i «•; "**, £> *3940 «' -r NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS TEST OF THE APPLICATION OF THE TYWAVES MODEL TO PREDICTION OF SWELL IN THE EAST CHINA SEA FROM THREE TROPICAL CYCLONES IN THE WESTERN NORTH PACIFIC by Lee, Hyong Sun December 1980 Thesis Advisor; J. B. Wickham Approved for public release; distribution unlimited T197870 UNCLASSIFIED ■MR. . - SECURITY CLASSIFICATION Q> THIS »Ar.E r *».««» Data Entarad) REPORT DOCUMENTATION PAGE ITS 2. GOVT ACCKUIOM MO 4 Tl TL £ mnd SubtltUi Test of the Application of the TYWAVES Model to Prediction of Swell in the East China Sea from Three Tropical Cyclones in the Western North Pacific 7. «uTMO*flj Lee , Hyong Sun READ INSTRUCTIONS BEFORE COMPLETING FORM ». KICl^llNT'SCiTtLOC NUMKD S TYPE OF »IPO»T A PERIOD COVERED Master's Thesis; December 1980 • ■ performing one. report numiih ». CONTRACT OH CHANT NOMl(«ri| t. •!»'0»MIN3 0«0iMiZATl0N NAME ANO AOORBSS Naval Postgraduate School Monterey, California 93940 10. PROGRAM Element. p»oj£c task AREA A WORK UNIT NUUIIKi M CONTROLLING OFFICE NAME ANO AOORESS Naval Postgraduate School Monterey, California 93940 12. REPORT OATE December 1980 IS. NUMBER OF PAGES 116 pages IT MONITORING AGENCY NAME A AQORESSCK dtllarmnt Irom Contrail!*! Olllea) Naval Postgraduate School Monterey, California 93940 IS- SECURITY CLASS, tol (M. r«v>" Unclassified IS«. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT tot thlt Xamart) Approved for public release; distribution unlimited 17. Distribution STATEMENT (at t». »*»trmet amfrdd in Rise* 30. II dlilmrmtl *•#<>«; • SUPPLEMENTARY NOTES '* KEY WOROS (Contlnud on rmworoa ••<»• It noeooomwr or>d Idrnntlty *y Woe* nuwaw) TYWAVES, typhoons, wave propagation. 20. ABSTRACT (Continue an eoomtmo Hd» II n»e»»««rr «r>« idontlir »T «•«* numaotj A method for predicting swell from tropical cyclones using a spectral wave model (TYWAVES) was tested. The model was applied to predicting swell propagating from three typhoons in the Western North Pacific through gaps in the Pyukyu Islands into a region of the East China Sea. The model involves a source region concept which considers only the swell emanating from regions o: peak energy in moving typhoons. For three representative typhoons predicted heights were not significantly different from the DO , '*?» 1473 (Page 1) EDITION OF I MOV «■ IS OBSOLlTt S/N 0 JO 2-0 14- A«.0 I 1 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOE (9han Data Kntatod) UNCLASSIFIED <*Cuwt» Cl*Ml»'C*Tton pir Twit »»Qt <■»».— n»tm htMl observed heights. The time of occurrence of the predicted peak height agreed well with observational values for the swell from two typhoons, but lagged by 6-12 hours for the third. The dominant swell period and direction predicted by the model were not verifiable by data available for this study. Shoaling and refraction effects were considered in the pre- diction, in a simplified way, but attenuation was ignored even for the passage of energy through the Ryukyu Islands. DD 1 jSn^D U73 2 UNCLASSIFIED S/N 0102-014-6601 stcuaiTv claudication 0' t*h *»otr**«- o«»« *»»•»•*> Approved fo public release; distribution unlimited Test ot Lhe Application of the TYWAVES Model to Prediction of Swell in the East China Sea from Three Topical Cyclones in toe Western North Pacific by Hyong Sun Lee Lieutenant Commander, Republic of Korea Navy B.S., Republic of Korea Naval Academy, 1972 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL December 19 80 ABSTRACT A method for predicting swell from tropical cyclones using a spectral wave model (TYWAVES) was tested. The model was applied to predicting swell propagating from three typhoons in the Western North Pacific through gaps in the Ryukyu Islands into a region of the East China Sea. The model involves a source region concept which considers only the swell emanating from regions of peak energy in moving typhoons. For three representative typhoons, predicted heights were not significantly different from the observed heights. The time of occurrence of the pre- dicted peak height agreed well with observational values for the swell from two typhoons, but lagged by 6-12 hours for the third. The dominant swell period and direction predicted by the model were not verifiable by data available for this study. Shoaling and refraction effects were considered in the prediction, in a simplified way, but attenuation was ignored even for the passage of energy through the Ryukyu Islands. TABLE OF CONTENTS I. INTRODUCTION 11 A. OBJECTIVE OF THE STUDY 11 B. TYPHOONS IN THE WESTERN NORTH PACIFIC 11 C. TYWAVES MODEL (THE TYPHOON WAVES PROGRAM) 12 D. FORECASTING AND VERIFICATION 13 E. TERMINOLOGY 22 II. PREDICTION OF TROPICAL STORM WAVES BY TYWAVES MODEL 2 5 A. LOCATION OF THE SELECTED POINT-SOURCES 25 B. SEA-SPECTRA AT THE POINT-SOURCES 2 8 C. SELECTION OF THE DIRECTIONAL ENERGY AT POINT-SOURCES 2 9 D. TOTAL AND DIRECTIONAL ENERGY AT POINT- SOURCES 3 0 1. Typhoon Hope 31 2. Typhoon Irving 31 3. Typhoon Owen 32 III. PREDICTION OF SWELL CHARACTERISTICS 36 A. THE SETTING OF THE FORECAST SITE AND ITS RELATION TO THE WAVE SOURCES 36 B. GROUP VELOCITY 37 C. TRAVEL DISTANCE AND ARRIVAL TIME 3 9 IV. THE ENERGY PROPAGATION PROCEDURE 45 A. PROPAGATION OF SPECTRAL ENERGY COMPONENTS 45 B. SHOALING AND REFRACTION FACTOR 4 7 1. Shoaling Factor 47 2. Refraction Factor 50 C. SHOALING AND REFRACTION OF THE SPECTRAL COMPONENTS 51 1. Shoaling Process (Computations) 52 2. Shoaling Energy Components From Each Source Versus Arrival Time 52 3. The Predicted Swell Waves at Prediction Site 5 3 D. OBSERVED DATA 53 E. COMPARISON OF SWELL PREDICTIONS AND OBSERVATIONS 6 3 F. ERROR SOURCES 64 V. CONCLUSIONS 67 APPENDIX A (Outputs of TYWAVES for Typhoon Owen on 12 GMT September 26) 68 APPENDIX B (Sea Spectra at Source Region for Three Typhoons and Significant Wave Distribution)- 76 APPENDIX C (Propagation Energy Arrival Time) 89 APPENDIX D (Shoaling of the Spectral Energy Components) - 94 LIST OF REFERENCES 113 INITIAL DISTRIBUTION LIST 115 LIST OF TABLES 1. 1979 Significant Tropical Cyclones 14 2. 1979 Significant Tropical Cyclone Statistics 14 3. Best Track for Super Typhoon Hope 19 4. Best Track for Typhoon Irving 20 5. Best Track for Typhoon Owen 20 6. Typhoon Centers and Selected Points Location 2 7 7. Period-Directional Spectrum at Point 4 of 06 GMT September 25, 1979 30 8. The Visual Observation Data by NODC and ROK Navy- 6 0 LIST OF FIGURES 1. Typhoon Tracks 15 2. Typhoon Hope, Best Track 16 3. Typhoon Irving, Best Track 18 4. Typhoon Owen, Best Track 17 5. Possible Refraction Diagram at Point 4 at 06 GMT September 25, 1979 29 6. Typhoon Hope, Total and Directional Energies at Point Sources 33 7. Typhoon Irving, Total and Directional Energies at Point Sources 34 8. Typhoon Owen, Total and Directional Energies at Point Sources 35 9. Typhoon Hope Swell Arrival Time 42 10. Typhoon Irving Swell Arrival Time 43 11. Typhoon Owen Swell Arrival Time ■ 44 12. Typhoon Hope, Directional Energy Propagation 54 13. Typhoon Hope, Total Propagated Energy Comparison 5 7 14. Typhoon Irving, Directional Energy Propagation 55 15. Typhoon Irving, Total Propagated Energy Comparison- 58 16. Typhoon Owen, Directional Energy Propagation 56 17. Typhoon Owen, Total Propagated Energy Comparison 59 LIST OF MAP AND PLATE MAP 1. East China Sea Bottom Contours 21 PLATE C-l. Illustration of Various Functions of =— 4 8 o FIGURE 2-19. Changes in Wave Direction and Height Due to Refraction on Slopes with Straight Parallel Depth Contours 49 ACKNOWLEDGMENT S I wish to express my deepest thanks to Professor J. B. Wickham for the concepts and methods in this thesis. The completion of this work is due to his effort, experience and guidance. I also wish to recognize the invaluable cooperation and assistance of Samson Brand, Naval Environmental Prediction Research Facility, Monterey, California, 9 3940; Kevin M. Rabe, Science Applications International, Monterey, California, 9 3940; and of Professor J. Von Schwind, Naval Postgraduate School, Monterey, California, 9 3940. 10 I. INTRODUCTION A. OBJECTIVE OF THE STUDY A serious problem for naval activities, ocean industry, shore protection and fisheries in the Korean south coastal area is the lack of adequate estimation of the waves re- sulting from typhoons. The objective of this study is to make a partial test of the TYWAVES for forecasting swell from tropical cyclones which arrive at a single observa- tion site near Cheju-do, Korea (33.2°N 126. 