FOR COASTAL ENGINEERING

TA7 n () ('' 0, 1 "3 _ (') } \,, (,-,-('' ' : \ ol - Rp~ 3 r 3 - HANDHELD CALCULATOR ALGORITHMS FOR COASTAL ENGINEERING Report 3 by Julie L Dean, Todd L Walton, Jr Coastal Engineering Research Center U S Army Engineer Waterways Experiment Station P 0 Box 631, Vicksburg, Miss 39180 oor:(s IR E ACCOUNTABLE PROPERTY CHARGED TO AN INDIVIDUAL BY NAME PLEASE DO NOT LEND TO OTHERS WITHOUT CLEARI NG YOURSELF December 1983 Report 3 of a Series Approved For Public Release; Distribution Unlimited LI BPr\RY BRANCH TECHNICAL INrG\ ' ',no;~ Cf~! T R 1 1S ARMY [N GW EE ~ "''\r r r,,-,, - t\ ~ ( 1\ ~ \ ~ - ~~ :'\ ~ ~ '" ' VICKSBU RG MI SSISS:PPt Prepared tor Office, Chief of Engineers, U S Army Washington, D C 20314

Unclassified SECURITY CLASSIFICATION OF THIS PAGE (When Oats Entered) {\ ~~ REPORT DOCUMENT AT ION PAGE READ l!':structio!'ls I REPORT NUMBER BEFORE C0\1PL ETING FORM 2 GOVT ACCESSION NO 3 RECIPIENT'S C ATALOG N UMBER ~ti scellaneous Paper CERC-83-9 8 4 TITLE (tmd Subtitle) HANDHELD CALCULATOR ALGORITHMS FOR COASTAL ENGINEERING: Report 3 5 TYPE OF REPORT & PERIOD COVERED Report 3 of a series 6 PERFORMING ORG REPORT N UMBER 7 AUTHOR( a) 8 CONTRACT OR GRANT NUMBER(s) Julie L Dean and Todd L Walton, Jr 9 PERFORMING ORGANIZATION NAME AND ADDRESS u s Army Engineer Waterways Experiment Station AREA & WORK UNIT NUMBERS ' Coastal Engineering Research Center P 0 Box 631, Vicksburg, Miss 39180 10 PROGRAM ELEMENT, PROJECT TASK II CONTROLLING OFFICE NAME AND ADDRESS 12 REPORT DATE Office, Chief of Engineers, U s Army December 1983 Washington, D c 20314 13 N UMBER OF PAGES 29 14 MONITORING AGENCY NAME & ADDRESS(If dlllorent from Controlling Office) IS SECURITY CLASS (of thla raport) Unclassified IS a DECLASSIFICATION 'DOWNGRADING SCHEDULE 16 DISTRIBUTION STATEMENT (of thla Report) Approved for public release; distribution unlimited 17 Dl ST Rl BUTtON STAT EM EN T (of the abetrsct entered In Block 20, If different from Report) 18 SUPPLEMENTARY NOTES Available from National Technical Information Service, 5285 Port Royal Road, Springfield, Va 22161 19 KEY WORDS (Continue on reveree 11ide II necesaary 11nd ldantlly by block number) Calculator algorithm Significant wave height Coastal eng1neer1ng Spectral wave height Peak spectral period 20 AfiJSrRACT ('CettfLaue 8!1<,,,_ efo II ntee\9e&ry ad ldenllfy by block number) This ls the third in a series of reports providing handheld calculator algorithms for use in coastal engineering The first and second reports in this ser1es were published as Coastal Engineering Technical Aids (CETA's) and are available from the U s Army Engineer Waterways Experiment Station Technical Report Distribution Center, Vicksburg, Miss Of these, CETA 82-1 presents a set of six algorithms for programs useful in performing certain wave (Continued) 00 FORM \JAN 73 1473 EDITION OF ' NOV 65 IS OBSOLETE Unclassified SECURITY CLASS! F'ICATIOP't OF THIS PA,E ( lrhen Data Entered)

Unclassified SECURITY CLASSIFICATION OF THIS PAGE(Whon Data Entered) 20 ABSTRACT (Continued) transformation and wave generation calculations with both the Texas Instruments TI-59 (Algebraic Operating System (AOS) notation) and the Hewlett Packard HP-67 (Reverse Polish Notation (RPN)); CETA 82-4 presents the same six algorithms for use on the HP-41CV (RPN) The present report provides algorithms for three calculator programs that forecast gravity water waves in deep and shallow water Two programs use the Joint North Sea Wave Project (JONSWAP) shallow- and deepwater wave forecasting equations as presented in the Coastal Engineering Research Center's Shore Protection Manual (revised edition to be published in 1984) The third program uses equations to predict a depth-limited significant wave height The programs are intended for use with the HP-41CV Unclassified SECURITY CLASSIFICATION OF THIS PAGE(W1um Dttts Entered)

PREFACE This report was prepared as part of the Littoral Data Collection ~lethods and Their Engineering Application Research Work Unit, Shore Protection and Restoration Program, Coastal Engineering Area of Civil Works Research and Development Technical Monitors from the Office, Chief of Engineers for the Coastal Engineering Area are Mr John H Lockhart, Jr, and Mr John Housley This work was accomplished during the period 1 July 1983 through 30 December 1983 by The Coastal Engineering Research Center (CERC) of the U S Army Engineer Waterways Experiment Station (WES), under the general supervision of Dr Robert W Whalin, Chief, CERC; Dr Lewis E Link, Assistant Chief, CERC; Dr Dennis R Smith and Mr Fred E Canfield, Acting Chiefs, Engineering Development Division; and Mr Thomas W Richardson, Chief, Coastal Structures and Evaluation Branch This report was prepared by Ms Julie L Dean, Engineering Assistant, and Dr Todd L Walton, Jr, Research Hydraulic Engineer Commander and Director of WES during the publication of this report was COL Tilford C Creel, CE Mr F R Brown was Technical Director 1

