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Application of WIS wave models in verification study

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Application of WIS wave models in verification study
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UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 90/013
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Lin, Li-Hwa
Wang, Hsiang
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Coastal and Oceanographic Engineering Department, University of Florida
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Water waves -- Models

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This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.

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UFL/COEL-90/013

APPLICATION OF WIS WAVE MODELS IN VERIFICATION STUDY
by
Li-Hwa Lin and
Hsiang Wang
December 1990
Sponsor:
U.S. Army Corps of Engineers Coastal Engineering Research Center DACW 39-86-K-0006




REPORT DOCUMENTATION PAGE
R eport"No. 3. Recipient's Accession No.
4. Title and Subtitle S. Report Date
December 1990
APPLICATION OF WIS WAVE MODELS IN VERIFICATION STUDY
6.
7. Author() 8. Performing Organizatio Report No.
Li-Hwa Lin UFL/COEL 90/013
Hsiang Wang
9. Performing Organisation Nme and "dress 10. ProJect/Task/fork Unit go.
Coastal and Oceanographic Engineering Department University of Florida 11. Contract or Grant No.
336 Weil Hall
Gainesville, FL 32611 13. Type of Report
12. Sponsoring Organization ame and Address
Wave Information Study Project Final
Coastal Engineering Research Center
U.S. Army Engineer Waterways Experment Station
14.
15. Supplementary Notes
16. Abstract
Hindcast waves from the 1979 and 1987 version deepwater wave models developed for the Wave Information Study (WIS) project at the U.S. Army Engineer Waterways Experiment Station's (WES) Coastal Engineering Research Center (CERC) were compared with measured Atlantic coast water waves for the year 1988. The wave parameters that are utilized in comparison are the significant wave height, the modal period, and the mean wave direction. The computed statistics show that the 1987 model yields slightly better results in significant wave height but worse in modal period than the 1979 model. Both models tend to overestimate the significant wave height for large waves and underestimate the significant wave height for small waves. Both models also tend to overestimate the swell components and, therefore, predict smaller modal frequency than the measured ones. The computed mean wave directions are similar from the two models. However, the comparison between the computed and measured mean wave directions from shallow water stations shows large root-meansquare errors. This may be due to the fact that computer models do not properly predict shallow water wave directions since they do not consider general shallow water effect, such as the wave-bottom interaction, percolation and bottom friction, etc.

17. Originator's Key Words 18. Availability Statement
hindcast model
verification wave
19. U. S. Security Classif. of the Report 20. U. S. Security Classif. f This page 21. No. of Pages 22. Price
Unclassified 1Unclassified J167




Preface
In 1976, the U.S. Army Engineering Waterways Experiment Station began a study to produce a wave climate for U.S. lake and coastal waters. This climatological information is produced by numerical simulation of wave growth, propagation, and decay driven by historical wind fields. Since then, an earlier version of deepwater wave model was developed in 1979 for the wave information study along the U.S. Atlantic coast for the period from 1956 through 1975. This version of computer model was later modified several times to include the nonlinear wind-wave and wave-wave interaction mechanisms. An updated 1987 version was utilized for the wave information study in the U.S. Great Lakes for the same 20-year interval.
The study here was to verify the hindcast waves from the 1979 and 1987 version deepwater models by comparing the hindcast results with the wave data collected along the Atlantic coast for year 1988. The specific task is to establish and compare model accuracy through the comparison of the hindcast waves with the measured data in various water depths and to assess the characteristic performance of the wave models in idealized sea and meteorological conditions.
This study was conducted during the period from July 1988 to July 1889 under the direction of Dr. Jon M. Hubertz, manager of the Wave Information Study (WIS) project at the Coastal Engineering Research Center (CERC), U.S. Army Engineer Waterways Experiment Station (WES), Vicksburg, Mississippi. Drs. Lihwa Lin and Hsiang Wang conducted the study and also prepared the report. Mr. Subarna Malakar was especially helpful in performing computer programming tasks.




CONTENTS

PREFACE ........ ..................
INTRODUCTION ...............
BUOY DATA AND WAVE GAGE DATA .......
STATISTICS . . . . . . .
ATLANTIC OCEAN WIND FIELD DATA ......
VERIFICATION OF PHASE I HINDCAST RESULTS VERIFICATION OF PHASE II HINDCAST RESULTS VERIFICATION OF PHASE III HINDCAST RESULTS MODEL CHARACTERISTICS .... ............
SUMMARY AND CONCLUSIONS .... ...........
REFERENCES ................

