimensional model is initiated from a condition of rest (qy E O) and                         from the two-dimensional model calibration runs.
                                                                                                      3)  For the landward grid and each time step, the contribution due to dynamic
    zero water surface displacement (n = 0).  The only boundary condition required is
                                                                                                           wave set-up is included to yield the combined total storm tide.
    that at the seaward end (i = l) of each transect where the "barometric tide" is                           wave set-up is included to yield the combined total storm tide.
                                                                                                      4) Determinine whether enough storms have been simulated for the n-year simulation.
    imposed as
                                                                                                      5)  After the required number of storms and associated storm tides have been simu-
                              P-                                                        (11-46)               lated, the peak water levels for each storm are ranked and the return period,
                              Pg
                                                                                                           TR, is calculated, according to

    Explicit Solution of the Finite Difference Equations                                                                           TR - 500                                                     (11-47)
         Eqs. (11-41) and (11-42) are solved sequentially for each time step with the                                                    M
                                                                                                           where M is the rank of the combined total tide level. (For example, if the
    hurricane advanced along its specified track with the initial position of the                             where M is the rank of the combined total tide level.   (For example  if the
                                                                                                           simulation was carried out for a 500 year period, the highest combined total
    hurricane at a sufficient distance to allow the longshore transport qy to be free                         simulation was carried out for a 500 year period, the highest combined total
                                                                                                           tide level would have a return period of 500 years, etc.)  Finally, by
    of any artificial transients.  The solutions of these equations are straight                              tin   es retn eio   p                              e , et          inal,
                                                                                                           presenting these results on semilog paper, it is possible to interpolate
    forward and free of any potential instabilities.  At the landward grid the wave
                                                                                                           for the return periods of interest, i.e.,^ TR = 10, 50, lO0 and 500 years.
    set-up is superposed as described previously for the two-dimensional model                                for the return periods of interest, i.e., TR   10, 50, 100 and 500 years

    (Section 2.5).

                                               47                                                                                                   48

                                                                                                            11.  APPLICATIONS OF STORM SURGE METHODOLOGY WITH7 SPECIFIC ILLUSTRATION BY
                                                                                                                  EXAMPLE TO CHARLOTTE COUNTY

                                                                                                            3.1 Two-Dimensional Model (Appendix A)

                                                                                                                 As noted previously, the two-dimensional model is first verified using storms

                                                                                                            of record and then employed to generate a data base for calibration of the one-
                                        _ andrFll
                             /lAp. R. R, . V \                                                                  dimensional model.
                                        YF' - AHM
       Random                                                                                 -Verification With Storms of Record
                                                                                        0 (Radom590
       _fR~ando                          Alonloshore             Generae Altrono.l r.l      Run iSimple                Several examples will be presented comparing measured and calculated storm
       Xo. Gen.)    A     1(RftNl6    a p, R.          "          Tide rA(t) randoly        I - Din madel
                                        L. - AMP               as boundary condition          nl)(t)           tides for storms of record.  In these comparisons, an attempt was made to extract
                                                               to slrple i-DOi model
                                                                                                            the astronomical tide and only tide measurements were generally used for comparison

                                        E3x itig                                                               since the more abundant high water marks can be shown to contain significant
                                       Ap. R. VF.
                                       |F-                                   AM                         P      extraneous effects.  The calculated storm tides were based on a parameterized

                                                                                                            hurricane which is undoubtedly responsible for some of the differences between

                                                                                                            the measured and compiled tides. The parameters were allowed to change along the

          sRrnk ~ cobinesd totalculate I~   S.~                         ].I                '                     hurricane path in accordance with measurements of these parameters.
       storn tides cnd talculate
       recurrence intervals culAe YeUdd qs)(t)'-.Sa (1)                                                                The only appropriate storm tide located for calibration for Charlotte County

                                       E1~  I                                           required was the September, 1947 hurricane.  The parameters for the 1947 hurricane used

                                                                                                            for input into the program are presented in Table 111-1. Water level measurements

    Figure 11-22. Flow Chart for Storm Tide Simulations (After Calibration to Determine (AMP)Lwere available at three locations: Manasota Bridge, Venice and Fort Meyers and
                  (AMP)ALONG and (AMP)ExIT)
                                                                                                            the comparisons are presented in Figures 11I-1, III-2 and 111-3, respectively.  It

                                                                                                            is seen that although the peak surges due to this hurricane were not large (= 4.0 ft),

                                                                                                            there is generally reasonable agreement between the peak measured and measured

                                                                                                            storm surges, with the maximum deviation being approximately 0.5 ft for the

                                                                                                            Manasota Bridge (Figure III-1).

                                                                                                                 Comparisons conducted for Franklin County included Hurricanes Agnes (1972) and

                                                                                                            Eloise (1975) with measurements available from the St. Marks tide gage.  These

                                                    49                                                                                                    50

                               TADLE 111-1                                                                            SEPTEMBER 1947 HURRICANE- Monosolo Bridge

                                                                                               5
                Input Parameters for Calibration Hurricane

                         Hurricane of September 1947

    date    ti~e         A    P            VF              R              11C                                                                             -  ~
              (EST)       (in.11g)      (knots)        (n.mi.)       (degrees)
    9/17       1900         -1.)S          5.4         3     4    0 9 .

    9/11      0100          -1.95          6.6           34.0           107.7                   at..uoed
              0700         -1.95         13.1           34.0           117.3                  W
                                                                                            O
              1300         -1.95         17.9          34.0            116.5                        2
              1900         -1.95         22.3          34.0            122.6
    9/19       0100         -1.40         21.0           34.0           121.6
                                                                                         0
                                                                                         Cl,
           Starting coordinates.                  Landfalling coordinates:
               Xs .  43.8 n.mi.                       XF= -4.2 n.mi.
               Y  = -60.5 n.mi.                       YF m 78.71 n.mi.

                                                                                                 9       10       11     12       13       14      IS      16        17      Is       19

                                                                                                                                 TIME (Hours)
                                                                                                                                Seplembet 0. 19.17

                                                                                       Figure 111-1.  Comparison between Measured and Computed Storm Tide at Manasota
                                                                                                      Bridge. Florida for the September 1947 Hurricane

                                    '51
                                                                                                                               52

                          -SEPTEMBER 1947 HURRICANE- Venice                                                                            SEPTEMBER 194       7 HURRICANE - Ft. Myers

                                  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4

                                                                                                                                      I ~~~~I-___ I  -             -.--2-"
    z3                                        I                                                                     3                                                                     '
                    It.           ..-.--*-   I                I        jm~~~~~~oSurted    LOi                                                                                 cew.Duled~
                                                                                                            73

                               2    ~~~~~,iErpled 2
    o                                                                                                            z

           /i

        0
          33       14      35       16       37      l8   1 9         20       21       22      23                    0
                                             TIME (Hours)                               I0                                      33      12        3   1 4   I 5            I6   1 7          .16      19       20
                                             Seplemberla,394;7                                                           �                                     TIME(Hours)
                                                                                                                                                          Seplembcr 38. 3947

       Figure 111-2.  Comparison between Measured and Computed Storm Tide at Venice.                                  Figure 111-3.  Comparison between Mreasured and Computed Storm Tide at Ft. Myers.
                       Florida for the September 1947 Ifurricane                                                                      Florida for the September 1947 Hurricane

                                                     53                                                                                                    514

                                                                                                                                                    TABLE 111-2

                                                                                                                                  Input Parameters for Calibration Hurricanes
    input data for these hurricanes are presented in Tables 111-2 and 111-3 and
                                                                                                                                            Hurricane Agnes (June. 1972)
    the comparisons are presented in Figures III-4 and 111-5 for Hurricane Agnes

    and Hurricane Eloise, respectively.  For Hurricane Agnes, the peak measured tide

    exceeds the computed by approximately 0.8 ft, whereas for Hurricane Eloise, the                           date         time             Ap             VF               R              eN
                                                                                                                               {EST)        (in. Hg)       (n. mi.)         (n. mi.)       (degrees)
    peak computed tide exceeds the measured by approximately 0.5 ft; on the average                                        (EST)         (in. H)        (n. mi.)         (n. mi.)      (degrees)

    this is considered reasonable agreement                                                                   6/18         1900           -0.92           12.0              20            180.0

         In the CCCL study for Nassau County, comparisons were carried out for Hur-                          6/19          0100          -1.04            13.0             20            180.0
                                                                                                                               0700          -1.04            11.0             20            184.5
    ricane Dora (1964) and Hurricane David (1979), using the input parameters presented                                      00           -1.04           11.0              20            184.5
                                                                                                                               1300          -0.89             9.7             20            201.11
    in Tables 111-4 and 111-5, respectively.  Measurements were available at Fernandina                                    1900           -0.79           10.0              20           205.8

    Beach and Mayport.  The comparisons are presented in Figures III-6, III-7, 111-8                          6/20         0100           -0,68           11.2              20            224.4

    and III-9.  In general the average agreement is considered good.                                                   Starting coordinates:                 Landfallng coordinates:
                                                                                                                          Starting coordinates:                 Landfalling coordinates:
         In summary of the comparisons shown (and others available but not shown for                                         Xs = 220.2 n. mi.                        XF=  4.2 n. mi.

    Dade, Broward and Walton Counties), the agreement between measured and computed                                          Ys =  45.4 n. mi.                        YF   40.2 n. mi.

    storm surges is considered good. We regard this comparison/validation phase as

    useful in demonstrating the validity of the model and ensuring that the nearshore
                                                                                                                                                   TABLE 111-3
    bathymetry/topography is represented adequately.  Differences that exist in the                                                             TABLE    -3
                                                                                                                                          Hurricane Eloise (September, 1975)
    peak surges are believed to be due to the wind field structure of the specific                                                    Hurricane Eloise (September, 1975)

    hurricanes, i.e., a measure of the deviation from the idealized hurricane used as

    input and other factors such as the difference in air-sea temperature which in-                           date         time              p             VF               R              eN

    fluences the wind surface stress coefficient.                                                                          (EST)         (in. Hg)       (n. mi.)         (n. mi.)      (degrees)

                                                                                                                 9/22         0100          -0.59            10.0              18           175.0
    Generation of Data Base for Calibration of One-Dimensional Model                                                       0700           -0.80            7.1              18            187.1
         With the two-dimensional model validated, a data base is generated spanning                                       1300          -0.98            11.2              18           224.3

    the hurricane parameters of interest.  This data base is subsequently employed                                         1900           -1.33           15.2              18            223.5
                                                                                                                 9/23         0100          -1.63            20.0              18           205.8
    for calibration of the one-dimensional model which includes more severe approxi-                                       0700           -1.72           28.5              18            190.5

    mations to the physics of the hurricane problem.                                                                       1300           -0.91           27.8              18            205.9

         To illustrate the range of hurricane parameters included in the data base,
                                                                                                                          Starting coordinates:                Landfalling coordinates:
    TablesIll6, 111-7 and 111-8 present the cases selected for Landfalling,                                            Starting coordinates:                Landfalling coordinates
                                                                                                                              Xs = 292.2 n. mi.                         XF - -31.8 n. mi.
                                                                                                                              Ys = 238.3 n. mi.                         YF =  76.6 n. mi.
                                                                                                                                                       56
                                                 55

                                                                                                                                     HURRICANE ELCOISE- St. Marks
                            HURRICANE AGNES - St. Marks

                                                                        I~~~~~~~~~~~~~~~~ 4
                           LO~~~~~~~~~~~~~~~                                                                                                         -  . .-

                               H                                                                                                                               I~~~~~~~~~~I

    Jun I              S      , 22Jn                      9         172TM HUS

                                           ~~~~~~~~~~~~~~~~~~~~~~~~~~Foid'-.ae for kurcn lie                                                                 I175

           Florid for97     JlurceAnes (1972                                                                                                           IM)(OUS

                                                           57                                             so

                                   TAOLC 111-4

                   Input Parameters for Calibration Hurricanes

                           Hurricane Dora (September, 1964)

    date      time*                         VF             R              eN
              (GMT)        (In. Hg)      (n. mi.)    (n. mi)          (degrees)

    9/8        1800           -1.48          13.1        20               98.80
              0000           -1.35           8.0         20             104.60                                              HURRICANE  DORA- Fernandina Beach
              0600           -1.21          10.3         20             112.88                      16
              1200           -1.27          6.0         20              120.13
              1800           -1.51          6.0         20               99.41
    9/10      0000            -1;45           6.1         20              99.41                      12-
              0600           -1.39           8.7         20              96.62
              1200           -1.30          6.1         20               96.62
                                                                                             ~                                    ...         ~    ....~ .........          measured
              1800           -1.25          3.5         20               90.00                                                                                                  mesred

        Starting  coordinates: Landfalling coordinates:
              Xs = 165.43 n.mi.                          XF = 5.17 n.m.
              Ys ' 90.00 n.mi.                           YF   36.00 n.mi.                        j  4

                                                                                                O-
                                  TABLE 111-5

                           Hurricane David (September, 1979)                                         18      19      20       21      22       23      00      01       02      03       04       05

                                                                                                                Seplember 9,1964                                September 10.1964

     date     time*            p           VF             R              eN
              (GMT)        (in. Hg)    (n. mi.)        (n. mi.)       (degrees)                       Figure 111-6.  Comparison between Measured and Computed Storm Tide at Fernandina Beach,
                                                                                                                 Florida for Hurricane Dora (1964)
     9/3       1200           -1.14        10.4           10              150.14
              1800           -1.17         8.4           10              162.07
     9/4      0000            -1.20        11.3           10              166.07
              0600           -1.23         11.0          10              175.52
              1200           -1.23        13.3           10              168.75
              1800           -1.23        10.0          10               184.92
     9/5      0000            -1.17        10.2           10              189.78
              0600           -1.05         14.2          10              190.46
              1200           -0.98        14.2           10              190.46

         Starting coordinates:                      Offshore coordinates:
              Xs - 51.70 n.mi.                           XL  15.51 n.ml.
              Ys - 150.00 n.m.                          YL    -60.00 n.mi.                                                                  60
                                      59

                                                                                                                                                      HURRICANE DAVID - Fernandina Beach
                                                                                                                       16
                                                                                                                       16        II                          I 1              1  I  ll
                                       HURRICANE DORA - Moyporl
    16                                          .1

                                                                                                                     12-

                                              o                                                                                                                                               *cmeasured

                                08~~~~~~~~~~~~~~~-

    0                                                                                              _

      18      19       20      21       22      23      00       01      02        03       04      05                  01     02       03       04       05       06      07       08      09        10       11      12
                19     20 2           I22        23      O0       01      02       03       04       05
                              Seplember9,1964                         Seplember 10.1964                                                                       September 4,1979

     Figure 111-7.  Comparison between Measured and Computed Storm Tide at Mayport, Florida                            Figure 111-8.  Comparison between Measured and Computed Storm Tide at Fernandina Beach,
                       for Hurricane Dora (1964).                                                                                        Florida for Hurricane David (1979)

                                                              61                                                                                                 62

                                                                                                                                                                                                                  Table 111-6.
             B~ ~~HURRICANE DAVID - Moyport                                                                                                                                                                          Table II-6.
                        I a   I           L          I           I           I          I                       j I                                                                      Parameters  Defining  11  Landfalling  Storms  Used

                                                                                                                                                                                         In Calibrating The One-Dimensional Model With
     6.                                                                                                                                                                                       The Two-Dimensional Model And The Results

                                                                                                                                                                                                  Landfalling           Starting
                                                                                                                                                      SAP       R             F          eN       Coordinates          Coordinates                                'nmax. (ft. H.S.L.)
                                                                                                                                          MODEL                               FO
                                                                                                                                                                                                     n. ml.)             (n. mi.)
                                                                                                                                          STORN
                                                                                                                                             SOM(In.-Mg)   n. mi.)   (n. ml.)   (degrees)    XI              r y         5        y           North Profile        Middle Profile        South Profile
                                                                                                                                                                                                                                             1-D       2-0      1-0          2-0   !     -0       2-0
                                                                                                                                              2I  1  -1.6       20          12           225       -2.5   12.0       102.29    -14.13         9.28    10.64    11.03         12.15       11.54   12.50
                                                                                                                                              2      -2.2       20          12            225      -2.5    12.0    102.29        -14.13      11.57    13.37    13.68         15.03       14.33    15.53
                                                                                                                                              esue *.3  -1.2    20          12           225       -2.5   12.0    102.29        -14.13         7.81      8.86      9.33      10.27        9.75    10.66
                                      a......0_~~~~~~~~~~~~~~~~~~~~ ~4                                                                                -1.6        12          12           225       -2.5   12.0    102.29    -14.13            9.47    10.30    9.95         10.24        9.34      9.49
                                                                                                                                              5     -1.6        30          12           225       -2.5   12.0       102.29     -14.13        9.27    10.81    11.13        12.51        12.43    13.63
                                                                                                                                              6      -1.6       20           a           225       -2.5   12.0        98.41    -13.16          8.88      9.78   10.43        11.20       10.88   11.54

     01        02           03         04          05          06         07          08         09           10          II          12       7      -1.6        20         s15           225       -2.5   12.0       99.38    -13.40          9.57    10.70    11.46        12.32       12.03    12.77
                                                              September  4, 1979                                                               8      -1.6       20          12            170       -2.5    12.0      36.20    -88.83         10.03    10.68   10.31         10.73       10.38    10.50
                                                                                                                                              9      -1.6       20          12            240       -2.5   12.0    105.48         13.88        8.59    10.43   11.03         12.64       11.73   13.33
                                                                                                                                            10      -1.6       20          12            225       -2.5    32.0    102.29         5.87       10.58     12.49    10.16       11.95        9.53    11.37
      Figure  111-9.   Comparison  between  Measured  and Computed  High  Water  Mayport, Florida  for                                        11      -1.6        20          12           225       .2.5   -8.0    102.29    -34.13            2.34       2.99     3.30       4.11         4.81    5.65
                            Hurricane David (1979)

                                                                             63
                                                                                                                                                                                                                     64

                                                                     Table 111-7.

                                              Parameters Defining 11 Alongshore Storms Used

                                               In Calibrating The One-Dimensional Model With

                                                 The Two-Dimensional Model And The Results

                                                          Offshore            Starting
       MODEL       P                   VF          eN      Coordinates        Coordinates                               nmax. [ft. M.S.L.)
                                                           Cn. rni.)          In. mil.)
       7STRH                                                                                         North Profile    Middle Prpfile    South Profile
              (in.-Hg) (n. mi.) in. mi.)  (degrees)    XL    YL              X5         Y5
                                                                                                1-D       2-D      1-D        2-D        1-D      2-D
          1     -1.6       20         12          150        40    12       41.88       -95.98      4.83      4.81    4.95        4.81       5.02    4.65
          2     -2.2       20         12          1SO        40    12       41.88       -95.98      6.54      6.38    6.71        6.36       6.82    6.22
          3     -1.2       20         12          150        40    12       41.88       -95.98      3.73      3.77    3.81        3.77       3.86    3.65
          4     -1.6       20         12          15        40    12        41.88      -95.98      4.83      4.81    4.95        4.81       5.02    4.65
          5     -1.6       12         12           150       40    12        41.88      -95.98      3.10      2.99    3.18        2.99       3.24    2.88
          6     -1.6       30         12          150        40    12        41.88      -95.98      6.69      6.75    6.84        6.77       6.92    6.57

          7     -1.6       20          8          150        40    12        41.81      -91.98      4.68      4.38    4.80        4.37       4.87    4.20
          a     -1.6       20        1I            140       40    12        23.57      -91.71      4.35      4.08    4.53        4.14       4.68    4.02
          9     -1.6       20         12          160        40    12        60.61      -94.02      5.46      5.71    5.51        5.65       5.50    5.43
         10     -1.6       20         12          150        18    1.        19.88      -95.98      7.33      7.47    7.49        7.44       7.59    7.18
         11     -1.6       20         12          150        62    12        63.88      -95.90      3.28      3.50    3.37        3.53       3.42    3.43

                                                                      Table III-8.

                                                  Parameters Defining 11 Exiting Storms Used

                                                 In Calibrating The One-Dimensional Model With

                                                   The Two-Dimensional Model And The Results

                                                             Exiting            Starting
                  oP         R          VF           ON     Coordinates         Coordinates               "max. (ft. H.S.L.)
                                                              (n. mi.)           (n. mi.)
        ST7ORM                                                                                       Ilorth Profile      Middle Prpfile    South Profile
     (tin.-Hg)  (n. mi.)  (n. mi.)  (degrees)    XF                     F        X5        Y5
                                                                                                  I-D       2-0      1-0         2-D       1-0      2-D
           1     -1.4       20          12          100       -2.5   12.0   - 84.01    -58.85         7.14      6.53    7.94        7.37      8.23    7.53
           2     -1.6       20          12          100       -2.5   12.0   - 84.01    -58.85         7.93      7.19    8.80       8.10       9.11    8.25
           3     -1.1       20          12          100       -2.5   12.0   - 84.01    -58.85         5.97      5.56    6.66       6.29       6.92    8.45
           4     -1.4        12         12          100       -2.5   12.0   - 84.01    -58.85         6.89      6.46    7.24        6.87      6.82    6.49
            5     -1.4       30          12          100      -2.5   12.0   - 84.01    -58.85          7.43      6.71    8.29        7.53      8.88    7.91
           6     -1.4       20           8          100       -2.5   12.0   - 80.99    -56.23         7.22      6.53    8.07        7.37      8.40    7.57

            7     -1.4       20          15          100      -2.5   12.0   - 81.74    -56.89          7.07      6.56    7.81       7.31       8.07    7.36
            8     -1.4       20          12           80      -2.5   12.0   -103.33    -26.70          6.12      5.50    7.63       7.00       8.14     7.46
            9     -1.4       20          12          120      -2.5   12.0   - 54.86    -82.46          8.00      7.71    8.35       8.07       8.47    8.02
           10     -1.4       20          12          100      -2.5   32.0   - 84.01    -38.85          7.70      7.54    7.41        7.27      G.95    6.85
           11     -1.4       20          12          100      -2.5   -8.0   - 84.01    -62.85          6.35      5.66    7.43        6.77      8.06    7.21

    Alongshore and Exiting Storms in the Charlotte County vicinity.  Note that eleven               and 11-8  and in Figures 111-10 through 111-12.  In each of these nine graphs,

    storms are selected for each hurricane path category.  The last columns in these                best fit least squares curves are shown of the form

    tables contain the maximum storm surges for the coastal terminus of the three

    transects shown in Figures 11-19, 11-20 and 11-21 and will be discussed in the                                       (nmax)2-D = K (nmax)l-D                                       (Ill-l)

    next section.
                                                                                                 where for perfect agreement, a value of unity would be obtained for K.  For

    3.2  One-Dimensional Model (Appendix B)                                                          landfalling storms, the range of K is 1.09 to 1.14, and the associated ranges
         In the following, the results will be presented of calibrating the one-
                                                                                                 for alongshore and exiting storms are 0.93 to 1.00 and 0.93 to 0.94, respectively.
    dimensional model with the data base generated by the two-dimensional model.
                                                                                                 These values are reasonably close to unity and are employed in the subsequent
    In addition, the results of the long-term simulation will be illustrated.
                                                                                                 long-term simulation which uses the one-dimensional model.