CONTENTS PREFACE CONVERSION FACTORS, INCH-POUND TO ~ffitrjc (SI) UNITS OF MEASUREl"lENT PART I: INTRODUCTION PART II: PROGRAMS 103R-41CV-REV: JONSWAP Shallow-Water Wave Forecasting Equations, Revised 106R-41CV: JONSWAP Deepwater Wave Forecasting Equations 107R- 41CV: Depth-Limited Significant Wave Height REFERENCES APPENDIX A: BLANK PROGRAM FORMS Page 1 3 4 5 7 11 16 24 Al 2

CONVERSION FACTORS, INCH-POUND TO METRIC (SI) UNITS OF MEASUREMENTS Inch-pound units of measurement used 1n this report have been converted t o metric (SI) units as follows: feet Multiply miles (U S statute) miles per hour (international) By 03048 1609347 044704 To Obtain meters kilometers meters per second 3

HANDHELD CALCULATOR ALGORITJillS FOR COASTAL ENGINEERING Report 3 PART I: INTRODUCTION 1 The advent of the handheld programmable calculator has led to the development of numerous programs in various fields of engineering and science Coastal engineering is no exception This report provides three programs to forecast waves in deep and shallow water Two programs use the Joint North Sea Wave Project (JONSWAP) wave forecasting equations for deep and shallow water as presented in the Shore Protection Manual (U S Army Engineer Waterways Experiment Station Coastal Engineering Research Center (CERC), in preparation, 1984) The third program predicts a depth-limited significant wave height using a spectral approach (Vincent 1982, Thompson and Vincent 1983) 2 The three programs presented herein are versions of Reverse Polish Notation (RPN) logic suitable for use on HP-41CV programmable calculators with or without accessory printer Each program is documented, assumptions are briefly described, and references to more detailed presentations of the theory are given 3 Each of the RPN programs incorporates HP-41 compatible-print routines which print and label all input and output parameters The user has only to enter the input parameters and the results are automatically computed and printed Since the printing routines 1ncrease program length by as much as 25 percent, use of a magnetic card for permanent program storage is recommended The print steps do not need to be deleted if a printer is unavailable 4

PART II: PROGRAMS report 4 Three programs (103R-Rev, 106R, and 107R) are presented in this Program 103R-Rev is a revised version of Program 103R (Walton, Birkemeier, and Weggel 1982) and is being published herein with slight changes for consistency 5 Program 103R-Rev forecasts s1gnificant wave height and spectral peak period in shallow water, using JONSWAP wave forecasting equations of the Shore Protection Manual (CERC, in preparation, 1984) Program 106R forecasts the deepwater significant wave height and spectral peak period for fetch-limited, duration-limited, and fully developed sea cases in deep water The JONSWAP forecasting equations used are presented in Table 3-2 of the Shore Protection Manual (CERC, in preparation, 1984) Program 107R calculates a depth-limited significant wave height based on an estimate of the peak frequency of shallowwater storm wave spectra Equation (14) from Vincent (1982) and equation (5) from Thompson and Vincent (1983) are used 6 Each program allows either English or metric input and output Program listings are annotated, making it possible to follow the logic of the algorithm and to make modifications if desired that have 7 There are undoubtedly many calculator programs not included here been developed on coastal engineering subjects Practicing eng1- neers who would like to share such programs (in either AOS or RPN) with other users are encouraged to submit them to the CERC If the response is great enough, additional reports presenting the programs will be prepared programs, or suggestions for programs should be sent to: Commander and Director U S Army Engineer Waterways Experiment Station ATTN: Coastal Structures and Evaluation Branch, CERC P 0 Box 631 Vicksburg, Mississippi 39180 Comments, 8 These and future programs will generally correspond to the following numbering scheme: Miscellaneous Waves and currents Inlets 0-99 100-299 300-499 Beaches Geology Structures 500-699 700-899 900-1099 5

9 In general, the documentation of programs submitted should be i n a format paralleling that of the programs presented in this report A blank set of forms which can be reproduced is included in Appendix A 6

Program Description Program Title Name 103R-4!CV-REV: JONSWAP Shallo" -Water Wave l'orecasttng Equattons, Rev1sed (RP~ L g Todd L Walton, Jr Date 7/83 Address Coastal Engineering Research Center Ctty Waterways Experiment Station Vick!';bun? State MS Program Description, Equations, Variables, etc ZtpCode 39180 This algorithm computes the wave height, H, wave period, T, and minimum duration, t, from input values of the water depth, d, fetch length, F, and adjusted windspeed, UA using ~quations (3-39), (3-40), and (3-41) of the Shore Protection Manual (CERC, in preparation, 1984) Equations (3-39) and 3-40) are for constant depth and unlimited wind duration Wave height and period in this algorithm are significant wave height and period Algorithm uses English or metric system of units REFERENCE U S Army Engineers, Coastal Engineering Research Center, Shore Protection Manual, Chapter 3 (in preparation) Operating Limtts and Warntngs 103R-41CV-REV-l 7