APPENDIX A: APPENDIX B: APPENDIX C: APPENDIX D:

Page
. I
. 3
. 4
. 7
. . . . . 12
. . . . . 18
. .. . . . 31
. . . . . .. 38
. . . . . 41
. . . . . 44

COMPARISON OF 1988 TIME HISTORY OF NMC AND NDBC WIND DATA ........ ....................
COMPARISON OF 1988 TIME HISTORY OF PHASE I MEASURED AND HINDCAST WAVE DATA ... ........
COMPARISON OF 1988 TIME HISTORY OF PHASE II MEASURED AND HINDCAST WAVE DATA ... ........
COMPARISON OF 1988 TIME HISTORY OF PHASE III MEASURED AND HINDCAST WAVE DATA ... ........

. Al BI Cl Dl




APPLICATION OF WIS WAVE MODELS IN VERIFICATION STUDY

Introduction
1. This report presents the results of hindcast waves from two deepwater wave models developed by the Wave Information Study (WIS) project at the Coastal Engineering Research Center (CERC), U.S. Army Engineer Waterways Experiment Station (WES). The two deepwater wave
models are: (1) WIS 79 model -- an earlier version of computer code for the wave information study along the U.S. Atlantic coast for the period 1956 through 1975 (Brooks and Corson, 1984), and (2) WIS 87 model -- an updated version for the wave information study in the U.S. Great Lakes for the same 20-year interval.
2. The purpose of this study is to verify the hindcast waves from the WIS 79 and 87 models by comparing the hindcast results with the wave data collected along the Atlantic coast for year 1988. The specific task is to establish and compare model accuracy through the comparison of the hindcast waves with the measured data in various water depths and to assess the characteristic performance of the wave models in idealized sea and meteorological conditions.
3. The verification was conducted for each of the three hindcast phases: (I) Phase I -- deepwater wave hindcast based on historical surface wind information, (2) Phase II -- transformation of the hindcast Phase I waves into intermediate water using a finer scale geometric grid to include the sheltering effects of the continental geometry, and (3) Phase III -- transformation of the hindcast Phase II waves into shallow water. Phases I and II hindcasts were carried out by using both WIS 79 and 87 models. The Phase III computation was based upon a shallow water wave model using Phase II results as input boundary condition. Three wave
parameters, the significant wave height, the modal period and the mean wave direction, were compared for each of the three phases. The
verification was performed by using the hindcast results in three-month and annual intervals for the entire year of 1988. A schematic diagram delineating the relationship among the three phases and their respective boundaries is presented in Figure 1 (Corson and Resio, 1981).




Hindcast Phase I: Deep Ocean II: Shelf Zone III: Nearshore Zone
Wave Active
Domain
Synoptic and Synoptic and Synoptic, Mesoscale,
Atmospheric Large Scale Mesoscale and Convective
Response Scale zx hundreds of miles, Ax tens of miles, Ax less then 10 miles,
At* greater than 6 hours At 3 to 6 hours Lt less than 3 hours
Primary Secondary Wave Transformation:
Energy Source; Energy Source; Refraction,
Wave Processes Air-Sea Interaction Air-Sea Interaction Shoaling, Sheltering,
Long Waves
*&x and At are space and time increments, respectively, considered in hindcast study.
Figure 1. A schematic of relationship of three wave hindcast phases.
Buoy Data and Wave Gage Data
4. At present, there are many data sources along the Atlantic coast. The main sources utilized in this study come from: (i) ocean buoy data from the National Data Buoy Center (NDBC), National Oceanic and
Atmospheric Administration (NOAA), and (2) shallow water wave gage data from a Florida's Coastal Data Network (FCDN) maintained by the Department of Coastal and Oceanographic Engineering, University of Florida (Wang, et al., 1990). Table I summarizes the information sources used including data type, water depth, and station location for year 1988. The NDBC buoy
stations are identified by the location identification numbers and the FCDN wave gage stations are identified by the names of the nearby cities or bay systems. A location map of these buoy and gage stations is shown in Figure 2.
5. The information contained in the NDBC and FCDN data are specific wave energy, one-dimensional energy spectrum, modal wave period, and significant wave height. The specific wave energy is defined as the sum of averaged potential and kinematic energies carried by waves per unit weight per unit water surface area. The one-dimensional wave energy spectrum is defined as the distribution of specific wave energy in the