    Calibration With Two-Dimensional Model Results                                                        Table III-9  presents the ranges of K values for the three categories of
          The one-dimensional numerical model represents the physics of storm surges                storms and all Counties completed to date.

    in a much greater simplified manner than does the two-dimensional model. Simpli-
                                                                                                 3.3 Long-Term Simulations
    fications in the 1-D model include, but are not limited to:
                                                                                                      As noted previously, long-term simulations are carried out using the one-
                       a) The onshore dynamics of the storm surge are not
                                                                                                 dimensional numerical model, usually for a duration of at least 500 years.  The
                           represented,
                                                                                                 study of historical occurrence ensures along with the directional distribution
                       b)  Only the hurricane pressure and wind stresses
                                                                                                  (presented for Charlotte County in Figure II-5) that the correct number and cate-
                           along the transect selected are taken into
                                                                                                 gory of hurricanes are selected.
                            account, and
                                                                                                      The long-term simulation is carried out for each transect selected, the peak
                        c) Convergences and divergences of flow are
                                                                                                 total storm surges ranked and their return periods calculated in accordance
                            not represented.
                                                                                                 with Eq. (11-47).
         Because of the omission of these and other realistic features from the one-
                                                                                                       For Charlotte County, five 500 year simulations were carried out and averaged
    dimensional model and the comprehensive nature of the validated two-dimensional
                                                                                                  for each of the three transect lines. The return period vs peak total storm
    model, the latter is considered as a reliable basis for calibrating the one-
                                                                                                  tide relationships for these transects are presented in Figure 111-13 and are
    dimensional model.
                                                                                                  summarized for selected specific return periods in Table III-10. It is seen
         Comparisons of the one-dimensional and two-dimensional peak surges along the
                                                                                                  that the 100 year peak storm tide ranges from 12.7 ft (above MSL) for the southern
     three transect lines for Charlotte County are shown in Figures 11-19, II-20 and 11-21
                                                                                                  profile to 13.1 ft for the northern profile.
     and   for each of the hurricane categories are presented in Tables 111-6, 111-7

                                              67                                                                                               68

                                                                                                                                    CHARLOTTE  COUNTY

                                                                                                                            LANDFALLING STORMS. SOUTH PROFILE
                                                                                                                      16

                                       CHARLOTTE COUNTY                                                                                   I                   I      I     �

              LANDFALLI G STORMS. NORTH PROFILE               LANOFALLING STORMS. --,;DDLE PROFILE                                   2I

          1,                                             1I
          12     i    I    I    I    I    I              ,,      i    I                                                                                                I  i  I(fi n a I  I
               Iz                        II             1011                   1,4<                                                  6                          c8:.8~

                                                          IlK  ILUL)

                6  II     !(,,,O~l 1I38 4.1-                                 ?.O.097lC                                                                  A                       lu I
                                                     I-              I' I                                                       2

           L?6  t     ~ ~~    I    Il~               IO 01C                                                                   c

                                                                                                                         0     2      4      6     6      10    12      14

            0     2  4    6   a      tO  12  14             0   2  a       6    6    tO(I4-NGV
                                                                   I-0

                                                                                                      Figure 111-10b. Calibration Relationship between the One-Dimensional
                                                                                                                       and the Two-Dimensional Calculations of Peak Surges at the
    Figure II-lOa.  Calibration Relationship between the One-Dimensional and the                                                     South Transect Line of Charlotte County for Landfallingj
                    Two-Dimensional Calculations of Peak Surges at tie north and                                                     Hurricanes
                   1iddle Transect lines of Charlotte County for Landfalling Hurricanes

                                           69                                                                                             70

                                                                                                                                                                 CHARLOTTE COUNTY

                                                                                                                                                          ALONGSHORE STORMS. SOUTH PROFILE
                                                                                                                                                 16

                                              CHARLOTTE COUNTY                                                  14

             ALCNGSHORG  STORM. NORTh 4CFIVLE                1   ALONGSHlCRE STCRMS, m.CL�  RE PRGFI                                                                                I
     '6                                                     16                                                                              12        I              I      I      I

      5    4I    I    I    I           I                                                                                                                                      0      'c
                                      ~~all~~~~~l~~~l     S 10111111                                                                                                     I~~~~~~~~~~~~1

                    12    I    I    I   I i                         I     I     I    I    I    I                                                       I_      1. 6Qmch        Oc

       0     i    I    I     I    !    I     a4           t    o la   t4                               0    2      4      6                                              a 10 121;0 2 4 6at  2   14
        ii~ ~ ~ ~~-                                                                 1-01

                    t--

                                                                                                                              Figure II-1ib. Calibration Relationship between the One-Dimensional and
    Figure 111-1a.  Calibration Relationship between the one-Dimensional                                                                      the Two-Dimensional Calculations of Peak Surges at the
                                                                                                                                                  South Transect Line of Charlotte County for Alongshore
                        and the Two-Dimensional Calculations of Peak Surges at                                                                Ilurricanes
                        the North and Middle Transect lines of Charlotte County
                        for Alongshore Ifurricanes

                                                     71                                                                                                 72

                                                                                                                                                         CHARLOTTE CO.

                                                                                                                                                    EXITING STORMS, SOLITH PROFILE
                                                 CHARLOTTE COUNTY                                                                                          10

              EXITING STORMS. NORTH PROFILE                                EXITING STORMS, MIDOLE PROFILE                                                         9
        tO                                                          10

                                        to to~~~~~~~~~~~~~~~~-

      9111                                                                                                                                                  z

       6O~~ 8                                                                                          *r                                                        N? ~�i�-~
                                                                             I 7* I               7

                                                        ZN.: 6                                                                                      -      6
    E
                      6~~~~ J/I ,,tU K
         5
                                    2-0           ID                          111

                                                                                                                                                 4   5   6   7   8 9                      10

                 5       6      7     8       9      0               4       5       6     7      8      9.      10
                         ('(mox)  (ft-NGVD)                                         lrhOc) I  (ft.-NGV0)

     Figure III-12a.  Calibration relationship between the One-Dimensional and the Two-Dimensional                                      Figure 111-12b.  Calibration Relationship betWccn the One-Diniensional and the
                     Calculations of Peal: Surges at North and M-liddle Transect lines of Charlotte County                                              Two-Dimaenslonal Calcula tilns of Peak Surges at th1e South
                      fI31 Exiting Ilurricanes                                                                                                          Transect li  e of Charlotte County for Exiting hurricanes

                                                                                                                                             74
                                                       73

                                                                                                                                 CHARLOTTE COUNTY
                                    TABLE 111-9

                           Values of 1-0/2-0 Peak Storm Surge
                Correlation Coefficients For Counties Completed to Date

                                                   Range of K
                                                     For
                                        Landfalling    Alongshore          Exiting                                 s
        County           Date of Study       Hurricanes      Hurricanes        Hurricanes

         Broward             1981             1.07*           1.07*               ***                            Co

         Charlotte           1984             1.09-1.14       0.93-1.00         0.93-0.94                                                                      9

         Dade                1981             1.03            1.34              1.13 3

         Franklin            1983             0.95-1.18         ***               ***

         Nassau              1982             0.93-0.99       0.84-0.90**       0.84-0.90**       '

        Walton              1982             0.99-1.05         ***               ***
                                                                                                     o    7

      *The calibration of the landfalling and alongshore hurricanes was combined.                                  C
                                                                                                           5          to        20             50         loo        200           500
     **The calibration of the alongshore and exiting hurricanes was combined.                                                                         Relurn Period(years)

    ***Due to their very small relative frequency of occurrence, alongshore and
      exiting hurricanes were not included.                                                      Figure 111-13. Comubined Total Storm Tide Elevation Versus Illtern P'eriod for Three Representative
                                                                                                     Transect lines in Charlotte County

                                                                                                                               76
                                           75

                                                                                             IV EROSION CALCULATION METHODOLOGY

                                                                                             4.1   Introduction
                                                                                                  The erosion calculation methodology is based on measurements of

                              TABLE 111-10                                                       beach profiles, both in an equilibrium and post-storm state and
                                                                                             reasonable approximations to the physics, where necessary. These

       Combined Total Storm Tide Values for Various Return Periods                                 methods have been under development for approximately seven years and
                                                                                             the numerical models are continually being upgraded, both as new and

    Return .Period ,   Combined Total Storm Tide Level* above MSL (ft) improved Information becomes available and in our continuing attempt to
     TR (years)            North             Middle            South                               include as much realism (for example, overwash) in the numerical model

         500                15.3               15.0              15.0                              as possible.
        200                14.1               14.0              13.8
        200                13.1               14.0              12.7                              4.2   Equilibrium Beach Profiles
             100    ~~~13.1 12.9 12.7
         50                11.7               11.5              11.4                                    A number of theories have been advanced attempting to describe the
         20                  9.3               9.3               9.0                              properties of and mechanisms associated with equilibrium beach profiles.
         10                 6.8                6.8               6.7                                    Based on a data set comprising more than 500 beach profiles ranging

    *Includes contributions of:  wind stress, barometric pressure, dynamic                         from the eastern tip of Long Island to the Texas-Mexico border, see

     wave setup and astronomical tides.                                                            Figure IV.1, the following form for an equilibrium beach profile was
                                                                                             Identified

                                                                                                                          h(x) = Axm                              (IV.l)

                                                                                             in which A and m are scale and shape parameters, respectively. Figure

                                                                                             IV.2 presents normalized beach profiles for various m values. It is

                                                                                             seen that for m < 1, the profile is concave upward as commonly found in

                                                                                             nature. Figure IV.3 demonstrates the effect of the scale parameter, A.

                                                                                                  The data from the 502 wave profiles were evaluated employing a

                                                                                             least squares procedure to determine the A and m values for each of the

                                                                                             profiles.  The results of this analysis strongly supported a value of

                                                                                             m = 0.667, (see Figure IV.4).  It can be shown that a value of m = 2/3

                                                                                             corresponds to uniform wave energy dissipation per unit water volume in

                                  77                                                                                               78

                                                                                                                           DEFINITION SKETC

                                                                                     145 ~~~~h/hI3

                                                                                                                              0.8     ~ ~~~~ (a) FOR n< I, BEACH

                                                          44~~~~~~~~~~~~.                                                                                       (b) FOR  m =I' BEACH  IS

                  504                              419      14O.0 1.0                                                                  0.6           0.6           0.4            0.2             0

                                                    50 4   4 1   --40 4            17                                                                    ~~~~~~~~~~~x/w

                                                                                                               Figure IV.2  Characteristics of dimensionless beach profile  h               xm
                                                                                                                              fo r va ri ous m va Iutes-(from Dean, (I11)).b

    IV.1   Location map of the 502 profiles used in the analysis  (from
           Hayden, et al., (10)).

                                             79                                                                                                    8

                                                                                               0.2  PREDICTED VALUE (0.4)
                                                                                                             BASED ON UNIFORM STRESS             PREDICTED VALUE  (0.67)
                                                                                                  OR ENERGY DISSIPATION                                       UNIFORM
                                                                                                  ACROSS THE
                                                                                                  ACROSS THE                         .>:          ENERGY DISSIPATION PER
                                                                                                  SURF ZONE----                                   UNIT VOLUME ACROSS
                               DISTANCE OFFSHORE  m).                                                                                                THE SURF ZONE

                                          100                               200        0                                        >        '

                                                                                         13-i

    E  i .

                                                                                                                               EXPONENT m

      Figure 1V.3 Equilibrium beach profiles for sand sizes of 0.2 ion and 0.6 mm         Figure IV.4 Histogram of exponent m In equation h = Axm for 502 United States East Coast and Gull
                  A(D   0.2 n) = 0.1 Im3, A(D   0.6 mm)  0.20    .                                    of Mexico profiles (from Dean, (11)).

                                          81                                                                                    82
                                                                                                        O~~~~~~~~~~~~~~~~~~~~. ..  ,:,
                                  10-                                                            0          0,2   0~~~~~~~~~~~~~~~~~.4  ...  0.. '... ':.:.. I.~.
                                  Ld                                                       ~'1               �                .       .       ~. ,: .,,....~. ..j~$�f:.',,NENT

                                     Figure 1Y.3 Equilibium beach profilesfor sand sizes of .21r~ and 0.6 mn   Fgure IV.4 Hlstogra  of exponent m In quation h ~ Ax" fo � �" :. :"  ..';:!:i." ".' .  a",  .u:
                                              A(D i 0.2 rm,) = 0.1 m1/3,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ '( ': 0.6 n   :.',' -'".';i roils(fo Da,'' ; .  ,.

                                                                 81~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"',''.; ,:,i .-
                                                                                                                                 :~..  .:. . ,..~'.,~...';.~  ,.

    the surf zone.  The physical explanation associated with this mechanism

    is as follows. As the wave propagates through the surf zone, coherent

    wave energy is converted to turbulent energy by the breaking process.

    This turbulent energy is manifested as eddy motions of the water

    particles, thus affecting the stability of the bed material. Any model

    must acknowledge that a particular sand particle is acted on by

    constructive and destructive forces. The model here addresses directly

    only the destructive (destabilizing) forces.  It was reasoned that the

    parameter A depends primarily on sediment properties, and secondarily on                                             Suggested Empirical
                                                                                    parameter  E                     Relationship
    wave characteristics, i.e.
                                                                                    U-j                           From Hughes'
              A - F(Sediment Properties, Wave Characteristics)           (IV.2)                                      Field Results
                                                                                                                        Field Resulls~jf~FFore Irndividual Field Profioles Where a
                                                                                                                                                Range of Sond Sizes Was Given
    where "F(" denotes "function of" and it would be desirable to combine
                                                                                         0.10
    wave and sediment characteristics to form a single dimensionless                    wj
                                                                                    -J
    parameter.                                                                          u
                                                                                    En
          A portion of Mr. Brett Moore's M.S. Thesis (12) was directed                                                     From Swart's Laboralory
                                                                                            Z   ~~~~~~Results
    toward an improved definition of the scale parameter, A.  Moore combined

    available laboratory and field data to obtain the results presented in                     .                     j        s
                                                                                                       ~~  0.01  0.1             1.0               t~~~~~~IOO         10
    Figure IV.5, thereby extending considerably the previous definition of
                                                                                                                            SEDIMENT SIZE, D(mm)
    A. Some of the individual beach profiles used in the development of

    Figure IV.5 are interesting. For example, Figure IV.6 presents the
                                                                                    Figure IV.5  Beach profile factor, A, vs sediment diameter, D, in relationship h   Ax2/3 (modified
    actual and best least squares fit to a beach consisting of "sand                                 from Moore, (12))

    particles" 15-30 cm in diameter (approximately the size of a bowling

    ball). Figure IV.7 presents the same information for a beach reported

    to be composed almost entirely of whole and broken shells.  Figure IV.8

     shows a profile with a bar present resulting in one of the poorer fits

     to the data.  It is emphasized that the analytical form (Eq. (IV.2))

     describes a monotonic profile.

                                                                                                                                84

         ~E
          0  Di~taric'  off~hore (rnetcr~ )
             cc g;.oo     1.50         25.00        317.50        50.00

                                         -   /Icu~  Prfila

                                   t-A~ ~ ~ ~ ~ ~ ~ ~~~~~~52   50.00  75.00   �00
                                                                                            ~~~~050
           �o

                                                                                                                          -  -AL.t squa.. Fitt
                                                                                         -n    -lrstsncc              -fe   [Aciu..  P.f
     Figure IV.6 Profile P4 from Zenkovich (1967). A boulder coast in
                 Eastern Kamchatka.  Sand diameter. 150 na - 300 nn.
                 Least squares value of A = 0.82 rn1!3 (from Moore,
                 (12))
            O
                                                          Laast Squwo.& Ftt.+St.r�.FL

                         ~~~~~~~~~~~~~~~~~~~~Figure    IV.8 Profile P  from  Zenkovich (1967). E  oldrcastern  K acata
                                                                                        '4-r

                                     ~~~~~~~~~~~~~~~~~~~~Measen sacata   and diameter:              0.25 mm. Lastsquresvale o
                                                                                        -, qr    auoA  0.07 m1/3 (from Moore13

                 A  .5V                                                                            fo  or,(12))  a

                                                85~~~~~~~~~~~~r
                              Oi~tz~ncc offihcre (mettcrz ) 8
              ccd~.OO     3.00         Sf2.00       90.00         �20.00                         ,

                 a                       ~~~~~- - L�aau  Sq �  Fit
                 a   ~~                   ~~~~ ~- Ac~.,a1 P;..it1~

                              o                                                          ~~~~~~~~~~~~~~~~~~Figure IV.8  Profile from Zenkovich (1967). Eastern Kamchatka.
                                                                                                 Mean sand diameter: 0.25 nasn. Least squares value of
                               3                                                                       ~~~~~~~~~~~~~~~~~~~~~A   0.07 rn1.3 (from Moore.  (12)).

    Figure IV.? Profile PlO from Zenkovich (1967). Near the end of a
                5pit inWe~ern Black Sea. Whole and broken shells.
                       A =  .25ml/j(frm More,(12))

                                  85
                                                                                                                     86

    4.3   Cross-shore Transport Models

          It has been noted that most equilibrium profiles correspond to

    uniform energy dissipation per unit volume with the scale of the profile

    represented by the parameter A which depends primarily on sediment

    characteristics and secondarily on wave characteristics, i.e.

                                                                                                                                               DISTANCE (M)
                                 h(x) " Ax2/3                            (IV.3)
                                                                                                  0.0      20.0      40.0      60.0       300      100.0     120,0     140.0     160.0
                                                                                               -Oll

         The parameter, A, and the uniform energy dissipation per unit                                        CH

    volume. v*, are related for linear spilling waves by                                         p                                                   MW0.0 -

                                                                                          o.o
                                               'p. 2/3

    It can be shown that for the spilling breaker assumption and linear                           a                                     .

    waves, the energy dissipation per unit volume, A, is proportional to the

    product of the square root of the water depth and the gradient in depth,              3                                                             -

                                                                                                                   INITIAL EStUIltIRIUMSIFACII PROIIlf
                                  5    312 2  1/2 ah                                            .
                                      h                                 (g3/22] a .5)                                                                               INItIAL =lEAK Pt.
                                                   ax 16 P9   K    T X                                             FINAL tXQUlLIURIUM IIIACII PROVILK
                                                                                                                         AITlR SEA lIVIL Rll                            3b 1.01 M

    Thus it is clear that an increase in water level such as due to a storm

    surge will cause wave energy dissipation to increase beyond the                      Figure IV.9 Model simulation of a 0.5 meter sea level rise and beach profile response with a

    equilibrium value.  It is also known that the beach responds by erosion                            relatively mild sloping beach (from Moore, (12))

    of sediment in shallow water and deposition of this sediment  in deeper

    water (Figure IV.9).  It therefore appears reasonable to propose as a

    hypothesis that the offshore sediment transport,  5  per unit width is

    given by

                                     87                                                                                          88

    where K is a rate constant that hopefully does not vary too greatly with

    scale. Moore (12) evaluated this relationship using large scale wave tank

    data of Saville (13) and found

                                 K _ 2.2x10'6 m4/N                       (IV.7)
    Figure 1V.10 presents comparisons of predicted cumulative erosion for

    various values of K with the measured values obtained from Saville's

    wave tank tests.

                         4.4~~~~~~~~~~~~~~~~~~~~~~~0
    4.4   Prediction of Beach and Dune Erosion Due to Severe Storms by                        ae        -
          Kriebel's Model

         Mr. David Kriebel carried out a Master's thesis on this subject.

    He incorporated previous work and developed considerable original                                                             *�.'      . �                                        S ' "
                                                                                             a ~~~~~~~~. -                                     -.- /.-
    contributions to this problem, including the capability to model single                    2

                                                                                                                                                              .volume .-'/011
    storm events and long-tern scenarios in which many storms occur.                                              ..
                                                                                    �                       .'                  - i,~
    Profile Schematization

                                                                                                rs-S
         The profile was schematized as a series of depth contours, hn, the             -         "'

    locations of which are specified by coordinates, Xn, measured from an                               /       ...                           K20, o

    arbitrary baseline, see Figure IV.11.  The profile is thus inherently                           /   .:/.                        a                   ..

                                                                                                       I *4f                    l~~~~~~units -f It, M4JHI
    monotonic and at each time step, the xn values of each of the active                           / .,

    contours is updated.                                                                            /N,

    Governing Equations                                     - - -                                  .......
                                                                                            0         1          tO        IIJ       10         32        :i0
         As in most transport problems, there are two governing equations.

    One is an equation describing the transport in terms of a gradient or                                                                  1110uss)

    some other feature. The second Is a continuity or conservation equation
                                                                               Figure IV.1D  Effect of varying the sediment transport rate coefficient on cumulative erosion during
    which accounts for the net fluxes into a cell.                                                the simulation of Saville's (1957) laboratory investigation of beach profile evolution
         As discussed previously, the offshore transport is defined by                           for a 0.2  mm sand size (from Moore.  (12))

    Eq. (IV.6) in terms of the excess energy dissipation per unit volume.

    Specifically, In finite difference form

                                    89
                                                                                                                        go

                                                                                                                                                      h5/2- h5/2
                                                                                                                                       V    - k         nt-I hn                          (IV.8)
                                                                                                                                        ni-    D (hi-n+ hn )(Xn+ID  Xn)

                                                                                                                  where

          xms1                                                                                                                                          k  .                                   (IV.9(
          Xmsl
                                                 _ F                                                                                                  k~~~~~~~~~~~                          ~~~~~~~~~~~~~~~~~~~~D X4      (Vg

                                         _ i~ ~~~~~~~~~~~~~~~~ _ t                                                        ~~~~The sand conservation equation is

                                   Xi'~~~~~-I~~~~ vSURGE LEVEL                                                                                             AtIV.10)
                      ___________ V___ I__n_|                                                           MSL                                         bxn . Ah- (on-                             D.+)

                                                               I\~~~~~~ l   { ~~~~~~~Method of Solution of Finite Difference Equations
          ,6h                                  I                                                                             A number of methods could be employed for solving Eqs. (IV.6) and
                             e\<      ~hi -I  I'
                             --        h      i        n                                                               (Iv.I0).  For example, explicit methods would be fairly direct and
                                                    hn
                                                               Lo-I0 hn+l                                            simple to program; however, the maximum time increment would be
                                          ~~~~~~XnI~~~~l~~~ > ,   >   | ~~~~relatively small resulting in a program which is quite expensive to
                                              _--~L -   _sp+1          I                                              run.  Implicit methods are somewhat more difficult to program, but have
                        Xn                                      ,'
                                                                                 -hn =A(  Xn-XmsI                   the desirable feature of remaining stable with a much greater time

                            Xn+1                                                                                      |step.  Because of the planned application to long-term simulation in
                                                                                  ~L  . .      .    .     .    _~ _   _   _which for a 500 year time period and on the order of three hundred
                                                                                                                   storms would be modeled, each with an erosional phase of six to twelve

                                                                                                                   hours, an implicit method was adopted.  This method will not be
    Figure IV.11  Model representation of beach profile, showing depth and transport relation to grid                    described in detail here except to note that a double sweep approach is
                 definitions (from Kriebel, (14))
                                                                                                                   used in which the Q5  values and the Xn values are updated

                                                                                                                   simultaneously at each time step. For ah values of 1 ft, and a time
                                                                                                                   step of thirty minutes, the system of equations was stable.

                                                                                                                                                    92
                                                            91

        The boundary conditions used were somewhat intuitive. At the

    shoreward end of the system, erosion proceeded with a specified slope

    above a particular depth, h*. The depth, h*, is the depth that the

    equilibrium slope and the slope corresponding to the beach face are the

    same. Thus a unit of recession of the uppermost active contour causes

    an erosion of the profile above the active contour that is 'swept" by

    this specified slope., This material is then placed as a source into the

    uppermost active contour.  The offshore boundary condition is that the                        R�

    active contours are those within which wave breaking occurs. If an

    active contour extends seaward, thereby encroaching over the contour

    below to an extent that the angle of repose is reached, the lower
                                                                                           (1)
    contour (and additional lower contours if necessary) are displaced E

    seaward to limit the slope to that of the angle of repose. LA

    Application of Method to Computation of Idealized Beach Response

         Kriebel (14) carried out computations for a number of idealizedW

    cases, some of which are reviewed below.  Details of the erosion model                          0                          0                       0                       0

    are presented in another report (Kriebel (15)).                                                                                 TIME  Whs)

         Response to Static Increased Water Level - Figure IV.12 presents

    the beach recession due to a static Increase in water.  The beach                          Figure IV.12  Characteristic form of berm recession versus time for increased

     responds as expected. In the early stages, the rate of adjustment is

     fairly rapid with the latter adjustments approaching the equilibrium

     recession in an asymptotic manner. Of special relevance is that the

     response time to equilibrium is long compared to the duration of most

     severe storm systems, such as hurricanes. The form of the response

     presented in Figure IV.12 is reminiscent of that for a first order

     process in which the time rate of change of beach recession, R, Is

     represented as

                                     93
                                                                                                                               94

                                  dR
                                  d-= _ KR                             (IV.ii)

    for which the solution is

                               R(t) = (i_e-Kt)                         (IV.i2)

    Figure IV.13 presents a comparison of the response from the numerical
                                                                                               R�

    model and Eq. (IV.12). This similarity forms the basis for a very

    simple and approximate numerical model of beach and dune profile

    response.  Such a model has been developed, is used currently in the                        Z
                                                                                           0
    CCCL program and will be described in the next section.
                                                                                           Lo
         Effects of Various Wave Heights - Considering a common increased                       LU
                                                                                           a:
    water level, but storms with different wave heights, the larger wave

    heights will break farther offshore causing profile adjustments over a                       LU
                                                                                           cm
    greater distance and thus a greater shoreline recession.  Simulations                           0
                                                                                                                       I 0  100               200
    were carried out to examine evolution of the beach under different wave                                                         TIME   hrs

    heights with the results presented in Figure IV.14. As expected, the

    greater shoreline recessions are associated with the larger wave

    heights. Surprisingly, however during the early phases of the

                                        evolutionthesdo not cause proportionally larger       Figure IV.13  Comparison of asymptotic berm recession from model {
                                                                                                          and as calculated by Eq. (IV.12) (o  *).
    erosions.  Thus, for storms of short duration, the sensitivity of the

    maximum erosion to breaking wave height may not be large.

         Effects of Various Storm Tide Levels - The counterpart to the

    previous case is that of a fixed wave height and various storm water

    levels. The results of these simulations are presented in

    Figure IV.15. In contrast to the previous case, the various storm tide

    levels cause recession rates in the early stages of the process which

    are nearly proportional to the storm water level.

                                     95                                                                                                96

                        24                                                          ~~~~~~~~~~~~~~~~~~~~~~DfCQ.3mnm                         S 2.4mn

                             ~~~~~~~~~~~~~~~~~~~MB =                                   :O 4.6m

      18-                                     ~O-                                                                                               :m -

    zz
                o~~~~~~~~~~~~~~~~~~B                                          0
    U)
     uj  2-                                                                 LiS-I.2m
                     U~~~~~~~~~~~~~~~
                                                                             20 -
                U~~~~~~~~~~~~~~~~~H 1.5
                                                                                                                                   S 0.6m
                                                                             10-

                         0   2 5      s     o           7     5         I(O       0    ~     ~ ~        ~~~~~~~~0 50  100            150              20(
                                  TIME Whs)                                                                      TIME (hrs)

         Figure IV.14 Effect of breaking wave height on berm recession (from Kriebel, (14))  Figure MIS.  Effect of static storm surge level on berm recession (from Kriebel, (14))

                                                        97 ~~~~~~~~~~~~~~~~~~~~~~~98

          Effect of Sediment Size on Berm Recession - The effect of two

    different sediment sizes on amount and rate of berm recession is shown

     in Figure IV.16. The equilibrium recession of a coarser material is

    much less; however, the equilibrium is achieved in a much shorter time

    than that for the finer sediment. The explanation for the lesser

    equilibrium erosion for the coarser material is that since the beach is

    steeper, the waves break closer to shore and thus less material is

    required to be transferred offshore to establish an equilibrium profile

    out to the breaking depth (considered to be the limit of motion).                            5

    Presumably the explanation for the slower approach to equilibrium for                               B  -1.5m

    the finer material is that, as will be shown by consideration of the                                Me =8:15
                                                                                                 ,2 S --0.3m
    initial and equilibrium profile geometries, a much greater volume of                                Hb =3.0m                         D50      =0. 2mm

    sediment must be moved a greater distance to establish equilibrium.

