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Ga i n-iesAv i Ie FL. 3 26 06 ii ci~~~~~~~~~~ ea c i-e s- a ncl Nh or e s R e so)ur c e Cen-i-c r .JI F Ior I- ci a S-i-a te [Jin i v er: si ty 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 (3 Ei [30 Funded by 11 El ~~~~~~~~~~~~~~~~~~~~~0 a A grant from the I.J., S. Of f i c~e o-f Coastal. Zone Maniagement 0 11 Nat oi oa Oceanic: arid A-tmfospter ic Aim in istra-rtion, 0 �3 ( under -the Coasita I. Zone Management Act of 1972, as amendled ) 0 o thirough a 0 ;: or ci F Lor I da 0-f-f i ce (if Coasta I1 ManiagemienltE 0 a Dep~~N art mend- oif ErvivIr(-omenita11 . Re ukia-ti on E GB Fl [or ida Department of Nat uralI Resourc~es El 4590 .F56b c no. 84-6 ]Ulca ciffff noooin niianooocorlooor aa lcohjoI 0'IoDarIor juIonjDbOIJEI moi.- IoE I - or f ,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