Table 1. Summary of ocean buoy and wave gage data information
NDBC ocean buoy data
station data length latitude and depth dir.
ID.# (1988) longitude (m) data
41001 Jan-Apr, Aug-Dec 34o54'N, 72054'W 4260
41002 Jan-Aug, Oct-Dec 32012'N, 75018'W 3660
41008 Mar-Dec 30042'N, 81006'W 18 x
41009 Aug-Dec 28030'N, 80012'W 41
41010 Nov-Dec 28054'N, 78036'W 830
44004 Jan-Dec 38030'N, 70036'W 3230
44005 Jan-Mar, Jun-Dec 42042'N, 68018'W 195
44006 Jan-Mar 36012'N, 75030'W 26 x
44007 Jan-Dec 43030'N, 70006'W 47
44008 Jan-Dec 40030'N, 69030'W 60
44009 Jan-Nov 38030'N, 74036'W 28
44011 Jan-Mar, May-Dec 41006'N, 66036'W 93
44012 Jan-Jun, Sep-Dec 38064'N, 740361W 24
44013 Jan-Dec 42024'N, 70064'W 30
FCDN wave gage data
station data length latitude'and depth dir.
ID.# (1988) longitude (m) data
King's Bay #4 Mar-Apr, Jun-Dec 30043'N, 810191W 12 x King's Bay #5 Jan-Feb, Apr-Dec 30040'N, 81016'W 18 x Jacksonville Jan-Dec 30018'N, 81022'W 10
Marineland Jan-Dec 29040'N, 81012'W 10
Cape Canaveral Jul-Aug, Nov-Dec 28025'N, 80035'W 8
Vero Beach Jan-Feb, May-Dec 27040'N, 80021'W 8
West Palm Beach Jan-Apr,Jun-Jul,Oct 26042'N, 80002'W 9
Miami Beach Jan-Jun 25046'N, 80007'W 7
* station that has directional wave data is checked by x.




4 5'N

40N
1.440. 9r... 0 04 o0
U.S.A.
. u ,iuua 35 N
S/ 1002 KING S.4AYii0
.ujltC A Al LANTIC OCEAN
ACK NVILLE A \
AR MELAND 30N
\ *41010,? @4100f
IP CANAVALI
E0 BEACH
E:kH BACH
IAN
20"N
85'W 80'W 75OW 70'w 65.W 60'W
Figure 2. A plan view of NDBC buoy and FCDN wave gage station locations.




frequency interval domain. The modal wave period is defined as the wave period associated with the peak energy in the one-dimensional spectrum. And, the significant wave height is defined here as four times of the square root of the specific wave energy. Other information are the magnitude and direction of sea surface winds measured from NDBC buoys, tide records of the FCDN stations, and directional wave data collected at a limited number of NDBC and FCDN stations.
6. From the NDBC data the directional wave information was collected at stations 41008 and 44006, where pitch-and-roll buoys were deployed. From the FCDN data, the directional waves were measured at King's Bay stations where several self-contained directional wave gages were installed in shallow coastal waters.
Statistics
7. The statistics used in this report for comparison of the hindcast and measured quantities are the mean value, the bias of the mean value, the root-mean-square error, and the correlation coefficient of the computed and measured values. The mean value is defined as X=EXi/N or P=EYi/N, where Xi and Yi are the computed and measured values,
respectively, of size N. The bias of 2 is defined as B= Bias= 2-1. The root-mean-square error of X is defined as c= erc =[Z(Xi-Yi)2/N]'12, and the correlation coefficient of X and Y is defined as 6-E(Xi-2)(Yi-T)/[Z(Xijt2(yi_p.)211/2.
8. The aforementioned statistics were computed for wind speed, significant wave height, and modal wave period. The root-mean-square
error was also calculated for wind and wave directions. Bias of the mean is an indicator of data tendency. The root-mean-square error is a measure of data scattering. The correlation coefficient, a unitless quantity between I and -i, is a measure of the linear relationship between the computed and measured values. A large positive correlation coefficient indicates a strong linear relationship between the computed and measured values. From the statistical aspect, small bias of the mean value and root-mean-square error coupled with large positive correlation coefficient indicate good hindcast results.




Atlantic Ocean Wind Field Data

9. The most critical information required in wave hindcasting is the surface wind fields. The wind information used as input to wave models in this study came from the U.S. National Meteorological Center (NMC). The NMC data contained the information of magnitude and direction of winds at a 1000 mb level. The data were digitized at twelve hour intervals on a 65x65 geographical grid covering the Northern Hemisphere. Figure 3 shows this grid for the NMC wind information on Polar projection of the Northern Hemisphere (Resio, Vincent, and Corson, 1982). The NMC wind information was mainly derived from numerical hindcast based on meteorological data. The computed values were then adjusted by ship observations, and by airplane and satellite data. The NMC data sets which included winter storm and hurricane events are considered best wind input information available.
10. In the present study the NMC wind information at 1000 mb level was treated as the surface winds in the wave models. Table 2 summarizes some of the statistics calculated between the 1000 mb NMC wind data and the measured sea surface wind data collected at six deepwater Atlantic coast NDBC buoy stations. The statistics were calculated for the 1988 hindcast results based upon three-month and annual data bases. The computed statistical parameters include the mean values of the NMC and NDBC wind speeds, the bias of the mean NMC wind speeds, the correlation coefficient between NMC and NDBC wind speeds, and the root-mean-square error values for both speed and direction. It is seen in Table 2 that the mean values of the NMC wind speed data are generally greater than those of the NDBC data. That is, the bias of NMC winds is usually positive. This positive bias is because the NMC wind is based upon the 1000 mb level rather than the sea surface. The largest bias value as computed for the NMC wind speed is 6.9 knots. This positive bias may-also be seen from the cross plots of the NMC wind speed data versus the measured buoy data, where more points are above a 450-sloped equal line -- also known as a line of equilibrium -- than below. Figure 4 shows an example at the NDBC buoy 41001 location.