         Effect of Storm Duration - The effect of storm duration on                        z    9-

    shoreline recession was investigated by considering a fixed wave height                    -
                                                                                        (y)
    and an idealized storm tide variation, expressed as                                    u
                                                                                        a  6-

                   n = 1.2 cos2(  ( 8))           It-18<T                                 c/
                                                                                        Li                                           D050O.mm
                                                                      (IY.13)

                     - o                     ,   It-181> T/2

                                                                                             0
                                                                                               0                  100                 200                  300                 400
    in which T (:- 2a/) is the total storm duration in hours.  The results

    are presented for three storm durations in Figure IV.17.  For the

    shortest storm duration (T * 12 hours), the potential volume eroded is
                           shortest storm duration (T   12 hours), the potential volume eroded is  Figure IV.16  Effect of sediment size on berm recession (from Kriebel, (14))
    approximately 70 m3/m whereas the computed actual maximum volume eroded

    is 10 m3/m. With increasing storm tide duration. the computed actual

    maximum volume eroded increases. Tripling the storm tide duration to

                                    99
                                                                                                                                  100

                                                                                                        36 hours doubles the maximum volume eroded to 20 m3/m.  It is noted that

                                                                                                        this is only approximately 28% of the potential volume eroded, again

                                                                                              a8  ~     underscoring the likelihood that most storms will only reach a fraction

                                                                                 S K    X  /  >  {   a   of their potential erosion limit.  This feature also highlights the

                                                                  /�~~~~ \~~~~                           ~ /     \significance of cumulative effects of sequential storms and of the need
                                                              ///\ Surge Height and Fbtential             to better understand the recovery process (especially the rates), a
                                                                Volume Eroded
                                                                                                        portion of the cycle not addressed in this project.

                                                                                          I  /\\-       Application of Method to Long-Term Beach and Dune Response Simulations

                                  |-~~~~~ /  \  /   \          \                              S ~~~~~~~~~~~The previous section has described the application of the model to
                                                                                                        idealized examples of beach and dune response.  The model can also be

                                                                                              lS~ l\applied to more realistic situations in which the initial beach and dune

                                                                                           I  I\@conditions are specified along with time-varying waves and tides.
                                                                                                              Evaluation of Method by Hurricane Eloise Erosion Data - Kriebel

                                                                                                        carried out an evaluation of the method by comparing erosion

               ~~I I /    /                 ~~24 IRS  \_#.... -                             ~ 8               computations for Hurricane Eloise (1975) with measurements reported by
                                                                                                        Chiu (16).  Although the wave and tide conditions were not measured

                 //  i2tI~RS -A -'~ ,-                \        ~Act ual I    e Eided          .9              along the beaches of Bay and Walton Counties (Florida) of interest, some
                                                     a1 - --(Computed)
                            / -~ // -~~ -,#'~ _- ~ - -  ' \                          \tide data were available and wave heights were estimated.  Erosion was
                            8t>/c_'.X$--~~~~~~ \~~~~~~~~~~~~~                                                                  ~ \computed for twenty combinations of dune slope, wave height and peak
       .no   {e'i �   i! Jt.eo00   I.Ot   113.oo  2i.0   24.Co   2'.DO   sb.oo   ab.00    -afil
                                        TIME - IIRS                                                         surge.  It was found that the volumetric erosion ranged from 21 to

    Figure IV.17  Comparison of the effects of 12. 24, and 36 hrs. storm surge on volumetric                   38 m3/m compared to average measured values of 18 to 20 m3/m for Bay and
                 erosion (from Kriebel, (14))
                                                                                                         Walton Counties, respectively and an average of 25 m3/m near the area of

                                                                                                         peak surge. Although the predicted values are somewhat larger than the

                                                                                                         observed, Chiu (16) states that the beaches had started to recover at

                                                                                                         the time of the post-storm surveys, with approximately 5 m3/m of sand

                                                                                                         having returned to the beach. Thus the maximum eroded volume would be

                                                                                                         30 m3/m compared to a maximum calculated value of 38 m3/m, a difference

                                                   101                                                                                        102

    of approximately 27%.  This reasonably close agreement was considered                          hurricanes was assumed to corenence from a fully recovered condition.

    adequate recognizing the uncertainty in the storm tide employed in the                         This is clearly an approximation as the recovery process occurs at

    computations; therefore no further calibration of the model was                                several rates of magnitude slower than the erosion process.  Study of

    considered warranted.  It is of interest that the erosion potential                            some recovery stages from severe storms has shown that up to seven years

    associated with the peak tide is approximately nine times that predicted                       may be required to achieve approximately 90% recovery.  The duration

    for the time-varying conditions included in the computations.  This                            required for recovery from milder storms would, of course, be less.

    again reinforces the fact that most storms in nature cause only a                                   Figure IV.18 presents a "flow chart" describing the elements of the

    fraction of the potential erosion associated with the maximum conditions                       long-term simulation.  In the Bay-Walton Counties area, hurricanes

    in the storm.                                                                                  making landfall within � 150 n.mi. of these counties were considered

         Long-Term Simulation - Wit h the model reasonably verified for the                        requiring a total of 393 hurricanes to simulate a 500 year record.  The

    Bay and Walton Counties area of Florida, a long-term simulation of beach                       return periods associated with various dune recessions as determined

    and dune erosion was carried out.  The hurricane wind and pressure                             from the simulations are presented in Figure IV.19.  As examples, the

    fields were idealized In accordance with a representation published by                         dune recessions for return periods of 10. 100 and 500 years are 4 m. 12

    Wilson (17).  The five idealized hurricane parameters                                          m and 18 m, respectively.  Based on these results, Hurricane Eloise is

                                                                                              judged to represent a 20 to 50 year erosional event, however based on
                       Ap =Maximum Pressured Deficit
                                        Rmax  =  Radius   to  Maximum Winds ~~results from a storm surge analysis, Hurricane Eloise was a 75 to 100

                        VF = Hurricane System -Translational Speed                                year coastal flooding event.

                                           8 = Hurricane Translational DirectionIt is also possible to present the results of the erosion

                                         yF -   Landfall   Point  ~~~~~~~simulations in a manner that is of maximum relevance to individuals or

    were selected by a Monte Carlo method in accordance with the historical                        agencies responsible for shoreline management.  This type of

    characteristics of hurricanes in the general area.  For each hurricane,                        presentation is demonstrated for the Bay-Walton County area in

    the storm tide was calculated using the Bathystrophic Storm Tide Model                         Figure IV.20.  This plot includes the contributions from storms and sea

    of Freeman, Baer and Jung (9).  With the time-varying storm tide and                           level rise.  As examples, without any erosion mitigation measures within

    wave height calculated, the beach and dune model was applied until                             the next 50 years, the erosion due to sea level rise (regarded as a

    maximum erosion was achieved.  As the recovery mechanism is not yet                            certainty or probability of 100%) is expected to be approximately 15

    understood to a degree for realistic modelling and because hurricanes                          ft.  Within 50 years, the probability of dune erosion occurring to a

    occur approximately on a biennial basis, the erosion for successive                            distance of 40 ft is 85% and for distances of 60 and 80 ft, the

                                     103                                                                                            104

                                                                                                                                                  RETURN PERIOD IN YEARS
                                                                                                                            5          10            25         50         100       200           500
                                                                                                                         20

                                                                                                                                                                                                7

                                  RANDOMLY CENERATE                                                                         15
                             U HRRICANE CHARACTERISTICS
         BEGIN                   IIN ACCORDANCE WITH
        NYEAR                 HItSTORICAL METEOROLGY.                                                                   - '
        EIOSION SELECT INTENSITY, SIZE,
      SIMULATION j             SPEED, DIRECTION, AND                                                                                                                           /
                             LOCATIOt, AS UELL AS THE  CALCULATE STORH                        CALCULATE WAVE            i

                                                                      INTEREST USIlA   INTEREST  USING I ERS
                                                           COL/ EBATIIYSTROPHIC             LOCAL WIND SPEED          5J                        O
                                                                     STORM SURGE  MODEL MODEL
                                                         /O NO                                    MODEt

                          IS  \                    /    IRSO  \                                                               . CALCULATE BEACH-DUNE EROSION  -
                       U N-YEAR \EyTS  /ESINLE STORM\                        FOR PROFILE AT SITE OF                                                                           O
                     SIHULATIOtI      -             SIHULATION   ~C       INTEREST USING BEACH EROSION  /
                      (frCOMPLETE   (14)).        \Caro COMPLETE?/      MODEL BASED Ol EOUILIBRIUM BEACH                                          /
                                                                                 PROFILE THEORY

        ANALYZE RESULTS:
        (1) STORM SURGE FREQUEINCY CURVE
        (2) EROSION FREQUENCY CURVES FOR:                                                                                                                     1
                DUNE RECESSIOtl                                                                                              .2          .1        .05      .03   .02       .01       005           .002
              VOLUMETRIC EROSION
                                                                                                                                      PRO8ABILITY OF OCCURRENCE OR EXCEEDANCE

    igure IV.18  Flow diagram of N-year simulation of hurricane storm surge and resulting beach erosion                Figure IV.19  Average frequency curve for dune recession  developed by Monte
                 (from Kriebel, (14)).                                                                                               Carlo simulation, Bay-Walton Counties, Florida (from Kriebel,
                                                                              ( fro mS~ K106iebe l,  (14)).                           ~~(14))

                                                            105                                                                                              106

                                                                                                 corresponding probabilities are 32% and 9%, respectively. Through the

                                                                                                  use of figures such as these it would be possible to weigh the costs of

                                                                                                 certain erosion control measures against the potential of damage if

                                                                                                 those measures are not carried out.

                                                                                                       These procedures provide, for the first time, a basis for

                                                                                                  conducting the necessary technical studies to implement the erosion

                                                                                                  component calculations of the Flood Insurance Act of 1973 which provides

                                                            so-  l~ - 18%                           for the application of methodology to provide the basis for insurance

                                                                                                  rates for flooding and erosion coastal hazards. Although the flooding

                                                                                                  component of this act has been Implemented, the erosion component has

                                                                                                  not.

                                                       -    /-/ /    J'    . ~'f   /   _--J .-"-  ~  4.5   Prediction of Beach and Dune Erosion Due to Severe Storms by
                             - - -                 - -       26%  - - - -                                   Simple Model

            L !/                       -                    -                                               For computational ease and economy, a much simpler erosion model

        W  40                                                                                          was developed and is applied in the CCCL process (Appendix C). This model is not
                                            � ~ '       ~    ~99.9X    ""''
                                                                                                  physically-based, yet retains the overall characteristic response

                                                                                                  described previously in the Kriebel model.

        2~0 ~'////~.,/.,,,~~             - . ...~-sc~xTER                                                   The model is based on the characteristic response exhibited in
                                                            EOSION TREND -
                                                        DUE TO SEA LEVEL                            Figure IV.13 and Eq. (IV.12) rewritten for reference purposes as
                                                              RIEOF 1

          . '~*J     ~R(t)   (l.-Kt)                                                                                                                                         (IV.14)
              0 ~~~25                       50                75                o
                                       2 5          7        5              ~~~~~~~~~100 R

                                 YEARS FROM PRESENT
                                                                                                  At each time step, for the instantaneous value of the time-varying water

    Figure IV.20  Probability or risk of dune recession of given magnitude
                                      occuring a  leas  oncein N-earsBay-Wlton  o., Foridalevel S(t) and the selected breaking wave height. Hb, the equilibrium
                  occurring at least once in N-years, Say-Walton Co., Florida
                  (from Kriebel, (14))                                                                profile and the associated equilibrium recession, R_, from the existing

                                                                                                  profile is established, see Figure IV.21. The characteristics of the

                                                                                                  equilibrium profile are:

                                                                                                  (1)  the eroded volume above the "hinge point" equals the deposited

                                         107                                                               volume below the hinge point,
                                                                                                                                  108

                                                                                                 (2)  The equilibrium profile is in accordance with Eq. (IV.I) with the

                                                                                                      scale parameter either specified by the user, or determined as a

                                                                                                      best-least squares fit to the measured profile during the field

                                                                                                      program, and

                                                                                                 (3)  the equilibrium profile above the instantaneous water level is

                                                                                                      characterized by a uniform slope, NMD, on the order of 2 or 3 as

                                                                                                      determined by post-storm profile measurements following Hurricane

                                                                                                      Eloise (1975) and other storms.

                                                                                                      With the equilibrium profile established, the erosion occurring

                                                                                                 from time t to time t+At,Ax is given by

                               ")>~~~~~~ '.  ~~~~~~ax - x(t+At) - x(t) - - R (1-e 'rt)                                                                                     (IV.15)

                                           Instantaneous Uater Level at Time, t
                          *.  ~~~~~~i ~~~-..~~~  ,-~ _- ~                                  _           _where, through calibration with Kriebel's model, a K value of 0.075

           ,x. b   ;      Bea ch Profile at Time, t  St)                                             sec-1 has been found.
                                                        I-ealSea Level
    t
                                                    ,,-Hean Sea evel                                     Figures IV.22 and IV.23 present examples of application of the

                                                        Beach Profile for ijater
                                                           _  ~ui~li~b(  BahPoiefr U   Xerosion model to two ranges in Martin County.
                                             Lov S( f'auted Beach Profile A
                                          ~'~.-  .  ~   -- --__   Time.taat                                Agetto
                                                            ;Aiaculated Beach Profie at          4.6   Augmentation of the Erosion Predicted by the Model for
                                                                                                       Recommending Position of CCCL

                                                                  -.^ - * - ~~~~ ..2S~As noted previously, the erosion model accounts only for cross-

                                                                                                 shore sediment transport and has been verified against the average

                           Figure  V.21 Features of simplified beach erosion model                   erosion occurring in Hurricane Eloise, see Figure IV.24.  As documented
    Figure IV.21 Features of simplified beach erosion model
                                                                                                 by Chiu, there are a number of factors which result in considerable

                                                                                                 variability about the mean value.  Probably the greatest causes of this

                                                                                                 variability are the gradients in longshore sediment transport as a

                                                                                                 result of the relatively small scale of the hurricane system, and

                                                                                                 natural variability due to inhomogeneities in the system (sand size,

                                                                                                 consolidation, offshore bay system, etc.).  Regardless, the variability

                                      109                                                                                              110

                                     20   .     .                                                                                                       20         f.....~~~~~~~~~~~~~~~~~~~~~~2
                                             ............                                                 4..                             ...                          .*...... ... *.:::.....*....... ....                                              ..*. I...........
                            ~~~~~~~~~~~......4. .+..    ............. f..*.                                                                                                                                                                           I...4.~.                        ....... ..-......
    ...... .                            , .....~                               .... r-   1....                                                                                                                            . .... ...                         .. 4.....  .4...4....4.4.4.
                                               10  .-.4....4.4..4..4....4.4.....,.....i.4.....4.....4.4.4.....4.4.....4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...........4...4... . . . . 1...  .... . .      . . . . . . . . . . .....*..

                                         .... ..*... ....1    4..... ..... ...... ....~.   .. ~.   4.        ~     .      .......                              .~..... .....    -    1                     ..... ....4.   ~-+...4.-....t*
                         ,   ~~                         ~~~~~~~~~~~~~~~~~..........4. .... . ......          ..*.... ..        4. 4......4. ..    ~ ...*N,.,                                                              -4.           -..4.-.4..4. .4.                         4...-...
                                                         .. . -.  .i  1 - . i..*.,*   I  I.  +     ~~~~~~~~~~~~~~~~~.- . ,  4          4    . 4                .4 . 4   .    4   ~ ~   ~ ~  ~  ~  ~  ~  ~ ~  ~ ~ ~    . 4 -~~~* . 4 . 4.....4~~~~~~~~....4 . *.....4.- . i....................I...... . . . ................. .
                                                                                                                                                                                                                                                ...4.. ...*....4..4             4
                               . ........ . ..-.~~~~~........ ~     ~ ~          4  4...4.....*....4.4.....*..-.4.4.+.-.4..~~~~~~~~~~.....         .      .       .     .           . . . . ............._4f...................... ....
              ~~~~~~~~~~~~~~~~~~~....... ..... ..*... ..... ...4. .  ...4......4.  .*.4. ....4.....4.   .     4....      4.....*.-..      .....*                                                              .                                                                                ..... �.
                                                 4.....4....4.4.....4....4.I . . 4 . 4.....4            ....4.4.4.....4.4.*.                                  .~~~~~~~~~~~~~~~~~~~~...+.....-......4........4   .--i.to-.........._4...... . . ... .......................................
                                 ~~~~~~~~~~~~~~~~~~~~... 4  . .        ..                             .. .....                                                                                            4....... ........
                                  . 4.4.-.4.~~~~,..* . 4..4    4  4....,   .     4.4      .    4....4.I          .     -.4~~~~~~~~                            ...J~~..4...........4..4....................4.............. .......:            4.... .... i .... ....
     -20: .       .               .               .               *.....,.          -                ...4.--   -0                                                                                          F----- --4-- ----.4-  ...~.. ,.........~
                                         ~~~~~~~~~~.4.4....    ...,...  I i..    . ........   . ~. 1                            1..... ....4...                                   ....4.... . ......i.....4. .4....'. .4... . ... ... ..4..                . .i.4.. ...4......4
                -~~~  ~~~~~~~~~~~~~~.-. .........~....... ...... ..... ..    ...........      ...4... . .. I..4...4.      ...4.... .       4.....              i.... ...~. .4...4. ...       .. .....   -. ......      ..,....    ..  ,.. ...i.. . . .... ... .     .....+.....j. ......-... .... .
                                                                                                                                                                          *    ~~~~~~     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.4...  ...
                .... ......4..4.i....4.i.                                                                                                                                                             .-.4..4...
             ..........~~~~~~~~~~~~~          ~      .         4........                                                                                                                                                                  .4.... ....                 .....
                      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... ... ..            i:.4...J.A................ . ... ......... .....4  A......... .                    .....A..A...
                                                                                                                                                  -....---- . .44 ..4-i--i---~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-                                                  4         . ... ..
                          . ..4...4.....4.......4.4*.... ..4....4......4                                   .      . . .*....4.4............4....                           .4.....4................ ..............4 .........................
                                                   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.                                                                                                    ..4.. .....4:  ..t2::::: ....4.....4.....                         -. .. ..-.....-....-. . . ......
                                                                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......*. . 4.4...~.......4..    ....t                                                                                                                                              4......
                                                                                                                                        .... ......... ;_4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .4~
                                                                                                                    ;4   .....   ......   .   .   .....   .....  ...... .......... ... ;.  ........~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-~
    -.............00 . 00                                                              800           .   ...............-...200 .                                                                    20              40           60            800           100           120            140           1
                                                              IlIONUNENII                                                                FEET                                     III0N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iIENTI                                                     FEET~~~~~~~~~:1  n   .....

                                                             I OFFSHORE    PROFILE  ~~~~~~~~~~~~~~~~~~~~~~~~~~~  MARTIN  I  I   R-1                         j OFFSHORE    PRO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iLE  C04J,41V.   MRR~~~~~~~~~~~~~~~~~~~~~~~~lN  ~ ~ ~ ~~~CE.    R-8......-----
                       ~~~~~~~~~~~~~~~~~-: -tNE  . .. .....
      10                                                         -~~KIA-40744I  iIiNO    EICE   4SOISIMH4EITEIBIIEI                                                    -     -    UVTIDVSO    FBRCE       HRSIIOUIEIEIB   iE: 1-
              _4 4    ., i   ...   ...  ...                                                    ...  ... ... ....... -4                                                             1N-11fl-4la~4i i__ -.-i;.   ...  4......                            I
                                                                            EI~~a~~iD-FMK 5440,  FLII.OEFI.OF  NATURAL  RESOURCES  BER~~~~~~~~~~~~~~~iND,   Out ,.40RrH  IIIAG.I  -.---.-  Eonozo-F.4~~~~~~~~~~~~~on 5440.  ....L....EF.. I.......U.......E.O...C....B........,...U....0.0044
                                                ....~~~~~~~~~~~~~~~~~~~~~~~Fgr   I.... ......... of- ....in   erosion  ....... to  Range--                                                                                                       .-9   .....i   ....... ......e               sad..................
                 Figue lV22 Rsult  of  pplyng  rosin moel t  Rane R-, 1-artn Conty  Hutcinso  Islnd),                                                     .         .        .         year.stom.tie,.aerag.ero.on
        .....10   ....  .....  .....  .vrg   erso...........

                                                                         ......... .......                                                                                                              .1....1..2..... .. ... .. ......... ......

                                                                                                                         of erosion is recognized and as documented by ChWu (16) in Hlurricane

                                                                                                                         Eloise, the maximum erosion was approximately 2.5 times the average

                                                                                                                         erosion.  This factor is incorporated in the erosion considerations

                                                                                                                         employed in the recommended CCCI position by modifying Eq. (IV.15) as

                                                                                                                         fol l ows

                                                                                                                                                     Ax  -  (2.5) R (I-e-Kt)                    (IV.15)

                                         Average weasured and computed erosion
                                         distance in Walton county by Hurricane
                                         Eloise (Septe ber. 1975).                                                     which, due to the long beach response time compared to the time scale of
        25
                                                                                                                         storms. results in a profile which is in approximate accord with the 2.5

                                                                                                                         factor.
        20

    z   15
              .�                                       ~~~~~~~K

        o 0

                                                                             %%com'puted
                                                measured              '      cospted
                           ,,'                    ~                             %'~t~~~~~~~~~~~~~~~~X K.-0.07. 1HD-3

               20        I0      0           -I0       -20      -30       -40        -50       -60

                                     erosion distance o vario us conlours {f)

            Figure IV. 24 Calibration of Simplified Erosion Model By Comparison with Erosion
                           Occurring at Various Elevation Due to Hurricane Eloise

                                                           113                                                                                            114

    V  WAVE HEIGHT DECAY CALCULATIONS                                                                National Academy of Sciences (NAS) (18) has developed recommended

    5.1  Introduction                                                                               methodology for calculating wave decay due to the various mechanisms

         If calculated erosion is not governing, the final recommended                             noted above.  The method employed in the CCCL establishment is basically

    Coastal Construction Control Line position is based on the location                             that recommended by the NAS report.  Each of the decay mechanisms Is

    where the significant wave height has attenuated to three feet.  This                           described briefly below; the interested reader is referred to the 1977

    three feet criterion is consistent with the Federal Emergency Management                        NAS report for greater detail.

    Administration (FEMA) criterion for delimiting the so-called "High                              Wave Height Decay Due to Shoaling Water

    Velocity Zone" and is considered to be the wave height (significant) at                              The maximum wave height, H, which can be supported In a water

    which structural damage is considered to be substantial.  This is                               depth, h, is

    presumably in recognition of the rather large piling forces and uplift

    forces that waves of this magnitude can induce.  (The wave force is                                        H = 0.78 h                                                    (V.1)

    proportional to Hn where 2 < n < 3.) A potential storm related factor

    not presently included in the methodology that could cause significant                          a result developed by McCowan for shallow water waves.

    damage is storm-tide induced current across barrier islands (the                                Wave Height Decay Due to Vegetation

    potential velocity due to a 2 ft tide difference across a submerged                                  Consider waves propagating through a stand of vertical cylindrical

    barrier island is on the order of 10 ft/sec.).                                                  elements of diameter, 0, (representing for example tree trunks) at a

         The following section describes the methodology for calculating                           uniform spacing, S.  For a water depth, h, an initial wave height, Hi,

    wave height decay.                                                                              and a propagation distance, Ax, the wave height, HT, after propagation

    5.2  Methodology                                                                                through the stand of elements is

         As waves propagate, energy can be added to or removed from the wave                                            H

    system.  The most common mechanism for energy addition is by wind                                          HT = I + AHiAx      (V.2)

    blowing over the water surface.  Principal mechanisms for energy loss

    (or dissipation or reflection) include wave breaking due to shoaling                            in which

    water, turbulent losses due to damping by vegetation and wave reflection
                                                                                                                 C0D
    by buildings.  In the present application, energy input by winds is                                        A = 5                                                         (V.3)
                                                                                                                3,r Sh
    neglected due to the short distances considered, for example the wave

    height decay usually occurs over a maximum distance of 600-800 ft.  The

                                     115                                                                                             116

    where CD is the hydrodynamic drag coefficient (taken as 1.0 in this                           VI  LONG-TERM EROSIONAL CONSIDERATIONS

    study) associated with flow about the elements.  Equation (V.3) would be                     6.1  Introduction

    modified, for vegetative elements extending only partially over the                                Prior sections have described methodology for calculating the

    depth.                                                                                       erosion associated with a single severe storm event.  In addition to

    Wave Height Decay Due to Buildings                                                           erosion due to relatively short-term events, the recommended location of

         Buildings serve to reduce the transmitted wave energy by blocking                       the CCCL includes consideration of any long-tern erosion trends.

    the waves and causing energy reflection.  For an incident wave                                6.2  Methodology

    encountering buildings with a decimal blockage density, B (perpendicular                           The methodology employed presently consists of accessing those

    to the direction of wave propagation), the incident and transmitted wave                      studies which have focused on and identified long-tern erosional

    heights are related by                                                                       trends.  These studies usually incorporate comparison of early surveys
                                                                                               (in chart form) and perhaps comparison of early and more recent aerial

                                                                        HT   1(1 - B) H1  (V.4)  photography.  Additionally, as counties are resurveyed as part of this

                                                                                               study, these data are examined to determine long-term trends.