6°E). Forecasting based on wave fields predicted in a typhoon area by the TYWAVES [13] developed by NEPRF (Naval Environmental Prediction Research Facility) are to be verified against swell observations made near Cheju-do. B. TYPHOONS IN THE WESTERN NORTH PACIFIC During 1979, the Western North Pacific experienced 2 8 tropical cyclones. Table I, from "1979 Annual Typhoon Report" [2], shows the significant tropical cyclones for that year. Table II from [2] shows the monthly distribu- tion of tropical cyclones in 1979 and other statistics. Most typhoons occur in the summer season and their tracks can be classified as one of three typical tracks. The first type is that passing south of Taiwan toward the west, the second is that crossing over Korea through the 11 Ryukyu Islands, and the third is that passing east of Ryukyu Islands. I selected one typhoon of each type; one each in July, August, and September in 1979. They are Typhoons Hope, Irving and Owen shown in Figures 1, 2, 3 and 4 from [2]. tropical cyclone "best track" information is shown in Tables III, IV, and V for Typhoon Hope, Irving and Owen, respectively. C. TYWAVES MODEL (THE TYPHOON WAVES PROGRAM) The SOWM (Spectral Ocean Wave Model) run at FNOC (Fleet Numerical Oceanography Center) utilizes a coarse operating grid system (100~190NM) which does not allow sufficient resolution to describe adequately the resultant sea state in typhoon areas. Thus, TYWAVES, an improved model for typhoons with a locally finer grid, was developed by NEPRF. FNOC judged that TYWAVES is worthy of evalua- tion as a possible operational typhoon sea state model [14]. The TYWAVES is intended to produce fields of signifi- cant wave height and spectral wave properties on a mesh size consistent with the scales of tropical cyclones and is designed, primarily, for the application to the western North Pacific. The detailed outputs of TYWAVES are in the form of fields, at each of 12 points, of spectral energy 12 components, significant wave heights, maximum wave periods, and the predominant wave directions, for 00, 12, 24, 48 and 72 hours, where 00 hours is the time of the first typhoon warning issued. An example of those outputs for Typhoon Owen is shown in Appendix A. Using these spectral energy components at selected source points, I was able to make predictions based on the propagation of these components as swell into the region, south of Cheju-do, Korea (see Map I, page 21). More details of TYWAVES are described in Ref. 11. D. FORECASTING AND VERIFICATION Extremely high sea states are known to be generated in the quadrant to the right of the direction of movement of typhoons. The wave generation in that quadrant of the typhoon derived in TYWAVES from a spectral model utilizing the Pierson-Moskowitz (1964) spectrum. The model describes the spectroangular components of the waves present at a number of grid points in the region of strong winds. Each spectral component of interest is then permitted to propagate at its appropriate group velocity to the fore- cast site. The method is applied to three western North Pacific typhoons in 1979 and the forecast products are compared with the observed swell data from the south coastal area of Cheju-do, Korea. 13 TAB>-t 1 . WESTERN NORTH PACIFIC 19/9 SIGNIFICANT TROPICAL CYCLONES ! CALENDAR MAX MIN NUMBER PERIOD DAYS OF SFC 08S OF DISTANCE CYCLONE TYPE NAME OF WARNING WARNING WIND SLP WARNINGS TRAVELLED 01 TY ALICE 01 JAN-14 JAN 14 110 930 51 2597 02 TY BESS 20 MAR-25 MAR 6 90 958 21 1804 03 TY CECIL 11 APR-20 APR 10 80 965 40 2535 04 TS DOT 10 MAY-16 MAY 7 40 984 24 2876 05 TD TD-05 23 MAY-24 MAY 2 30 998 6 2170 06 TY ELLIS 01 JUL-06 JUL 6 85 955 22 1612 07 TS FAYE 01 JUL-06 JUL 6 40 998 20 1837 08 TD TD-08 24 JUL-25 JUL 2 20 1004 5 1264 09 ST HOPE 27 JUL-03 AUG 10 130 898 33 3928 10 TS GORDON 26 JUL-29 JUL 4 60 980 13 1058 11 TO TD- 1 1 03 AUG-06 AUG 4 25 997 14 1088 12 TY IRVING 09 AUG-18 AUG 10 90 954 38 2732 13 ST JUDY 16 AUG-26 AUG 11 135 887 39 2502 14 TD TD-14 18 AUG-20 AUG 3 20 1006 9 605 15 TS KEN 01 SEP-04 SEP 5 60 985 13 1418 16 TY LOLA 02 SEP-08 SEP 7 90 950 23 1298 17 TY MAC 15 SEP-24 SEP 10 70 984 35 1831 18 TS NANCY 19 SEP-22 SEP 4 45 993 14 528 19 TY OWEN 22 SEP-01 OCT 10 110 918 37 2151 20 TS PAMELA 25 SEP-26 SEP 3 45 1002 6 984 21 TS ROGER 03 OCT-07 OCT 6 45 985 16 1920 22 TY SARAH 04 OCT- 15 OCT 12 no 929 43 1194 23 ST TIP 05 OCT-19 OCT 16 165 870 60 3972 24 ST VERA 02 N0V-07 NOV 6 140 915 23 1868 25 TS WAfNE 08 NOV- 13 NOV 6 50 990 22 1559 26 TD TU 26 01 OEC-02 DEC 2 30 998 6 1070 27 TY ABBY 01 DEC-14 DEC 14 110 961 52 4044 28 TS bEN 21 DEC-23 DEC J 60 990 10 2245 1979 TOTALS 149* 695 •OVERLAPPING DAYS, INCLUDED ONLY ONCE IN SUM. TABLE 2. J 1979 SIGNIFICANT TROPICAL CYCLONE STATISTICS | '8)1 WESTERN (1959- NORTH PACIFIC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC TOTAL AVERAGE I TROPICAL j DEPRESSIONS 0O0O1O 1 2 0 0 0 1 5 4.8 * TROPICAL STORMS 0 0 0 0 10 2 0 4 1 1 1 10 10.0 i TYPHOONS 10 1 10 0 ? 2 ? 2 1 1 13 18.0 i ALL CYCLONES 10 112 0 5 4 6 3 2 3 28 32.8 • (1 959-78) AVERAGE 0.6 0.4 0.6 0.9 1.4 2.1 5.2 6.8 6.0 4.8 2.7 1.3 32.8 FORMATION ALERTS 23 of the 27 (85%) Formation Alert Events developed Into tropical cyclones. 5 of the 28 (18t) tropical cyclones did not have a Formation Alert. WARNINGS Number of warning (lays: 149 Number of warning days with ? cyclones: 38 Number of warning days with 3 or more cyclones: S 14 Figure! Typhoon tracks ' IRVING OWEN LQ1A EiTERN NKDRTH PACIFIC TYPHOONS 1979 itHMII !■— — — — ■ ■ 5ARAH WESTERN NORTH PACIFIC SUPER TYPHOONS 1979 'tip 15 ■'■' A Figure 2. TYPHOON HOPE , BEST TRACK TC-09 '■;,. 27 JUL -03 AUG 1979 MAX SFC WIND 130 KTS 28/OOT MINIMUM SLP 898 MBS LEGEND 06 HOUR BEST TRACK POSIT A SPEED OF MOVEMENT B INTENSITY C POSITION AT XX 0000Z - IROPICAL DISTURBANCE ... TROPICAl DEPRESSION TROPICAl STORM TYPHOON ♦ HJPER TYPHOON START <.- iUPER TYPHOON END EXTRATROPICAl ••• DISSIPATING STAGE if 'IRST WARNING ISSUED •fr LAST WARNING ISSUED T> :*4 •30V- i — t- -♦—- 1— I I I I P - A/ 20 1 / 20 / 0" ->5 1 JO 03/0*>Z ^ . B35 50 70_ flc / / I ! H5 i i / -i — i- ■sr ■ rxr h .-Chi • ^ -/r 06 HOUR BEST TRACK POSH SPEED OF MOVEMENT INTENSITY POSITION AT XX 00O0Z - TROPICAL DISTURBANCE ... TROPICAL DEPRESSION - — TROPICAL STORM TYPHOON ♦ SUPER TYPHOON START O SUPER TYPHOON END EXTRATROPICAL • • DISSIPATING STAGE if HRST WARNING ISSUED -fr -AST WARNING ISSUEO -^ 17 Figure 3- TYPHOON IRVING BEST TRACK TC12 09AUG-18AUG 1979 MAX SFC WIND 90 KTS MINIMUM SLP 954 MBS LEGEND ■"■H 06 HOUR BEST TRACK POSH A SPEED Of MOVEMENT 8 INTENSITY C POSI'IONATXX 0000Z IROP ' Al DISTURBANCE -■ ROf A. DEPRESSION - ■ RO* LAI STORM _. 'YPHOON ♦ .UPfR TYPHOON >FART SUPtR TYPHOON ENO 5XTRATROPICAL •• DISSIPATING STAGE IT f'RST WARNING 'SSUEO -.1 LAiT WARNING SSUEO 18 Table 3. Best track SUPER TYPHOON HOPE 90/J4/MJ 0'2*l2t oUnUJ 0 7231B/ o '23002 072BU6/ u7<:3i2/ aii! i mi 0 l£l 7.a l->6. / l?4.7 l?3.? Ml.* I'd. I I 14.? 116.4 lll.i 111. 7 119.* 1"7.S 1 IS. 4 II). I 1 .1 1 . 7 111.4 19.? • 7.9 •>6.7 2.7 92. 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'I i. •10. 1 i 1 19 3 . 3 . • rs 092 '192 --0.3 1 '9 a -S ?5.6 1 29. 7 B5. a. 1 . >9.n I3n.- '3. it . 3 1.6 133.7 30. 1-9. •16. |4 .0 1 -3 3 .3. 1 1 ) lHouc/ J'.o 1 39 pi 27.1 1 29. o 85. i. 0 . '9.* I3n.7 lb. y. . 3°. 3 133.8 60. 1 44. -10. Is .0 140 1 40. 337 p 92 BOO/ 2'. 3 1 />« u -n 27,5 1 29. a BO. ! p. lO.l 131. i lb. 12-. ► ' p . a 136.1 33. in 3, -10. " .0 1 0 0. -il 0 9231c:; 2'. a 1 -9 ll /' 2'. 1 i 29. a '5. * 39. S 1 3«.n 10. 2-». -- .3.1 1 32.0 60. l«l. 3 . 0 .0 0 ) J. - J9<:9ln/ tl.x 1 '9 .J ;c 11. 1 1 29. a '5. , . 78.' 129.9 11. ao ■ ■ s < 1 ./ 131.2 60. -6*. i 6 . II ■ 0 J 1 J. -0 DV29UU2 P8.1 1'9 3 rs 28.0 1 39. a E«fl» 15. *«i» [MTvmSIff -4G9i'uOF t«9ua 2. ««6 lH-rs-^ii I 1 H[»5 -n. •<\}»i^<* 3f fjaec«.ST< 37 7P-. 33'. 2'*. 20 MAPI. East China Sea Bottom Contours SOUNDINGS IN FATHOMS AND FEE! ;epth contours O, -I A° = Long x cos 10 .*. ° Long = 2° Lat/cos 10° = 2.128° E = 126.7 + 2.128 = 128.8° E Therefore, point 4 * 20.0°N 128. 