Figure 3. NMC wind information grid on the Northern Hemisphere.




Table 2. Summary of statistics between NMC and NDBC wind speed and wind direction data.
station data Vc -m* BUC cum 8UctU m 6 c&,l
length
ID.# (1988) (kt) (kt) (kt) (kt) (deg)
41001 19.8 14.7 5.1 7.9 0.78 40
41002 Jan, 17.3 14.0 3.3 7.0 0.74 44
44004 Feb, 19.5 14.1 5.4 8.2 0.64 34
44008 Mar 18.3 15.4 2.9 6.4 0.70 36
44011 20.1 13.2 6.9 10.1 0.70 36
41001 12.3 10.9 1.4 5.9 0.73 40
41002 Apr, 14.0 13.9 0.1 5.5 0.62 44
44004 May, 15.3 12.7 2.6 6.1 0.73 39
44008 Jun 14.0 12.9 1.1 5.0 0.77 47
44011 12.0 8.4 3.6 6.2 0.65 53
41001 12.1 11.5 0.6 4.2 0.63 40
41002 Jul, 12.1 10.7 1.4 3.7 0.53 32
41009 Aug, 9.9 9.0 0.9 3.7 0.57 40
44004 Sep 11.5 11.4 0.1 4.3 0.61 35
44008 11.3 10.1 1.2 4.1 0.69 43
44011 11.9 7.8 4.1 6.1 0.60 41
41001 15.9 15.3 0.6 4.9 0.72 39
41002 Oct, 13.9 12.5 1.4 4.4 0.75 44
41009 Nov, 10.6 11.6 -1.0 4.1 0.70 45
44004 Dec 16.7 14.8 1.9 5.9 0.67 39
44008 16.9 16.5 0.3 5.4 0.73 33
44011 18.0 12.7 5.3 7.6 0.72 34
41001 15.4 14.1 1.3 5.6 0.72 39
41002 14.6 12.8 1.8 5.4 0.69 43
41009 Annual 10.4 10.6 -0.2 4.0 0.66 43
44004 15.6 13.3 2.3 6.1 0.68 37
44008 14.7 13.5 1.2 5.1 0.76 40
44011 15.6 10.6 5.0 7.5 0.74 40
* Uc and Um are NMC and NDBC wind magnitude data. resoectivelv

** 9c and em are NMC and NDBC wind

direction data, respectively.

I




CROSSPLOTS OF NMC/NOBC U'S(JAN-OEC,1988)
STATION: NDOBC BUOY L41001
6 = 0.72. enns S5.6 (KT) BIns = 1.3 (KT)
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Figure 4. Cross plots of the 1988 NMC and NDBC wind speed data at the NDBC buoy 41001 location.
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O'N
10#H 900H 75'W 60,0 L5'H 30WH 15.0 0 'E 15E
Figure 5. Phase I numerical grid for WIS 79 model hindcast study. Computational domain is bounded by thick lines; hindcast waves are saved at deepwater buoy (x) and Phase II boundary (*) locations.




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Figure 6. Phase I numerical grid for WIS 87 model hindcast study. Computational domain is bounded by thick lines; hindcast waves are saved at deepwater buoy (x) and Phase II boundary (*) locations.

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11. The root-mean-square errors of the NMC wind speed with reference to the measured data are generally large. As shown in Table 2 the values of the calculated root-mean-square errors range from 3.7 to 10.1 knots. The large root-mean-square errors of the NMC wind speed data indicate that individual NMC wind speed values do not agree well with those of the NDBC data. In the cross plots of NMC and NDBC wind speed data, large rootmean-square error is evident by the scattering of data points. An example is also shown in Figure 4. The correlation coefficients of the NMC and NDBC wind speed data given in Table 2, all showing reasonably high values, indicate a linear relationship between the NMC and NDBC wind speed values. The root-mean-square errors of wind directions are also large, ranging from 33 to 53 degrees, as shown in Table 2.
12. One of the possible sources causing large root-mean-square errors of both wind speed and direction is that NMC information was based upon 12 hour time interval whereas NDBC data were based upon one to three hours. The comparison of wind data from NMC and NDBC for year 1988 is given in Appendix A.
Verification of Phase I Hindcast Results
13. Both WIS 79 and 87 models were applied independently in Phase I hindcast study. The geographical grid systems used for the WIS 79 and 87 models are, however, different. The grid system utilized for the WIS 79 model in the Atlantic Ocean is a spherical orthogonal grid as shown in Figure 5, where the computational domain is bounded by thick lines. This spherical orthogonal grid has great circle paths for quasi-east/west lines and orthogonals to the great circle paths for quasi-north/south lines (Corson and Resio, 1981). The results were saved at four deepwater buoy locations as indicated by x, which were later compared to the measured data from five nearby buoy stations, and along the Phase II offshore boundary points marked by .. The one utilized for the WIS 87 model is a latitude-longitude parallel grid as shown in Figure 6, where computational domain is also bounded by thick lines, and the results are also saved at the deepwater buoy locations and Phase II boundary points, as marked by x and ., respectively. For both models the hindcast waves were produced at four hour increments for the entire 1988 study period.