    If n rows of buildings, each with the same blockage density, are                                   Studies of value may be directed toward a particular county or may

    present, the corresponding result is                                                          be broad in scope, such as the National Shoreline Study (19) of the
                                                                                               U.S. Army Corps of Engineers. Some of the early studies by the
              HT = (1   B)n/1 HI                                                                 University of Florida, Coastal Engineering Laboratory quantified long-

    Combined Effects of Topography, Vegetation and Buildings                                      term erosion around the State, Figure VI.1.

         For an incident wave height, HI, and both vegetation and buildings                            With the long-term erosion rate established, the recommended
    effects present, the transmitted wave height is                                               location of the CCCL includes accounting for a 5 year duration of this
                                                                                               erosion.  That is, if the long-term erosion rate is 5  ft/year and the

              HT       AH1Ax (1 - B)n/2 H1                               (V.5)                   methodology described heretofore indicates that the CCCL should be
                 HT=I + AH IAx
                                                                                               located x feet from shore, then the recommended position is specified at

         If the transmitted wave height as calculated by Eq. (V.5) is                            x +25 ft from shore.

    greater than the depth-limited value givern by Eq. (V.1). the wave height

    is set equal to the depth-limited value.

                                    117                                                                                           118

                                                                                              VII OVERALL VERIFICATIONS OF CCCL METHODOLOGY

           s-              -o -                                                                       As might be expected, due to the relative rarity of storms of the

                               {~ ~~  _          f  -' FERNANDINA                                100 year severity level and of the difficulty in conducting meaningful
                                                                                              measurement/observations before and after such a storm, there is only

                                                         I ACKSONVILLE  1                       limited direct data available to evaluate the CCCL methodology.  Two

                                                          ST.AUGUSTINE  '                      examples which provide varying degrees of evaluation/confirmation are
                                                                 '-q'o+ ~ o   .,5AND
                                 'a   O               __&MAPARINELAND    2                       presented below.

                                             B  t    LEGEND  orAYTONnA      n7.1  Hurricane Agnes, St. George Island, Franklin County
                                                                +NEW 1SMY'RNA                       This example is of interest, in part, because the extent of storm
                                           ANMA SS~ELj ( RECt53C-
                                           _,Ipo ..lo0..to  �I   \impact was discovered after the recommended position of the CCCL had

                                                                    CC" APE CANAVERAL          been established.

                            CLEARWATER     | OE wTA � SI                         0                     Slightly to the west of the center of St. George Island (Range 105-

                         UADEIRA BEACH                                  v IVERO BEACH             106), the recommended position of the CCCL was some 500 ft landward of
                      O   PASS-A-GRILLE,                                                          the mean sea level contour.  The position of the line was challenged by
                            ANNA MARIA                                  T. PIERCEt
                                 *NNPILCASEY KE YE                                               a developer who, by counsel, requested a delay from the Governor and

                                  ENGLEWMOD.                        ?        JUPITER 1.           Cabinet to develop proof that the recommended line was too far landward;

                                     so    CAPTIVA 1.t                w   | PALM BEACH           the delay was granted.  After the delay was granted, DNR located aerial

                                                       EVERGLAOES                               photographs flown on June 21, 1972, the day after the passage of
                                                                            SEERFIELD
                                             � NAPLES MPANO                                      Hurricane Agnes, which documented the almost completed destruction of

                                                                   NAPLES*  HAULOVER            the only road along this portion of St. George Island and landward of

                                                              4  ondgtl ., ~ IAMomunents 104 and 105.  The roadway is located some 100 ft landward of

                                                                                               the recommended position of the CCCL, see Figures VII.l(a) and (b) and

             ~- Y                                                   -I ILI  do                    photographs on display as a part of this workshop.  It is noted that the

                                            KEY WESt.        /.                                  storm tide accompanying Hurricane Agnes in Franklin County is believed
                                                                                               to be on the order of a 40 year event with the erosion event on the same

    Figure V1.1  General erosion conditions in Florida (Bruun, Chiu, Gerritsen                      order.
                 and Morgan, (20)).

                                         119                                                                                        120

    30 .............**... .*..A I i*-*  ..                                   *...                 .........       .           30  DOT.*.                         .ti

                                   1***~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F......g.....i... ,.                             E....-....-. .
                               hI  a a a a ~~~~~~~~~~~~ ~~~~~~~..a.. .... . ... .....I.j i  ..... ....a.......a.........                     1.... E                    ..                           I     ...a. .... .... ....a....~......t..... .
                                                                                          3...j~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- 4                                                             I
                                         I~~~~~~~~~~~~~~~~~~~~..... ... ..~.......---"-
                                           1.  I -  a . 3 . 3   i....a....,   ~ ~ ~ ~ ~ . ,            -. . ......1.........,...    *..,...., . a....r...a....,.. . a....I........a . . . .     . . . . -. . . . . . . . . .   ... 4-
                                                                                                          . ... . ....,                        ...j. ......     j....... .....a....
                                                              -~~~~~~~~~~~~~~~~~~~                                                                   ~    ~~~..a  ....a.... .a  ~.   ....J...-
                              ~~~~~~~~~~~~~~~~~~~~.. a...a. ..........                                                                                                                                                      -I - -.-.- .I
                                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a.a....-....                                                          .                                              .....a        a.~.i           I ~     .....a....a.
                                                                                                            S....,  ...~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..  z  ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~1~~~~~~~~~~~~....... ... ...
                                                 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.i....  .   3....3..3...                                                          I.-.'.         3       .I.                -
                                                                       -.-a.-.5.-                       ..::::::     ~        ~        ~        ~        ~            1::4.a   ...j.[~...a....I....a.   ....I..-.-..                           ... ]
        50  .  .. .       ... 150                       .    0       .    .    .     .    .    .     .    4 045                 5           004         0-        00-         5          002         02          0         5
                                                                  IHONUHENTI                                      FEET                                                                                                                       FEET~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I4 4--_
                                                    13000. 01335 BaR 53181301 31135ME~ 007033000 071.01330 BY T~lE330II~a(AT AT SOT 3ISOTBGAA3IETIE Eaaa~ouaas  tOI~a tillS 0331350331301 0335 31000 LEI~aISBB 331.33330 07 THC 31033033031! IT001 7IIOTAGA...1....C.l.......
                                  BERCH   PROFILE  cow~~~~~~~~~~~~~~~~~~~~~~~~~~u..   .......N  33A0E   :-1             I            BEC         PRF                                                                          .:araF~iKI  :~o f-lSII
                   02~ J . ...                 IIIO   FBECE  ISO              ...UHN  ETBLSE. .... ....                       . .         .--.-           .     ..                .        i  IVSO   FBAHE  HRSIHOUETETBISEHT1

                                         and   amaed  oaday  ue t  Huricne  gne.  192 (ee  igue VI.1()  fr etenionof.d...d.rad.dueto.HrrianeA.ns,..7.
                  -f .... profle)

                                                      ... .... .... ... .. .1  II                     lzz: I:.-:    I.-      ----            -     ------~~~~~~~~~~~12
                           .......    ..   ......... .... ... ......... ....... .....1

         Stressing again that the evidence of storm impact cited in this

    example was located after the CCCL location had been recommended, we

    interpret the line location in this area to be somewhat too far Gulfward

    in the vicinity of Monuments 104 and 105.

    7.2 Hurricane Eloise Damage in Walton and Bay Counties

         The set-back line was established in Walton and Bay Counties in

    April, 1975, and August, 1974, respectively.  Hurricane Eloise made

    landfall in Walton County on September 23, 1975, as shown in Figure                                     20-                                             -20

    VII.2.  The hurricane storm tide is ranked as a 75-100 year occurrence                                                                        m,- 200-OOF.

    and, due to the relatively high translational speed of the hurricane,                                                                                   -o- ,-U

    the erosion is ranked only as a 20-50 year event.                                                      ~                F

         Two types of information will be presented by way of comparison of                                                                                 -0 gd

    the measured zone of impact versus location of the (then) set-back                                     d  IU"ILE fea COAT

    line.  Figures VII.3 and VII.4 compare the eroded zone with the location20                                        2

    of the set-back lines in Bay and Walton Counties, respectively.  The

    location of the pre-hurricane vegetation line is also shown.  It is

    clear that the limits of erosion correlate reasonably well with the                       ,ve-                                       ._S

    location of the set-back line.                                                                                         Vex"" '"E,'"' A

         The second type of information available from Hurricane Eloise

    relates to the per structure damage costs relative to the location of

    that structure with respect to the set-back line. Of course the quality

    of construction is very important in terms of the damage that an
                                                                                         igure VII.2  Landfall location of Hurricane Eloise, September 23, 1975
    individual structure will experience.                                                                  and some resulting tide and uprush characteristics (from
                                                                                                      Chiu, (16)).
         Based on a survey of 540 structures, Figure VII.5 presents the per

    structure damage costs as a function of the structure position relative

    to the set-back line. Of general relevance is the quite steeply rising

    damage costs as a function of proximity to the shoreline. Of specific

                                   123                                                                                           124

                               BAY COUNTY
                                Plan View

                                                     SHELL SLAND

    tad-

      :                                                                   /                                      Wc 200-

               0JLAJA MACH            AMAMA CITY   -Mean i Sea  evel  ine _                          -Il Y

                                                 . .d[I.,,    IStAND
                     WVe LUn f!fl EroEle duce to hirricen Ebit se
              ---�letback Ua  Stble or emling beach
                     Enmote Starpt

      Figure VII.3  Relation of erosional characteristics and pre-Eloise                                      150-
                   vegetation line to set-back line, Bay County, Florida
                   (from Chiu, (16)).                                                                   CD\

                                 WALTON COUNTY    -'   8 0
                                    Plon View                                                         CD

                                                                     ION   SCARP
                                                                                               c:

                                                                                                                   Distance  From  CL (Ft.)

                               HUlRICANE ELOISE         NOTEVlgetoti n lme sthan s prior
                                                   o   hurrica ne Elo i se

                      'eAg. Line           to hurrica                  e E lan,                   Figure VII.5  Damage to structures in relation to location of set-back control
              --      Setback Un                         fllE ra        rin   e       l ine (based on study of 540 structures in Bay County after

                -    ErosIon Scarp           /Hurricane Eloise,  by Shows, (21)).

       Figure VII.4  Relation of erosional characteristics and pre-Eloise
                    vegetation line to set-back line, Walton County, Florida
                    (from Chiu, (16)).
                                                                                                                             126
                                         125

    interest is that average damage costs for a structure situated on the
                                                                                                                               REFERENCES
    set-back line were approximately $8,000, whereas the average damage
                          set-back line were approximately $8,000  whereas the average damage        1.  National Oceanic and Atmospheric Administration, "Flood Insurance Study -
    costs for a structure located 150 ft seaward of the set-back line was in                                 Sarasota County, Florida," October 1971.
                               excess ~~~~~~~~ of $5~200,000.  ~2.  U.S. Department of Commerce, National Oceanic and Atmospheric Administration,
    excess of $200,000.                                                                                      "Meteorological Criteria for Standard Project Hurricane and Probable
                                                                                                  Maximum Hurricane Windfields, Gulf and East Coasts of the United States,"
                                                                                                   NOAA Technical Report NWS 23, September 1979.

                                                                                               3. Van Dorn, W., "Wind Stress on an Artifical Pond," Journal of Marine Research,
                                                                                                   Vol. 12, No. 3, 1953.

                                                                                              4.  Christensen, B.A. and Walton, R., "Friction Factors in Flooding Due to
                                                                                                   Hurricanes," Proceedings, National Symposium on Urban Stormwater Management
                                                                                                   in Coastal Areas, Blackburg, Virginia, June 19-20, 1980.

                                                                                               S.  Saville, T., "Experimental Determination of Wave Set-Up." Proceedings,
                                                                                                   Second Technical Conference on Hurricanes, 1961, pp. 242-252.

                                                                                              6. Bowen, A.J., Inman, D.L. and Simmons, V.P., "Wave 'Set-Down and Set-Up' ,
                                                                                                  Journal of Geophysical Research, Vol. 73, No. 8, 1968, pp. 2569-2577.

                                                                                               7.  Lo, J.M., "Surf Beat:  Numerical and Theoretical Analysis," Ph.D. Disseration,
                                                                                                   Department of Civil Engineering, University of Delaware, June 1981.

                                                                                              8. U.S. Army Corps of Engineers, "Shore Protection Manual, Volumes I, II and
                                                                                                   III," U.S. Government Printing Office, 1977.

                                                                                              9. Freeman, J.C.,Jr., Baer, L. and Jung, G.H. "The Bathystrophic Storm Tide,"
                                                                                                  Journal of Marine Research, Vol. 16, No. 1, 1957.

                                                                                              10. Hayden, B., et al., "Sysmetic Variation in Inshore Bathmetry" Tech. Report
                                                                                                  No. 10, Department of Environmental Science, University of Virginia, 1975.

                                                                                              11. Dean, R.G., "Equilibrium Beach Profiles: U.S. Atlantic and Gulf Coasts,"
                                                                                                  Ocean Engineering Report No. 12, Department of Civil Engineering, University
                                                                                                  of Delaware, January 1977.

                                                                                              12. Moore, B., "Beach Profile Evolution in Response to Changes in Water Level
                                                                                                  and Wave Height," M.S. Thesis, University of Delaware, 1982.

                                                                                              13. Saville, T., "Scale Effects in Two-Dimensional Beach Studies," Trans.
                                                                                                   7th Meeting of Intl. Assoc. of Hydraulic Research, Lisbon, 1957.

                                                                                              14. Kriebel, D.L., "Beach and Dune Response to Hurricanes," M.S. Thesis,
                                                                                                  University of Delaware, 1982.

                                                                                              15. Kriebel, D.L., "Beach Erosion Model (EBEACH) Users Manual," Volumes I and
                                                                                                   II, Division of Beaches and Shores, Florida Department of Natural Resources,
                                                                                                   1984.

                                                                                                                                  128
                                         127

    16.  Chiu, T.Y., "Beach and Dune Response to Hurricane Eloise of September
         1975," Coastal Sediments '77, ASCE, 1977.

    17.  Wilson, B.L., "Hurricane Wave Statistics for the Gulf of Mexico," U.S. Army
         Corps of Engineers, Beach Erosion Board, Technical Memorandum 98, 1956.

    18.  National Academy Sciences, "Methodology for Calculating Wave Action
         Effects Associated with Storm Surges," Washington, D.C., 1977.
                                                                                                                                         APPENDIX A
    19.  U.S. Army Corps of Engineers, "National Shoreline Study - Regional Inventory
         Report," South Atlantic Division, Atlanta, Georgia, August 1971.                                                                 2-D STORM TIDE MDDEL*

    20.  Bruun, P., Chiu, T.Y., Gerritsen, F., and Morgan, W.H., "Storm Tide
         Study in Florida as Related to Coastal Topography," Bulletin Series No. 109,
         Florida Engineering and Industrial Experiment Station, University of
         Florida, 1962.

    21.  Shows, E.W., "Florida's Coastal Setback Line - An Effort to Regulate Beach
         Front Development," Coastal Zone Management Journal, Vol. 4, Numbers 1/2,
         pp. 151-164, Crane, Russak and Company, Inc., 1978.

                                                                                                                 *This program represents a numerical modeling procedure that is subject
                                                                                                             to change due to: 1. newly encountered topo-bathymetric and hydraulic
                                                                                                             boundary conditions, and 2. incoporation of new advancements quantifying
                                                                                                             coastal processes. This program is applied on a county-by-county basis and
                                                                                                             is subject to acceptable calibration constraints recommended by the Beaches
                                                                                                             and Shores Resource Center and approved by the Florida Department of Natural
                                                                                                             Resources.

                                                                                                                                              130

                                         129

                                                                                              C     06        ~~~CORIOLIS PARAMurTER (0 OR 0.0000727)

    CC                                                                                                             FEET, NO CONVERSION TAK(ES PLAC.'E

    C     P RO GRAM:  2-D STORM TII)E
                          C ~~~~~~~~~~~~~~~~~~~~~~~~COMMON /A/  JUtX (I 10.11i0) , uUY iI(1 10,110) , P(1 I10,11i0> ,H11(l i I0.11I0)
    C                                                                                             -DPDX(l 1 0,11 i0) ,DPDY ( 1i0, 1 10) , DX
    C                                                                                              COMMON /P/ ETA(1I1I0, 11I0) , QX ( i0,11i0) , QY ( 1 0,11 I0) , NQPX (1 10) , TJDE,
    C                                                                                             -            1Y,NNX,lEND
    C                                                                                              COMMON /C/ IsJ
    C                                                                                              COMMON /E! PINF,DT,NNY
    C                                                                                              COMMON IF/ JJ
                          C                                                                     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~COMMON /G/ CVAR(600,3,39),CTIME(600),CAEE,11PtOT(7F.),f.C2,
    C                                                                                             -INTERV,NPLOT
      C                    NOTE ~~-----------                          NOECOMMON /H/ IFFACT(l10,1i0)
    C                                                                                              COMMON /BAR/  ODR5)IA(0,JAR)XDR~)HtR5)
    C     DEFINITION OF PARAMETERS;                                                                  oR~)FAc0,IE(0,OIN(0,IL5)JN(0,I~5)
    C-DPN(0,EEX0)FN(0XLN()
    C          CASE       20 CHARACTER TITLE TO IDENTIFY A SPECIFIC OUTPUT
    C          DX         HORIZONTAL GRID I)ISTANCE, IN NAUTICAL MILES                             DIMENSION Y(110-),NQAX'T(il1),ETAT(110),UJ(l10,i10),YNM(110),XNM(1i10)
    C          DY         VERTICAL GRID DISTANCE, IN NAUTICAL MILES                                DIMENSION ETMX(110,1 10),IEETLUP(110)
    C          DT         TIME INCREMENT FOR EACH TIME STEP, IN HOURS                              DIMENSION DXA(`110),DYA(11I0)
    C          PINF       REFERENCE PRESSURE(ATMOSPHERIC) USED TO CALCULATE                        DIMENSION D(110,110),DETA(110,110),X(110),UJX(l10,IiO),
    C           BAROMETRIC TIDES                                                                  -U(1,1),X(1,1)
    C          DF    B     OTTOM FRICTION COEFFICIENT(0,02 - 0,002)                               -UYR(i10,l10),JNET(liO),NET(iiO,iiO),
    C          RHAX       RADIUS FROM CENTER OF HURRICANE TO THE POSITION-NX(11i)NY101),B1)
    C                     OF MAX. WINDS                                                            DIMENSION ETAMAX(39,3)
    C          YS         INITIAL Y-COORD. OF THE HURRICANE CENTER, IN                             DIMENSION  S101),A(1,l)
    C                     NAUTICAL MILES                                                           DIMENSION QC(1I0),ETA)C(110)
    C     D     P         HURRICANE CENTRAL PRESSURE INDEX, IN INCHES OF                           DIMENSIONAC10,C1)CC1)DC1)
    C                     MLURCURY                                                                 DIMENSIONAC(1),C11>  C(10,)C(1)
    C          VF         FORWARD VELOCITY OF THE HURRICANE SYSTEM IN KNOTS                        DIMENSION ETASO(110),E~TAS1(110),ET'AS2(I10)
      C       ~~~~NIT    0DIMENSION VT':IME(15) ,VDP(i5),VVF(15),VRMA)X(1'5),VTHIETA(i5)
    C          Wsc        WIND SHEAR STRESS COEFFICIENT                                            DIMENSION FCTX(110, I 1),FCT'Y(1 10,110),W41XX(110,I10),WWYY(l 10,110)
    C          INTERV    -~TIME STEP INTERVALS AT WHICH TO PRINT OUT                               DIMENSION WSF(110,i0)
    C                     AN OUTPUT FOR THE GRID SYSTEM                                            CHARACTER*20 CASE,SYSTEM
    C          THETA      LANDFALL HURRICANE TRACK W.R.'T. NORTH AND                               CHARACTER*1 D1RY,WET,AR~EA(i10),PER(110,lio)
    C                     CLOCKWISE IN DEGREES                                                     DATA IFLAGZ /I/
    C          XHDf       INITIAL DIST OF THE HURRICANE, IN NAUTICAL MILES                         DATA DRY,WET 1'    '
    C                     (MAY BE OUTSIDE THE GRID SYSTEM, W.R.T. ORIGIN)
    C          XHE        FINAL DIST OF THE HURRICANE, IN NAUTICAL MILES                    100FORMAT(/)
    C                     (MAY DE OUTSID)E THE GRID) SYSTEM, W.R.T ORIGIN)
    C          TIDE       ASTRONOMICAL TIDAL ADJUSTMENT IN FEET, POSITIVE             I10 KOUNT=-1
    C                     ABOVE MEL                                                                I C2=0
    C          XCB        THE X-COORD DIST OF THE LEFT-EDGL OF THE GRID                            G=32.2
    C                     SYSTEM, IN NAUTICAL M ILF                        E                       RHOA=0,.0024
    C          XCF:       THE X-f-OOI-D D)1ST OF THE RIGI.H1-EDGE OF THE GRID                      RIAOW--- I.9
    C                     SYSTEM, I.N NAUTICAL.  M IL E                                            NFIN=~-i
      C ~~YCDf           THE YDOOIE )[T OF THE 'IPHrEDGE,  OF1' THE. CRID                        D4=2 . SE-08
    C                     SYSTEM, IN NAUTICAL MI3.LLE. 9             (:OU N=0
    C          YCF        THE Y -- CUOOD )[S T OIF TlEfOI : OIDC  OF WE GRI1)
    C                     SYSE-1:M, IN NAUTICAL N I I-PS1                                  C
    C          TMAX       THlE MAX 1)URAT] ON OF: TI.E PROZTOTYPE- HJURRIC'ANE              C~x**x*INPUT GRID) SYSTEM DATA (D1IMENSIONS,   ~
    C                     MOD1FL SYSTEM, IM NH:LJORS                                       Cu****COSATATYMRYFITONFACTORS) ***~*K  *XX
    C          TMIN       THE T INC- ()",TTE:R WHIllCH OUTIPUTS ARE CENERATEI)              C
      C       ~~~~NDELT  0                                                                        READ('5, 20) SYSIEM

                                   131                                                                                     132

          WRITE(i, 25) SYSTEM                                                                           DO 160 I=2,NNX
       ''0 F ORMAT (A20 )                                                                          1 60 H(1,J.)'1-I(I, J).#0.O
        25 FRMAT(iliii U/,i IA20-)                                                                1'70 CONTINUE

          READ(5,40) NNX,NNY                                                                       1010 FORMATIIHi.. ASSIGNMENT OF FRICTION FACTORS FOR EACH  RI'
       40 FORMAT(213)                                                                                  -/IHO0,'I(TOWARDS  CA)>',I   'J(NORTH)'/iHl