8°E. 26 H CQ C o •H 4-> o 0 CO c •H o o -P U 0) H 0 CO C rd CO CD 4J C 0) u c 0 o >i Eh I CM H I CO I jy _w r^- co r^ cN^u)tNOinmvo cyiHcoro-^Lnin^ocnTr in (N cri ko ro co co cm cn cm i— I rH rH r-i H I 1 I I I m< ^o ko ko in oc7\cococor-r--r- fOCNCN(NfNCNCN(N rHi-HrHrHrHr-HiHrH I I I I I I I I cococMeorocooococo^ cocooooocooococococo H H H H H r- IHHHH I I I I I I I I I I ro^in-TiriLnrocoLnco r^ co a\ o rH HHH (N tN orMfO^Lnr^o^rH CMCNCNCNCNCNCNCO CMCNCNCNCNCNCNCNCNCN o> m co co cm cohojmdo^oh •>5rr-'^^ooo^ro>i co h co uo cn ro 00 (N CN CN rH rH -H rH rH I 1 I I I ^ vd ^o >^> m cocor-«v£>v^Ln<£>'^) CMCMCMCMCMCMCNCN r-\r-ir-ir-ir-{r-\r-{r-\ I I I I I I I I ooirnooMnkor- CNHHHHCMCNCMCMCM OOCOCOOOOOOOOOCOeOCO r-\r-At-\<-\r-\r-\r-i^r-^r-\ I I I I I I I I I I nvDin^ininfocomco m ko r^ co a\ cooHCNromr^cri HCNCNCNCMCNCNCN HCNCNCNCMCNCMCNCNCN cn un co ^r on coojcMMiiooH mr^^roo^HHH^rcri roHCOincs n n cn cn cn H H H rH H I I I I I ^ CMHrHHHCMCMCMCMCN rocococococococococo HHrHHrHHrHHHH I I I I I I I I I I ro^inrrininrocoi/ico en o H cn co H CN CN (N CM cM^Ln^Dr-cnHro ro^in^r^coatdiOH CMCNCMCNCNCNOOCO CMCMCMCNCMCNCNCMCOCO c^ in n ro cn cocNtsMnooH ^^,^)c^cnHH^,cn 0 1 CO rH CO LO CM CO CO CN CN CM H rH H H H ^ "o ^o ^o in cocor-»^x>>sO^>(Ln|sor^ CMrHHHHHCNCNCNCN cococococococoeoeooo rHrHHHHHHHHH I I I I I I I I I I n^DLifiriLnncoinco hcooiOH ocNn^iriMTiH HCNco^mkDr^r-coc^ HHrHCNCM CNCMCMCMCMCMCNCO CMCMCMCMCNCNCNCNCMCM cof cn cm h r^oomcor-»r-r- coincNt,r ^O CO O CO CM CM CM CN H iH H H rH I I I I I ^ KD VD U3 m "sO^OLD^r^cocooo CNCNCNCMCMCMCNCM HHHHHHHH I I I I I I 1 I ooLn^o^mvDo- OCiCTiCnCTiCnCPiCTiOO rOCNCNCNCNCMCMCNOOCO HHHHHrHrHHHrH i i i i i i i : i i nvoin^inmroooinco r^cocTiOH ocNroTcuir^aiH HCNcntinwr^t^com r_|,H(_|fMCN CNCMCNCNCMCMCNCO CMCNCNCNCMCMCNCNCMCM CN O CN O CN H O H O H O H H H rH cn co co o o r- r^ r- co co o o o o o OCNOCNOCNOCM OHOrHOHOH convfini/na^D rHHrHHHHHrH cococooococococo oooooooo VT)COVOCOV£)COU3CO*X)CO OHOHOHOHOH ininvavDr^r^cocooiu* CNCMCMCMCMCMCNCMCMCN CTiCTiCTiCTiO^iO^cTiCTicricri oooooooooo 27 B. SEA-SPECTRA AT THE POINT SOURCES The description of the wave fields using the spectral component method developed by NEPRF was used in this study. Only those directional components able to propagate to the forecast site need be considered. A schematic example of the TYWAVES spectral prediction in a typhoon area is given below. The whole spectral table for the selected sources is shown in Appendix B. 1 1 — 1 ean tion nds 6U0! ^> si U LINE l\Vft\ J 1 ea: Figure 5. Possible refraction diagram at point 4 at 06 GMT September 25, 1979. The curves around typhoon center are contours of wave height (H 1/3 in feet) . The detailed bottom contours are shown on Map 1. 29 TABLE 7 Period-Directional Spectrum at Point 4 at 06 GMT September 25, 1979. The energy units are 26- kiloerg/cm2. TYPHOON WAVES 3C I IT U. H.i/lu= j , 1 M NORTH- CORRESPONDS TO THE AZIMUTH 36C N ■i * U r j j J NN£ 3 * £ G c J * u ME [j * rt Q 4 J c ENE u * -1 n v ~ lj 0 P 1 * 0 Q >". J J Q zSE 32 * 0 6 b 17 1 Q SE 9 3 * n 8 25 27 Zk 8 S S E 7*» * G 7 2 n 71 3 L c 3 1 * u <+ 1 ". _^ u 2 SSW * - u - - - u sw u G '. U u G j WSW 0 * r j •^ - I Q w J * j 0 L T r 0 - WNW Q *■ n c u 'J y G NW G * U u w ^ C NNW a * - u c « Q u TOTAL 232 0 26 69 86 3d. 1C PEPIOOS 4 7 IJ 13 16 19 D. TOTAL AND DIRECTIONAL ENERGIES AT POINT SOURCES Figures 6 , 7 and 8 show the energy components at each selected grid point in the typhoon area. Each line is labeled by selected grid point (source point) . T indicates total energy given by TYWAVES at point n and D represents the sum over all periods of the energies with proper direction to reach Cheju-do. . 30 V9o> =il1 Ei i -gS-OOL) ABjaug 33 CN (iu)OI./|.H 00 m 6 o 00 en 00 o o 00 CO CO CO o CO CO o 00 m "Tf CN i^ co m ^t co (2uio/BJ30|i>i -gSOOl-) ABjaug CN m o' 34 (w)OL/LH COO) h- (0 10 ^ w (sluo/Bj30|!>i -gSOOL) ABjaug in d 35 III. PREDICTION OF SWELL CHARACTERISTICS The periods of high waves due to typhoons are usually in the range of 7~19 sec. They travel in deep water with the group corresponding velocities 10-30 kts. It normally necessitates 1-4 days for conspicuous swells generated in a typhoon in the far south seas to reach Cheju-do, Korea. The group velocities of periods 7 and 10 sec are constant along their paths since they remain in "deep water." But for periods 13, 16 and 19 sec, the group velocities vary because of depth variations. Thus, I considered two distance components: in deep water R and in shallow water R for periods 13, 16 and 19 sec. The travel distances between grid points and observa- tion points are calculated with the assumption of plane geometry. Then, group velocities, travel distances and travel times are derived for each period in this section. A. THE SETTING OF THE FORECAST SITE AND ITS RELATION TO THE WAVE SOURCES The passes of the Ryukyu Islands act as windows between the energy sources and the forecast site, Cheju-do, Korea. Since the largest land length for blockage of energy is only about 40 NM, this length is not sufficient to inter- rupt totally the energy propagation. Thus, as a further simplification, I neglected the effect of the Ryukyu Islands 36 against the energy propagation. The window is assumed sufficient for total propagation. B. GROUP VELOCITY Some simplications are used in assigning group velocity values along the route from typhoons to the observation site. From linear wave theory group velocity, C is given by y Cg " 2 [C + sinh 2kh] = nc (all the symbols are defined below) and phase speed c is given by c = - tanh kh. In deep water this is well approximated by c = g/a = 3.03 T (ktc) for T given in seconds, and in shallow by c = /gh. But in the general case c varies with both the depth of water and the wavelength. The classifications "deep" and "shallow" are given in terms of "relative depth h/L , described below. Since there is no "shallow water" between the wave sources and Cheju-do, Korea, (corresponding to the periods used by TYWAVES) , I will use only the general equation and the deep water approximation. In these equations C = group velocity c = phase speed (c in deep water) n = the fraction of energy propagated at phase speed 37 g = gravity acceleration h = water depth a = wave angular frequency (2T/T = 2kf, where T is period) k = local wave number (2W/L, where L is wave length) f = wave frequency (1/T) It is important to note that c and group velocity, Cg must be found as functions of both h and a. A straight- forward method is illustrated below, where the dependence on kh is replaced by the deep water wavelength L = 2T~ g/T . The local wavelength is then found from L/L , a function of the relative depth h/L . Since C/C = L/L , the phase speed c can be found from h and a. To estimate the group velocity by definition, C = y i c [1 + — « — r-nr] = nc where, n takes on the following 2 L smh khJ values for corresponding h/L : general case (y > h/L _> jq) : l>n>y , deep water case {h/L > y) : n = y • In order to simplify calculations, I used n = 3/4 in the waters between the Ryukyu Islands and Cheju-do where, for the longer periods, the relative depth range 1 >h/L >-W . With this simplication, the corresponding 2 ~ o 20 group velocities become the following: 38 T = 13 sec; C = 2 9.4 kts y T - 16 sec; C = 33.6 kts T = 19 sec; C = 35.8 kts The influence on the calculation of C of the use of g these representative constant values is discussed in Chapter IV. D. For deep water Cq = 3.03T (kts for T in sec) C = nc = T C = 1.515T (kts for T in sec) y o Therefore, group velicity in knots and depth at which C replaces C are shown below: T (sec) 7 10 13 16 19 C /C (kts) 10.6/- 15.2/- 18.7/29.6 24.3/33.6 28.8/35.C go g Lo h(-j- in ft) 126 256 433 656 924 C. TRAVEL DISTANCE AND ARRIVAL TIME The travel distance between grid points in the storm and the observation point 33.2 N 126.6 E are calculated with the assumptions of plane geometry. Consider this example. On 12 GMT July 30, the grid point 4 was at 17. 4°Nl33 . 9°E. Thus, the north-south component is given by 39 y = [lat (site)c - lat (grid point)0] x 60 MM = [33.2 - 17.4] x 60 = 94 8 NM and the east-west component is approximated by x = [long (grid point) - long (site)] cos (mean lat)] x 60 NM = [133.9 - 126.6] cos (17.4) x 60 NM = 418 NM Thus, the travel distance, D, is given by 2 2 ^ D = (x + y ) 2 and for grid point 4, D = (4182 + 9482)^ = 1036 NM The travel time, t, is given by R R t = _£ + 7r- , where R + R = D c c o 9 g ^o 3 R = the deep water distance R = the remaining distance Therefore, the arrival time, tar of each period band is given by tar (T) = t + t, where t = leaving time from o o 3 typhoon area t = travel time The Figures 9, 10 and 11 show the swell arrival time for each of the three typhoons. Each curve indicates the arrival time of energy from a source at a specified leaving time labeled with various periods (from 7 to 19 sec). 40 Appendix C shows the arrival time calculations for each typhoon. 41 5 a E > £ < (oas)pou9d £ 42 (oas) pouad a> (09S) POUSJ Q 44 IV. THE ENERGY PROPAGATION PROCEDURE A. PROPAGATION OF SPECTRAL ENERGY COMPONENTS The spectral forecast permits the forecaster to deal with only that range or periods which have important energy. Each spectral component is tracked with its respective group velocity, only those directions being chosen for which waves can reach Cheju-do. When the typhoon is moving with a velocity component toward Cheju-do, only spectral components with a group velocity greater than the movement of the typhoon are considered (as in Typhoon Irving) . Wave energy generated in a relatively small region at all frequencies will spread over a much larger region as it propagates outward from its source, and the wave character- istics change in such a way as to become more "swell like." There are essentially three processes which contribute to this change in wave characteristics: dispersion and angular spreading, which are modified by shoaling and refraction, and attenuation. In the procedure followed here, I have ignored attenua- tion for waves of long period. Dispersion and angular spreading are accounted for by simply following components to Cheju-do with appropriate shoaling and refraction factors. 