User lnstruetions 103R-41CV-REV: JONSWAP Shallow-Water Wav Forecasting Equations, Revised (RPN Logic) SIZE: 01() STEP INSTRUCTIONS INPUT FUNCTION DISPLAY I LOAD PROGRAH ( FOC ASTJ [X EQ]"FOCA-Sr' EtJR H? 2 CH-OOSE ENGLISH OR HETK!c UAJIT: ~ 3 ENTER ADJVST J) WIND5PEED E or/'1, [R/s] UA? (md-ts Per hour or mt:fcrs ptr stcj " t{a [R!s] FETCH? 4 ENTER FETCI-1 (Ret or km) F [R/s] PEPTH_? 5" ENTER PEPTH (k~t tjr m) ot [R/s] - ~ READ SI&N! FICANT WAVE /-lelght {kef ()y rneffrs) /-I 1 REJCJ D SIGNIFICANT WAllE PERIOD {sec) T 8 READ HINIHtJH PUR An ()1\J (hours) TIH FYamnle Pl-IJhf~ I'YJ tia ~ 50 mph = 22 mjsec F = B~ooof-J = 24 4 km d= 35ff = /1m SMOLLOW FO~'ECPSTP!~ t:;>!p~ LO F~I~EI 14: T! w Etll~l! ;H l1f I T::; METRE IJ~IE!JC= - UA= 5r (1ai4Q, 22 ~fo;~,:: Ht I ~E HH= - FET(l-!= 813 eee ee13e lf'1l, 4 c1 ~H:~ -;, - O f I;EPTH= - [I~PTH= 3: ~ ),j ; :ti 11 10ti~, H=4 ~? ~; I I - - ~=4 T=4! a; - - ---- -- 1-1:' 49i!j I - 4~44 T! fl = i, '589c, - "'H1~-1 -lc" ' ~-, t -'-' 103R-41CV-REV-2 8

Program Listing STEP KEY ENTRY KEY CODE ljj t P_ I)~I(,T ~2 "SHQLLO~ FODE"J~ ''7 ~TT"l' '!:'~ 1 r : ~4 O'Jl~ll ~S LBL ~5 ~ E 011 1'1? 07 OQ~I ~~: TQ~c 1 13~ PPOI1PT 1e Q~FF 11 PSTO V 12 Clll 13 ""'" 14 PSTi) X l':i ClA 16 )I:Y" 17 GTO e1 19 E~GLISH UHITS 19 PYIEW 2e 122 21 qro!19 22! 47 23 STO!17 24 I 8 25 STO!l! 26 GTO 132?7t LBL e~ 28 ~ ETPT~ UNITS" 2q PYIEW 3e 98 1 31 STO!lG 32 1 8 33 STO!l7 34 1 ij9~ 35 STO 131 3E LBL ij2 37 "UIP :e TOHE 2 39 PPOIIIPT 413 JJQ= 41 FS" 55 42 XEQ ~4 43 STO 13?, 44 -~ETCIP 45 TO~E? 46 PPOI'IPT 47 FETCH= 48 ~S" ':i"i 4C! XEQ ~4 S 1 srn ~~s 51 "DEPTH 1 " '52 TOHE 4 53 PPOI1PT 54 D PTH:" 55 J:")? ':i"i 56 '>';Ff ~<1 57 str1 e6 58 Pfl 133 ~q PI'" A~ _ - ( q Ocn 1~ 5h 9 COMMENTS ~ Koq n 9 CiJnverS,fra -"> Ro1 Eng Co11VeYSI dy1~ RD, q ~ Roct d flefr1c Hcfy,-c (t;r1 ve "5,m, Hefn c (or?vly"s''tm ~Ro, ' I STEP KEY ENTRY KEY CODE t)~~ # ; ~Tfl A~ - ( ;,? PrJ fjq -""" -- 63 PCL 97 "5 I 1), 6 STO!lS f:j7 PCL!16 Ge ' 6':1 STO ee 7!1 PCL!1:3 71 PCL et 72 * 73 PCL 135 7'4 * 75 no ~1 76 PCL ~fl 77 7~?e YtX 79 'i~ -} J3~ * 31 XEQ 93 82 ST~' 94 :;!7 P1'1 141 - - 84 ')~OT as ~13565 % 87 PCL e4 88 I 8!! XEQ!11 q14 PCL 04 9?, ';14 Pt:'l 99 q5 / % "H= G? l'li1cl ~ % PYIEU 9Q TONE ~ tee PrL a~ 1 A 1 '7"i - ~ HE v '-' 1 ~p ~33!ec; ":EQ e1 1 H~ qn A4 - - 1137 PCL ~: 113? y+x II 13 9379 111 * 112 RCL 134 113 I 114 XEQ 133 115 PCL 94 116, 117 754 ~------------------~ ---~~~18 * COMMENTS tjfuf ~Roe ~/{)! -:, Roo 41S tanh&-53 {~ 1) ] ~ 103R-41CV-REV-3 9