          RLAD(5,50) (DYA(J),J=1,NNY)                                                                   DO 210 J=1,NNY
       >0 FORMAT(OFD.D)                                                                                 IF(IFL.AGZ.EQ.1) READ(5,190)(IFFACT(I,J),I=1 ,NNX)
          WRI1CE(6,60)XCDE,YCB,PIN4F,T]IDE,DT',XCF,YCF,EI6,INTE--RV,THIETAC                        190 FORMATCIDIS)
       60 FORMAT(1H0,'GRID SYSTEM P-ARAMETERS-,//,IH ,' XCD= ',F9,2,                             C      WRITE(6,200) J,(IFFACT(I,J),I=1,NNX)
             I YCDl= ',F9.2,' PINF= ',FB.2,' TIDE= ',FD.2,' D= ',F10.2,                            200 FORMATCill ,I2,3X,25-15,/IH ,5X,2515)
             -   AIMl  ' XCF= '924YCF= ',F9 .2,1 6= ' ,EiO.4,                                      210 CONTINUE
             -     INTERV= ',16,' TIIETAC= ' ,F6.2)                                             C
          WRITEC6,70)NNX, NNY                                                                    Cx**M*x***INITIALIZE/CONVERT GRID SYSTEM DATA >********
       70 FORMAT(IHD, ' NNX= '.19,' NNY= ''19)                                                   C
          bJRITEC6,O0) (DXA(I),I=1,NNX)                                                                 CNM=60'76. I
          bJRITE(6,SO) (DYA(J),J=i,NNY)                                                                 CHS=3600.0
       80 FORMAT(IHDiIFI0.0)                                                                           XCD=XCDMCNM
                                                                                                   XCF=X CF* CNN
          READ(5,90) NDAR,NINL                                                                          YCF=Y CF*CNM
          WJRITE(6,95) NBAR,NINL                                                                        YCI= YC B*CNM
       90 FORMAT(213)                                                                                   PINF-470.51 *PINF
       95 FORMAT(lHO,2I3)                                                                               NNXMI =NNX-1
          IF (NDAR.EQ.0) GO TO 130                                                                      NNXP1 =NNX+i
          DO 110 N=1,ND(AR                                                                              NNYMI =NNY-1
          READ(5,100) NORBAR(N),IDAR(N),JBAR((N),XLBAR(N),HDAR(N),                                      NNYPi=NNY+1
            -          UD~~~WAR(N),FDAR(N),XKEX(N)                                                     IEND=NNX
    C       ***ADJUST HEIGHT OF BARRIER TO MEAN SEA LEVEL ***                                             ENDMi =IEND-1
          HBAR(N)=HBAR(N)+0.8                                                                           DO 12 J=1,NNY
          WRITE(6,105) NORDAR(N) ,IDAR(N) IJBAR(N) DXLBAR(N) ,HB1ARf(N),                             12 ISETUJP(J)=40
             -          UD~~~WAR(N),FBAR(N),XKEX(N)                                                     ISETUP(4B)=54
      100 FORNAT(313,5F10.3)                                                                            ISETUP (54) =52
      1 05 FORMAT( iHO,3I3,5F10.3)                                                                      ISETUP (60) =52
      110 CONTINUE
                                                                                                   X(1 )=XCE>
          IF (NINL.EQ.0) GO TO 130                                                                      Y(1 )=YCB
          DO 120 N=I,NIlNL                                                                              XNM(1 )=XCD/CNM
          READ(5,100) NORINL(N),IINL(N),JINL(N),XLINL(N),DPINL(N),                                      YNM(1 )=YCD/CNN
            -         ~~~~WINL(N),FINL.(N),XKENEX(N)                                                   DO 220 I=2,NNXP1
          DPINL (N) =DPINL..(N) +0.D8                                                                   X(,I)=X(I-1>)+(DXA(T),fDIXA(I-1) )/2.0
    C      **** ADJUST DEPTH OF INLET TO MEAN SEA LEVEL ***220 XNM(I)=X(I)/CNM
          WRITE(6,115   NOIRINL(N),IITNL.(N),JTIN(N),XLINL(N),DPINL(N),            DO0230 J=2,NNY

      115 FORMAT(IHO,313.5F10.3)                                                                    230 YNN(,J)=Y(J)/CNM
      1 20 CONTINUE                                                                                     NRITE(6,240)(JJ,0
      1 30 CO0NTIN ()E                                                                              2.40 FOR M A T (IHII , / /, ,  I I X A ND1 Y DIST 9TAN CE S(N.MI) ' - ,/IOI    10 11)
                                                                                                   WR ITF(6, 25D) (XNM (J) ,J=1i , NNX)
    C              RE--AD IN DATHYMETF.Y. ELEVATIONE=-H1, DCTSUTR)+.WURITE(6, 12000)
          DO 170 J=1 ,NHY                                                                               IJRITE(6,250) (YNM(J),J-l ,NNY)
          IF(T-IFLAGZ.EQ.1 )RA(,10(IIJ,11,N)                                                       250 FORMATUili ,10F1.2)
    C     FJIE6  5)(I ,J  I1  H)WRITE(6,260)
      1'50 FORMAT(10(-F'7. 2)                                                                       260 FORMAT (il
          (1 ,J)=-9V.
    C         ***ADJUST DATHYMET'RY TO MEAN SEA LEVEL *M*270 00 300 IX(0=1 ,NNX

                                     133                                                                                           134

                IF(H( :r~~~GO,*J  1C0.0  Gf  ()90                                                          VF=VVF(i
          ARE A(IN(:))= )RY                                                                                TH ETA =V T HETA ( i
          "E R( I S 0,J1)'R Y                                                                              CTH=.-COS ( (THETAC-90. 0) /.-7.2956)
           Go TO :110                                                                                       ST1H=SIN( ITEA-0.)5.96
      290 AREA(iso)=wJEr                                                                                   XHl-M=XHfcj(CTH 4. YHB*STHM
          PER(1S0, J)=WET                                                                                  YHl- =-XHB*STH + YHDl*CTHl
      31)0 C:ONTINUJE                                                                                      XHDl=XH-ID
                                                                                                           YHB=YllH~l
          DO 310 I=l,NNX                                                                                   XH=H#N
          DO 310 .J=1,NNY                                                                                  YHB=YHB0*CNM
          ETA(IJ)=0.0001                                                                           C      THETAC=THE--TAC/57 .2956
          QX(I,J)=o.oooi                                                                                   T'MAX=T MAX *CHSl
          QYCI, J)1=0.000i                                                                                TMIN=-TMIN*CH9
          NET( I.J)=0                                                                                     I<OLJNT=- i
          WJSF(I,J)=1 .0                                                                                   IC=
      310 CONTINLIE                                                                                         I ICOUN=0
          DO 315 1=8,35
      315 WSF(I.29)=0.0                                                                                    READ(4,39i) (IPLOT(J),,J=1,24)
          00 316 1=26,30                                                                                   IF (IPLOT(24).NE.0) READ(4,391) (IPLOT(J) ,J=24,48)
      316 WSF(I,9)=0.0                                                                                 391 FORMAT(i2(13,iX,12))
          DO 317 1=24,26
      317 WJSF(I,i0)=0.0                                                                                   NPLOT=0
          DO 320 I=1,NNX                                                                                   DO 392 JPLOT=1,48,2
          DO 320 J=iNNY                                                                                   IF(IPLOT(JPLOT).EQ.0O.R.IPLoDTJPL.OT+i).EQ.0) GO TO 394
          luUX(I,J)=0.001                                                                                  I,.J=(JPLOIT+1 )/2
          UUY(I,J)=0.001                                                                                   JI=IPLOT(JPLOT)
          P(I,J)=0.0001                                                                                    J2=IFLOT(,JPLOT+1 )
      320 CONTINUE                                                                                          I SETUP(IJ2 )=J i
    C                                                                                                       N FLOT=NPL.OT+ i
    C   **~*~*~    INPUT HURRICANE PARAMETERS                                                               DO 392 JJJJ~i .3
    C                                                                                                       ETAMAX(I.J,JJJJ)=O.O
      325 READ(4..330,END=i1130)CA9E                                                                   392 CONTINUE
      330 FORMAT(A20)                                                                                  394 CONTINUE
          READ(4,340)XHB,YHB,TMIN. TMAX,NPARM                                                              NFLC)T2=NFLOT*2
      340 FORMAT(4F8.1,13)                                                                                 WRITE(6,396) (IPLOT(J),J= , NPLOT`2)
          WRITE(6,345)CAEE                                                                            396 FORMAT~iHO,'GRIDS FOR PLOTTING:    ,,iHO.
      345 FORMAT(iHi,//,4H ,A20)                                                                                    i 51' (12'I,))
          WRITE(6,350)XHB,YHD. ,TMINt,TMAY,N'ARiM                                                   C
      350 FORMAT(IHO,' HURRICANE PARAMETERS   M/,I-0'XD=  ',FB.1 .  YHD='
              MlF,1,   TMIN=  ,FL, TMAX= 'F1, NAr,(FM=  1,13)                                       C
          WRITE(6, 360)                                                                                    NTIMES=IFIX((TMAX-TMIN)/DT) + 1
      360 FORMAT(IH-, 20X,-VARIADL-E PARAME.TER9:',//lH ,21X,-TIME-,SX.  OF' ,7X,                          WRITE(4,39B)NTIMES
         - 'VF',6X. 'RMAX',6X, 'THET-A,/)                                                             398 FORMAT1IHO,-NTIMES (MAIN LOOP VALUE)    '.)
          1)0 390 1Ii,NF'ARM                                                                        C
          READ(A,370) v-IML( I), VVF( I),VRMAX(I), VDPII), VTHIETIA1 I)                             C       ID(J) = T. DE"NOTES I INDEX OF FIRST SUBDMERGED GRID) OF JTH 17OW
      370 FORMAT C F7.)                                                                             C    - STARTING SECTION TO DETERMINE ACTIVE ETA ELEMENTS
           WR ITE (6 1I      iIM 3     O CI),VFII  RA    ),VHT I)                                    C       NET (I._0)=0 IF1 DR-'~Y AND = i IF FLOODED.
      380 FORMAT(iH  1X1'S   l''XP   ,X  416,A16,51
           Vr'IMEM=VTIMI C1)M-CCHS                                                                          DC) 420 Jr.1i,NNY
           VDP(I=VD)P(I)N70()  i                                                                            DC) 420 I=1,NNX
           VVF(T)=VVF(Tx1  '9                                                                               IFTAI)--(,)) 400,400,100
           VRMAXM=)VRMAXCI)CNM                                                                        400 NET( T J) --

      :91) CONTINUE                                                                                        I~):+
           R11AX=VRMAXM                                                                                     GO TO 420
           DP=VI)P(1                                                                                   410N.TI)I

                                        135                                                                                              136

      420 CONTINUE                                                                                        DO 2100 *.j:=i,NNYMi
                                                                                                       DY=DYA W )
                                                                                                       DO 2090 1=i ,NNXM1
    c     ESTABDLISH RE.FE RENCE: HURR I CANE VA LUIES FORk WAVE   El TUP                                 DX=T)XA(I)
    (2    CALCULATIONS                                                                                     IF (JJ.NE.i.OR.NET(I-J).NE.1) GO TO 2030
                             (2                                                                          ~~~~~~~~~~~~~~~~~~~~~~~~~~~CALL JIURCIH(USII,,I,,J,X,Y,VF,FPINI-,D)P,FMAX,TtiETA,D'T,DY,
          IT5-0                                                                                                        RHOW, XH, YH)
          CALL HLIRCH(USEQ, I,..J,X, Y, VF,PINF,DP~,RMAX,THiETA,D)TI)Y,                                  ETA(IJ)=0.01!562F)*(PINF-P(I,J)))
            ~~~~~.aox-I RLAXH, YND.-)                                                             2030 IF (NET(I,J)*NET(I+iJ)) 2040,2040,2050
          USQM=USfQ                                                                                 2040 NQX ( I .1,J) =(. 0
          UMAX=EQRT(USQ)/i .69                                                                            QX(I+1 ,J)=O.O()i
          AA=-RMAX *I)P*04                                                                                NQBX (J) =I1.1
          AA2=0. I60m VF/SIQRT(IUMAX)                                                                     GO TO 2060
          HMAX=16.5*EXP(AA)*(1 .0+AA2>                                                              2050 NEQX(I,J)=i
          TNAX =8. 6*EXP (AA/2. Wm ( i (.)+AA2/2.)                                                  2060  FNT(,JNTI.+1)2070,2070,2000
          IPARM=2                                                                                   2070 NQY(I,J+i)=0
    (2    WIRITE(6,430)                                                                                    QY (I 'Ji  ) =0. 001
      430 FORMAT ( i1-0,    I    THR      ETA NET        QX   EQY  D(53,60)',//)                          GO TO 2090
    C                                                                                                2080 NQY(I,J+A)=l
    C ****         ***    ~***MAIN LOOP                                                              2090 CONTINUE
    C                                                                                                2100 CONTINUE
          DO 40500 JJ=i,NTIMES
          XJ=JJ-i                                                                                         CALL ETABCS (XHI,YH,T, X,Y,VF,DP',RMAX,THiETA,RI-OW)
          T=XJ*DT+TMIN                                                                                    DO 2110 J=i,NNY
          THR=T/3600.                                                                                     DO 2110 I=i,NNX
          TS=T                                                                                      2110 D(I,J)=ETA(I-J)+H-(I,J)
          IF (NPARM.EQ.0.OR.IPARM.GT.NPARM) GO TO 2020
          IF (T.L-E.VTTME(IPARM)) GO TO 2010                                                       C
          IF (IPARM.E1Q.i) GO TO 2000                                                              C      TVIlS PORTION OF PROGRAM FOR SWEEPS IN THE X-DIRECTION
          XHB=Xl-ltI+(V'TIME( IPAR~M)-VTIME( IPARM-1 ))*VVF(IPARM-1 )                              C
          -*COS(VTHETA(IPARM-1))                                                                          IMPDIR=i
          YiiB=YHB+(VTIME(IPARM)-VTIME(IPARM-l ))*VVF(IPARM-1)                                            DO 3090 J=2,NNYMI
          -*SIN(VTHETA(IPARM-i1))                                                                         D)Y=DYA(, ))
     2000 IPARM=IPARM+l                                                                                    DO 3030 1=2,NNX
     20`10 IF (IPARM.GT.NPARM) GO TO 2020                                                                  DX=0.5*(DXA(I-l )+DXA(I))
          DPCT=(T-VTIME(IPARM-1))/(VTIME(IPARM)--VTIME(IPARM-i))                                          DX2=DXA(l)
          DP=VDP(IPARM-1 )-fDPCT*(VDP(IPARM)-VDP(IPARM- ) )                                               FACTX=1 .0
          RMAX=VRMAX(IPARM-1 )+I)PCT*(VRMAX(IFARM)-VRMAX(IPARM--1)                                       CALL lHURCFI(US(,I,I,J,X,Y,VF,rPINF,DP,RMAXTlHETA,DT,DY,
          VF=VVF(IPARM-1)                                                                                -RHOW,XH,YH)
          THETA=VTHETA( IPARM-i)                                                                          CALL CALLFR(I-,BF)
          TS=T-VTIME(IPARM-1)                                                                             WX=0 .5
     2020 CONTINUE                                                                                         CALL INLT(I,.J,I-F,I)T,FACT-XFACTY,WX,WY,TICOIJN,NF3AR,N.TNL,IMPDIR)
          XH=XHB+TS*VF*COS (THEl:TA)                                                                      FT(,)AT
                                  YH=YHD+TS~~~~~ VF * S IN (THETA) ~~~~~FCT'Y(I,,J)=FACTY
          XHN= X H/CNM                                                                                    WWXX(I,_J))WX
          YHH=Y H /CNm                                                                                    WWYY(I'J)=WY
          IF (T.G.T.TMAX) Go TO 11000                                                                     IF (NT(IiJ  NTIJ).E00.ADXL.40)Go T  3000
          DO 202.5 J=1,NNY                                                                                AC '(I) =O.(
          DO 2025 1=1 , HX                                                                                BcII) =0.0

     2025 ETrAS ( I,J)=ETA (I , J)1
    (2                                                                                                     Go TO 3010
    C     ESTABILISH ACTIVE (DISCHARGE) JUNCTIONS                                                    3000 DA=.*D  1-  J+(  J
    C     USE BOUNDARY CONDI FT1ON OF NO FLWACROSS A BOUNDARY                                              IF ( D   DR).Lr.0)DBAR=0 .001
       (2 NQEDX (.J I IS IHE POSITION OF TII(E NO FLOW(ZOA FIH  ON TlE. JTrH  COLU,(.MACI)G*)RXT/XFCX

                                     -137                                                                                             138

          (,Q--zSQ)R I( X( I, JI *f2IYBAR* it 2)                                                          DC(J)=QY( I, J).-A("( j) x(ErsI,.jA .r(   ]..l j ).41( -D liARl*IOPDY (I, JI/k;) I i.
          liC(l:( 1 .0fI�(OT(0,DRx2)-                                                                            HoYc I, JI) /RHow-#rt6*QxArm  I xDT,
          IF (WX. GT.025) DC( I )--::1J                                                             4010 IF (NET(I-J).NE.0) GO TO0 4020
          CC(TI A(:,A( I)                                                                                 ACE (,jI '0o. 0
          Dc ( :r =QX (I,lJ) If C  'sTA*1P                                ( I   I /RO)IX(,.  /HW-D*)ARI*fiCC J   . =0.
     301 0 IF (NET(I ,J) WN.".0) GO TI) 3020                                                              CCS (JI=0. 0
                                 ACE~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C (I =0.                          DCS(J).0(
          DCE (I)=0(. 0                                                                                   GO TO 4030
          CCS ( 1) =0.0                                                                             4020 ACS (J) DT/ (2. 0xDY2)
          DCS (II=0. 0                                                                                    ICS(,J)=i .0
          CO0 TO 3030                                                                                     CCS(j)=-ACsCj)
     302-0 ACS(I)=1)T/(4,0xDX2)                                                                             C()EAIJDT(.DX*QXI1vxIj+

                                CCE(I)=-ACE(I)                                                     ~~~~~~~~~~~~~~~~~~~4030 CONTINUE
                   DCS(I)=ETAIJ)--ACS(I*CQX(I+1  JI-QX(I,J))--DT/(2-.OxOY)*                              11)I0=2
             -   (QY(I ,J.Ii )-QYC I,J)                                                                  COLLDWEPIDNNA.CCCABECSCET,  ,IE)
     3030 CONTINUE                                                                                  4050 DO 4060 J=i,NNY
          101R=1                                             Ply ( II J) =QC (,I
          CALL DEEIIRNXACCCDCCCCETCCNT)4060 ETA(IJ)=E-TAC(jI
     30!50 Do 3060 I=1,NNX                                                                         C4090 CONTINUE

     3060 ETA(I,,J)=,ETAC(I)                                                                       C      REESTAILISH [JET AND DRY GRIDS; DRY=O, FLOODEDO1
     3090 CONTINUE                                                                                 C      START AT TEND-1
                           C                                                                      ~~     ~~~~~~~~~~~~~~~~~~~~C DRYS UP IF ETA+H<=0.0
    C     THIS PORTION OF PROGRAM FOR SWEEPS IN THE Y-DIRECTION                                    C      O 53   =,NM

       C  IMPDIR=2                                                                                        DO 5030 1=2,NNX
          DO 4090 I=2,NNXMI                                                                               IS=NNXMI-f-2-I
          DX=DXA (I)
          DO 4030 J=2,NNY                                                                                IF (NET(IS,,JI  EQ. 0) GO TO 5030
          DY=0.5*(DYA(J-1 )+fDYA(J))                                                                     ETIA(IS,J)=0.67TXETACIE,J)+0.33*ETASCITJI
          DY2=DYA(J)                                                                                     IF(ETA(IS,JI  + H(IS,J)) 5000,5000,5010
          FACTY=1 .0
          CALL NUtR~Cl(USQ,I,J,X,Y,VF,PINF,DP,RMAX,THE-TA,DT,DY,                                   5000 EAII-CS,)000
            -        ~~~~RHOW,XH,YHI-                                                                    D(I9,J)=ETA(IS,,j)+HcI~S,j)
          CALL CALLFR(I,J,D~FI                                                                           NET(IES,J10(-
          WY=0.5                                                                                         GO TO 5020
          CALL INLT(I,J,DIF,DT,FACT'X,FAC-TY,WX,WY,IICOUJN,NBFAR,NIINL.,IMFPDIR)
          FCTX(I,J)=FACTX                                                                         .5010 NET(IES,J)=1
          FCTY(I,J.)=FACTYD(,JH(EjETTSJ
          W1WXX (I,.J) =WX
          WWYY(I,,J)=WY                                                                            5020 CONTINUE
          IF (NTIJ1*E(,IN...N.J.T400 GO TO 4000                                                    5030 CONTINUE
          AC(CJ 1=0.0
          BC (J) =0. 0                                                                            C
          CC(,J 1=0.0                                                                             C REESTABL ISH) ACTIVE (Of ECHARCE) JUNCTIONS
          DC (.)1=0).0                                                                            C USVE BOUNDARY CONDIT ION OF NO FLOW ACROSS A BOUNDARY
          Go TO 4010                                                                              C NjQDX(..J) IS THE P"OSITION O'F THE NO FLOW COASTLINE ON THE J * TH COLUMN
     4000 ODR05()  ,i-  +(I  )IC                                                                          00065 J.)=.NNYM1
          IF (ABS C ODAR)I. L.T .0.001) ODAR"0 .001                                     O
                                 AC C J I '~~~~GXIIDA~~xI)T/ (2.0" DY I *FACT y ~~~~~Do 5060 I =1,NNXNI
          QXOlAR=0.25*(QX (I,&-- I I+X(I-f-1, .J-1- I+X(I.,J) QX( I+ , JI                                IF (NE ,T(I,'  NTIIJI53,0554
                                Q~~i=SQ~~~r C QXOAR~~~~x2+QY C IJfltx2I ~~~~~5035 NQX(I�1- ,))=0O.0
                                 DCC .11=1 . 0+BF~~~QW~OT/( S. OtOOA~~mu2 I                             QXCItlJ0.1
          IF CWYG.(1 ,05I  CJ:                                                                         NQrtX(,J)zI+1
                                  CCCJ)=-ACCJ)                                                          GO ~~~~~~~~~~~~~~~~~~~~~~~~~~~TO 5,04.15

                                      139                                                                                            140

     5040 NQ(,)1DY=DYA (.-1
     5045 IF (NET( (II J)* NET r( I JF IA)  50,0 5050,15,0515                                            NE'( IC_.1-i )=
     .5 0 NO~,Y ( I , .J+ I ) - 0)                                                                       Q Y (I C , J -1 )- DY*(ET A(IC, J -    I +( I C J--  1))/T

          GO TO 5060                                                                                     D  C  )T(IJ+(IJ
     5 0 5 5 NCY (I ,J-.I)=1                                                                       6140 CONTINUE
     .5060 CONTINUE                                                                                 61 50 CONTINUE
     506)5 CONTINUE                                                                                      IF(MOD(,JJ..i)NE.0) GO TO 10000
    C                                                                                              C****x.* STORE ETA VALUES' FOR TIME SEr~IES' OF GRIDS IFOR PLOTTING ****
          DO 6020 Jm2,NNYMi                                                                              IC2mlC2+i
          ICtJR=INETtiP(_J)                                      DO                                         8000 NPLT=1 ,NPL.OT
          CALL VIIJr~CH usoT,TCI.JR,.J, X ,Y ,Vl-,F;INE,I)P riMAX,TH-ETA,                                JPLo~hr= NPLT-1 ) *2+1-
            -        ~~~~~DT, DY, RHOW, XH, YH)                                                         K PLO T= IPLOT(CJPLO T)
          HO=NM AX*UEQ/USQM                                                                              LPLOT=IPLOT(JrLlOT+i)
                                 AAA=S(~~RTCUUX(ICIJR~j)**2+UUY(ICURJ)~~*2)                            CVAR(1C2,1I,NPLT)=ETA(K<PLOIT,LPLOT)
          H0=H0*ABS(UUX(ICIUR,J) )/AAA                                                                   CVAR ( C2, 2, NPLT )=ETASl (LPLOT)
          T0=2. i 3*S(QRT (H0)                                                                           CVAR (IC2, 3, NPLT) --ETAS2 (LPLOT)
          HD=0. 936xH0                                                                            C****ff* FIND MAXIMUM ETA'S OF GRIDS FOR PLOTTING ***~*x******
          IF (UUX(ICUR J).GT.O.0) H10=0.1                                 DO                                0000 JJJJ=i .3
                                 WSU=0.19*(1 .0-2.02*SRRTCND/(G*TO*TO) ) )*ND                          ~~IF(ETrAMAX(NPTF'.I,,JjJJ) .LT.CVAR(IC2,JJJJ,NPLTF)) ETAMAX(NPLT,JJJJ)=
          LJSUI =14LJi1 . 0                                                                             -   CVAR(IC2,JJJJ, NPzLT)
          WSU2=WSU*1 I 5                                                                           0000 CONTINUE
          IF(NSETUP.EQ.0) WEu=0.0                                                                 C****** FIND MAXIMUM ETA VALUES (NO SETUP> FOR ALL GRIDS  *******
          ETAS0(,J)=ETA( ICUR,J)                                                                         DO 9000 JJJJ= , NNY
          ETAS (,J)=ETA(ICUR,J)+WSUi                                                                     DO 9000 lllI=1,NNX
          ETAS2(J)=ETA( ICUR, J)4-WSU2                                                                   IF (ETA(1III,JJJJ) .GT.ETMX(II1I,J.JJJ)) ETMX(1III,JJJJ)=-ETA(IlIII,
          NQBXT  J) =ICUR                                                                                    JJ)
     6020 CONTINUE                                                                                 9000 CONTINUE
    C                                                                                                    CTIME( 1C2)=T/CH9
    C ESTADLISH MOST SHOREbJARD FLOODED STATION.
    C NOTE-NEW SHORE ELEMENTS ARE ACTIVATED ONLY BY FLOODING IN X-DIRECTION                        10000 CONTINUE
    C                                                                                                    NFIN=NFIN+1
          DO 6150 J=2,NNYMi                                                                              IF (MOD(JJ-1,i8).NE.0) GO TO0 10020
          IC=NQBX(J)                                                                                    WRITE(6, 10010) THR,XHN,YHN
          DX=DXA(IC-1)                                                                            10010 FOr~MAT(IHO,'*****',THR=',FiO.2,'  XHN=I,Fio,2,1  YHN=',FiO.2)
     6060 IF(ETA(IC,J)+H(IC-1,J)) 6080,6080,6070                                                         IF (MOD(JJ-1,36)..NE.0) GO TO 10020
                                                                                                       CTHi=COSE((90. 0-TH~ETAC >/57.2956~)
     6070 ETA(-IC-i,J)=-HC(IC--1,J)-f0.2t'*(ETA(1C,J)+H(IC-i,J))                                         STH=SIN( (9(.0.-TH~ETAC)/57.2956)
          D(IC-1 J)=ETA(IC-i J)q.H(IC-i J)                                                               XHB2=XHN*CTIH + YHN*STH
          NET'(IC-1 J)=                                                                                  YHP2=-XHN*STH 4+ YHNjfCTH
          QX(IC,J)=-DX*(ETA(IC-i J)+1-(IC--1,J) )/DT                                                    WRITE(6, 1001 5)TH-R, XHDL2, YHDE2
                      ETA(ICJ)=-H(IC-1,J)+0,75*(ETA(ICJ)+H(IC-1,J>)                            1 001i5 FORMAT(iHO,I UNROTATED COORDINATES:  THR= ',FiO.2,
                                                                                                          I XHN= IFiO.~2,  I YHN= I,FIO.2)
     6080 IF(NET(IC,j4-l)) 6090,6090,6110                                                         10020 CONTINUE
     6090 IF(ETA(IC,J)4-H(IC,J+1)) 6110,6ii0,e6100)                                                      '11F((NFIN.EQ.7).AN). (XH-.L-T.45.0-AND.XI-.G'T.-45.0)) GO TO 10030
     61 00 ETIC-I)-(C,+1+.5(T:CJ+H(IC,J-i1))                                    11F (NFIN.EQ.14) NFTN~i
                                 D(IC,,J~~l )=ETA(IC, j+1 )+HC IC, j+1                                  GOG TO 10080
          NE ( IC ".01 >=I                                                                        C
          DY=:DYA(J+1                                                                             C     THIS DO LOO1::' CALCULAT'ES VELOCITY AS A FUNCTION OF FLUX DIVIDED DY
          QY( IC,J+1 )=)*EA.C jl)H(Cl ) )/DT                                                     C    .AVERAGE DEPTH OF TWO ADJACENT GR1I) ELEMENTS
          ETA( IC,,J)=-Hl( IC,J+1 4O7(EgC,)H  IC,,J+1l                                            C
                                                                                                10030 DO 10050 I=1,TENj)
     6110O TF(NE-TTCIC,J--1 )) 6120,6120 ,6140                                                           1)O 10050 J= , NNY
     6120 IF( ET(C.)HIJ1))6140,6140,6130                                                                UXK(I,j)=0.001