45 For ease of calculation shoaling and refraction processes are simplified as described below. As seen on Map 1, a slightly curved contour of 100 fathoms (590 ft) connects the northern tip of Taiwan to the south-western tip of Japan. The slope from 590 ft bottom line to 413 ft (70 fathoms) is very steep. But most bottom topography along the path to Cheju-d0/ north of the 413 ft bottom contour is almost flat with the depth of 45 fathoms (266 ft) up to the forecast site (33.2°N 126. 6°E). Therefore, I have approximated to underwater topography by assuming only two water depths, a deep water and a shallow water (intermediate water depth) region with an abrupt jump between them. To compute the wave characteristics at a shoal water site, the shoaling and refraction are considered using the values of Cg and n from Chapter III.B. The energy of component Eq (t,9) in the typhoon area (deep water) is transformed after shoaling and refraction to its value at the forecast site according to Ed, J) = Eq (i, j)-k2 (±# -j k2 {if j} where E (i, j) is the energy of the component of period T\ and which had the direction 9 . in the -J • generating area, and ks (i, j), kr (i, j) are the respective shoaling and refraction factors of those components. 46 Details of calculation of k and k are given in the S r following sections. The refraction and shoaling calcula- tions for three typhoons are shown in Appendix D. The following is a sample calculation on 12 GMT July 3 0 for Typhoon Hope at source point 4. T 7 10 13 16 19 ks 1 1 0.92 0.89 0.90 kr 1 1 1 0.989 0.972 (ks kr) 1 1 0.8464 0.7748 0.7653 EQ 7 19 11 9 14 E 7 19 9.3 7.0 10.7 where k is derived from plate C-l [6] with h = 40 fathoms = 2 36 ft k is derived from Figure 2-19 [5] with h = 413 ft and a = 40°. o B. SHOALING AND REFRACTION FACTOR 1. Shoaling Factor The shoaling factor, k = H/H ' was derived from the 3 so plate C-l [6] with depth and period of the appropriate spectral component. The shoal site depth near Cheju-do (33.2°N 126. 6°E) is 40 fathoms, and the relative depth h/L and shoaling factor of each period are shown below. 47 10 8.0 T-rq 0.00 0.0001 0.0002 0.0004 0 00. 0.002 0.004 0.01 0.02 0.04 0.06 0.1 0.2 0.4 0.6 1.0 d Lo iftM Wiegel. R.L., "OitilUtory W.»c" U.S. Amy, fl««ch Eroaon Bo^rd. DuJcon, Special Imu* No. 1. Juiy 1948. Plate C-l Illustration of Various Functions of -£- 48 V Q. O to e o c o o: s 3 Q — i/> 1> i- X§ T3 — ss = u 2 * = Q Q — » — o o 5 3 c Q. »/> *- 4) -c Ss -C — 0> 3 0< 49 10 13 16 19 0.46 0.24 0.18 0.13 1 0.92 0.89 0.90 T 17 h/LQ 0.94 ks 1 2 . Refraction Factor Generally, two basic techniques of refraction analysis are available — graphical and numerical. Several graphical procedures are available, but all methods of refraction analyses are based upon Snell's law. Refraction may be treated analytically in any region with straight and parallel contours, by using Snell's law directly: c sin a = (— ) sin a , where a is the angle between the wave co ° crest and the bottom contour, and aQ is the angle between the deep water wave crest and the bottom contour. Figure 2-19 [5] shows the relationships among a, a , period, depth and refraction factor in graphical form. I derived the refraction factor from using this graph, Figure 2-19, the bottom contour and period. Also, I assumed that the refraction factor is 1 if the angle a 3 o (between crest and bottom contour) is less than 10 and that the refraction occurs only one time at the depth of maximum bottom gradient where waves are refracted because of the wide flat-bottomed portions over most of the inter- mediate water propagation path as seen on Map 1. 50 With these considerations, I derived the refraction factor and predicted the shoaling energy. Those procedures are shown in Appendix D. C. SHOALING AND REFRACTION OF THE SPECTRAL COMPONENTS Each deep water wave spectral component derived from the TYWAVES model moves with its respective group velocity. I considered the 80 energy components to behave as mono- chromatic component waves. To assess the shoaling and refraction of each to the shoal-water site I assumed that the wave power transmitted between a given pair of orthogonals remains constant at all depths (this means no frictional losses, diffraction or scattering, and also implies that a steady state exists) . With these assumptions the wave power P is given by P = EC b=E C b g o gQ o C bQ Thus, E = Eq _!o_^ = Eq x k2 k2 m 1 pgH2 g where E = the average wave energy per unit area of sea surface for waves transformed by shoaling and refraction. P = water density g = acceleration of gravity H = wave height of transformed waves C C group velocity gQ' g 51 bQ,b = orthogonal separations k = shoaling factor kr = refraction factor The energy in each spectral component of the swell at the observation site was calculated by modifying the energy spectrum at the selected sources for the effects of shoaling and refraction according to equation E = E -k2-k . o s r The energy associated with the various components as a function of time of arrival at observation site, as seen in Figures 9, 10 and 11. The total energy in the swell at any given arrival time is estimated by summing all the shoaling components at that time. In summary, each component in typhoon area's T - 6 spectrum is shoaled and refracted using the k and k 3 s r values appropriate to it to find the energy at the observa- tion site. 1. Shoaling Process (Computation) See Appendix D. 2 . Shoaling Energy Components From Each Source Versus Arrival Time As seen in Figures 12, 14 and 16, the energy of the components from all sources is shown as a function of its arrival time at Cheju. See Appendix D. 52 3. The Predicted Swell Waves at Prediction Site As shown in Figures 13, 15 and 17, the predicted swell waves are the sum of all transformed components at given time at the forecast site. For Typhoon Irving (see Figure 15) beginning 12 GMT August 16, the forecast site is already inside typhoon area. Therefore, there is no prediction done after that time. These predictions are discussed in Chapter IV. D. D. THE OBSERVED DATA Observations of wave conditions for verification of the swell forecasts were obtained from the sources, the National Oceanographic Data Center (NODC) and the Republic of Korea (ROK) Navy. All listed heights are based on visual estimates. Following Table VIII shows the visual observation of swell heights (H 1/10) for each typhoon. The data from NODC are sparse and often far from the forecast site, but they appear to be samples from the same set as those of the ROK Navy. The data from ROK Navy visual observa- tions were made at 33.2 N, 126.5 E close to my point of interest (33.2°N, 126. 6°E). So I considered this point exactly the same as my forecast site. 53 (w)OI./lH CO in m CO CO CO CO CO CO CO in CM CN O) O CO T h- CN CN _1 yml om oo i- 9 CO "cT o CO o r- s o m o CO o CN (jUio/BJSOijyi -92)A6j9U3 54 Or- v„ 0) £ > (2uio/6jao|!>t-92 ) ABjsug 35 o CO 00 CN (LU)Ol/LH 0) <0 E CD > (3ujo/ Bj90|!>fg2)ABjaug 56 (uOOUI-h ( ujo/BJ30|!>i g3)ABjaug 57 (ui)OL/l-H I- O v E CD > ^- CO CM (2tuo/Bjao|!>i -gS-OOI.) ABj9U3 58 ( siuo/ Bjson^.gg) ABJ3U3 59 TABLE 8 The Visual Observation Data by NODC and ROK Navy For Typhoon Hope DTG ( GMT ) Location ( N- E) H 1/10 (meters) Source 79080100 33.6-125.2 2.5 NODC i 0104 32.3-126.0 2.5 NODC I 0112 31.2-126.7 4.0 NODC I 0118 27.7-124.6 6.5 NODC i 0121 27.8-125.4 6.5 NODC I 0200 29.1-128.0 6.5 NODC I 0206 28.0-129.0 5.5 NODC i 0218 26.9-125.8 5.0 NODC i 0300 28.7-128.6 3.0 NODC i 0306 31.4-126.2 3.0 NODC I 0312 32.3-125.9 3.5 NODC I 080100 33.2-126.5 3.0 ROK Navy 0104 33.2-126.5 3.5 ROK Navy 0108 33.2-126.5 3.7 ROK Navy 0112 33.2-126.5 4.0 ROK Navy 0116 33.2-126.5 4.5 ROK Navy 0120 33.2-126.5 4.5 ROK Navy 0208 33.2-126.5 5.0 ROK Navy 0212 33.2-126.5 4.5 ROK Navy 0216 33.2-126.5 5.5 ROK Navy 0220 33.2-126.5 4.5 ROK Navy 0308 33.2-126.5 3.5 ROK Navy 0312 33.2-126.5 3.5 ROK Navy 0316 33.2-126.5 3.0 ROK Navy 0320 33.2-126.5 5.0 ROK Navy 0408 33.2-126.5 4.0 ROK Navy 0412 33.2-126.5 3.0 ROK Navy 0416 33.2-126.5 3.0 ROK Navy 0420 33.2-126.5 2.5 ROK Navy 60 2. For Typhoon Irving DTG (GMT) Location (°N-°E) H 1/10 (meters) Source 79081400 29.10127.6 2.5 NODC 1403 28.5-127.6 4.0 NODC 1406 28.7-129.3 3.5 NODC 1409 27.7-129.7 4.0 NODC 1412 29.2-131.1 4.5 NODC 1500 30.0-125.0 6.0 NODC 1503 30.7-127.3 4.0 NODC 1515 28.3-130.3 8.0 NODC 1518 27.2-130.0 9.0 NODC 1521 26.5-128.8 8.0 NODC 1600 27.1-130.0 6.5 NODC 1603 27.3-128.5 8.0 NODC 1606 29.6-129.2 5.5 NODC 1700 27.4-125.5 6.0 NODC I 79081400 33.2-126.5 2.5 ROK