STEP KEY ENTRY 1 '(j "i"l l & rt - t"' '2A l - I 121 RL'L f:l~ ~: 1 ""''"' 1 ')7 _, - '- - 1-1,_ '4 '~ r \ol, - - Y 125 P~IE!J 1 - " y " IJ r _, f One b 127 F'C~ 09 ')( " LC' -T 12'? RL'L 87 13~ I 71 ) 777 1_ ~ vj,!12 YtX!311 *! 7 5 ~:CL i\7 ~~ 1 :: ~~c~ (19 i?cr 1 -"- 1~4 L 1601~ ', 14~ '! 4 j "Tit1E= 142 HPCL X ~43 CNfEI!! 44 T011E ~ 14~ :;TIP 146 GTO 135 147+LBL 133 148 :;TI) i;2 149 EtX 1 '5e PCL 92 15: CHS! l I S' Et" _,, 153 -!54 PCL 62 1'55 ft'r'! 56 PCL 132! 57 (H') jc" ; '~ E+" il"t 15'3 +! Gtt t 161 ~:TH 1t>2+LBL ij4 1 ~ - -= ~ PR~ 164 ;:-~ ~E' 165 RTN 166 L ~~T -,_ KEY CODE COMMENTS STEP KEY ENTRY KEY CODE ' COMMENTS ~----r---------~--------~ ~---+---------+--------~ 103R- 41CV-REV -4 10

Program Deseription Program Title Name Address Ctty 106R-41CV : JONSWAP Deepwater Wave Forecasting Equations (RPN Logic) Julie L Dean Date 7/83 Coastal Engineering Research Center Vicksburg State MS Zip Code 39180 Program Description, Equations, Variables, etc This program takes the fetch length, F, adjusted windspeed, UA ' and duration, t, as input values and calculates the deepwater spectral wave height, HMO, and the peak spectral period, Tm, for fetch-limited, duration-limited, and fully developed sea cases in deep water The equations used are presented in the Shore Protection Manual, Table 3-20 The algorithm uses either English or metric units REFERENCE U S Army Engineer Waterways Experiment Station, Shore Protection Manual, Chapter 3 (in preparation) Operating Limits and Warnings 106R-41CV-l 11

User nstruetions 106R-41CV: JONS\JAP Deepwater Wave Forecasting Equations (RPN Logic) SIZE: 010 STEP INSTRUCTIONS INPUT FUNCTION DISPLAY I LOAD PROGT<AH {DEEP FOR) r- ],,,, XEC,_ DEEPFtJR E CJR fi? ' 2 CH005E EN6LISH OR!1ETRIC VNI rs E or H, [T</s] FETCH? 3 ENTER FETCH ( rnt!es or kdometer s) F [1</s] VA? 4 ENTER ADJUSTED WIN f)spe E E (mdes/hr or t11effrs /sec) LiA L'R/s] DURATJ()N? 5 ENTER DUR ATIDN (hours) t rr/s] (p FETCH- LIN/TED CA-SE!<EfJD I-IHo, 5PEC TR /J L WRVE lit HNo (f -1 orm' f<efjd TH, P /lk 51'ECTI<AL f?l ~RIOD Tl1 (sec) 7 DUI<flTION -LIH I TED CA-SE REfiD HHol SPECTRitL WINE YT HNo (rr ~rm: I<EfiD TH PEt:JK SPECTRFJL PERIOD 7H ( sec ) g FULLY ])EVE LOPED CA-SE REfJD Htv~o~ 5PECTRI1L WfJVE HT fihfj iff 11rm ) R fjd TH~ PE/11< SPECTR/1L PERioD TH ( se c) q PRESS R/s TO ENTER A NE w f/?t J8LEH Exam Pit frob/em: DffPl IQEP FOPE:w: 7 1 1,- DEFPWQTFP ~o~etp st;n F= 9 2 I m1lt s::; /183 km tja = 4005 m/lts/hr: = 2()59 mererslsfc t= 20 hours I EtlGI_IS!-1 1lt!:T:; MnP!( U ~l!t'; J:"- :1-l= t::etch= - : t ih~ p ~ 1 ()ii1 ~ 1 ~ & "t - J - $':1 lip= IJC: ~ ~ l'50c :t:t ; f: :-~,-~P '- - ~ _1 - r P~Tl i,; = 11 I~-- 'ij - I :t+= - -- ~ )~ f1i1hf' >»~?i' lll1~i1 ( I,, - I,, f:"ei- k l PI! TEI! ~J:FH - ' L nc L rq - ~w~ :J?A?c; Hli0=1?814 I Ttl:! 0, QyC -M 4 ~-- 1 :: :~~:1t, I ~CiPOH L :l'!n : D tn:tiijtj 1 I"';rn ~ -~ ~-~~1r: )\ "7~fl rr:, i~=r 4 I ' ' - 0 HM't-7 - t ;;, iu: _ Tf-4 = ~ -' ~ ~--- - ' -', ~ - - - ~llll" fie"' 't O?Fit Fll~l_, DE'Jt'O~ a ~~ 0=?& 4':3: H'1"-ji' IJ- - ~ c-: K -) L; T11='"' v,;,;' TH,~ = { ' ij!:''; ---- '" I '" 106R-41CV-2 ~ 12

PROGRAJ'1 DEEPFOR FLOHCHART START PROGRAM XEQ "DEEPFOR" ENTER A"'D STORE VARIABLES COMPUTE : '' FETCH LIMITED H =1 6xl0-3 I gf \ ~ 2 UA mo ua2} g T =2 857x10-l (gf )l/ 3 ua m ua2 g COMPUTE : DURATION LIMITED ( gt ) (6 88xtol)uA 3/2 T - m 2 857xlo-l (gfeff) ua2 1/3 CO~~UTE : FULLY DEVELOPED H =2 433x10-l DA 2 mo g T - m 8 1 34 UA g 13 106R-41CV-3