                DCICJ-1 )=ETA(IC,,.J- f 1 )(C , J-1 i                                                   I F (J. EQ.   DDUMlY--1DI J)

                                       141                                                                                            142

          IF(I.EQ1.IEND) S)UX)  [,)iI 000 FORMAT (i1 H , 'ETAMAX FOR CR15) 12 i,                                                                       1 :2,    3 1:-93529
                1F( I- ES~ lEN) - O. . E .1)GO TO I0,1 OO-                                         119 goCONTINUE

          DDUMY=(D(I ,J)-fD( :, J-1  )/2.O                                                                 WRITE(6, 11100)
    10040 UX(IJ)=QX(IJ)/DOUjMX                                                                    11100 FORMAT(I Hi , //, -MAximum ETA VALUSES FOR ALL GRIDS  (No SE'Tup)  .
    1 0050 UrY( II J) =QY( II J) /DS>UMY                                                                   DO 11120 JJJJ=1,NNY
          00 10070 1='2,1EN!)Mi                                                                            IJRITE(6,i1i10) JJJJ,L)(ETMX(11II,JJJJ),IIII=1 ,NlJx)
          00 100)70 J=2,NNqYMl                                                                      11110 FO)RMAT(1Ill0,13,3X, 10F7.2,/,10(IHA  6X,10F7.2,/))
          IF (I.EQ.2) DUY=2.0/0(:I-:,J)+D(I,J-i))                                                   11120 CONTINUE
          IF (I.EQ.2) GO TO 10060                                                                          IFLAGZ=0
                                DUY=8/(O(+1 ,-1 )D(I+1,J)+(I-- ,J- )+D(-1 ,)+2*(IJ1 )+GO TO 270
           - 2*D(I,..J))                                                                           11130 STOP
    10060  UXO/(I.J-)BI1-1+D(J)2OI1JDC+J1)END
            -   1 +(1, J+i)                                                                         C
          QYR=(QY( I J) +QY( I, J-4l ) +QY( I+i ,J) +QY( 1+1 , J+1  )/-q. 0                        C�---------------------

          UXR(I,J)=EQR'Y(QX(I,,J)X-i2,i(IYRxm2)*DUX                                                        SUBROUTINE HUR'Cl (USQW,T.,J, X, Y, ISS,FINF * OF-,FRMAX, THETA,
    10070 UYR(I,J)=SQRT(QY(I,J)*)(2-iQXR*i*2)*DUY                                                                               Di, Dy,Rim, XH-,YHI)
          NTENT=0                                                                                          COMMON /A/ 1JUX (11I0, I10), ULY (l1 0, 110) , P(1I1Io,lI    H -( 110,1I1Io)
    10000 CONTINUE                                                                                                      DPO)X(110,110),DFPDY(110,1l0) ,IX
          0010110O J=iNNY                                                                                 DIMENSION X(110),Y11i0)
          DO 10100 IsO=1,NNX                                                                       C       **  BEWARE ** SOME SIGNS HAVE BEEN MOI)IFIED TO ACCOUNT
          IF(ETA(ISO,J).tH(ISO,,J)GE.-0.000i) GO TO 10090                                          C      FOR LEFTHANDED COORDINATE SYSTEM.
          AREA (ISO) =DRY                                                                                  COR=0. 6563E--04
          GO TO 10100                                                                                      UCR=23.6
    10090 AREA(ISO)=W'ET                                                                                   RHOA=0 .0024
    10100 CONTINUE                                                                                         IF(I.NE.0) GO TO 1
    10110 CONTINUE                                                                                         XP=-RMAXx-SIN (TH-ETA)
    10500 CONTINUE                                                                                         YP=RMAX*CO ( TI-SETA)
    CI
    C ***~********END OF MAIN LOOP   *******~******J1
    C                                                                                                      GO TO 20
    11000 CONTINUE                                                                                      10 XI=I
          WRITE(6, 11005)                                                                                  xjmj
    11005 FORMAT(iHI,//,IHl* 'TIME SERIES FOR PLOTTING GRIDS',//)                                          XP=X(I)-XHA
          15=-i                                                                                           yp=Y(J)-YH
          DO 11040 J=1,NPLOT                                                                           20 R=SQiRT (XF*XF,+YP*Yr,)
          15=15+2                                                                                  C
          WRITE(6,`11010) IPL0T(I5),IPLOT(I5+1)                                                            IF(R-LT.2200.0) R=2200.0
    11010 FORMAT(1i1    'GRID ('1,,'1,'')RAT=RMAXIR
          WRITE(6,i1020) (CTIME(l(6),(C-VAR~(1(6,I,,J),1=1,3),1(6=i,IC2)                                  EXPD=EXP(-RAT)
    11020 FORMAT(IH ,F6.2,3FiO.3,5X,F6.2,3F10.3,5)<,F6.2,3F10.3)                                           UG-S/kO~)RTEP/O
          WRITE(6,i11030)                                                                                 UJC=SQiRT (-DP/RliJAi~RAT*EXPO)
    11030 FORMAT(IHI,/I)                                                                                   ALFHA=ATAN2 (YP, XP)
    14040 CONTINUE                                                                                         DETA=AL rHA-THETA
          WJRITE(33,11050) CASE                                                                           OS)=N-BTA
    11i050 FORMAT(A20)                                                                                     VF`RIMF '7:LJSHI N (DO)
          DO 11i090 I=i , NLTGMA(       (V[PRI ME/UC+lJC/UJSG)
            1=(-1 )*2+1                                                                                     AIi'SR  FM   *+  .0)-GAMMA
          1(=11-11OT(J)                                                                                   UUlCi(RAT rIS((-).9
          L= IPLOT(J-1 i                                                                                  U.SQ=Ui x
          WRITE(33,i11060)  UPO(),ILTJ1)*12IXX=-IUhf1*YIN(AS PHIA+0.31)
    11i060 FI)RMAT(213,15)                                                                                 UYY=-tJ.1Q)(fOS ( -ALPHA i0. 31

    11070 FORMAT(AF7._2,3X,4f-7.2)                                                                         1)P 1) R     P R AT / R E X P
          WR IITE (6, I10 80 )   , L , (ET A MA X(I , M),=, 3)                                            DFI) X (I, J . P1) ROPS)RC) S ( ALPSF  IA)

                                     143                                                                                              144

          DI1DY( I,J.i) --DF1R*.SIN (-PHAO)                                                                 ENM IENDMI
          WSC-1 .(-E-06                                                                                   NNYPI "NNY-1-
          IF (U..LT .I.UR) GI) TO 30o                                                                     NNYMI =NNY-1
          WSC=~WS('+2.5E--O6m ( I . O--t.CR,/U) 3(.)2                                                     RHObJ'1 .99
    30O    CONT INUE                                                                                       G=32 .2
          AA=1 .0                                                                                         AA~i .O/ (RHOW*G)
               OUX (I * ) =AA~RH*WSC:IJX                                                                  DO 45 J=1,NNY
          LUUY (I ,J) =AY~A* xRlI0*ECx-I.J                                                                 IF(H-(IEND,J)+ETA(IENI),J).L-T.O.0) GIO TO 45
          I JK( -                                                                                         CALL I-IIRCH(UJSQIEND,J,X,Y,VF,PINF,DP,FRMAX.ITHE'TA,L)I, DY,
                                  IF (IJK.ER.1 ) CO TO 00                                                1~~~~~~~~~~~~~ RHOW,XH-,YH)
          IF(MO(I,0.R.   AOJKEQ.10) GO '0                                                                 TETA=ETA( TEND, J)
                   IF(NSP.EO.1) CO TO 00VP=                                                               ETA(IEND),J)=T.IDE-AA*(P(IEND,J)-PINF).#AST'
          WRITE(6,40)1Ij,Xli,YHi,XP,Y14,r~,RMAX,RAT,P(I,J),DPDX(I,J),                                     QX (IEND-f1 , J) =QX(TEND, J) -(ETA (IEND, J) -TETA) *DX/DT
             -         ~~~~DPDY (1, J)                                                                 45 CONTINUE
      40  FORMAT (IHO,-I=' 13, ' J=' ,13, 'XH=, E12.4,  YH=', El2.4, ' XP=', E12.4                  C
            -     ,' ~YP=' , El2.4, 'R=' , El2.4,  RMAX=' , EI2.4,                                 C      ESTABLISHl ETA AT TWO LATERAL BOUNDARY ELEMENT ROWS AND BOUNDARY
                          /Im                     ~~~~~RAT=',Ei2.4, ' NI,J)=,E12.4,                C      FLOW, QY(I,i) AND QY(I,NNY) INTO AND.FROM THESE ROWS
              I D PDX(1,J)=1,Ei2.4,  '  PDY(I,JW.'E12.4)                                            C
          WRIT-E(6,50) I,J,EXPO,C-OR,RHOi(A,US(;,DP,r'INF,AL.F-H-A,DiETA,V'R~IME                           QDO 50 J=N1,XNN Y~ l
      50  FORMAT(1HO, I=',13,' J.h,13,1 EXPO=',Ei2.4,' COR=',E12.4,                                O5   =    N
           I RH-OA=' ,E12.4,' LUSG',E12.4,1 DP=,E12.4,' PINF=',E12.4,                                     NLIMIT=NQDX(.J)
           - /iH ,50  XNMT,)001
            - E12.4,' BETA- ,E12.4,' VF'RIME=',Ei2.4)                                                      JiBP~0X()+
          WRITE(6,60) 1,J,LUH,GAMMA,RATIO,USG,UJ,UXXLUYY                                                  IP=~j()-
      60  FOMT10I,3'J=',13,' UH'l',Ei2.4,' CAMMA=,C.12.4,                                                  DO 70 I-:DFP2,TEND
                RATIO=',EI2.4,IUSC=1,E12.A,' U=I,E12.4,1 UJXX', E12.4,                                     IS=IEND+IBtP2-I
                UYY-=C',E24)                                                                               IPI-
          WRITE(6,70) I,J,WSC,UUX(I,J) ,UUY(I,J) ,THErTA                            GFHIPJ+T(SLT00    O TO 70
      70  FORMAT(iHO,'I=',I3,  J=' ,1,                                                                     CALL HURCH(USQ, ISP,J],X,Y,VF,PINF,DFP,rHA)(,THIETA,DT,D)Y,
           - WSC=',Ei2.4,                    UUJX(I,J)-'~,El2.4,' LUY(I,J)W,Ei2.4,                       -RHOW,XI-1YH)
           - THAETA=-  Ei2.4)                                                                             TETA= ETA(ISP,l)
          mSP='1                                                                                           ANT=O.0
      80  CONTINUE                                                                                         ETA(ISP,J)=TIDE-AA*(P(IRP,J)-FPINF)-iAET
          RETURN                                                                                           QY(ISP,,J)=QY(ISr,2).t(ETA)(I.P,.J)-TETA))*DY/DT
          END                                                                                          70 CONTINUE
    C                                                                                                       J=NNY
    C                                                                                                       IBP2=NQBX(NNYM1 )+2
    C                                                                                                       DO 00 I=IDP2,IEND
          SUBROUTINE ETABCS (XH,YH-,TS,X,Y,VF,DP,RMAX,THiETA,RHOW)                                         I9=1END+IBP2-I
          COMMON /A/ UIJX(110, 110) ,t.UY(iiO,110),FP(10, 1io),Hl(i10,i0) ,                                ISP=IS--i                            C   O0
             -        ~~~DFDX(11O,110) ,DFDY(iiO,110),DX                                                   IF(Hl(ISF,,J)+ETA)(ISr,,J).LT0.(-).)GTO8
                                  COMMON  0/ ETA110, 11) ,QX(  10,110,QY(11,110>,NBX(1l0,TIDECALL I-IURfCIA(UEQ,1ISP-,.J,X,Y,VF,rINF,DP,RMAX,THETA,DT,DY.
             -        ~~DY,NNX,ITEND-RHWHY)
          COMMON /C/ Is~                                                                                   TETA=ETA (ISP, J)
          COMMON /E/ PI NF, DT, NNY                                                                        ET-A(Isp"J) =TIDE-AA*-(P (ISP, J) -PINF)
          COMMON /F/ ..IIj                                                                                 BY (IS P ,N N Y P  =Y ( I S P, N NY)ETA (I SP ,J) - TET A 1)*Y/) T
          DIMENSION X(11),Y(iio)                                                                       0 0 CONTINUE
                                                                                                     90 RETLJRN
         C  THIS SUBROUT'INE ESTIABLI-SHES E.TAS Al SEAWARD GRID IN BALANCE WITH                            END--------
    C       BAROMETRIC F:ESi   AND SETS ETAS AT TWO LATERAL BOUNDARY ELEMENT                                SBOTN   ALR  ,J  F
    C       ROWS IN BALANCE WIT H T DlE DAR0METRY.C P VRESSURECOMN//UX1.11)ULY10,1) F1010)H(1,11)
    C       ESTABLISH ETA Al'FSHR   END  AND FLOW INTO OFFSHORE ELEMENT DUE                       C        OMO DI.D 11,10  DrD  10,10
        C   TO CHANGES IN ETA                                                                               COMMO  /0/ IT( 10 110 ) , XCYI 0 10)  Y( I          I)NB~   10) ,TIDE
    C       JH- IS X HIUERRICANE. I NDFX                                                                    -OMN  B
          USQ=0.O                                                                                         -             IY, NNX, TEND

                                                                                                                                      146
                                       145

           C.OMMNC)N /I I/ I FFAC T (  C) j j C)                                                          ftF=F /A 2
           l.F9UM=O. 0                                                                                     RETURN
           TF U M = 0. 0                                                                                   END
           DO05 IF = i,
           IPM   lp--l+I                                                                                   SUBROUTINECMPFH   l*AAAA   DOFTF02
           OVA   ET'A(IPM,J).(+I(IPM,J)                                                                    A6=A4+A5*D2/l 0.0
           02   OVA                                                                                        IF(A6.GT,l O)A6=4 .0
           IFA =IFFACT(IPM,j)                                                                              TF=TF+FA6
           CALL FRICT(IFA, OVA,1FlF,-TF,D2):)                                                              03  =02
           OF SUM =BFSU M # OF                                                                             IF(A3.EtQ.5.47) D3m=01
         5 TFSLJM=TFSUM+TF                                                                                 IF (fl. EQ). I . 0) CO TO 1 0
           OF   = FSLJM/1.0                                                                                PHI =10(o(1A~r~3*i33)*.
           TF = TFEUM/2.0                                                                              10 BF   12/*2*AoO(3D+.))2�I
    C      TF    1 .0                                                                                      RET URN
           UUX(IJ)=UUX(I,J)*TF                                                                            END
           UUY(I,,J)=.ILJY(I,J)*Ti:'                                                                C�-----------------------------------------
           RETURN                                                                                          SUBROUTINE  sAr~R(N, I,.J,F,DT,FACTX,FACT1Y,14X,t4Y,fICOUJN,NINL-)
           END                                                                                             COMMON /BAR/NOAR5)IA()JO(5)XLR50HAR0)

           SUBROUTINE FRTCTITREM,01 ,DF,TF,D2)                                                              DPN(0XE XS IN 0) LNL )
           IF(IREM.GE.io) GO TO 10                                                                         COMMON /A/  UCI,1)UY10I0)P1010,(1,1)
           12=1                                                                                           -             DPDX(1 l0,iiO),DP0y(JJ(,iiO),DX
           G0 TO 40                                                                                        COMMON /0/ ET'A(IiO,IiO),QX(IiO,i10),QY(410,i110),NQ13X(110),TIDF,
    10(    IF(IREM.rGE.100) GO TO 20                                                                                    D Y,NNX,IlEND
           12=2                                                                                            0= 32.2
           G0 TO 40                                                                                 C
    20     IF(IREMGE.1000) GO TO 30                                                                C      THE PRESENT TREATMENT IS FOR SUBMERGED BARRIERS ONLY
           12 =3C
           GO TO AO                                                                                        NORB=NORBAR (N)
    30     IF(IREM.LT.lIOOOO)I2=4                                                                          IMI =I-l
    40    PE=O.O                                                                                           IC=I
           TF=0.0                                                                                          JMI =J
           IDIV=li0**12                                                                                    JC=,J
           DO 90 1=1,12                                                                                    OL=:DY
           IDIV=IDIV/1 0                                          DS.--OX
           ITEST=IREM/IDIV                                                                                 QC___-X(ICl JC)I
           GO TO (50,60,70,B0,85),ITEST                                                                     IF (NORB.EQ.i) GO TO 1
       50 PHT=1.0                                                                                          IMI =1
           IF (Di .LE. 110,0) D1=l0,0                                                                      JM1 =J-1
           02 = Di                                                                                         DS==DY
           CALL COI)I000054.1  0000   OT,2                                                                 L=DX
          00 TO 90                                                                                        Q=YIC
       60 PHI=O.0                                                                                      10 CONTINUE
          CALL COMP(PI-'i,O.999,0,34, 10-94,0.3,0.0,D1 ,BF,TF,D2)0lHM1JM)ET(M    MI
          GO TO 90                                                                                         1)3=I-( IC, JC) tETA( IC,_JC)
       '70 rH I =1  0                                                                               C
          C AL L. LOMP(PI I I , 0. 0, 0. 0, 0. 91 , I  00,0.0,I  , DF, Tr-, 02)  2                    --AVI. RAG'E WATER SURFACE ELEVATION
          GO T0 90                                                                                 C
       UOC30   H=0.0                                                                                       ETABAR=O.5)((ET ACIMI .JMi )+ETA(IC,JC))
          CALL                                                                                             14 =ODPI,.6,  54,1.9,.,.,1,F  F  2  I..0
          GO TO 90                                                                                         W 3: 1) L
    05    P I II  0 .0                                                                                      D X i= O .5*1) S-- XL BA R (N
          C A L.L. fO M -( PHI , O.6 4 ,O. 2  ,iO . 9 4,   0 , O).0 1)1  ,F ,TIF ,1) 2                     D)X3=)Xi
    90     1 RCM=  1REM -I T ES T itI 1 Iv                                                          C
          A2-FLHAT 12)                                                                             C       THIS NEXT LOOP11 DETERMINES WHETHER THE RE IS AN INLET
          TFml'F/A2                                                                                 C      1000O011 THE BARRTICR OF CURRU7NT INTEREST

                                       147                                                                                              148

                              C                                                                               ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~SA I =SRT(AL PHA I
           DC) 20 NI=ININL                                                                                      SAB=SQRT ( ALPHAI.')
           IF GIN(I.E.   RJN.(I.Ej    O TO 20                                                                   T2-(Tr21*WI*1)1.f.T22xtWI:(*DrtAR) *IX2/(W11+lJIu
           NINC=-NI                                                                                              XMI.J-Ti/(DI *Wi41-)DX2/(WDf+WI )*(,21 +T22)-lT'3/(D3*iiW3)
           WI =WI NL (NINHE)                                                                                     FACT= 2. 0/(XMI.J*DL) x.(TI +T2+T3) /(D-412o)
           IF  GNRN  N)E.1031   O TO 30                                                                         TEMPv.ALI-1-AI*WI*DI/ (1 .+SAI/SAB)**2+ALPNIAO*KWI.')DDORI7/ (1. O4Si-13/,Tt ) *i2
       20 CONTINUE                                                                                              WS= (DL/Dg) *(T4+T!5+TEMP) *A119(QC)
           141=o 0                                                                                               WS=W9*DT+i .0
    C                                                                                                        70 CONTINUE
    C----DEPTH  OVER BARRIER                                                                                     IF(NORBAR(N).EQ.l) GO TO0 00
    C                                                                                                            FA.T Y=FAf_'T
       30 DBAR=ETADAR+HfsR MN)=W
           DXTJ=XLDAR(N)                                             GI                                             TrO 90
           FB=FDOR (N)                                                                                      130 FACTX =FAC:T
          WB=WBAR(N)                                                                                           WX= WE
           IF (D)OAR.LE.0.0) 140=0.0                                                                         90 CONTI NUE
           IF GW.T00O.WT00    O TO 40                                                                          NZIP = 0
    C                                                                                                            IF (NZIP .EQ. 0) GO TO 250
    C      IF DBOR 1S GREATER THAN ZERO,  DARRIER IS OVERTAPPED                                             100 IF (IICOUN.GE.10) GO TO 250
    C                                                                                                       i10 IF (IICOUN.GE.20) GO TO 250
          145=500.                                                                                              I ICOON=I IGOUN+l
          FAC`T=0,0                                                                                             WRITE(6,120) IICOLJN,N,NINC,NOR~BAR(N),IEIAR(N),JEtOR~(N)
          CO TO 70                                                                                              WRITE(6,130) IMiJMi,IC,JC,1)L,DS,QC,Dl,D3
    c                                                                                                            WRITE(6,`140) H(IC,~.)C),H(IM1,JMi),ETA(TC,JC),ET-A(I~i1,JMI),ETABAR~
    C      THIS SECTION FOR GRID LINES WITH INLET THROUGH BARRIER                                                WRITE(6,`150) Wi,W3,D)Xi,DX3,DX3, DX2,DE4AR,I-IAr~(N)
    C      WHETHER OR NOT BARRIER IS OVERTOPPED                                                                  WRITE(6, 160) WI,FB,D1,FI,DXX,DX2
    C                                                                                                            WRITE(6,170) Ti,T3,T4,T5
    40     DI=DPINL(NINC)+ETABAR                                                                                 WRITE(6,180) T21,T22,T8,T9,T_99
          FI=FINL(NINC)                                                                                        WRITE(6,190) Ti,T7,T67,T2,XMIJ,FACT
          DXI=XLINL(NINC)                                                                                      WRIT-E(6, 200) 145,CDT,FAC`TX,FACTY,WS, WX, WY
          CONTINUE                                                                                             WRITE(6,210) WN,F
          IF (WB.NE,0,0) DX2=D)<B                                                                              WRITE(6,220) QX(IM1,JMI),QX(IC,JC),QY(IM,,JM1),QY(IM1,JC+i)
          IF (WI.NE.O0.) DX2=DXI                                                                               WRITE(6,230) iU(MJIJXICu(MM)IUyIC
          Ti--DXi/(D1*Wi)                                                                                      WRITE(6,240) OPDX(IMi,JMi),DP-DX(IC,,JC),D)PDY(IMi,JMi),DPDY(IC,,IC)
          T3=DX3/(D3*W3)                                                                                120    FORMAT(iHi, -IICOUN=',I3,/iHO,1N=',13,    NINC=',I3,'  MOREAR<N)=1,
          T4=F*DXl/(8.0*Wim*01**2)                                                                            * 13,1  IBAR(N)=',I3,'  JBAR(N)=' ,I3)
          T5=FitDX3/ O. 0*W3*D)3**2)                                                                    130    FORMAT(fIH      M=,3          JMI=',I3,'  IC=',13,'  JC=  13.   DL=',
          T21=0.0                                                                                             * FB.1,1  DSB,               C=',F8.3,'  Di1=,F8.3,1  D3=1,FB.3)
          T22=0.0                                                                                       10     FOR1IAT(IH-  'H(IC,JC)=',FO3,'  H(IM`I,JNi)=',F8.3,'  ETA(IC,.JC)=',
          T6=1 0000.0                                                                                         * FS,3,'  ETA(IMl,JMl)=1,FO.3,'  ETABAR=1,FO.3)
          T7=iOOOO.O                                                                                    1 50    FORMAT(iH  ,W-F.              W3=', F8.1i,'  DXi=',F8.l1,   D13=', FB.1i,
          T8=iOOOO.O                                                                                          * .   XB= ,F8. I , DX2=',F8.1,'  DBAR  , F8.3 I             HBAR(K)=1,FB.3)
          T9= 0000.0                                                                                   '160    FORMATCI l     WHFO1           FB=',F8.5,'  DI-'F-B.3,'  FI=',FB.5,
          T67=1 0000.0                                                                                        it   I)Xl=  FCJ3 i    DX2=',FB.1)
          T139=1 0000.0                                                                                 170    FORMAT(IR 111,-T      , El2.5, -T3z-' , E1i2. 5,    T4= 1,i2.5,'  T5=',El2.5)
          IF (WEC.EQ.0.0) GO TO 50                                                                      1010    FORMAT(iHi  .'12=',Ei2.5,'  T22=' ,El? 5,1  T1    , E12. 5,    T9='
          T22=WD/(CDBARmUB))(V-2                                                                              *( E12.5,'  TO9='E12.5)
          TO=-Fj-*I)Xr/ (.0WWD)ARX 3)                                                                   190    FORMAT ( I H , 'T6:- EI C2. 5, 'T7=', E1 25, '   67=  El12.5,'-  T2:=',E1l  5,
          T9-XI(EX (N) / (2. 0*DIARM1)=RXWDEWI                                                                      XMU    FV'         FACT=',E12.5)
          Tfl9= (TO I ?1)x(W1'/(WB-f WI X))  2                                                          200    FOfalAT(  (IH , 'WS~  , F S.5,    O )T=' , FB. 3, '  FACTX= , FO .5, 'FACGTYg-
       50 IF (WI.EQ-.00) CC) TO 60                                                                             * F8.5,1  Wsm   F8.5,   IWX= ' -1. 5, 'WY=1FR.5)
          T21 m:WI/CDI~*W:f ) x 2                                                                       2`10    FORMAT (1iH'W=I 141  ,F1.1I,   DF-'  F0. 5)
          T6=FI*DXI/(8,O*DIx*39WIy*2)                                                                   220    FORMATCIH    '4X (I Ml , JMI   EI ,E2  .4, '  QXXCIf, Jl;)- , El2 12,
          T7=-XI<ENE-X MNG)C/ (2. 0)(1:*oX-I iWI*WI 3                                                         * .QYC]:M , JMli) , ElI.?. 4,    QYCIMIl , JC+1 )=  El  2A)
       60 A LPHOAI-T 6 4T7-                                                                             230    F 0R MA T lI I,  UJXC(IM I ,JMI )' ,E 12. 4,  1UJUX (IC_`)-   El' 2.a,
          ALPHAB=TB iT9                                                                                       *     ULIY (:ItH , JM1 )=,E1 2.4,    CJUY(I- JM =' E12 .4)