Navy 1408 33.2-126.5 2.5 ROK Navy 1412 33.2-126.5 3.0 ROK Navy 1416 33.2-126.5 3.5 ROK Navy 1420 33.2-126.5 3.5 ROK Navy 1508 33.2-126.5 4.0 ROK Navy 1512 33.2-126.5 4.5 ROK Navy 1516 33.2-126.5 5.0 ROK Navy 1520 33.2-126.5 6.0 ROK Navy 1608 33.2-126.5 8.0 ROK Navy 1612 33.2-126.5 9.0 ROK Navy 1616 33.2-126.5 8.0 ROK Navy 1620 33.2-126.5 8.0 ROK Navy 1708 33.2-126.5 8.0 ROK Navy 1712 33.2-126.5 9.0 ROK Navy 1716 33.2-126.5 8.0 ROK Navy 1720 33.2-126.5 7.0 ROK Navy 61 3 . For Typhoon Owen DTG (GMT) Location (°N-°E) H 1/10 (meters) Source 79092600 31.4-128.0 4.0 NODC 2606 33.6-129.1 3.5 NODC 2615 31.8-129.5 3.0 NODC 2700 28.1-126.9 6.0 NODC 2703 27.1-126.6 6.5 NODC 2706 32.6-125.7 4.0 NODC 2709 31.6-125.7 5.5 NODC 2712 30.7-129.8 6.5 NODC 2715 28.7-125.3 6.0 NODC 2800 32.8-128.3 5.5 NODC 2803 30.6-125.7 6.5 NODC 2806 31.5-126.8 6.5 NODC 2809 31.6-126.6 6.0 NODC 2812 31.7-126.6 6.5 NODC 2818 34.0-128.3 6.0 NODC 2900 32.7-127.7 6.5 NODC 2606 32.1-127.3 5.5 NODC 2912 31.0-126.4 5.5 NODC 2918 34.0-129.7 5.0 NODC 3000 29.0-124.7 4.0 NODC 3006 30.8-127.7 3.0 NODC 3018 30.4-131.6 4.0 NODC 79092600 33.2-126.5 2.5 ROK Navy 2608 33.2-126.5 4.0 ROK Navy 2612 33.2-126.5 5.0 ROK Navy 2616 33.2-126.5 5.0 ROK Navy 2620 33.2-126.5 4.5 ROK Navy 2708 33.2-126.5 5.5 ROK Navy 2712 33.2-126.5 5.0 ROK Navy 2716 33.2-126.5 5.0 ROK Navy 2720 33.2-126.5 5.5 ROK Navy 2808 33.2-126.5 4.5 ROK Navy 2812 33.2-126.5 5.0 ROK Navy 2816 33.2-126.5 5.5 ROK Navy 2820 33.2-126.5 5.5 ROK Navy 2908 33.2-126.5 4.5 ROK Navy 2912 33.2-126.5 4.0 ROK Navy 2916 33.2-126.5 4.5 ROK Navy 2920 33.2-126.5 4.5 ROK Navy 3008 33.2-126.5 5.0 ROK Navy 3012 33.2-126.5 4.0 ROK Navy 3016 33.2-126.5 2.5 ROK Navy 3020 33.2-126.5 3.0 ROK Navy 62 E. COMPARISON OF SWELL PREDICTIONS AND OBSERVATIONS The predicted and observed heights are plotted in Figures 13, 15 and 17, and are good agreement. Detailed comparisons for each typhoon follow: 1. Typhoon Hope The first predicted swell arrival times from each of three sources, and the NODC and ROK Navy observations are almost the same with similar energies (see Figure 13) . The peak energy arrival times are also nearly the same, but the peak predicted energy is slightly higher than the observations. This is reasonable agreement since it is estimated that the visual observations can be error. Verploegh 1961 [18] estimated the average observational error for a visual observation of wave height varies from 1 ft at 5 ft wave heights to 3 ft at 18 ft wave heights. 2. Typhoon Irving As seen in Figure 15, the predicted swell arrival time nearly matches the time shown by both sets of observations. However, the predicted energy of the rise is slightly higher than the observational values. The peak energy (around the time of 2 0 GMT August 15) is also the same as the observa- tional peak. After 00 GMT August 16, the prediction ' site is within the typhoon's wind circulation area. Most wave heights (H 1/10) are 8m and the highest observation is 10m. These waves 63 dominate the entire wave field and no swell can be dis- tinguished later than 00 GMT August 16. 3. Typhoon Owen In Typhoon Owen (see Figure 17) , the swell arrival time indicated by observations is earlier than the predicted time by about 6-12 hours. The predicted peak energy lies close to the observational values. In fact, the NODC values are higher than those of the prediction, and ROK Navy observations are lower. Except near the peak both observation sets show similar time variations. Therefore, the observed values are con- sidered consistent and probably accurate. F. ERROR SOURCES I have made several assumptions in this study in order to simplify calculations. The most serious error sources involve assumptions about the windows in the Ryukyu Islands, group velocity in shallow water, and simple bottom contours in shallow water. There are also differences between the predictions (which include waves dependent on the local weather conditions) that make it difficult to evaluate the prediction. Regarding the assumptions about group velocity in Chapter III.B, I used n = 3/4 in shallow water for calculation of group velocity C = nc. In Typhoon Hope, which has the longest shallow water travel distance, miscalculation of C would have its g 64 greatest effect. Yet the observed and predicted energy peaks are not greatly separated. This may mean that the approximations are realistic. The bottom contour assumptions seem to be reasonable through three tests. The local weather condition is the most serious factor contributing to differences between the observations and the predictions. The local wind pattern was the following at Cheju-do, according to the ROK Navy data set. 1979 072900-073100: SW 5-8 kts (preceding Hope swell) 080100-080300: SW 6-10 kts (during Hope swell) 1979 081200-081300: S 6-8 kts (preceding Irving swell) 081400-081700: S 30-60 kts (during Irving swell) 092400-092600: E 5-8 kts (preceding Owen swell) 092600-093000: E 20-30 kts (during Owen swell) Therefore, before the swell arrivals, the local wave heights were considered less than 1-1.5 m. During Irving and Owen there were important local sea contributions to observed height. Lastly, the original error sources, i.e., those involving input parameters for the TYWAVES model, the location of the typhoon center, the winds in the source region, and typhoon 65 size, etc., are ignored in this study. Those errors are discussed in Refs. [2] and [17]. 66 V. CONCLUSIONS From Figures 13, 15 and 17 , I can conclude that most predicted swell heights are lower than those of the obser- vations (combined sea and swell) . The times of occurrence of the predicted peak heights agreed reasonably well with those of observations for the swell from each typhoon. These results on the basis of this limited test suggest that TYWAVES predict satisfactorily those swells in the East China Sea which originate in tropical cyclones in the western North Pacific. Computer aided predictions may improve the quality of the forecasts by reducing the need for simplifying approximations/ as in the case of the treatment in this thesis of the shoaling and refraction processes. Such predictions would also provide a larger base for assessing the accuracy of the method. Additional verification is required to draw more specific conclusions. 67 APPENDIX A Outputs of TYWAVES For Typhoon Owen at 12 GMT September 26 The following tables and figures show the computer anal- ysis for Typhoon Owen by TYWAVES. a. Period-directional spectrum at each of 12 sources. b-1. The significant wave height (H 1/3 in feet) distri- bution in typhoon area. "0" indicates the land area and the distance between the grid points is 40 NM. b-2. The maximum wave period distribution in typhoon area. "-1" indicates the land area. b-3. The maximum wind wave directions distribution. The direction indicated with 16 unit point rose, from North (1) to NNE (16) with CCW direction. c. 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W, 75 APPENDIX B Sea Spectra at Source Region for Three Typhoons and Significant Wave Distribution The following tables and figures show the period-direction spectrum at selected source grid point and NEPRF typhoon wave program analysis for wave height (H 1/3 in feet) distribution around the typhoon center, respectively. a-1. NEPRF Typhoon Wave Model (period-direction spectrum at each selected grid point) for Typhoon Hope. a-2. NEPRF Typhoon Wave Program Analysis for Typhoon Hope. b-1. NEPRF Typhoon Wave Model (period-direction spectrum at each selected source grid point) for Typhoon Irving. b-2. NEPRF Typhoon Wave Program Analysis for Typhoon Irving. c-1. NEPRF Typhoon Wave Model (period-direction spectrum at each selected source grid point) for Typhoon Owen. c-2. 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M r^j — t '-• -- —• '— 'NJ K. -* W -« J~ ir> m (T N a: 85 J -3 U O o o U> in o u o o o E9 O o T -• C > Q O o rj -» f\J ^ ^ f\J <^-> o o o w fj c - CI 1 (T *T ra er — eg -» « 3 « r* J <-» o o •^J O ** cd o ioa « O "3 *-» «-•" o e> a o 3 O O a *T» *3 O VI o c inj or -T UJ a -•« J3 -iJ #4 UJ Uj Uj z z z z Z uj Uj Uj uj in in UJ j- six (/I (/> 0* (/^ it oo x X XXX z z z X z 5 * c — -i - — ■ j .3 o rt N n j i O O O a 3 i p o o o K fvj n RS a 01 C UJ XXX XXX -j O u 2ZZZWWW V) 1/1 1/1 1/1 l/l X z z z 2 UJ UJ (/» t/» XX z Z ZZ ZUiV)i rH m e < 6 to u Cn O n Hi > c (13 i Eh fa « H I u ;/*f*CX:S>. 87 WLYS15 FOR 052 21 3EP_ 79 ]2 HQUR PROG. & 88 APPENDIX C Propagation Energy Arrival Time The following tables show the components from each source grid point, travel time and arrival time (GMT). R and R are determined from Map 1 (U.S. Navigation Chart No. 94027, Scale 1: 927.700 at lat 32°15') from the critical depth of each period. 