Program Listing STEP KEY ENTRY KEY CODE 91+L8L "DEEPfOP 92 "DEEPkATER FOPEC" tl3 "I-4STIHG" 04 AYIE!I 05+L8L ~i f16 "E OP ~'!') (17 AOH 118 TO~E 2 139 PPOMPT 19 AOF"F t! PSTO Y 12 CLQ r: r~ - - - - - - - COMMENTS STEP 5'~ KEY ENTRY lip-: _ ~r t: F""~ ~ """,_1,_1 62 ')TO 82 63 DIJRA TI Oh i E~ TQHE 5 E5 ::;; tji'fpt 66 DIJI?iH I Orl= t, ~ ~ 8 Y(Q ff3 7 r-c'> """ lj t~ ST(t ~1 79 Q~~ 71 FETCH LIMITEP' 72!WIEW 73 RCL 91 74 SPRT 75 PCL P2 7{: * 77 RCL 94,0 ( 0 'I 79 "111'10= 3& flpc~ ~ 8! QVIE :32 TOHE 4 :33 J;>CL 9: 84 PCL ~; 85 ~ 8E? 37!!'>' B~: Y+'t' 39 PCL e5 9 1 't 9! "H1=" q, ;:~('I v l ~- ~ 93 Cl'll E~ '=i4 T )l't- " n ' 95 fhi' 96 "DUPATION LIMITE" ~? -~n qo: nv T C 1 ' ' ' f"4 ~-~"" KEY CODE 1 t ~ "Ro3 ~ COMMENTS os J/No= R04 UA f 'n ~ ~"!t!_ tj c;ft TON 3 52 uj;~--h: ~7 ~ : 'j - - - c;c; 24 ')(Eb ~3 ""5 - - e: n- ~, 57 T(l"'~! 58 ~POMiiT - - - F-" Ro, - - c iloi-j 186 ~ cl if~ 197 ;j 198 "4"1j=! 13'~ C~ (t X 1 _,_!f\ r "JE t'ff " 111 TONE 6 112 F'CL 93!!3 ~:CL 92!14 ll! 15 '3t;IPT!1E RCL &7-106R-41CV-4 14

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS 11"' :t ~ 5 os 1 H TI'J: TM=- R 01 UA t 1: ~ OR(L, - a: 'A uv ~, pl T!)NE ~- 1 v -~ '' H "Dii, 123 FULLY DEVELOPEr 124 OVJE~ 125 t:(l A : -~ -- \'+'i - I P~- 127 F,'l'' -L A'' -- pg :t '' 2 pq '-- - ~ ~ o= HMo"' Ro8UA 13e APe,_ X 13! C'f TEIJ 1 ---c i'' TnHE 8 133 PCL A" -( 134 D 'L,_ ~9 ~ ~c ll ~' -',~, ~ t j77 JI,-, "T"= APCL X 1 ~ (4 A'!JEIJ 139 TOllE s!4e ~T J)P 141 GTO ~4 142+LBL 83 143 PPR 144 PR~' 145 DTH 14t END irt :: R, fll U A 106R-41CV-5 15

Program Description Program Title l07r-41cv: Name Address Crty Depth-Limited Significant Wave Height (RPN Logic) Julie L Dean Coastal Engineering Research Center Vicksburg State MS Date 4/83 Zip Code 39180 Program Description, Equations, Variables, etc This program calculates a depth-limited significant wave height as given by equation (14) from Vincent (1982) and equation (5) from Thompson and Vincent (1983), given depth, peak frequency of the wave spectrum, and Phillip ' s equilibrium coefficient The low cut-off frequency is 0 80 fp The upper cut-off frequency is 2 0 fp, where fp is the peak frequency Simpson ' s Rule is used to numerically integrate the frequency spectrum The algorithm uses either English or metric units REFERENCES Vincent, C L 1982 "Depth-Limi te d Significant Wave Height: A Spectral Approach," Coastal Engineering Research Center Technical Report 82-3, U S Army Corps of Engineers Coastal Engineering Research Center, August 1982 Thompson, E F, and Vincent, C L "Significant Wave Height for Shallow Water Design," (submitted to ASCE for publication, June 1983) Vincent, C L "A Method f or Estimating Depth-Limited Wave Energy," Technical Aid No 81-16, U S Army Corps of Engineers Coastal Engineering Research Center, November 1981 Operating Limits and Warnings 107R-41CV-l 16

frogram SWH Flowchart START PRO&~AN XEQ "S w 1-1 11 NT R AND SToRE Vfl Rl A 6L ES S SET SIEPS/2 SET COUN'IER c =o COMPVTE R{w 11 )ti) tp(lajn)( i) I USE SJHPSONS f(ijle COMPUTE SIGNIFICANT WAVE HEIGHT - 4-t3h) (oz28'd 1 Hs=1_e l07r-41cv-2' 17