                                       14910

     240   FORMAT(1III , 'DFIX( IMI, JMi ) -  ,E2A4    DPDOX(ICj)    C23                     ~N).TCN
            .  1)1-DY( IMI _JM1 )--J`I2.4, El DPY:CJ)          2.4,/////)                            C

            ENDC

            SUBROUTINE DEE(JDRNNA,,C,,AS  SCSOSETCQCJNT)C  80 FORMAT( I II , -  SWEE.P:  JJ=',1.                                                     16
     C                                                                                               C      IF (.JJ.NE-07-OR~~JC~NE.40.ANI).JC.NE.10)) GO TO 60
            COMMON /B/ ETCII),X11,10,~(1,1)NO(1)TDC                                                       WRITE(6,90)
              -        ~~~~DY,NNX.IEND                                                              C  90 FORMAT( I I-,                 I      AUI)      B(I)      CU).    0I.
            COMMON /F/ JJ                                                                            C    -EUl)       FU)I    AS(I)       B (I)      CSU)       5()       ESUI)     FS(I
            DIMENSION A (1l 0) , El(1 I0) , C  10) , D 1I0) , E(11I0) , F I 10)                      C    -)  ETACUI)    ~(,
            DIMENSION AS10,S1I)C(1)D(1)E(1)F(1)C                                                            WRITE(6, 100)  IAI,()CIDI)E),F)AS).OICI)
            DIMENSION QC(il0),ETAC(I10)                                                              C    I                D()E()F()EA()Qc)I,   NI
            DIMENSION NET(110,Ii0)                                                                   C 100 FOR~MAT(16,3F9.4,F9,2,5F9.4, F9 .2,2F9,.3,2F'9.2)
            DATA 11COUN/O/                                                                             110 RETURN
     C                                                                                                     END0
     C     IF IDIRmli, SWEEP IN X-DIRECTION                                                         C------------------------------------
     C      IF IDIR=2, SWEEP IN Y-DIRECTTON                                                                SUBROUTINE INIT~l(1,J,BlF,DT,FACT-X,FACTY,WX,WYIICOUt.N,NDARNINL,
     C                                                                                                                        IM PD IR)
            NNMI=NNI-i                                                                                      COMMON /F/ .JJ
            IF (IDIR.EQ.2) GO To IO                                                                         COMMON /BAR/ NORBAR~(50),IBAR(50),JI1AR(50),XLDAR~(t5O),HTJR(50),
     C- WBAR(0),FBAR(5)X<EX(5x~(0),NORINL(!50),TTNL(50),I,JIL(50),WINL(50),
     C     CARRY OUT FII;~ST SWEEP TO CONDITION COEFFICIENTS                                              - OPINL(5(-)),XlrENEX(50) ,FINL(50) ,XLINL(50)
     C                                                                                                     FACTX=I .0
            E(NNI )=O.0                                                                                     FACTY=1 .0
            F(NNI )=ETA(NNI, JC)                                                                            IF (NDAR.EQ.0) GO TO 20
            ETACCi )=ETA(1 ,JC)                                      DO                                        IO N=I,NOiAR
            GO TO 20                                                                                       IF (IDAR(N) .NE.I.OR.,IDAR(N).NE.J.OR.NORDAR(N) .NE.IMPDIR)
         10 CONTINUE                                                                                      -     GO TO 10
            E(NNI )=O.O                                                                                    CALL BARR(N, I,J,DF,DT,FACTX,FACTY,WX,WY,IICOUNNINL)
            F(NNI)=ETA(JC, NNI)                                     IO                                     CONTINUE
            IF (NET(JC,NNI).EQ.0) F(NNI)=0.O                                                            20 RETURN
            ETAC(1i)=ETA(JC,NNI)                                                                           END
         20 DO 30 1=2,NNMI
            IC'~NNM1 2-I
            I CP= IC+ i
            DEN=A(1CP)*E( ICP).iB(1ICP)
            IF (DEN.EQ.0.0) DEN=1.0
            ES( IC)=-C(ICP)/DEN
            FE(IC)=(D(ICP)-A(ICP)*F(TCP))/DEN
            DEN=AS(IC)*ES(IC)+DS( IC)
            IF (DEN.EQ.0.0) I)EN=1.0

    *30 CONTINUE
     C
     C     CARRY OUT SECOND SWEE-I:P TO EST AOLI._'.7I ETA AND Q
     C
            DO 40 .1=2,NNI
            IM4= I-I
            (TAc ( I )=Es( im ) m'c (' Sf )F'( I)
     4()   CONTINUE

            E(1 >=ETAC(l )

                                                              151                                                                   ~~~~~~~~~~~~~~~~~~~~~~~~~~152

                                                                                            ccCCCcc  ccc CccCCCCC cC(ccc .C cc   cc C           cICC,      ccccc cc 1; c cCCC

                                                                                            c      ONE-DIMENSION NUMERI:CAL STORM SUIRGE MODIEL
                                                                                            C,
                                                                                            C
                                                                                            CCCCCCCC CC3CCCCCCCCC      CCC CCC(CCC cCcccccccccc     CCcccc  c  ccccccc
                                                                                            C

                             APPENDIX B                                                             DIMENSION CTS(3,5,1200)  COUNTY(4),FOFIL(i),CASEI5),OATE(6)
                                                                                                  DIMENSION 1-1(200) ,X(200) ,ETi(200), QY(200),EMXMILN(5,2)
                        1-D STORM TIDE MODEL*                                                     10 FORMAT(5A4)
                                                                                               20 FORMAT(5A4 ,15,2F7.2)
                                                                                               30 FORMAT(5(F9.0,F7.2))
                                                                                               (40 FORMAT(10F7.l ,313)
                                                                                              100 FORMAT(iH )
                                                                                              11I0 FORMAT(`IHi, ONE-DIMENSION NUMERICAL STORM SLURGE MODEL',T49,
                                                                                                 I 'RUN DATE:  ',6A4,/IH ,41('-'),///)
                                                                                              120 FORMAT(IH ,4A4,4X,5A4,/IH ,40('-')///)
                                                                                              130 FORMAT(1I- ,'PROFILE DATA -- (DISTDEPII):
                                                                                              135 FORMAT(5(iH ,5(F7.0,F7.2,2X) ,/))
                                                                                              `140 FORMAT(4VI-,'INPUT PARAMETERS:',//III
                                                                                                 i     I  PINF=' , FS. 2, T26, I PO=m I , F - 2 T5  , DP=:', FE). 2, /11
                                                                                                 2        'ZLAT~' , FB.2, T26, 'RMAX-' ,F 8.2,/1HI
                                                                                                 3        'COR=',Ei2.4,T26,'VF=',F8.2,//1H
                                                                                                 4        'THETAC=' , F9.2,T26, 'TIHETAN='' FS.2, T51, 'THETAW , FS.2,/IH
                                                                                                 5        'XSITE=' , FS. 2, T26, 1 XVIC= I, FS.2,T51 , 'XI.ID=' , FS.2, /I H
                                                                                                 6         YSTI'E=' , F8.2,T26, 'YI-'C , FS.2, T51, 'YH:=' ,F-8. 2,/1H
                                                                                                 7        'XOFF=' , FS . 0, T26, 'DTIST=' , FS.2,/1HV
                                                                                                 a 'DT=',FG.2,T26,'TMAX=' FS.2,T51-,NTIMES=',I5)
                                                                                              145 FORMAT(1H ,4A4,4X,5A4,20X.X5A4,/iH ,80('-'),///)
                                                                                              150 FORMAT(IH-,-'TIME STEP ',15,5X,'TIME=',FS.3,' IIRS.',SX,'XHl',
                                                                                                 I F9.2, ' N, MI.', 5X,'YI-I=',,F9.2,' .MI'//1
                                                                                                 2        'STORM SURGE, ETA(I) IN FEET ADOVE MSL -- (I,ETA):',//,
                                                                                                 3        (IN ,6(15,F9.3)))
                                                                                              160 FORMAT(iH ,20X,'CONDENSED TIME SERIES OF STORM SURGE ETAS',//iH
                                                                                                          4A4,4X,5A4,20X,5A4,///I-
                                                                                                 2        2(' TIME   SURGE   SETUP U/SETURP W/DYNM)
                                                                                              170 FORMAT(i-I ,F5.2,4FB.3,6X,F5.2,4F8.3)
                                                                                              175 FORMAT(F5.2, 41F.3, 6X,F5.2,4FB.3)
                                                                                              100 FORMAT(iVI--,'MAXIMUM SURGES FOR ',4A4,2X,5A4,2X,5A4,//I  .5X,4F8.3)
                                                                                            C
        This program represents a numerical modeling procedure that is subject
    to change due to: 1.  newly encountered topo-bathymetric and hydraulic            I110F- 0
    boundary conditions, and 2.  incoporation of new advancements quantifying                         kHAi, 0.0024
    coastal processes.  This program is applied on a county-by-county basis and                        OON II� .99
    is subject to acceptable calibration constraints recommended by the Beaches                       G;-32. i
    and Shores Resource Center and approved by the Florida Department of Natural                     1`3 i 417
    Resources.                                                                                        i C, r 0.0025
                                                                                                   CNM=6076 .
                                                                                                   CLHR=600.
                                                                                                   CIHG=70.51
                                                                                                   C 1) E G::N  1 0 0. 0/ / :1
                                                                                                   OME GA ::2. Oi(-P ]/ (24. 0H ClHR
                                  153
                                                                                                                             154

          DETIA2=i .5                                                                                 TEATE  /IE
          TIDE =0. 0                                                                                  XHB=X H * CNM
    C                                                                                                  Y H =YHFJ*tC NM
    C                                                                                           C
          READ (5, 1 0) COUNTY                                                                        DO 31i0 I1=1 , IHPI
          READ(5, 20) P-ROFIt..,]'MAX, XS'IITE-,YSITE                                                 QY(I)=0.0
          READ(5,30) (X(If-1 ),HI) ,I=i ,IMAX)                                                    310 CONTINUE
    C                                                                                           C
                                WRI-TE~~~~~~s~~ilo) DAIE  ~ ~ ~ ~ ~DO 320 1=1,5
          WRITrE(6, 110) DA.LjTE,'OFI                                                                 EMXMN(I,1)=0.0
          WRITE(6, 130)                                                                               EMXMN(1,2)=0.0
          WRITE(6,135) ((1HI)=1IA)320 CONTINUE
                          C                                                                   ~~~~~~~~~~~~~~~~~~~~~~~~~~C
                            C                                                                         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~TIMSC=:-D'T
          IMF-1 =IMAX+1                                                                                Is=0o
          XOFF= XSI TE *CNM                                                                     C
          XCI =0.0                                                                                    CALL. HURFCH-(IS, X,XSITF,YSIT',XH,YHI,PINF,DOP,RZMAX,VF,ITHET-A,
          DO 290 I=1, IMPi                                                                            I            RHOW, RHOA, CORD 050, P, TAIX, TAUY)
          X(I)=X(I)+-XOFF                                                                       C
      290 CONTINUE                                                                                     USQM=USQi
          DO 295 I:=i , IAX                                                                           UMAX=SQRT( US ) *CH1R/CNM
      295 H(I)=H1(I)+0.0                                                                               AA=-RMAX*DP/(CCNN*CHr*I 00.0)
          WRITE(6, 135) (XC 1+1) ,H-(I), 1=11IMAX)                                                     AA2=0.1 60*VF/SQRT(UMAX)
    C                                                                                                  HNMAX=16.5*EXP(AA)*(1 ,0+AA2)
    C                                                                                                  ITlAXI =8.6*EXP(AA/2.0)*(i .0+AA2/2. 0)
          XSIT=XSITE*CNM                                                                        C
          YSIT=YSITE*CNN                                                                        C
      300.READ(5,10,END=999) CASE                                                                      DO 600 NTIME=1,NTIMES
          READ(5,40) DT,TH-ETAC,ZLAT                                                            C
          READ(5,40) PINF,DP,RNA~X,VF,THAETAN,XHBI,YHDf,DIST,-TMAX,TMIN,                               WSU"0.0
            i        ~~NPARM,NTIDE,ION                                                                TI MSCT IMSC-fD'T
                                                                                                    XHi=XHD+VF*TIMSC*COS (THETA)
    C                                                                                                  YH=YHD+-VF*TIMSC*SIN (THETA)
          PO=PTINF+DP                                                                                  TI MHR=T IMSCCIC HR
          THETA=THETAN-THETAC+90.0                                                                     XHN=XH/CNM
          IF (THETA.GT.360.0) THETA=THETA-360.0                                                        YHN YH /CNN
          IF (THETA.LT.0.0) THETA=THETA4-360.0                                                  C
          COR=2 .0*OMEGA*SIN(Z LAT'/CDEG)                                                       C
          NTINES=IFIX(TNAX*CHR/DT )+1                                                                  ETASUM=0.0
          INTERV=IFIX (CHR/O)T/2 .0)                                                                   SLIM.ST R= ~0 .0
          INTER4=4*INTERV                                                                              CSUM=0.0
          NSTORE=IFIX(i100.0/OT)                                                                C
          IF (NSTORE.EQ-,.0) NSTORE=1                                                                  DO 500 I=I,IMAX
    C                                                                                                   IS=IM1AX-I1-i
          WRITE(6,1I0) DATE                                                                            CALL. HUR.1CHl( IE,X, XSTl, YSIT , XHi,YH,rPINF,DOP. RMAX, VF,I'THETA,
          WRITE (6,1 45) CONYiRFICS                                                                               RHOW, RHOA, COR, USQ, P, TAUX, TAUY)
          WRITE(6, 140) PN,,DSATRNCODVTTAHATHAETAPR='I .0-/(CRHO)W*G )*(PINF-P)
                                     XSITE, XC, XHOYSITE, HC, YII, XOFFDIST, D, THAXNTIMESDX=-X( I5+1 )--X( IS)
    C                                                                                                  TDTHH(I)4+ETASUM
          PINr-'F P1NF * C H;                                                                          IF (T EQ. 1) TDPTHl=H( IS)f-TIDE
          F0p )-;pOeV.H (;                                                                             IF (TD)PTIll.CT 0.0) GO TO 400
          DP-Drl*CHC CGO TO 4150
          RNMAX=RMA XH*CNN                                                                        400 SLIMS TR=SU.MST R TAUX*DX/ (RHO('W*G*TDPTHi)
                                 VF=~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~E VI:* N/  REA (IS) =ET''rA I'R---SUINS TR:+ TI1 IE
          TUE  I T A C= T IHE I AC/Cl) G                                                               E ETASUIM=E TA( IS)
          THE TAN=TH UI TAN/CDF. ERTDT-I(S)+TASI.M

                                                           155                                                                  ~~~~~~~~~~~~~~~~~~~~~~~~~~156

           BD IV i .0 + 1)I xFF RI C T*A 1.S7 ( Q Y (I) ) / I DDPTIITOr 1) 1-, F1P  I 1+1
            RY (I S   (QY (I S +Dr / RI io w ~r  .T  y     Li                                                W RI TE ( 6, 1 7)   C (TX (  ,J , K ,J I ,5 ,K =I IFI'I
           C:CTI DE-DIX*(',(:)Y (iS/ y( t~*T                                                                WRITE(8, 175) ( CT S I  J , K .J i ,5 ,i<=<i, Ill)
           CSUM'=CSUI1 f  I' IDE                                                                        61 0 CONTI NUE

           ETASUM=ETA (I 9)                                                                          11I    1ORMAT (2F i0,i )
    C                                                                                                C
           IF ( INS NE 1 i) GO TO 500                                                                       WRITE (6, i 0) COUNTY, PROFIL, CASE, (EMXMNXI), I =:2,)
       450 H0=HMAX*8S (USQ) IUS('M                                                                           WRITE(10,4130) COUNTY,PROFIL.,CASE,(EMXMN(l,i),Ip'2,'5)
           I F (L)EQ. GT~ 0 0) 101r  . 0                                                             C
           T0=2.1 3*SQRT(jI-0)                                                                               I ON'- i
           Ilr.'0  936 XI I0                                                                                 VO TO 300
    C                                                                                                999    RETURN

                              C                                                                            ~~~~~~~~~~~~~~~~~~~~~~~~~SUBROUTINE HLIJRCH(IS, X, XSITrE, YsiTE, XH, YHi,PFIF.F,YPr~MAX. VF-,TH-ETA,
                                 C  ~~~~~~~~~~~~~~~~                                                       I        ~~~~~~~~~~~~~~ Ri-OW, RI-IDA, COR, USQ., P, TAUX, TAUY)
           ETASU[1l=EASUM-f-EtIA2*tWSt.                                                                      I)IMENSION XCI)
           IF ((ETA(IS)+HCIS) ).GT.0.0) GO TO 500                                                    C BEWARE  SOME SIGNS HAVE BIEEN MODIFIED TO ACCOUNT FOR LEFT-HAN)EI) COORD
           ETA(1 )=O.O                                                                                       UCR=23.6
           GO TO 5`10                                                                               *        IF (IS.NE.0) GO TO 4
    C                                                                                                        XP=-RMAX*SIN (THETA)
      500 CONTINUE                                                                                           YP=RMAX*COS (THETA)
    C                                                                                                        GO TO 6
    510   CONTINUE                                           4                                               XIE=O 5*(X(IS+l)+X(IS)
           NTM=(NTIME-1 )/NSTORE+i                                                                           XF'~XIS-x1-
                                   CTS(1 .1 ,NTM)=TIMHR                                                    ~~~~~~~~~~~~YP=YS ITE- Yl
                                 CTS (1,2, NTM ) =ETA (1)                                           ~~~~~~~~~~~~~~6 R=SQRT(XFP**2+YP**2)
          *CTS(I ,3,NTM)=WS'U                                                                                IF(R.L.T.2200.0) R=2200.0
           CTS1`,4,NTM)=ETA(l)+WSIJ                                                                          RAT=RMAX/R
           CTS(i ,5,NTM)=ETA(1 )+1 .5*WEU                                                                    EXFO=EXP (-RAT)
    C                                                                                                        I.JSG=-DP/ C RHOAAR) X-RAT*EXPO/COR
           DO 520 1=2,5                                                                                      LJC=SQRT(C-,DP/RIAOA*RAT*EYPO)
           IF- (CTSCi,I,NTM).GT.EMXMN(I,i)) EMXMN(I,i>=CTS(J,I,NTM)                                          ALPI-A=ATAN2(YP,X)P)
           IF (CTS(l,I,NTM).LT.EMXMN(I,2)) EMXMN(I,2)=CTSC1>,I,NTM)                                          BETA=THETA--AL.PI-A
      520 CONTINUE                                                                                           VPRrME=VF*SIN(BETA)
    C                                                                                                        GAMMA=0. 5*(VFRIME/UC-tUC/tJEG)
           IF (MOD(NTIME,INTERV).NE.l) GO TO 600                                                             RATIO=NQRT (GAMMA**2+1 .0)-GAMMA
    C                                                                                                        IF(RATIO.LT.1 .OC--05) RATIO~1 .OE-05
           IF (MOD(NTIME,INTER4).EQ.1) WRITE(6,1i0) DATE                                                     U=UCi(RATIO*0. 9
           IF (MOD(NTIME,INTER4).EQ.1 ) WRITE(6,1,45) COUNTY,PROFIL,CASE                                     USi=LWA2
           WRITE(6,15O) NTIME,TIMI-IR,Xf-N,YHN,(I,ETACl)I=I,1IMAX)                                           UXX=-USQ,*ElNC -AEP-HA+O.31)
           WRITEC6,151) (CTS(1,I<,NTM),=2, 5)UY=SG*O(-LFA01
    151    FORMAT(IHO,'FTA:',FB.3,4X,'WVI.:',Ff..3,4X,'ETA4-USUJ:',FO.3,4X,                                           O~I~D*1.-EXPO)
              -   'ET-f I f  5-KWU; ,Ff.].3)                                                                 WgC=1 .OE-06
    C                                                                                                        IF(U.LT.LJCR) GO TO 20
      600 CONTINUE                                                                                           WSC=WSC� f2.151E,-06* (1 .0-UCR/U) **2
          DO 605 T.- 1,5                                                                             20     CONT .INUE
      605 CTS (I,1,,NTM'1) =0 0                                                                             AAm;  .0

          WRI TE (  515 )NI'M                                                                               IF CI.E.)UG=X
    152   FORMAT(15)                                                                                         RETURN
          1)O 610  =1 1NHIM2                                                                                E EN
          I F (M i)( I I100) ELI 1) iW  IJTE(6, 11i0 ) DAVIE
          IF  MO(110    .1)WR~ITE (6, 160) COUNTY, PrOFn', CASE
          IF (MOI1)(   )WRIIEC6,400)

                                      157                                                                                                158

                                                                                          C     EROSION MOIEL
                                                                                          C
                                                                                          C

                                                                                          C
                                                                                          C

                              APPENDIX C                                                     C

                        BEACH-DUNE EROSION MODEL*                                            C
                                                                                          C     NOTE:   THIS PROGRAM WAS USED FOR CHARLOTTE COUNTY, APRIL 1i94.