89 Cgo/Cgs 10.6 15.2 18.7/29.4 24.3/33.6 28.8/35.8 12 Jul (GMT) 30 PT4 17.4-133.9 T Ro/R t tar .7 1036 97.74 031344 10 1036 68.16 0202809 13 896/140 52.67 011640 16 873/163 40.78 010447 19 866/170 34.82 312249 PT12 17.4-135.3 Po/R t tar 1071 101.03 031702 1071 70.46 021028 941/130 54.74 011844 876/175 42.08 010605 884/187 35.91 312355 00 Jul 31 PT4 18.6-131.5 Ro/R t tar 919 86.70 031443 919 60.46 021228 749/170 45.83 012150 719/200 34.94 011056 709/210 30.49 010629 PT12 18.6-132.9 Ro/R t tar 946 89.29 031717 946 62.24 021414 816/130 48.06 020004 781/165 37.05 011303 770/176 31.66 010740 12 Jul 31 PT4 19.6-128.3 Ro/R t tar 822 77.55 031731 822 54.08 021847 610/212 39.83 020350 555/267 30.79 011847 550/272 26.70 011442 00 Aug 01 PT4 20.6-125.3 Ro/R t tar 780 73.56 040134 780 51.32 030319 410/370 34.52 021031 370/440 27.43 020326 365/415 24.26 020014 PT12 20.6-126.8 Ro/R t tar 756 71.32 032319 756 49.74 030144 501/255 35.46 021128 476/280 27.92 020355 471/285 24.31 020019 12 Aug 01 PT4 21.5-122.2 Ro/R t tar 744 70.19 041011 744 48.95 031257 324/420 31.62 021937 284/460 25.38 021323 279/465 22.68 021041 PT8 19.5-122.2 Ro/R t tar 858 80.94 042059 858 56.45 032027 446/412 37.86 030152 408/450 30.18 021811 406/452 26.73 021444 12 Aug 01 PT12 21.5-123.7 Ro/R t tar 720 67.92 040755 720 47.37 031122 350/370 31.30 021918 305/415 24.90 021254 300/420 22.15 021009 00 Aug 13 PT4 20.0-128.8 Cgo/Cgs Ro/R t tar 10.6/- 802/- 75.66 160340 15.2/- 802/- 6.76 150446 13.7/29.4 562/240 38.22 141413 24.3/33.6 550/252 30.13 140608 on 0/-}C p i- w • o/ -) -J • O 546/256 26.11 140207 PT12 20.0-130.2 Ro/R t tar 817/- 77.08 160505 817/- 53.75 150545 617/200 39.80 141548 607/210 31.23 140714 600/217 26.89 140253 90 12 Aug 13 PT4 22.0-138.2 Ro/R t 678/- 63.96 678/- 44.61 433/245 31.49 423/255 25.00 413/265 21.74 tar 160358 150837 141929 141300 140945 PT12 22.0-129.6 Ro/R t 692/- 65.28 692/- 45.53 467/225 32.63 452/240 25.74 442/250 22.33 tar 160519 150932 142038 141345 141020 00 Aug 14 PT4 23.5-127.2 Ro/R t 583/- 55.00 583/- 38.36 323/260 26.12 303/280 20.80 300/283 18.32 tar 160700 151422 150207 142048 141819 PT12 23.5-128.6 Ro/R t 592/- 55.85 592/- 38.95 362/230 27.18 352/240 21.63 350/242 18.91 tar 160751 151457 150311 142138 141855 12 Aug 14 PT4 24.6-126.7 Ro/R t 516/- 48.68 516/- 33.95 239/277 22.20 196/320 17.59 191/325 15.71 tar 161241 152157 151012 150535 150343 12 Aug 14 PT12 24.6-128.2 Ro/R t 523/- 49.34 523/- 34.41 288/235 23.39 278/245 18.73 263/260 16.39 tar 161320 152224 151123 150614 150424 00 Aug 15 PT4 25.9-126.5 Ro/R t 438/- 41.32 438/- 28.82 155/293 18.25 108/330 14.27 103/335 12.93 tar 161719 160449 151815 151416 151256 00 Aug 15 PT12 25.9-128.0 Ro/R t 444/- 41.89 444/- 29.10 214/230 19.27 204/240 15.53 199/245 13.75 tar 161753 160513 151916 151532 151345 12 Aug 15 PT4 27.5-126.0 Ro/R t 343/- 32.36 343/- 22.57 13/330 11.92 -/343 10.21 -/343 9.58 tar 162022 161034 152355 152213 152135 PT8 25.5-125.9 Ro/R t 464/- 43.73 464/- 30.53 144/320 18.58 119/345 15.16 109/355 13.70 tar 170744 161832 160635 160310 160142 PT12 27.5-127.5 Ro/R t 345/- 32.54 345/- 22.70 105/240 13.78 95/250 11.35 85/260 10.21 tar 162033 161042 160147 152321 152213 00 Aug 16 PT4 29.6-126.0 Ro/R t 218/- 20.57 218/- 14.34 -/218 7.41 -/218 6.49 -/218 6.09 tar 162034 161421 160725 160629 160605 PT8 27.6-126. Ro/R t 337/- 31.79 337/- 22.17 20/317 11.85 -/317 10.03 -/317 9.41 tar 170747 162210 161151 161002 160925 91 PT12 29.6-127.5 Ro/R t tar 221/- 20.85 162051 221/- 14.54 161432 -/221 7.52 160731 -/221 6.58 160635 -/221 6.17 160610 06 Sep 25 PT4 21.3-132.4 Cgo/Cgs Ro/R t tar ; 10.6 784 73.96 280758 15.2 784 51.58 270935 18.0/29. 654/730 39.39 262123 4 24.3/33. 621/163 30.44 261225 6 28.8/35 611/173 26.05 260803 PT12 21.3-133.9 Ro/R t tar 822 77.55 281133 822 54.08 271205 702/120 41.62 262337 662/160 32.00 261400 658/164 27.43 260926 18 Sep 25 PT4 22.6-131.7 Ro/R t tar 696 65.66 281140 696 45.73 271547 563/133 74.63 270438 513/183 26.56 262034 508/188 22.89 261653 PT12 22.6-133.1 Ro/R t tar 731 68.96 281458 731 48.09 271805 610/121 36.74 270644 577/154 28.32 262219 574/157 24.32 261819 06 Sep 26 PT4 23.5-131.4 Ro/R t tar 639 60.28 281817 639 42.04 280002 509/130 31.64 271338 469/170 24.36 270622 419/220 20.07 270204 PT12 23.5-132.8 Ro/R t tar 675 63.68 282141 675 44.41 280225 555/120 33.76 271546 522/153 26.03 270802 515/160 22.35 270421 18 Sep 26 PT4 24.4-131.6 Ro/R t tar 542 51.13 282108 542 35.66 280539 417/125 26.55 272034 382/160 20.48 271429 371/171 17.66 271140 PT12 24.4-135.3 Ro/R t tar 667 62.92 290855 667 43.88 281353 607/60 34.5 280430 562/. 05 26.26 272016 562/105 22.44 271626 06 Sep 27 PT4 25.5-131.9 Ro/R t tar 544 51.32 290919 544 35.79 281747 484/60 27.92 280955 410/134 20.86 280252 407/137 17.96 272358 PT12 25.5-133.4 Ro/R t tar 591 55.75 291345 591 38.88 282053 526/65 30.34 281220 446/145 22.67 280440 443/148 19.52 280131 18 Sep 27 PT4 26.5-132.0 Ro/R t tar 496 46.79 291648 496 32.63 290238 430/66 25.24 281914 348/148 18.73 281244 345/151 16.20 281012 92 PT6 28.5-132.1 Ro/R t tar 406 38.30 290818 406 26.71 282043 306/100 19.76 281346 251/155 14.94 280857 245/160 13.01 280706 PT12 26.5-133.5 Ro/R t tar 547 51.60 292136 547 35.99 290559 487/60 28.08 282205 417/130 21.03 281502 407/140 18.04 281202 06 Sep 28 PT4 27.3-132.1 Ro/R t tar 460 43.40 300124 460 30.26 291216 400.60 23.43 290526 318/142 17.31 282319 315/145 14.99 282059 PT12 27.3-133.5 Ro/R t tar 511 48.21 300612 511 33.62 291537 414/97 25.44 290726 386/125 19.61 290136 381/130 16.86 282252 18 Sep 28 PT4 27.8-132.1 Ro/R t tar 436 41.13 301108 436 28.68 292241 371/65 22.05 291603 291/145 16.29 291017 289/147 14.14 290608 06 Sep 29 PT4 28.5-132.4 Ro/R t tar 416 39.25 302115 416 27.37 300922 361/55 21.18 300311 291/125 15.70 292142 288/128 13.58 291935 93 APPENDIX D Shoaling of the Spectral Energy Components For refraction factor computation at 00 GMT August 13 from Point 4 of Typhoon Irving, the critical water depth is 32S feet and the angle between the swell crest and the bottom contour of 325 ft depth is 40°. Thus, with h/gT2 and the Figure 2-19 [7], the refraction factors are derived like the following: T (sec) =7 10 13 16 19 K (-— ) =1 1 1 0.98 0.963 r h o In the same way, the other refraction factors are shown in shoaling computation, in the following tables: 1. Shoaling Computation a. Typhoon Hope b. Typhoon Irving c. Typhoon Owen 2 . Shoaling Energy and Arrival Times a. Typhoon Hope b. Typhoon Irving c . Typhoon Owen 94 1. Shoaling Conputation a. Typhoon Hope 12 Jul 30 PT4 T k PT12 a =35 o 00 Jul 31 PT4 SSE. a = 45 SSE o s PT12 (ovrr) 17.4-133.9 (k k r 1 h = 413 SSE 7 o a =40° SSE o s 17.4-135.3 (k k r 1 s r h = 413 SSE 8 18.6-131.5 (k k )2 1 s r h = 413 SSE 4 o 10 13 1 0.92 E (2 • kilo- 16 19 H 1/10 (in 0.89 0.90 ^A^ meters J 1 1 0.989 0.972 1 0.8464 0.7748 0.7653 E H 1/10 19 11 19 9.3 9 7.0 14 63 10.7 53 3.17 2.91 11 1 0.98 1 0.8464 0.7921 0.7779 28 31 36 42 147 4.85 28 26.2 28.5 32.7 123.4 4.44 1 1 0.984 0.962 1 0.8464 0.7670 0.7496 15 20 13 15 69 3.32 15 16.9 10.0 11.2 57.1 3.02 1 1 0.982 18.6-132.9 (k k r 1 s r h = 431 SSE. a = 35 SSE o 1 0.8467 0.7921 0.7811 37 43 19 19 123 4.44 37 36.4 15 14.8 106.2 4.12 12 Jul 31 PT4 K 19.6-128.3 (kskrr 1 n = 413 a = 45 o 1 1 0.984 0.962 1 0.8464 0.767 0.75 23 30 46 20 23 25.4 35.3 15 121 4.40 98.7 3.97 00 Aug 01 PT4 20.6-123.2 (k k ) 1 s r h = 236 SSW a = 60 SSW o s 1 0.935 0.875 0.825 1 0.7399 0.6065 0.5513 23 30 19 40 118 4.35 23 22.2 11.5 22.1 83.8 3.66 95 PT12 k r 1 20.6-126. 8 (kk)2 s r 1 h = 413 S o 0 a = 35 o S s 0 12 Aug 01 PT4 k r 1 21.5-122. 2 (kk)2 s r 1 h = 236 ssw o 0 a = 30° o SSW s 0 PT8 k r 1 19.5-122. 2 (kk)2 s r 1 h = 295 SSW o 1 rrO a = 55 o SSW s 1 PT12 k r 1 21.5-123. 