METHODOLOGY USED IN THE PROGRAM Find lab max Equations Reference = 4Jf' Equation (6): Vincent 1982 (A)= 271f and f = 2 p If e: wh - max 1 2 3 10 * = _!_ "'gh)~ -1 HJ Equation (16): Vincent 1982, c * ( rl oc Equation (15) : Vincent 1982 2 H,t - H A 0 0081 ( -0 43642) H - H exp 0 02289d s 1 Equation (5) : Thompson and 2 Vincent 1983 df - h p Where d - - T 2 g g p If wh > max 1 2 3 10 R (tub) tanh ("b R ~h) ) - 1 2 2l1 2 R ("h) -1 Equation (7) : Vincent 1982 ~ ~) = R~)-2 1 + sinh(~ 2 R(~)) Equation (5) : Vincent 1982 2-54> Eh - JZOfp Jg f ~) 08fp ( 271--) 4 df Equation (13) : Vincent 1982 Simpson's Rule is used to numerically integrate Step 3 f(x)dx h -- 3 y +4y1+2y2+ +4y, 1+y 0 1-1!: 4 H( * = 40 (E ) 2 h 5 H) - * ( c<: )~ H,t 00081 Equation (14) : Vincent 1982 Equation ( 15): Vincent 1982 ( -0 4364, 6 H - H_t exp 0 02289d s d h df 2 p 2 gt g p - - Equation (5) : Thompson and Vincent 1983 107R-41CV-3 18

User lnstrug!tions 107R-41CV: JONSWAP Depth-Limited Si gni ficant Wave Height SIZE: 033 STEP INSTRUCTIONS INPUT FUNCTION DISPLAY I LOAD PROGRAH (SWH) X ~J \\sw H '' EOR M? 2 Cl+a>SE ENGLISH 0~ H r!<ic U/VJj t-s E or H )[R/5] DEPTH? 3 ENTER DEPTH ( Het~r-melers) d CR!s] PEAk F? 4 NrEI< SPECT!<J1L Pe/lK ff<equenc'i -fi, [P/s] ltlphfl? --r 5 ENT R- " PH ILL IPS E(i)UJLI8RJIJJ ~ CO F-FICENT oc' [R/s] 6 REifJ) SIGNIFICANT W/tt!E HEIGHT (/?et tjr me:fers), lis== Note: vvlth 4 inte:; rahot7 t!7l'reme;; r-s) +he, 'Drogrom fa lees 2 YntfJUffS to ruil 107R- 41CV 4 I 19

User Instruetions /, 2 Example Problems input: inpllt = d= 3f+ = oq/44 rn fp- {)08 75 ~ = 0010 I d = 30f+ = 9 J44rn +f 00875 oc = ~010 I 3 it1ptlt: d = J Of+ = 3048 m -fp ~ 61875 ~= 002152 ' I~N ~ --~,;- ~ ~ IJ a r 1 h WC~t': T EHI~L ISH l1h ITS fieptt<= 3~1399fl&9~~ t~t PEPt J:: e &8?5eHOei3 *"' ALPHt:l= eetutflflill313 ;fya HS=7712829318 l"~ ~ fit:r 4_!Q16027?? ~T si,~nifrcqhr \tii-1ye I ' EIIGL I 5H lj~: ~; DfF"I-l= 301313999991} :r=t:t PEAt' J:: ees?5eeeee -:*-1- ALPHP= e e H:ll eeee ~ HS-t"i ** - -' 914- '6,,n,, : L I HJ J} 1}4655~?~ :JZ,- SIGtm:wu~ WHYE EHGLI SH IJNiiS [IEPTH= teeeeaeeee PEH~ F= e ta?seeefh) Qlf'liA= 13 02' 1 c'ih8yh )'- HS=68e4891352:: Hi 509468898S ~ ~ 0: _ T(;14'r ~ l r T al ~PH T iol~yc: HT t'eh'! C LIH ITS BEor,: 8914400 16& PEAk -_ r- ees?se~!3e~ l-:f t th ALPHA= e a t ete~~~~3e :t1 :, HS=2 3S09?649' llt = 1 Th8l_lli37 *'~' '' SIGil ifich"f lrloye HT METPE ijnie [IEPT~: 9 t44&e~eee PE~LI ht _ r- lj, - 97'e e ::; J loj \l~ ts ~LPH~ eeteteeeee I k0:':4 - ' ~44 7 ' ) ''11 iii li(~ 1Q7494!}~~( 'H --- -- I, m;~ 1 FI unn W ~YE HT, "1 H IC IJH ITS ** **''' :j:lj::t "'** [I~PTi-l= PHi~ 4LPI-lq: 1 e43 9et~ee~ C:: e t87seeeee 8 i( 1 152~1P'~O J i-1:3= 1 fl?qrr)~3b -'- -'-~' ' til~ l ~"i??h25'~ 1 ** :;- ; JL: d= 15{1 = 45?2m tp =- ()1815 o1 = o 02 I 52 SIG~!riCAN T W~ E HT, EfIGU ;H 1_1~; T S DEP H= PE~~ 15 9999~909 * ~ J:: e 1 875909!39 '~'"' QLP4Q= 9921529899 *~~ HS=796tl469425 H( = f 15) 18546 t ~*-= - _ SIGNitl(QWT ~~ E H~TP I c IJ ~d -, fiepth= HT 4, 572~B999~ PEO~' F= 9 1875il099f HLPHP: '» 892152~3Q9 H;:~!'54 51~853 h(:: 1 B773:3(7~r: h Exampl~ problems 1 and 2 correspmd tv -txample prvhjem #J of ee{eyence {3) Example prvblen?s 3 ana 4 co'yrtsp()nol to LX amp/~ pyo/olem #z of efe,rtnce {3) Values of 1-/1 ( stor~d,(] R 08 ) have been py-,flt-ed ouj for- ~mpar- {son Wtffl +11t ;_xample prolilwjs of Re{f:-rence {3) rnese_; pro9r:am va~uts dt'fftr fvvyyj Re(aence {3) va/uls betms6 fitle 1()kg~-h~n J'm'fs irj +h/s paj!jram art fort1 o8{p to 201; and #1e f,m, ts usect 1r1 +h~ TZeftrmce (3) ave- fyuyy> 0/1 fr fo I Hl 107R-41CV-5-20