14. The Phase I hindcast results at nine locations were used as the boundary input information to the Phase II wave hindcast process. In
cases where actual grid point location is in shallow water, the
correspondingly computed data are regarded as estimates for a point further offshore in deep water. Six parameters describing simple wave characteristics of height, period, and direction for waves and swells are recorded for each synoptic time step, which is of four-hour interval in the Phase I process. The wave characteristic parameters are selected here as the significant wave height, modal period, and mean direction for swells and for combined waves and swells determined from wave spectrum. It should be noted here that the hindcast results from the WIS 79 model do not contain swell information.
15. Tables 3 and 4 summarize the statistics calculated on significant wave heights and modal periods between hindcast and measured results at five deepwater Atlantic coast NDBC buoy stations. The statistics were calculated for seasonal and annual intervals for year 1988. A summary of the figures showing the comparison of hindcast and measured significant wave heights and modal periods for year 1988 at five buoy stations is presented in Appendix B.
16. The significant wave height was found to have strong correlation between the Phase I hindcast waves and measured data for both WIS 79 and 87 models. The bias of the mean value of significant wave height and the root-mean-square error of the significant wave height are generally smaller for the WIS 87 model than the WIS 79 model. The wave period had poor correlation between the Phase I hindcast results and measured data from both models. The bias of the mean modal period and the root-meansquare errors of the modal period are generally greater for the WIS 87 model than the WIS 79 model. Nearly all the biases of the mean modal period from the WIS 87 model are positive. This is probably by the
tendency of overestimating the swell component in the WIS 87 model.
17. According to the statistics calculated for the Phase I hindcast results, the WIS 87 model appears to yield slightly better results on significant wave heights but worse results on modal periods than the WIS 79 model. Both wave models tend to overestimate the significant wave height for large waves and underestimate the significant wave height for small waves. The WIS 87 model tends to generate long waves if significant




Table 3. Summary of the bias, root-mean-square error and correlation between computed and measured values of Hs for Phase I hindcast study
station data Hs,m(m) BHC Hsm(m) HSC HSm(m) HS,c HS,m length
ID.# (1988) NDBC W1S79* WS87* WIS79 WIS87 WIS79 WIS87
41001 2.4 0.9 0.6 1.3 1.2 0.72 0.73
41002 Jan, 2.2 0.5 0.3 1.1 1.0 0.66 0.71 44004 Feb, 2.2 1.1 0.7 1.5 1.2 0.53 0.59 44008 Mar 1.8 1.6 1.2 1.9 1.5 0.46 0.51 44011 2.4 1.2 0.6 1.7 1.3 0.68 0.73
41001 1.5 0.0 0.2 0.6 0.6 0.61 0.62
41002 Apr, 2.0 -0.1 -0.2 0.7 0.7 0.73 0.75 44004 May, 1.8 0.2 0.0 0.8 0.6 0.73 0.77 44008 Jun 1.5 0.5 0.4 0.9 0.7 0.78 0.78 44011 1.5 0.2 0.0 0.7 0.7 0.61 0.56
41001 1.5 -0.5 -0.3 0.7 0.6 0.68 0.68
41002 Jul, 1.2 -0.3 -0.1 0.5 0.4 0.52 0.58 44004 Aug, 1.4 -0.3 -0.1 0.6 0.5 0.57 0.55 44008 Sep 1.1 0.0 0.1 0.5 0.5 0.62 0.61 44011 1.3 0.1 0.0 0.5 0.5 0.73 0.48
41001 2.1 0.0 -0.2 0.7 0.7 0.75 0.78
41002 Oct, 1.9 -0.2 -0.3 0.6 0.6 0.76 0.77 44004 Nov, 2.3 -0.1 -0.3 0.8 0.8 0.78 0.79 44008 Dec 2.0 0.1 0.0 0.8 0.8 0.73 0.75 44011 2.5 0.1 -0.3 1.0 1.0 0.72 0.74
41001 2.1 0.2 0.1 1.0 0.9 0.75 0.76
41002 1.9 0.0 -0.1 0.8 0.7 0.72 0.74
44004 Annual 1.9 0.1 0.0 0.9 0.8 0.70 0.73 44008 1.6 0.4 0.3 1.0 0.8 0.68 0.70
44011 1.9 0.3 0.0 1.0 0.9 0.74 0.73
* WIS79 and WIS87 indicate the WIS 79 and 87 wave models,
respectively.
** Hs,c and Hs,m are computed and measured wave heights,
respectively.