7 (k k )2 s r 1 h = 295 SSW o 0 a = 50° o SSW s 0 b. Typhoon Irving 00 Aug 13 PT4 (GMT) 20.0-128.8 11 1 0.98 I 0.8464 0.7921 0.7779 20 71 98 52 243 6.24 20 60.1 77.6 40.5 198.2 5.63 1 0.99 0.98 0.97 1 0.8296 0.7607 0.7621 II 33 3 10 58 3.05 11 27.4 2.3 7.6 28.3 2.78 1 0.97 0.93 0.88 1 0.7963 0.6851 0.6272 22 51 8 13 98 3.96 22 40.6 5.5 8.2 77.3 3.52 1 0.977 0.95 0.915 1 0.8079 0.7149 0.6781 6 17 49 31 104 4.08 6 13.7 35.0 21 75.7 3.48 deep SSE 3 39 46 21 27 137 4.68m shoal k 111 0.98 0.963 r h= 325 ft (k k )2 1 1 0.8464 0.7607 0.7512 s r = 40° SS o a = 40° SSE 3 39 38.9 16.0 20.3 117.2 4.33 96 PT12 20.0-130.2 deep SSE 5 25 38 20 11 100 4.00 shoal k 1111 1 h = 325 (kk)2 1 1 0.8464 0.7921 0.81 s r a = 10 SSE 5 25 35.0 15.8 8.9 89.7 3.79 o 12 Aug 13 PT4 22.0-128.2 deep SSE 4 30 31 25 13 105 4.10 shoal k 1111 1 r h = 325 (kk)2 1 1 0.8464 0.7921 0.81 s r a = 10 SSE 4 30 26.2 19.8 10.5 90.5 3.81 o PT12 22.0-129.6 deep SSE 3 24 20 15 4 67 3.27 shoal k 11111 r h = 325 (kk)2 1 1 1 0.8464 0.79210.81 s r a = 10 SSE 3 24 16.9 11.9 3.2 59 3.07 o 00 Aug 14 PT4 23.5-125.0 deep & 4 17 22 18 17 79 3.56 shoal k 111 0.97 0.95 r h = 325 (kk)2 1 1 0.8464 0.7453 0.7310 s r a = 4.5 S 4 17 is. 6 13.4 12.4 65.4 3.23 o 97 PT12 23.5-128.6 deep SSE 4 shoal k 1 30 30 28 20 114 4.27 1 1 0.98 0.963 h = 325 (kk)2 1 1 0.8464 0.7607 0.7512 s r a = 40 o SSE 4 30 25.4 21.3 15.0 95.7 3.91 Aug 14 PT4 24.6-126. .7 deep S 1 19 31 13 8 74 3.44 shoal k r 1 1 0.975 0.94 0.91 h = 266 (kk)2 s r 1 1 0.8046 0.7 0.6708 a = 50 o S 1 19 24.9 9.1 5.4 59.4 3.08 PT12 24.6-128. ,2 deep SSE 1 28 33 34 27 125 4.47 shoal k 1 1 1 0.98 0.963 h = 325 (kk)2 1 1 0.8464 0.7607 0.7512 s r a = 40 o SSE 1 00 Aug 15 PT4 25.9-126.5 deep S 9 shoal k 1 28 27.9 25.9 20.3 103.1 4.06 40 36 23 22 132 4.60 1 0.99 0.976 0.948 r h = 266 (kk)2 1 1 0.8296 0.7545 0.728 s r a = 40 Q 9 40 29.9 17.4 16.0 112.3 4.24 O o 98 PT12 25.9-128. ,0 deep SSE o 3 shoal k r 1 h = 325 (kk)2 s r 1 a = 45 o SSE s 3 deep S 3 shcal k r 1 h = 472 (kk)2 s r 1 a = 50 o S 3 12 Aug 15 PT4 27.5-126. ,0 deep S 0 shoal k r 1 h = 266 (kk)2 s r 1 a = 45 o S 0 PT8 25.5-125. ,9 deep s 1 shoal k 1 29 20 17 40 110 4.20 11 0.98 0.95 1 0.8464 0.7607 0.7310 29 16.9 12.9 29.2 91.0 3.82 34 41 33 12 125 4.47 1 1 0.985 0.96 1 0.8464 0.7685 0.7465 34 34.7 25.4 9.0 106.1 4.12 19 13 24 15 73 3.42 1 0.983 0.957 0.93 1 0.8179 0.7254 0.7006 19 10.6 17.4 10.5 57.5 3.03 17 15 14 13 62 3.15 1 0.988 0.967 0.95 r h = 261 (kk)2 1 1 0.8262 0.7407 0.7310 a = 40 s 1 17 12.4 10.4 9.5 50.3 2.84 o ° 99 PT12 29.5-127. .5 deep SSE 1 shoal k r 1 h = 325 (kk)2 s r 1 a = 45 o SSE 1 PT12 27.5-127. ,5 deep S 0 shoal k 1 21 56 55 75 212 5.82 1 1 0.97 0.95 1 0.8464 0.7353 0.7310 1 47.4 41 54.8 145.2 4.82 17 38 50 43 153 4.95 1 1 0.975 0.94 r h = 384 (k k )2 1 1 0.8464 0.7530 0.7157 s r a = 51 ^ o 0 00 Aug 16 PT4 29.6-126.0 deep S 0 shoal k 1 17 32.2 39.9 30.8 119.9 4.38 15 14 19 15 65 3.22 111 1 h = 266 (kk)2 1 1 0.8464 0.7921 0.81 s r a = 0 o S 1 PT8 27.6-126.0 deep s 0 shoal k r 1 h = 266 (kk)2 s r 1 a = 45 o s 0 15 11.8 15.0 12.2 54 2.94 16 20 31 21 90 3.79 1 0.983 0.957 0.93 1 0.8179 0.7254 0.7006 16 16.4 22.5 14.7 69.6 3.34 100 PT8 27.6-126.0 deep SSW 0 shoal k 1 33 62 47 31 175 5.29 1 0.976 0.93 0.87 h = 325 (kk)2 1 1 0.8063 0.6851 0.6131 a = 60 o SSW 0 33 50 32.2 19 134.2 4.63 PT12 29.6-127. .5 deep SSE 1 24 54 60 38 179 5.35 shoal k r 1 1 1 1 1 h = 354 (kk)2 s r 1 1 0.8464 0.7921 0.81 a = 15 o SSE 1 24 45.7 47.5 30.8 149 4.88 PT12 29.6-127. ,5 deep S 1 21 40 40 19 122 4.42 shoal k r 1 1 1 0.96 0.93 h = 384 (kk)2 s r 1 1 0.8464 0.73 0.7001 a = 50 o S 1 21 33.9 29.2 13.3 98.4 3.97 101 c. Typhoon Owen 06 Sep 25 PT4 kr 2 (ksV 1 1 1 1 0.98 (GMT) 21.3-132. .4 1 1 0.8464 0.7921 0.7779 h = 413 ft (SSE)Q 7 26 31 8 0 74 3.44 "SCO a = 35 o (SSE) 7 26 26.2 6.3 0 65.5 3.24 PT12 k r 1 1 1 1 0.98 21.3-133. ,9 (kk)2 s r 1 1 0.8464 0.7921 0.7779 h = 413 SSE o 5 28 19 14 10 78 3.53 a = 35 o SSE s 5 28 16.1 11.1 7.8 68 3.30 18 Sep 25 PT4 k r 1 1 1 0.989 0.973 22.6-131. ,7 (kk)2 s r 1 1 0.8464 0.7335 0.7716 h = 413 SSE o 3 38 36 10 0 89 3.77 a = 40 o SSE s 3 38 30.5 7.3 0 78.8 3.55 PT12 k r 1 1 1 1 0.985 22.6-133. ,1 (kk)2 ::s r 1 1 0.8464 0.7921 0.7859 h = 413 SSE o 2 27 34 15 9 88 3.75 a = 30 o SSE s 2 27 28.8 11.9 7.1 76.8 3.50 06 Sep 26 PT4 k r 1 1 1 0.985 0.95 23.5-131. ,4 (kk)2 s r 1 1 0.8464 0.7685 0.73 h = 384 SSE o 2 39 54 42 1 140 4.73 a = 47 0 SSE s 2 39 45.7 32.3 0.7 119.7 4.38 102 PT12 kr 111 1 0.985 23.5-132.8 (kskr)2 1 1 0.8464 0.7921 0.7859 h = 384 SSE 2 33 49 26 19 132 4.60 o a = 33 SSEo 2 33 41.5 20.6 14.9 112 4.23 o s 18 Sep 26 PT4 k 111 1 0.983 24.4-131.6 (k k )2 1 1 0.8464 0.7921 0.0827 h = 384 SSE 0 32 54 48 53 188 5.48 o a = 35 SSEo 0 32 45.7 38 41.5 157.2 5.01 o s PT12 k 111 1 1 r 24.4-135.3 (k k )2 1 1 0.8464 0.7921 0.81 s r h = 431 SE 0 9 15 17 15 o a <10 SE 0 9 12.7 13.5 12.2 47.4 2.75 o s 06 Sep 27 PT4 k 111 1 1 25.5-131.9 (k k )2 1 1 0.8464 0.7921 0.81 s r h = 354 SSE 0 17 54 31 56 150 4.90 o a <10 SSE 0 17 45.7 24.6 45.4 132.7 4.61 o s PT12 k 111 1 1 r 25.5-133.4 (k k )2 1 1 0.8464 0.7921 0.81 s r h = 413 SE 1 9 11 7 8 37 2.43 o a <10 SE 19 9.3 5.5 6.5 31.3 2.23 o s 103 18 Sep 27 PT4 26.5-132.0 (kk) 1 s r h = 413 a <10 o SSE SSE. h = 431 a <10 o SE SE PT6 28.5-132.1 (kk)4 1 s r 11 1 1 I 0.8464 0.7921 0.81 30 58 49 39 180 5.37 30 49.1 38.8 31.6 150.5 4.91 II 1 1 1 0.8464 0.7921 0.81 18 39 32 30 123 4.44 18 33 25.3 24.3 101.6 4.03 PT12 26.5-133.5 (kk)' 1 s r h = 431 a <10 o SE SE 11 1 1 1 0.8464 0.7921 0.81 15 18 23 17 15 15.2 18.2 13.8 75 3.46 62.2 3.15 PT4 26.5-132.0 (kk) 1 s r h = 413 a <10 o 06 Sep 28 PT4 SE. SE h = 431 a <0 o SE SE 27.3-132.1 (kskr) 1 11 1 1 I 0.8464 0.7921 0.81 26 57 81 35 201 5.67 26 48.2 64.2 28.4 166.8 5.17 II 1 1 1 0.8464 0.7921 0.81 26 44 52 36 161 5.08 26 37.2 41.2 29.2 134.6 4.64 104 PT12 27.3-133.5 (k k ) 1 s r 2. h = 431 SE o 1 a <10 o SE s 1 18 Sep 28 PT4 k r 1 27.8-132.1 (k k )2 s r 1 h = 431 SE o 1 a <10 o SE s 1 06 Sep 29 PT4 k r 1 28.5-132.4 (k k )2 s r 1 h = 431 SE o 2 a <10 o SE s 2 Shoaling Energy and Arrival Time a. Typhoon Hope T 7 12 Jul 30 PT4 t 97.74 (GtfT) +--.-W mi -3/t A 11 1 1 I 0.8464 0.7921 0.81 15 25 24 14 15 21.2 19 11.3 II 1 1 I 0.8464 0.7921 0.81 10 15 16 5 10 12.7 12.7 4.0 II 1 1 1 0.8464 0.7921 0.81 10 18 12 11 10 15.2 9.5 8.9 10 13 16 81 3.60 67.5 3.29 49 2.80 40.4 2.54 55 2.96 45.6 2.70 19 SUM 17.4-133.9 SSE PT12 17.4-135.3 SSE t 97.74 68.16 52.67 40.78 34.82 tar 031344 020809 011640 010447 312049 SSE o 7 19 11 9 14 63 SSE s 7 19 9.3 7.0 10.7 53 t 101.03 70.46 54.74 42.08 35.91 tar 031702 021028 011844 010605 312355 SSE o 8 28 31 36 42 147 SSE 8 28 26.2 28.5 32.7 123.4 105 00 Jul 31 PT4 t 86.72 60.46 45.83 34.94 30.48 tar 031443 021228 012150 011056 010629 18.6-131.5 SSE o 4 15 20 13 15 69 SSE s 4 15 16.9 10.0 11.2 57.1 PT12 t 89.29 62.24 48.06 37.05 31.66 tar 031717 021414 020004 011303 010740 18.6-132.9 SSE o 3 37 43 19 19 123 SSE s 3 37 36.4 15 14.8 106.2 12 Jul 31 PT4 t 77.51 54.08 39.83 30.79 26.70 tar 031731 021847 020350 011847 011442 19.6-128.3 S o 0 23 30 46 20 121 ss 0 23 25.4 35.3 15 78.7 00 Aug 01 PT4 t 73.56 57.32 34.52 27.43 24.26 tar 040134 030319 021031 020326 020014 20.6-132.2 SSW o 5 23 30 19 40 118 SSW s 5 23 22.2 115 22.1 89.8 PT8 t 71.32 49.74 35.46 27.92 24.31 tar 032319 030144 021128 020355 020019 20.6-126.8 S o 0 20 71 98 52 243 Ss 0 20 60.1 77.6 40.5 198.2 12 Aug 01 PT4 t 70.19 48.95 31.62 25.38 22.68 tar 041011 031257 021937 021323 021041 21.5-122.2 SSW o 0 11 33 3 10 58 SSW 0 11 27.4 2.3 7.6 48.3 106 PT8 t 80.98 56.45 37.86 30.18 26.73 tar 042059 032027 030152 021811 021444 19.5-122.2 SSW o 1 22 51 81 13 98 SSW s 1 22 40.6 5.5 8.2 77.3 PT12 t 67.92 47.37 31.30 24.90 22.15 tar 040755 031122 021918 021254 021009 21.5-123.7 SSW o 0 6 17 49 31 104 SSW s 0 6 13.7 35.0 21 75.7 b. Typhoon Irving 00 Aug 13 PT4 T t 7 75.66 10 52.76 13 38.22 16 30.13 19 26.11 SIM tar 160340 150446 141413 140608 140207 20.0-128.8 SSE 3 39 46 21 27 137 o SSE 3 39 38.9 16.0 20.3 117.2 PT12 t tar 20.0-130.2 SSE c SSE 77.08 160505 5 5 53.75 150545 25 25 39.80 141548 38 35.0 31.23 140714 20 15.8 26.89 140253 11 8.9 100 89.7 12 Aug 13 PT4 t tar 22.0-128.2 SSE c SSE 63.96 160358 4 4 44.61 150836 30 30 31.49 141929 31 26.2 25.00 141300 25 19.8 21.74 140945 13 10.5 105 90.5 PT12 t tar 22.0-129.6 SSE c SSE 65.28 160517 3 3 45.53 150932 24 24 32.63 142038 20 16.9 25.74 141345 15 11.9 22.33 141020 4 3.2 67 59 107 00 Aug 14 PT4 t 55.00 38.36 26.12 20.80 18.22 tar 160700 151422 150207 142048 141819 23.5-127.2 S o 4 17 22 18 17 79 Ss 4 17 18.6 13.4 12.4 65.4 PT12 t 55.85 38.95 27.18 21.63 18.91 tar 160751 151457 150311 142138 141855 23.5-128.5 SSE o 4 30 30 28 20 114 SSE s 4 30 25.4 21.3 15.0 95.7 12 Aug 14 PT4 t 48.68 33.95 22.20 17.59 15.71 tar 161241 152157 151012 150535 150343 24.6-126.7 S o 1 19 31 13 8 74 Ss 1 19 24.9 9.1 5.4 59.4 PT12 t 49.34 34.41 23.39 18.73 16.39 tar 161320 152224 151123 150614 150424 24.6-128.2 SSE o 1 28 33 34 27 125 SSE s 1 28 27.9 25.9 20.3 103.1 00 Aug 15 PT4 t 41.32 28.82 18.25 14.27 12.93 tar 161719 160449 151815 151416 151256 25.9-126.5 S o 9 40 36 23 22 132 S s 9 40 29.9 17.4 16.0 112.3 PT12 t 41.89 29.10 19.27 15.53 13.75 tar 161753 160513 151916 151532 151345 25.9-128.0 SSE o 3 29 20 17 40 110 SSE s 3 29 16.9 12.9 29.2 91.0 PT12 t 41.89 29.10 19.27 15.53 13.75 tar 161753 160513 151916 151532 151345 25.9-128.0 S o 3 34 41 33 12 125 S_ 3 34 34.7 25.4 9^0 106.1 108 12 Aug 15 PT4 t 32.36 22.57 11.92 10.21 9.58 tar 162022 161034 152355 152213 152135 27.5-126.0 S o 0 19 13 24 15 73 S s 0 19 10.6 17.4 10.5 57.5 PT8 t 43.73 30.53 18.58 15.16 13.70 tar 170744 161832 160635 160310 160142 25.5-125.9 S o 1 17 15 14 13 62 S s 1 17 12.4 10.4 9.5 50.3 PT12 t 32.54 22.70 13.78 11.35 10.21 tar 162033 161042 160147 152321 152231 27.5-127.5 SSE o 1 21 56 55 75 212 SSE s 1 21 47.4 41 54.8 145.2 PT12 t 32.54 22.70 13.78 11.35 10.21 tar 162033 161042 160147 152321 152231 27.5-127.5 S o 0 17 38 53 43 153 Ss 0 17 322 39.9 30.8 119.9 00 Aug 16 PT4 t 20.57 14.34 7.41 6.49 6.09 tar 162034 161421 160725 160629 160605 29.6-126.0 S o 0 