t rogt am Listi11g STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS I" I" I" r I I" I ~~ -~lru r cnt~ uno 'J( ' CJ I"' 1 l I"', 1'1 M 03 "I-E HT 134 A \II E~ e: r OR ~? r f\"l ljr; 111_1 137 TOHE 2 138 PROMPT I)Q Q(lrF 1r CISTO Y 11 CLH 12 r 1 7 Cl~";) X 14 ~~~A 1 c! '1'-'J",,-I 1 GTO 17 17 METF!C Uh!TS 1S Clv!EII 1" 9Sl 20 GTO 13 21 +LBL 17 22 "EHGLiSH UHIJS, nvtel' '-~ r'r " 24 322 25+LBL 13 'l' r r ct :10 ~t 27+LBL 2e 28 "DEPTH? 29 TOH 3 3~ PPi}~PT 31 "DEPTH= vl 7~ F '? ) ""'i J_?? XE' 19 34 STO et 35 "PEAt' F? 36 TOHE 4 37 Pl?lj!APT 3:: PECI~ F = 39 FS? 55 4(1 XEQ 19 41 ~H (12 42 J 43 * 44 Pf 4: * 4 -: -, ~1 t - I - 47 RCL e2 48 ose 4<; * 5~ ~TO Ot 51 "HlPki;'l 52 TOHE '5 53 PPO~P"' ')<l "lilph~= 55 FS:' 55 5E- XEQ IQ 5"' SH e"" Sif't'l>!e, SOivtJO() Wn~ < J O \ sq R~- J: 1 ' E! SQRT og f~ ~ rl 171"' - J ~ t? * 64 :;TQ e"' rr: 1 ~ ', ';;' tl tt ' 7 v Y' t I f}! - fhl J IP 69 ~(las! 7e RC~ ~c "'t :t ( 7~ RCL ~l 73-; 74 SI}~T 1:" r ; 7,, r' I 8~ O&t1:31 81 I 1~ SQR, ')7 ;: ~- 8' :TO 17iS <J"" ' ' w c~til ~ 1 10 ' B6+LPL 132 87 PC~ ~2 ~ 3 * 9e sto ~9 9! Pr:"L ~4 "5 :~o! e 9E PeL &4 97 STO II 98 1?1? ~(j )TI) I? tee LBL IH 10i!~ 132 PCL 12 113? ~ 1134 STO 1? 1135 PCI_ 13 I!(IE RC~ ft6!if l 113;? ')(II?~! e ~ PCL ~ 1 lltl:i; l!i 2 \12:t: ' I 13 PI 114": ;1:" 1 ',;'+; -" -- - -----~ dt: ~ R,o [( (i)~r,, c_t)(jnftr ~ Rn 107R-41CV-6 21

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS 116 ;ro 13 whln z 172 '50 ~ R,3 : 17 ee ln YtX - { < ) I -' ~ 17C: PI, f I 1 :3 -;q i I q 100@1) - -' ~ ~~') 176 12~ STO * ~~ J, '7, l ( 121-16~ t ;> ; ;ij"l STO!78 v x 1 ; I ~~ ~- p~ B' pq ~-: L L ~~ * 18~ 11" 124 XEQ f'h' ~ L, f' 181 0J~I3Si 125 1 01 1 rr - f}( 126 '/f}'y' * 127 X\P ans > /01 7 c -7! C PCL er; 12:? nn!84 1~t2 " - e~ "He 1"- 1 - _1 l~ GTI~ ~? * 130 LBI_ et;,~4 j!'8' t; RCL 16 131 RCL!B? lj ~ w (00081),~ 1~(Wn) ~- 132 STO,,, lb8 ~n!7 - J I - i I ~Rn ll t"\q RCL 12 fli) 5 i 0 {m)+,~~ - jj P'",t-L "' :I 134 + 1913 10 13~ ~36 -~ 1'31 <! {,, >Y I 192 X=Y? 1~ ' GTC e: 193 GTO 1~ -~ ( 1-38+LBL H" 1'34 PCL 12 -{ jqc: ~~- f1 ~q _,l 5'1 j ';J - ' 14~1 \! }' - ' 1% \''( \}; ' \ i I-\ '! 4! \1\ ''? ans- "> oct'l 7 197 'x'=y'j \ l T -,_, 142 GTO ~ ) 198 no 11 1 ii ro('" 199 ze PCL 12 - 'L "'= L?1-111 14d ;ro EHTERt ')1 ~-- qc- ~- ;A I PCL?" -~ ~- :: " ~' ~ ~ - 14t MOD 1" ~-' i47 )?~1 )<::11? ~ ' - - <- ~ 4:: t 14Ci GTO 15,-4 d:1 GTO 12 rr: t\ _1 RCL 17 'i!j' r:- 1 8-1 ~ t; 1 ;l:l - L 11'~ :: ",, 151 2f17 'u~rx L J I * i ~ I' '3TI) i4 Rlwnld)~ Rt4,-o GTO,, ~11-1-: \<'\ 1c~ n;ot j I -_:?AfHLB' _, '--- L r! t " ~ 1 H 1 7 L-- ''14 F'Cl RCL i I l - 13 jcc ;j - )-J ' I - _t, ~-" ~1 # 1"'' ;~ ) 1 - -~ ' [z(~y"r{~~ li) -l R, 5 '-! - 't, '7 GTO 13 ' ~C~ ;I; 1 - -' {,-,fl 214 LBL C"o'r r: i, ' 1 - JC: :t - I -~ ~1 c "f'i ",-, ' ~q 1 - "EQ SIHH" ~ '!E-0 I /V "! t~ t, -:; 17 ' 1 jc DCL =;Tfi - ~, ) ~-' 1 t - "' _I - " ~1 r1 rf'l 1 f1 '; :-: :: - = r -L 11 --~ -7 l?f1 ~-rl 1~ l t - - 1 - _, + 22& t 1 "" -:r j J r: -: rj -c: 1 r' ~~- I I, t! 1 _1 -,, -' '"r4 - - J ~~: RCL 14 GTO lj l ~ t - - L ::: r - L l ) - "J,,, ") ;ii ~ Ir L - L-l 1e j ~7 1 - - 1 l'z' be l fl, r r-!0:1 * r?a F:CL I 7 L~'t ~ ~ ) Jr LL J ::io 1 I J,_, j?~, l<'l' i 11 17t1 :;ro 16 <f>(wn){t)~ Ruo ~~- - :,7,:_ ~! I 71 PCL_l~--- ~ RCL 1& ------ 22::; t - - ~ covnitr= /O? covnftr= 50? flt)tdx-==> Rn 107R-41CV-7 22

- STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS??Q - - - _ STO I 1 2~'1 ' B 1 I 230 GTO 84 286 RCi_ fri ' 23! +LBL 1 I 2:37 - Yt2 232 RCL 18 rnp [_( _, RCL ~I l'"roj9 233 RCL 17 ~'J 1 234 ~ '1 '!&\ - RCL ~ ij6 2"'C' J J RCL 113 ~ Q1 2 jt_\ ~ ' 2 2 -e43642 "7 * l-j 3 29~ YtY "ls t:'l,; I 294 13~2289?:\Q 2qc * J -' _ SPRT 248 4 296 +',: 241 :j 2'37 RC ~ 88 242 RCL 95 29B * 243 13 0BSI 299 -~"-,_ 244 I 3ee ARCL X? c- ~ 'f,_,l 246 * ~QR~ J i 3Bl fl'fl E~ ~ij'' ~ c TQHE 6 f ( o( 'fl ~ 247 - n ~s H1 -:: 1-1 1 o~ I =, 3133 SiOP :ol - 248 GTO t' 1 24':1 LBL ca~c 2'50 STO 29 2'51 RCL!3 ] C',,, - -''-,~ 253 STO,J 254 EtX )C'C' _ J-1 RCL 3J 256 I'W - ~ "c:-7 l J "lct""t,jl~ EtX T 2'59 STQ 3! )'A,- Lh RCL ~E! lj f"' '"' ~t C l'f Et:~ P'l 7j< f :>~, ~ '--- CH~ '>ht! '-- ')hc '- - _f - Et:r:, - 266 RCL 31 2t"' / -( 268 RCL 28 269 A 27~ PTH 271 LBL "SINH 272 ;ro, 7 ) 273 EtX 274 PCL 7" ', 275 CHS 276 EtX '>T' ~ i -?]0, ) <, ' 279 2')13 P T~ - 281 +LBI 19 232 PR4 283 PR :~ 2:34 PIN L """ 15 ' 3~4 GTO 28 3i35 EHD d= hfe ~ 2 H J1 exp&ozzsqrf ~ s i j 107R-41CV-8 23

REFERENCES Thompson, E F, and Vincent, C L 1983 "Significant Wave Height for Shallow-Water Design," submitted for publication to The American Society of Civil Engineers U S Army Engineer Waterways Experiment Station, Coastal Engineering Research Center (CERC) 1984 Shore Protection Manual, revised edition in preparation, U S Government Printing Office, Washington, D C Vincent, C L 1981 "A Method for Estimating Depth-Limited Wave Energy," Coastal Engineering Research Center Technical Aid 81-16, U S Army Engineer Waterways Experiment Station, Vicksburg, Miss Vincent, C L 1982 "Depth-Limited Significant Wave Height: A Spectral Approach," Coastal Engineering Research Center Technical Report 82-3, U S Army Engineer Waterways Experiment Station, Vicksburg, Miss Walton, T L, Birkemeier, W A, and Weggel, J R 1982 "Hand-Held Calculator Algorithms for Coastal Engineering," Coastal Engineering Research Center Technical Aid 82-1, U S Army Engineer Waterways Experiment Station, Vicksburg, Miss 24

APPENDIX A: BLANK PROGRAM FORMS Al

Program T1tle Name Date Address Clly State Z1p Code Program Oescnption, Equat1ons, Variables, etc Operating L1m1ts and Warnings A3

Use Instructions STEP INSTRUCTIONS INPUT FUNCTION DISPLAY SIZE: A4

Program Listing 001 STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS 060 010 070 020 080 030 090 040 100 050 110 AS

STEP KEY ENTRY KEY CODE COMMENTS STEP KEY ENTRY KEY CODE COMMENTS A6