Table 4. Summary of the bias, root-mean-square error and correlation between computed and measured values of Tm for Phase I hindcast study
station data mn,e(s) Brm,c Ts) Tm,c Tm,m~s 5Tm,c Tm,m length
ID.# (1988) NDBC WIS79- WIS87- I' S79 NI S87 WLS79 WIS97
41001 8.3 0.6 2.1 2.2 3.4 0.31 0.47
41002 Jan, 8.3 0.0 1.0 2.3 3.2 0.13 0.42 44004 Feb, 8.0 2.7 4.0 2.8 5.2 0.20 0.25 44008 Mar 8.1 1.6 3.8 2.6 4.8 0.17 0.42 44011 8.5 1.2 3.6 2.4 5.0 0.16 0.10
40001 8.7 -0.2 4.1 1.6 4.8 0.74 0.66
41002 Apr, 7.8 -0.5 1.7 2.2 4.2 0.46 0.34 44004 May, 7.8 -0.3 1.7 2.0 3.8 0.42 0.17 44008 Jun 8.1 -0.6 1.5 1.8 3.5 0.43 0.21 44011 7.6 -0.4 1.0 1.9 3.5 0.34 0.05
41001 7.3 -1.5 0.0 3.0 3.6 -0.04 0.16
41002 Jul, 7.1 -2.6 -2.0 3.2 3.2 -0.04 -0.13
44004 Aug, 7.1 -0.9 0.9 2.7 3.6 0.07 0.14 44008 Sep 7.7 -1.5 0.3 2.9 3.4 0.09 0.19 44011 7.6 -1.0 0.6 2.5 3.5 0.16 0.17
41001 7.7 -0.1 1.2 2.2 3.9 0.25 0.22
41002 Oct, 7.9 -0.6 1.2 2.3 4.0 0.41 0.30 44004 Nov, 7.7 0.2 2.4 2.3 4.5 0.25 0.14 44008 Dec 7.9 0.0 2.3 2.3 4.3 0.27 0.22 44011 8.1 0.0 1.3 2.2 4.1 0.32 0.17
41001 7.9 -0.2 1.4 2.4 3.7 0.30 0.36
41002 7.9 -0.7 0.8 2.4 3.7 0.38 0.35
44004 Annual 7.6 0.0 2.0 2.4 4.2 0.28 0.21 44008 7.9 -0.4 1.6 2.4 3.9 0.25 0.25
44011 8.0 -0.1 1.5 2.3 4.1 0.31 0.20
* WIS79 and WIS87 indicate the WIS 79 and 87 wave models,
respectively.
** Tm,c and Tm,m are computed and measured modal periods,
respectively.




wave height is small. A comparison of hindcast wave directions with wind directions measured by NDBC buoys, by using figures presented in
Appendices A and B, shows that the hindcast wave directions are in good agreement with the local wind directions.
Verification of Phase II Hindcast Results
18. The Phase II model, which is essentially the same as the Phase I model, also numerically simulates the wave growth, propagation, and decay from given wind fields. Phase II wave hindcast was used as an intermediate step between the deepwater Phase I and shallow water Phase III models to provide a better representation on the effects of coastline geometry to wave generation near the Atlantic coast. The Phase II model receives the Phase I hindcast results as the deepwater boundary condition, and then generates the intermediate water boundary condition as an input to the Phase III model.
19. The numerical grid utilized in the Phase II model is as about five times dense as the one used in the Phase I model. The spherical orthogonal grid is again utilized in the Phase II for the WIS 79 model (Corson et al., 1982). Figure 7 shows this grid and the boundary limit and locations at which the hindcast results are archived. Also shown in Figure 7 are the deepwater boundary points, as marked by -, where input wave information was provided from the Phase I results. The grid utilized for the WIS 87 model is shown in Figure 8, which is a latitude-longitude parallel grid and is similar to the one used in the Phase I model.
20. The Phase II hindcast results were archived for every four hour intervals. The results contained the general information of significant wave height, modal period, and the mean wave direction. The results also contained the information of one-dimensional wave spectrum at grid locations marked by x in Figures 7 and 8.
21. Tables 5 and 6 summarize the statistics calculated for
significant wave height and modal period, respectively, between the hindcast and measured values at six Atlantic-coast NDBC buoy stations in intermediate and deep waters. These statistics were based upon threemonth and annual intervals for the 1988 data. A summary of figures




45I 5N

358N
30*N
25N
20'N
85'W 80'W 750W 70'W 65'W 60'W
Figure 7. Phase II numerical grid for WIS 79 model hindcast study. Computational domain is bounded by thick lines; hindcast waves are saved at deepwater buoy (x) and Phase II boundary (.) locations.




hx"
ITTI1 I 1 u,
I II I DT I IT

30ON

250N

20'N

85"W 8O'W 750w 70'W 65'W 60OW
Figure 8. Phase II numerical grid for WIS 87 model hindcast study. Computational domain is bounded by thick lines; hindcast waves are saved at deepwater buoy (x) and Phase II boundary (*) locations.