15 14 19 15 65 S s 0 15 11.8 15.0 12.2 54 PT8 t 31.79 22.17 11.85 10.03 9.41 tar 170747 162210 161151 161002 160925 27.6-126.0 S o 0 16 20 31 21 90 S s 0 16 16.4 22.5 14.7 69.6 PT8 t 31.79 22.17 11.85 10.03 9.41 tar 170747 162210 161151 161002 160925 27.6-126.0 SSW o 0 33 62 47 31 175 SSW 0 33 50 32.2 19 134.2 109 PT12 t 20.85 14.54 7.52 6.58 6.17 tar 162051 161432 160731 160635 160610 29.6-127.5 SSE o 1 24 54 60 38 179 SSE s 1 24 45.7 47.5 30.8 149 PT12 t 20.85 14.54 7.52 6.58 6.17 tar 162051 161432 160731 160635 160610 29.6-127.5 S o 1 21 40 40 19 122 S 1 21 33.9 29.2 13.3 98.4 c. Typhoon Owen T 7 10 13 16 19 SUM 06 Sep 25 PT4 t 73.96 51.58 39.39 30.41 26.05 (oyrr) tar 280758 270935 262123 261225 260803 21.3-132.4 SSE o 7 26 31 8 0 74 SSE s 7 26 26.2 6.3 0 65.5 PT12 t 77.55 54.08 41.62 32.00 27.43 tar 281133 271205 262337 261400 260926 21.1-133.9 SSE o 5 28 19 14 10 78 SSE s 5 28 16.1 11.1 7.8 68 18 Sep 25 PT4 t 65.66 45.79 34.63 26.56 22.89 tar 281140 271547 270438 262034 261653 22.6-131.7 SSE o 3 38 36 10 0 89 SSE s 3 38 30.5 7.3 0 78.8 PT12 t 68.96 48.09 36.74 28.32 24.32 tar 281458 271805 270644 262219 261819 22.6-133.1 SSE o 2 27 34 15 9 88 SSE 2 27 28.8 11.9 7.1 76.8 110 06 Sep 26 PT4 t 60.28 42.04 31.64 24.36 20.07 tar 281817 280002 241338 270622 270204 22.5-131.4 SSE o 2 39 54 42 1 140 SSEs 2 39 45.7 32.3 0.7 119.7 PT12 t 63.68 44.41 33.76 26.03 22.35 tar 282141 280225 271546 270802 270421 23.5-132.8 SSE o 2 33 49 26 19 132 SSE s 2 33 41.5 20.6 14.9 112 18 Sep 26 PT4 t 51.13 35.66 26.55 20.48 17.66 tar 282108 280539 272034 271429 271140 24.4-131.6 SSE o 0 32 54 48 53 188 SSE s 0 32 45.7 38 41.5 157.2 PT12 t 62.92 43.88 34.5 26.26 22.44 tar 290855 281353 280430 272016 271626 29.4-135.3 SE o 0 9 15 17 15 57 SE s 0 9 12.7 13.5 12.2 47.4 06 Sep 27 PT4 t 51.32 35.79 27.92 20.86 17.96 tar 290919 281747 280955 280252 272358 25.5-131.9 SSE o 0 17 54 31 56 160 SSE s 0 17 45.7 24.6 45.4 132.7 PT12 t 55.75 38.88 30.34 22.67 19.52 tar 291345 282053 281220 280440 280131 25.5-133.4 SEo 1 9 11 7 8 37 SE s 1 9 93 5.5 6.5 31.3 18 Sep 27 PT4 t 46.79 32.63 25.24 18.73 16.20 tar 291648 290238 281914 281244 281012 26.5-132.0 SSE o 1 30 58 49 39 180 SSE 1 30 49.1 38.8 31.6 150.5 111 PT4 t tar 26.5-132.0 SE c SE 46.79 291648 0 0 32.63 290238 26 26 25.24 281914 57 48.2 18.73 281244 81 64.2 16.20 281012 35 28.4 201 166.8 PT6 t tar 28.5-132.1 SE c SE 38.30 290818 1 1 26.71 282043 18 18 19.76 281346 39 33 14.94 280857 32 25.3 13.01 280706 30 24.3 123 101.6 PT12 t tar 26.5-133.5 SE c SE 51.60 292136 0 0 35.99 290559 15 15 28.08 280205 18 15.2 21.03 281502 23 18.2 18.04 281202 17 13.8 75 62.2 06 Sep 28 PT4 t tar 27.3-132.1 SE c SE 43.40 300124 1 1 30.26 291216 26 26 23.43 290526 44 37.2 17.31 282319 52 41.2 14.99 282059 36 29.2 161 134.6 PT12 t tar 27.3-133.5 SE c SE 48.21 300612 1 1 33.62 291537 15 15 25.44 290726 25 21.2 19.61 290136 24 19 16.86 282252 14 11.3 81 67.5 18 Sep 28 PT4 t tar 27.8-132.1 SE c SE 41.13 301108 1 1 28.68 292241 10 10 22.05 291603 15 12.7 16.29 291017 16 12.7 14.14 290608 5 4.0 49 40.4 06 Sep 29 PT4 t tar 28.5-132.4 SE c SE 39.25 302115 2 2 27.37 300922 10 10 21.18 300311 18 15.2 15.70 292142 12 9.5 13.58 291935 11 8.9 55 45.6 112 LIST OF REFERENCES 1. Pierson, W. J., G. Neumann, and R. W. James, 1955, Practical Methods for Observing and Forecasting Ocean Waves by Means of Wave Spectra and Statistics, Naval Oceanographic Office, H. 0. Pub. 603, 284 pp. 2. Murray, T. R., and D. R. Morford, 1979, 1979 Annual Typhoon Report , Joint Typhoon Warning Center, Guam, Marina Islands, 191 pp. 3. Kauffmann, C. F. , 1973, Swell Prediction by A Multiple Point-Source Swell Generation Model, Master's Thesis, Naval Postgraduate School, Monterery, 7 3 pp. 4. Czaja, B. F. , and D. W. Stevenson, 1964, Simplified Spectral Forecasts of Sea and Swell Waves by Graphical Means, Master's Thesis, Naval Postgraduate School, Monterey, 307 pp. 5. U.S. Army, Corps of Engineers, 1977, Shore Protection Manual Volume I, U. S. Army Coastal Engineering Research Center, 4-180 pp. 6. U.S. Army, Corps of Engineers, 1977, Shore Protection Manual Volume III, U.S. Army Coastal Engineering Research Center, D-15 pp. 7. U.S. Army, Corps of Engineers, 1953, Analysis of Moving Fetches for Wave Forecasting, Technical Memorandum No. 35, 39 pp. 8. U.S. Navy Hydrographic Office, 1951, Techniques for Forecasting Wind Waves and Swell, H.O. Pub. No. 604, U.S. Navy Hydrographic Office, Washington, DC, 37 pp. 9. U.S. Army, Corps of Engineers, 1953, On Ocean Wave Spectra and A New Method of Forecasting Wind-Generated Sea, Technical Memorandum No. 43, Beach Erosion Board, Office of the Chief of Engineers, Washington, DC, 42 pp. 10. U.S. Army, Corps of Engineers, 1955, Graphical Approach to the Forecasting of Waves in Moving Fetches, Technical Memorandum No. 73, Beach Erosion Board, Office of the Chief of Engineers, Washington, DC, 31 pp. 113 11. Brand, S., K. Rake, and T. Laevastu, 1977, Parameteriza- tion Characteristics of a Wind-Wave Tropical Cyclone Model for the Western North Pacific Ocean, Journal of Physical Oceanography, Vol. 7, No. 5, September 1977, pp. 739-746. 12. Brand, S., J. W. Blelloch, and D. C. Schertz, 1974, State of the Sea Around Tropical Cyclones in the Western North Pacific Ocean, Journal of Applied Meteorology, Vol. 14, No. 1, February 1975, pp. 25-30. 13. Brand, S., Rabe , K. , and T. Laevastu, 1976, A Wind Wave Tropical Cyclone Model for the Western North Pacific Ocean, NAVENVPREDRSCHFAC Technical Paper No. 8-76, Naval Environmental Prediction Research Facility, Monterey, CA 93940. 14. Reynolds, F. M. , 1976, Climatological Wave Statistics Derived from FNWC Synoptic Spectral Wave Analyses, Master's Thesis, Naval Postgraduate School, Monterey, CA 93940, 141 pp. 15. Sediny, D. G. , 1978, Ocean Wave Group Analysis, Master's Thesis, Naval Postgraduate School, Monterey, CA 9 394 0, 90 pp. 16. Hubert, W. E. and B. R. Mendenhall, 1970, The FNWC Singular Sea/Swell Model, Fleet Numerical Weather Central, Monterey, CA 93940. 17. Brand, S., et al , 1978, An Analysis Pacific Tropical Cyclone Forecast Errors, Monthly Weather Review, Vol. 106, No. 7, July 1978, pp. 925-937. 18. Verploegh, G. , 1961, On the Accuracy and the Interpretation of Wave Observations from Selected Ships, WMO Commission for Maritime Meteorology working Paper. 114 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Technical Information Center 2 Cameron Station Alexandria, Virginia 22314 2. Library, Code 0142 2 Naval Postgraduate School Monterey, California 93940 3. Chairman, Code 68 1 Department of Oceanography Naval Postgraduate School Monterey, California 93940 4. Chairman, Code 63 1 Department of Meteorology Naval Postgraduate School Monterey, California 93940 5. Professor J. B. Wickham, Code 68Wk 1 Department of Oceanography Naval Postgraduate School Monterey, California 93940 6. LCDR Lee, Hyong Sun 2 Korean Naval Academy Jin Hae, Kyung Nam, KOREA 7. Academic Dean 1 Korean Naval Academy Jin Kae, Kyung Nam, KOREA 8. ADCNO for Education and Training Division 1 Korea Navy HQs Seoul, KOREA 9. Dr.. Na, Jung Yul 1 Jin Hae Machine Depot P.O. Box 18 Jin Hae, Kyung Nam, KOREA 10. Chairman, Department of Oceanography 1 Seoul National University Kwanak-Gu Seoul, KOREA 115 11. Chairman, Department of Meteorology Seoul National University Kwanak-Gu, Seoul, KOREA 12. Dr. Lee, Byung Don Director Korea Research Institute of Ocean P.O. Box 151 39-1 Hawolgok-dong Sungbuk-Gu, Seoul, KOREA 13. Commanding Officer Fleet Numerical Oceanography Center Monterey, California 93940 14. Director, Naval Oceanography Division Navy Observatory 34th and Massachusetts Avenue NW Washington, DC 20390 15. Commander Naval Oceanography Command NSTL Station Bay St Louis, Mississippi 39529 16. Commanding Officer Naval Environmental Prediction Research Facility Monterey, California 93940 17. Samson Brand Naval Environmental Prediction Research Facility Monterey, California 93940 18. Library Scripps Institution of Oceanography P.O. Box 2367 La Jolla, California 92037 19. Library School of Oceanography Oregon State University Corvallis, Oregon 97331 20. Chairman Oceanography Department U.S. Naval Academy Annapolis, Maryland 21402 116 Thesis L386 Lee c i Test of the applica- tion of the TYWAVES model to prediction of swell in the east China Sea from three tropical cyclones in western north Pacific. 191457 Thesis L386 Lee c. 1 Test of the applica- tion of the TYWAVES model to prediction of swell in the east China Sea from three tropical cyclones in western north Pacific. thesL386 Test of the application of the TYWAVES m II mi inn mil iiiii iiiii mi u n 3 2768 002 11996 8 DUDLEY KNOX LIBRARY jwbw ifliiilH iCiCflWJSBL ™fflffl HmfiHt ■■'.•■■'■.'';.'':' '...■.■-.. i. US MP raw HI Hi! Wis SI ' ■ .'■>■■ IBs « bsqSSSS KfflBBr KfflF1 HI9 ■ ■ • i raw Swsn "'■V.'.y':;.'t HHflfe