                                                                                                DIMENSION DH1(200)',DX(200),DPTC(200),
                                                                                                           STA](12(),STA(120),XAO(200),XAW(200),HiW(200),
                                                                                                           X(2(0,2),NCON(200),
                                                                                                           XASAVE(200),HASAVE(200)
                                                                                                DIMENSION XTOT(6),DXTOT(6),NTC1T(6)
                                                                                                COMMON /A/ HI (200) ,XA(200) IHA(200),NELM,X1 (200),NPl.NELMi
                                                                                                CHARACTERK8 RNG, RNGDAT, DOTDAT, DCHDAT, OFFDAT
                                                                                                CHARACTER*3 CNTY.CNAME3(5)
                                                                                                CHARACTERKI0 CNAME(5)
                                                                                                DATA NCNTY/5/
                                                                                                DATA CNAME3/'WAL','NAS', 'FRA', 'CHA', 'MAR'/
                                                                                                DATA CNAME/'WALTON', 'NASSAU', FRAN(LN',K'CHARLOTTE', 'MARTIN'!
                                                                                          C
                                                                                          C     H(N) VALUES ARE DEPTH VALUES TO CENTER OF ELEMENT.
                                                                                          C     ELEVATIONS ABOVE MEAN SEA LEVEL ARE NEGATIVE.
                                                                                          C
                                                                                          C
                                                                                                DATA XK/0.07/,XMD/3.0/,HB/iO.O/,A/0.13/,PERIOD/0.5/,DY/i.O/
                                                                                              5 FORMAT(/)
                                                                                             10 FORMATI1OXF10.2)
                                                                                             15 FORMAT(FO.4)
                                                                                             30 FORMAT(5(F7.1,IX,F7.2))
                                                                                             37 FORMAT(A3)
                                                                                             40 FORMAT(A8,13)
                                                                                             62 FORMAT(IH ,5X,F8.1,3X,F8.l,5X,F8.l)
                                                                                             65 FORMAT(13)
        This program represents a numerical modeling procedure that is subject                10050 FORMAT(iI-11 ,/I,34X,A10,' COUNTY',
    to change due to: 1. newly encountered topo-bathymetric and hydraulic                           -         ,25X, 'SIMULATED DUNE EROSION - DEAN-S MODEL'
    boundary conditions, and 2. incoporation of new advancements quantifying                        -         /,25X,            FOR DECEMBER 1982
    coastal processes.  This program is applied on a county-by-county basis and                     -         /,25X, '      100 YEAR STORM TIDE USED',!)
    is subject to acceptable calibration constraints reconmmended by the Beaches               10055 FORMAT(I-1H0, 'NOTE:  XMD/SLOPE=',F3.i,'  K VALUE =',F4.2,/,
    and Shores Resource Center and approved by the Florida Department of Natural                    -         IH           PROFILES CONTAIN ADDED OFFSHORE DATA',/)
    Resources.                                                                                 C
                                                                                                VOLTOT.0-:0,0
                                                                                                PFROF=0.0
                                                                                                DO 913 I=1 ,6
                                                                                                NTOT(I )=0
                                                                                                XTOT ( I) = 0,0
                                                                                          98    DXTOT(I)O0. 0
                                                                                                DO 100 K I   1,120
                                                                                                RIEAD(5Ii0.END=150) STAI(I
                                 159
                                                                                                                          160

      I 00 CONTINUE                                                                                      TMAX=IFIX(lil ( IDUNEM)
      150 NTIMFS=I(-1                                                                                    IMINI =IFI-X(Hi (MINI  )
    C                                                                                                     JMIN2=~IFIX(HI-JIMIN2) )
    C     REAl) H, X VALUJES                                                                              NFILMI=IMAX-IMj:N1 41-
           tJRITE(0, 201)                                                                                 NL2XA-MN+
      201 FORMAT( 'INITIAL SURVEY DATA'                                                                  NELM=NELMAX-NEMN2+
          W'RITE(9,202)                                                                                  NL =NELM
      202 FORMAT( 'INITIAL SMOOTHED) DATA'                                                               II1=i
          IJRITE(IO, 203)                                                                                IMAXMi =IMAX-i
      203 FORMAT( 'ERODED--SMOOTHED DATA' )DO 179 I=I'MlNi,IMAX
          READ(4,37)CNTY                                                                                 H4A(1II)=I
          DO 155 I=I,NCNT'Y                                                                              II  =II
          IF (CNTYEQ.CNAME3(l)) GO TO 160                                                          179 CONTINUE
      155 CONTINUE                                                                                       DO 1791 I=IMAX,IMIN2..-1
      160 ICNTY=I                                                                                        N-A( II )m
    C                                                                                                     11 = II +I
    C                                                                                               1791 CONTINUE
      175 READ(4,20,END=9999)RNGRNGDAT,ICODE,YNORTH,XEASTAZMLITFI                        D       O          2 I=1 ,NELM
          READ(4,-5)DOTDAT,BCHDAT, OFFDAT',NP,NF'O)OT,NPEICH, NF'OF                                      NCON(:[)=i
       20 FORMAT(AB,A8, 12,2F12.3,F7.2)                                                                2 XA(I)=O.G
       25 FORMAT(AB,AB,A8,413,I)                                                                         CALL SMOOTH(IDUNEM,i,2)
    C                                                                                                     CALL 9MOOTH(IDUNEM,NF',i)
          IF (AMOD(PROF,6,O).NE.0) GO TO 1750
          W4RITE(6, 10050)CNAME(ICNTY)                                                                   NELMIM = NEL-Mi - I
          WRITE(6, 10055)XMD,XI(                                                                         N2=NELM14+1
     1750 PROF=FROF+1 .0                                                                                  N3=NELM-i
          DO 176 1=1,200
          X(I,1 )=0.o                                                                                    DO 17000 M=I,NELMI
          X(T,2)=O.O                                                                                     XASAVE(M)   =-XA(M) + Xi(IDUNEM)
          XI (I>=0.0                                                                                     HASAVE (M)= -HA(M)
                                HI (I)=0.0                                                        1~~~~~~~~~~~~~~~~~7000 CONTINUE
          NCON( x =O                                                                                     DO 17B20 M=N2,NEILM
          XA(I)=O.O                                                                                      XASAVE(M)   =XA(M) + XI(IDLUNEM)
    176   HA(I)=0.0                                                                                      HIASAVE(M)=-HA(M)
                                                                                                17020 CONTINUE
          READ(4,30)WX(I),Hl(I),11,NF.)                                                           C      FILE 9 CONTAINS INITIAL SMOOTHED CURVE.
          NPOFF=O                                                                                        NFDOT  =0
          NP~DOTmO                                                                                       NPBCH =NL
          NPBCH=NP                                                                                       NPOFF = 0
    C     FILE 8 CONTAINS INITIAL SURVEY DATA.                                                            WRITE(9,20)RNG,RNGDAT,ICODE,YNORTH,XEAST,AZMUTIA
          WRITE(B,20)RNG,RNGDAT',ICODE,YNOF(TH,XEARTAZMUTIA                                             WRITE (9,25) DOTDA'T, BCHDiAT, OFFDAT, NL, NPDOT, NPDCH,14NPOFF
          WRITE(a, 25)DOTDAT,EtlCHOAT,)FF'DATr,NNP,NDOT,NpBCH-, NPOFF                                    WRITE(9,0)(XASAVE(I),HASAVECI),I=I,NL)

                                                                                                       DO 1780 Ml=1,NELMI
          DO 177 I I IP                                                                                 NCON(T)"2
          IF (HI (I) .GT . Hi ( IDUNEM) )  DNM IXr-l )   =-XA(.f) + Xi (IDUNEM)
      177 CONTINUE                                                                                        X(M, I)=-XA(T.)
          MINi~i                                                                                  1700  CONTI NUE -
          D)017 I     78  1,11UNEM                                  D00  7172 M=N2, NEL.M
          IF (HI1 (I) L1.T, 1-I (MINI)  MINI    I                                                        IMLLM
      178 CONTINUE                                                                                        XA(M)   XA(M) +Xi (IDUNE.M)
          MIN2=1                                                                                         X(1I,2)='XA(M)
          DO 1701 I = IOLUNEM,NP                                                                         HA(I)=--HlA(M)
          IF (HI (I)  !-T.  I(I2   MIN2 = I                                                             NL.S~l
    1701 CONTINUE                                                                                 1702  CONTINUE

                                     1651                                                                                            162

    C      INITIALIZEF  ACTIVE'  PROFILE                                                                      AA = 100A'o
          N L =NLS                                                                                           1)0 600 I =i , NL
          X (N E L.M1i,1)=--)0 00.0                                                                          B B        AB(DrITC cr.  - DPn'Tl'
          DO 1705 1=- ,NL                                                                                    IF (Dri .(;T. AA) CO TO 550
    1'703  XA(I)=X(I,2)                                                                                       AA = 01
          NPDOT =0                                               I                                            E =I
          NPDGHI   NL                                                                                   550 IF (AB.S(DlPTC(I)) .LE. 81(l)12) IW'L =I
                                   NPOFF = 0             ~~~~~~~~~~~~~~~~~IF CAE'S(HSTAR - DPTC(I)) .LE. DH(I)/2) ISTAR =I
          CALL SRGF7CT(CICNT'Y,RNI.,,SMULTI, SSUJRGE; IRNG)                                             600 CONTINUE
    C     WRITE(6,184)ICN-TY,RNG,EMULt.T                                                                      IE'=NPA
       14 FORMAT(' ICNTY,RN4G,SMUL..T'w ', I,A8,F7,3)                                                        DO 1200 lIT'   l ,10
          DO 185 I = 1,NTIMES                                                                                SLJMi   0. 0
          STA(I) = STAI(l) * SMULT                                                                           SUM2 =0.0
      i185 CONTINUE                                                                                          SLIMS    0.0
    C                                                                                                         SUM4     0.0
    C     CALCULATE H-STAR T'O NEAREST FOOT                                    D0 700 I  Is, ISTAR
    C                                                                                                         SUMi = SUMi + (HA(I) +ST - HSTAR)   DHONI) /XMD + DXS *DH(I)
          80 200 I = 1,NL                                                                                    SUM') = SUMA) + DIH(I)
          XAO(I) = XA(I)                                                                                     SUMS =. SUMS + XA(I) *DH(I)
      200 CONTINUE                                                                                      700 CONTINUE
           HE     (0.667 * A**1.5 /XMOX*92                                                                    ISP = ISTAR + i
           OXS    (HE / A)**1.5                                                                               DO 000 I = ISP, IE
           HSTAR = HE                                                                                         SUM') = SUM') + DHCI)
                              0                                                                             ~~~~~~~~~~~~~~~~~~~~~SUM2   =SU.M2 + (OPTCCT)/A)**1, 5   DIAQ1()
           DO 300 I = 1,NL                                                                                    SUMS = SUMS + XAIl  * 811(1)
           XA(I) = XAO(I)                                                                                800 CONTINUE
      300 CONTINUE                                                                                           IEP =IE +1
           XR =0.0                                                                                            DO 850 I = IEP,NL
           DH-(1)  =1.0                                                                                       IFILL =  -1
    C                                                                                                         IF (XR + XE'  LT. XA(I.)) GO TO 1000
    C      ESTABLISH INSTANTANEOUS WATER LEVEL, ST                                                           SUMS = SUMS + XA(I) * D1NCI)
    C                                                                                                        SUM') = SUM') + DH(I)
           AMP =0.0                                                                                           SUM2 = SUM2 + XB' * OH(CI)
           P102    i .5708                                                                                    IFILL =I
           DT = PERIOD                                                                                   850 CONTINUE
           DO 400 I = 2,NL                                                                             '1000 CONTINUE
           DH(I) = (HACI) - HA(I-1 ) -D(1)/0)20XRO =XR
      400 CONTINUE                                                                                           XR   =1.0/SUJM'  * (SUMS3   SUM2 - SUMi)
    CC
    C     NTIMES LOOP - LOOP FOR EACH SURGE VALUE                                                     C      ESTABLISH NEW VALUE OF ID

           SZ=1 .0-EXP(--XK<*T)                                                                               1180 = IE'
           IBP=1                                                                                            FOSTAR:' C- Xr+D--IXS'-XA(CISTAR)-f-DPTC(CISTAR ) -IITAR )/XMD
           NPA=1                                                                                             BSTAR=BLST AR* 5
           DO 1600 NTIME    1 ,NTIMES                                                                        XSTAR=XAC S'T'AR)I+D'STAR
           TIME = CNTIM--1)ltDr                                                                              3:' =NP-A
           ST = STA(NTIME)                                                                            C      WRITEC6,1106)
           00 '500 I   i 1,NL                                                                         '16FRA(
           OPTECI I = HA CI) -f ST                                                                           IITA'(T.Z   -
      500 CONTINUE-                                                                                         IDO-1 0        NA,
           DPTB  HT'/OO                                                                                      O  i~
           XD     DTE     A) *I.5                                                                            E0XTR   FCC)-UTRI/M-X  I
    C                                                                                                        IF GO'CE''L.)      iUT0  11
    C     ESTABLISH THE- INDICES OF- STIlL. WATER LEVEL ANT) HSTAR                                           I    -1+
    CC                                                                                                       WIT(6115NTMIITII'   ,XTRLTA
           IF =                                                                                       C     -XCSA)DT()HTRXN)z

                                        163                                                                                               164

    1105  FORMAT (414, B F7 .2)                                                                    i 732 C(LIONTI NU11E
     11i0 0 CONTINUE                                                                                       VOL=Si /27.0
     111i0      0NTrI N UE                                                                                VOL TOT= VOL TOT+ VOL
          IF (IDj.l-T.i)ID~1
          I F (ID .E I'D   0) .A ND.  IA US X R   X R  .L.    0 1) C O TO0 1:30()0                        WRITE(6..11001 )RNG,IMAX
                                        .F+++-I+I+++4-++~~~~+ + i ++ ++ + + ++ ++-i+44..          11001++++ii~    FORMAT(//, 6X, AD,-DUNE ELEVATION:  -12,
       1200 CN T I NUE                                                                                   -       LOG. RELATIVE TO MONLI.IFT.)   DISTANCE EROD)ED (FT .)/
     1300 CONT INUE                                                                                        DO '1550 IJII = 1,NL
    C   W4RITE (6,1i302)                                                                                   IF (HA(IJK) NME. -25.0) GO TO 1532
     1302 FORMATW/)                                                                                        XTOT(6)=XTOTW6+XAI IJK)
    C                                                                                                      DXTOT(6) =DXTOT (6) .DX ( IJII
    C     CALCULATE DX VALUES                                                                              NTOT(6)mNTOT(6)+1
    C                                                                                                      WRITE(6,1 1000) HA(IJl0),XA(IJI() ,DX(IJI()
          DO 1400 I   =IB,IFILL                                                                    11000 FORMAT~iI  ,15X,F5.1,' FT. CONTOUR:  -,IOX,F9.`1,`7X,F9.1)
          IF (I .CT. ISTAR .AND. I .LE. IE) GO TO 1325                                            `1532  IF (HA(1-I() .NE. -20.0) GO TO 1534
          IF (I .CT. IE) GO TO 1350                                                                       XTOT(5)=XTOT(5)+XAI IJK)
          DX(I)   =XA(T) - (XR + DXS + (MA(I) + ST-HSTAR) /XMD)                                           DXTOT(5)=DXTOT(5)+DX(IJl()
          GO TO 1400                                                                                      NTOT (5)=NTOT 15) +1
     1325 DX(I) = XA(I) - (XR + ((HAlI) + ET)/A)~*1,5)                                                     WRITE(6,11000) H-A(IJK) ,XA(IJI0,DX(IJl)
          GO TO `1400                                                                              1534  IF (HA(I-1i) .NE. -15.0) GO TO `1536
     1350 DX(I) mXA(I) - (XR + XB)                                                                         XTOT (4) =XTOT (4) +XA ( IJK )
     1400 CONTINUE                                                                                         DXTOT (4)=DXTOTI(4) +DX ( I.JI
          VOLCHG = 0.0                                                                                    NTOT(4)=MT'OT(4)+1
          IIA =(1.0 - EXP(-Xl<*DT))                                                                       WRITE(6,1 1000) AA(I.JK) ,XA(IIJK),DX(IJK)
          DO 1500 I = IB,IFILL                                                                     1538  IF (HA(IJ() .NE. -10.0) GO TO 1538
          BB = -DX(I) * DIA                                                                               XTOT(3)=XTOT(3)4-XAI IJK)
          VOLCHG    VOLCHG + BB  DH(I)                                                                    DXTOT(3)=DXTOT(3)+DXI IJK)
          XA(I) =XA(I) + BE                                                                               NTOT(3)=NTOT(3)+1
          IF (NCON(NPA).EQ.2.AND.XA(NPA).LT.X(NP~A,i)) NPA=MPA+i                                          WRITE(6,11000) HIA(IJl<)XA(IJIJ),DX(IjK)
     1500 CONTINUE                                                                                  1538  IF (NA(IJK) NME.   -5.0> CO TO 1540
    C      IF (MOD(NTIME,5).NE.O.AND.NTIME.NE.1) GO TO 1510                                                XTOT(2)mXTOT(2)-*XA(I IJI)
    C     WRITE(6,1505)NTIME,NPA,1ID,IWL,ISTAR,IE,ST,                                                      DXTOT(2)=DXTOT(2)4-DX(IJK)
    C    -     IA).(INCNINTOT(2)=MTOT(2)+1
    C    -X(I,1),X(I,2;,I=1,NP)                                                                            WRITE(6, 11008) HA(IJl<),XA(IJK) ,DX(IJl0
     1505 FORMAT('11-1,'NTIME  NPA  IB  IWL  ISTAR  IE   ST',/,iH                                   i 540  IF (HA(IJK) .ME.   0.0) Go TO '1550
              -   215,15,15,17,14,F5.2,/,iH  ,XTOT(1 )=XTOT~i)+XA(IJi()
             H, A(I)   XA(II  NEONIX)         XiI,i)    XI(1,2)',/,                                       DXTOT(1 )=DXTOT(1 )+DX(IJK)
          -(I5,F5.i,Ff3.i,I8,Fi0.2, FIO.2))                                                               NTOT~i1)=NTOTI'I)+1
     1600 CONTINUE                                                                                         WRITE(6, 11000) HAl IJK),*XA( IJl) ,DXI IJII)
    C                                                                                                1550 CONTINUE
    C *** END OF TIME LOOP                                                                                 WRITE(6, 1734)VOL
                           C                                                                      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1734  FORMAT( i1-0, 13X, 'VOLUME EROI)ED:  'SF10.2,' CUBIC YARDS FER FOOT
          DO 1700 I = 1,ML                                                                               -MEASUikED rFROM MSL UP' .1)
          DX(I) = XA(I) - XAO(I)                                                                          NP=NL-NrPAll
     1700 CONTINUE                                                                                  C  1FILE 10 CONTAINS EROaDED SMOOTHED CURVE.
                                 51=0.0                                                                 ~~~~~~~~~~~~~~~~~~~~~~~WI:IITE~iO,2() )R~NGRNGI)AT. ICCODE, YNORTHi,XEAST,AZMUJTH

          IF  GNAE.     O TO 1721 iIE  0  0  X(I),HII),(~PL
          DO 1720 lm1,Nl.'AM                                                                              GO TO( I 5
          IF IHA(II>.T,0.0) CO TO 1732                                                             9999  IF (PROF.LEI I0) CO TO 99999
     1720 E1=9i+(X(I,2)-X(I, 1))                                                                           WRITE(6, 10050)C NAMEI ICNTY)
     1721 DO 1730 I-MPA,NL                                                                                 WRI'TE(6,`10055>XMDXi(
          AA=X 11,2) -XA II)                                                                              WRITE(6, 1560)
          IF (HA(I).GCT.o.0-) GO IL) i732                                                          1560  FORMATI///,6X, 'TOTALS FOR AlI... PROFILES                LOC. RELATIVE TO N
          IF (AA.l.T,0.0) GO TO 1732                                                                     -DM0. (FT. )   DISTEANCE EROD)ED  (FT. )',/)
    1730  9!=9ii-AA                                                                                        DO 1570 I   16

                                      165                                                                                             166

          IF GNO()N.    O TO 1575-
          XTrOT(I)=.-) 0                                                                      00  DO 300 NE L. =-N 1.L i , NEL2, INC,
          D)X T TI)   0                                                                            IF (H(.',D T  H)G  TO 400
          CO TO i577                                                                         300  CONTINUE,-
    1 575XTTIXT1)NTT)
                              DXTOT(I) DXTOUI)/NTOT(I)                                     ~~~~~~~~~~~~C400  WRIf'E(6,3())NEL-,Nf: -Li,NEL2,HA(NEL),HLU
    1 577  CONT=FLOAl'I- 1)*fj.O                                                             30   FORMAT(' NEL.,NELI,NEL.2,HA(NEL),HIJ',31.5,2F7.2)
          WRITE(6..i580) CONT,XTOT(I),DXTOT(I)                                              400   NB.mNEL
    1 500  FORMAT (IH 1-  5X, J-.    FT. CONTOUR:  ',iOX,F9.1 ,17X,F9.1 )                          NEL2 = NELM
    1570  CONTINUE                                         IF (ICOI)E .EQ. 2) NEL2=1
          VOLT=VOLTOT/PROF
          WRITE(6, 1590)VOL'TOT,VOLT                                                              DO 700 N   =NB,NEL2,INC
    1590  FORMAT(1H0,5X,'TOTA)L VOLUME ERODED FOR ALL PROFILES;   ',FIO.2,/                        IF (HA(N).GT.1HL) GO TO 600
             -   IH ,5X,'AVERAGE VOLUME ERODED FOR ALL PROFILES: ',FIO .2,//)                     XA(N)=X.A(N)4-DX
    C                                               GO TO 700
    99999 STOP
    C                                                                                        600  DELI   (HU - IAA(N))/DH
          END                                                                                     XA(N) =XA(N) + DX * DELI
          SUBROUTINE 9MOOTl-(NBEG, NMAX, ICODE)                                             C     WRITE(6,40)N,HAA(N),HL,X(N),XA(N),DELI
    C                                                                                        40   FORMAT(' N,HA(N),HL,X(N),XA(N),DELi ',15,5F'7.2)
    C     SUBROUTINE TO SMOOTH SURVEY DATA.                                                  700  CONTINUE
    C     IF ICODE EQUALS 2, SUBROUTINE HAS BEEN CALLED TO SMOOTI-  REAR
    C     OF DUNE; IF (CODE EQUALS I * SUBROUTINE HAN BEEN CALLED TO                         000  CONTINUE
    C     SMOOTH FRONT OF DUNE.  SMOOTHING OCCURS FROM HIGHEST ELEVATION                           RETURN
    C     TO EITHER FIRST OR LAST SURVEY POINT.                                                    END
    C     SUBROUTINE USES SURVEY H AND X VALUES TO SET VALUES FOR XA,                              SUBROUTINE SRGFCT(ICNTY,RNGSMULT,SSURGE,IRNG)
    C     GIVEN PREVIOUSLY SET HA VALUES (FROM MAIN).                                       C
    C                                                                                       C      THIS SUBROUTINE CALCULATES A SCALING FACTOR WHICH WILL BE APPLIED
          COMMON /A/ HI(200),XA(200),HA(200),NELM,Xi(200),NP,NELMI                          C     TO THE STORM TIDE TIME SERIES.
          NSTART=NDEG                                                                       C
          NFINI=NMAX-1                                                                            DIMENSION SSVAL(5) ,NRNG(5)
          IF (ICODE .EQ. 2) NFINI =NMAX                                                           DIMENSION IBND(22,5),SRG(22,5)
          IF (ICODE .EQ. 2) NSTART =NBEG -I                                                       DIMENSION SRGCAL(13)
    C     WRITE(6,10)NETART,NFINI:                                                                 CHARACTER*8 RNG
     10   FORMAT(' NSTART,NFINI ',2I5)                                                             DATA NRNG/8,A,22,6,0/
          INC = I                                                                                 DATA IBAND/
          IF (ICODE .ER. 2) INC  =-1                               I                                         1,22,43,74,84,98,ii2,129,i4*0.0,
                                                                                               2           1i,17,34,50,67,83,16*0.0,
          DO 80001 = NSTART,NFINI,INC                                                            3           1,15,30,.60,75,92,101 ,I10,I25,i38,15O,i62,172,183,
          HI 1=HI (I)                                                                            -                 194,200,206,212,217,223,228,240,
          1H22=HI (1+1)                                                                          4           i,16,31 ,46,61 .69,16*0,
          I)H=ADE (Hi I -H22)                                                                    5           22*0-/
          DX=XI (1+1 )-XI (I)                                                                     DATA SRG/
          HU=Hii                                                                                 1 11.4,11 .3,11 .2,11 .1 1.,07I51.51~.,
          HL=H22                                                                                 2 13.9,13.,i,3.7,13.45,l3.2,13.2,l6i(.O.,
    C     WRITE(6,20)HiI ,H22,D)H,DX,HU,HL                                                        3 12.0-5,12.1,12.15-',i2.2,12.25,12.3,i2. 4,12.45,i2.!),i2.",i2.95,l3.O,
     20   FORMAT(' HI,H2,DNH,DXHU,HL -,6F7.2)                                                   --        31,331.,45.I.,40,50I.5   53,1.0
          IF (H22.LT.Hi1) GO TO 100                                                              413.1     301.,201.,27  600
                                                                                               S 22w0.0/
          H-U= H22                                                                                DATA SGA/.,.,.,.,.,.,.,1.,07
          IHL=H-I 1                                                                                            1111.6, 1 2.0.1 2.5/
     1 00  NELA = NELMI                                      D)ATA SVL~001.,37,29,   0
          NEL2  =HE'LM                                                                            DATA ICIAL/0/
          IF ( IC(DE .N1E 2 ) GO TO 200                                                     C
          NELi = NEL.Mi                                                                     C     CONVERT CHARACTE'R RANGE TO INTEGER RANGE
          NEL2 =I                                                                           C

                                   167                                                                                     168

          J=1 +2

          IF (K.I.-T.240) GO TO 100
          I RNG I RN~x I04.(K(-.?40)
       50 CO0NTINULIE
      100 IF (ICAL.EQ.(-) GO TO i5(o

    C     SCALE CALIBRATION STORM SURGE (WJALTON COUNTY HURRICANE ELOISE)
    C
          D0 110 I,1i13
          IF  IN.G.E-)1)NDNGL.I10    GO TO 120

      120 SStJRGE='SRGCAL. ( I)
          SMULT=SSURGE/8. 35
          GO TO 300
    C
    C )*~* SCALE 100 YEAR STORM SUJRGE FOR CURRENT RANGE
    C
      150 N=NRNG(ICNTY)
          DO 160 1=2,N
          IF (IRNG.I;EADNO(I-l4ICNTY).AND.IRNG.LT.IBND(I,ICNT-Y)) GO TO 170
      160 CONTINUE
      170 SSURGE=SRG(I-i ,ICNTY)
          SKLULT=ESSJRGE/SSVAL (ICNTY)

    C     WRITE(6,99)ICNTYIRNG,RNG,ESURGEEMULT
       99 FORMAT(15,I5,AB,2F7.2)
      300 RETURN
          END

                                    169