-r - - -
I AX 1 II
I I .L I

Ld 04 1 1 3 1 L-. I I I I I I I
7

5*N

0 N

a Mj




Table 5. Summary of the bias, root-mean-square error and correlation between computed and measured values of Hs for Phase II hindcast study

station data s,m(m) BHSC HS,m (m) CHs,c Hs,m (m) 6HsC Hs,m
length
ID.# (1988) NDBC WI1S79 WS87 YIS79 WIS7 W1S79 W1S87 41001 2.4 1.3 0.0 1.7 1.0 0.63 0.58
41002 Jan, 2.2 0.7 0.1 1.3 0.9 0.61 0.64 44004 Feb, 2.2 1.7 0.3 2.1 1.2 0.48 0.49 44005 Mar 2.0 1.0 0.3 1.5 0.9 0.48 0.72 44011 2.4 1.0 0.6 1.8 1.5 0.55 0.65
41001 1.5 0.2 -0.1 0.7 0.7 0.56 0.33
41002 Apr, 2.0 -0.2 -0.3 0.8 0.7 0.73 0.76 44004 May, 1.8 0.6 -0.1 1.0 0.8 0.75 0.73 44005 Jun 1.4 0.3 0.1 0.6 0.5 0.47 0.48
44011 1.5 0.1 -0.3 0.7 0.8 0.62 0.51
41001 1.5 -0.5 -0.4 0.6 0.6 0.73 0.52
41002 Jul, 1.2 -0.4 0.0 0.5 0.2 0.64 0.63 41009 Aug, 1.0 -0.3 -0.2 0.4 0.4 0.63 0.60 44004 Sep 1.4 -0.1 -0.2 0.7 0.6 0.57 0.53 44005 1.1 0.0 0.2 0.4 0.4 0.56 0.58
44011 1.3 0.0 -0.1 0.6 0.6 0.64 0.47

Oct, Nov, Dec

2.1 1.9
1.4
1.4 2.3
2.1
2.5

0.1
-0.1
-0.2
-0.2
0.1
0.0
-0.2

-0.5
-0.3
-0.3
-0.3
-0.4
-0.2
-0.3

0.7 0.6 0.5 0.6 0.9
1.0
1.2

0.9 0.6 0.6
0.3
1.0
0.8 1.1

0.77 0.61 0.74 0.75 0.63 0.65
0.71 0.73 0.69 0.71 0.58 0.70 0.60 0.70

41001 2.1 0.4 -0.3 1.2 0.9 0.71 0.64
41002 1.9 0.1 -0.2 0.9 0.7 0.70 0.71
41009 Annual 1.2 -0.2 -0.2 0.5 0.5 0.68 0.66
44004 1.9 0.4 -0.2 1.1 0.9 0.65 0.69
44005 1.7 0.3 0.1 1.0 0.7 0.62 0.73
44011 1.9 0.2 0.0 1.1 1.0 0.65 0.70
* TQ70 ,,A TTQ7 ; A; +- i-., LITQ 70 ,nA Q7 A

41001 41002
41009 41010 44004 44005 44011

respectively.
** Hs,c and Hs,m are computed and measured wave heights,
respectively.




Table 6. Summary of the bias, root-mean-square error and correlation between computed and measured values of Tm for Phase II hindcast study

station data ,m(s) BTm,c Tm,m(S) CTm,cTm(S) Tm,cTmn,m
length
ID.# (1988) NDBC YI1S79* YIS8-7 W1S79 W1S87 YIIS79 YIS87 41001 8.3 1.1 1.5 2.4 3.5 0.21 0.33
41002 Jan, 8.3 0.6 1.5 2.5 3.1 0.13 0.42 44004 Feb, 8.0 1.9 2.0 3.0 4.0 0.19 0.37 44005 Mar 7.6 1.8 4.2 3.4 5.9 -0.05 0.11 44011 8.5 0.6 2.9 2.6 4.6 0.05 0.16
41001 8.7 -0.4 5.6 1.7 5.4 0.76 0.54
41002 Apr, 7.8 -0.2 2.1 2.2 4.2 0.43 0.26 44004 May, 7.8 0.2 2.1 2.1 3.8 0.39 0.24 44005 Jun 7.7 0.3 0.7 1.6 2.1 0.62 0.72 44011 7.6 -0.5 0.9 1.9 3.3 0.39 0.21
41001 7.3 -1.5 -0.2 2.7 3.3 0.13 0.16
41002 Jul, 7.1 -2.7 0.1 3.5 2.4 -0.29 0.22 41009 Aug, 7.9 -2.2 2.6 3.2 3.6 0.22 0.20 44004 Sep 7.1 -1.0 1.7 2.7 3.2 0.08 0.13 44005 6.9 -0.8 1.4 2.5 3.4 0.26 0.18
44011 7.6 -1.2 0.3 2.4 2.7 0.31 0.09

41001 41002 41009 Oct, 41010 Nov, 44004 Dec 44005 44011

7.7 7.9
8.1 8.2
7.7
7.0 8.1

0.2 0.0
-0.4
0.1
0.3 0.8
-0.6

1.8 2.1 1.9 1.6 2.0 2.1 1.5

2.1 4.1 2.4 4.2 2.7 4.5 2.7 3.6 2.2 4.2 2.9 4.5 2.4 4.1

0.32 0.18
0.24 0.20 0.20 0.09 0.14 0.28 0.25 0.15 0.01 0.14 0.22 0.20

41001 7.9 0.1 1.3 2.4 3.8 0.32 0.29
41002 7.9 -0.2 1.6 2.6 3.7 0.30 0.30
41009 Annual 8.1 -1.1 2.2 2.9 4.2 0.20 0.10 44004 7.6 0.2 2.0 2.4 3.8 0.28 0.23
44005 7.2 0.5 2.5 2.9 4.6 0.16 0.19
44011 8.0 -0.6 1.3 2.4 3.7 0.29 0.22

respectively.
** Tm,c and Tm,m are computed and measured modal periods,
respectively.

3




showing the comparison of hindcast and measured significant wave heights and modal periods versus time at the six Atlantic-coast buoy stations is presented in Appendix C.
22. Based upon the statistics presented in Tables 5 and 6,
conclusions similar to the Phase I study can be drawn for the Phase II study. Also, similar statistics were obtained from Phase I and II hindcast results at the same buoy stations. The correlation was found to be strong between the hindcast and measured significant wave heights using either WIS 79 or 87 models. The bias of the mean value on significant wave height and the root-mean-square error of significant wave height are generally smaller for WIS 87 model than WIS 79 model. The correlation was poor between the hindcast and measured modal periods for both WIS 79 and 87 models. The bias of the mean modal period and theroot-mean-square error of the modal period obtained from WIS 79 model are generally smaller than those from WIS 87 model. Again, most of the biases of the mean modal period from the WIS 87 model are positive.
23. According to the statistics calculated for the Phase II results, the WIS 87 model seems to hindcast better significant wave heights than the WIS 79 model but give worse modal periods than the WIS 79 model. Examples showing the cross plots of the 1988 hindcast and measured significant wave heights from the WIS 79 and 87 models at the NDBC buoy 41001 location for the Phase II study are given in Figures 9 and 10, respectively. Examples showing the cross plots of the 1988 hindcast and measured modal periods from the WIS 79 and 87 models at buoy 41001 location for the Phase II study are given in Figures 11 and 12, respectively.
24. The Phase II hindcast results contained the information of onedimensional wave spectrum at grid points marked by x in Figures 7 and 8. Figures 13 and 14 present the January 1988 time history of wave spectra at the NDBC buoy 41001 station from WIS 79 and 87 models, respectively. Figure 15 presents the January 1988 time history of wave spectra analyzed from the buoy 41001 data. It is seen in these figures that the WIS 79 model apparently overestimates wave energy when actual energy level is high, and the WIS 87 model generates more long waves and swells than measured. Nevertheless, spectral shapes indicated by both WIS 79 and 87 models are similar to the measured ones.




PHASE II STUDY RESULTS (JAN-DEC, 1988)
STATION: NDBC BUOY L41001
6 =0.71. ERMS= 1.19(M). Bis= 0.L42(M)
10
S -.
im8
LU
*** **..* .. ...
S-
- ......
2
0 I
0 2 L 6 8 10
Hs (M) BUOY DATA Figure 9. Cross plots of the 1988 measured and Phase II hindcast H8 from WIS 79 model at the NDBC buoy 41001 location.




PHASE II STUDY RESULTS (JAN-DEC, 1988)
STATION: NOBC BUOT 941001
6 = 0.64., enMS=0.89(M), BiAs -0.27(M)
10
8- ..
8 -:
o =o
C3C
C3
I-L
.....-- .. ...... .
4
7- ... ....- ....... .
: .: .. : .
... ...*: .:: ....:: : : :. : :. ::.
2%
0 I I
0 2 4 6 8 10
Hs CM) BUOY 0DATA
Figure 10. Cross plots of the 1988 measured and Phase II hindcast H, from WIS 87 model at the NDBC buoy 41001 location.




25
CC
20
15 z C
U
* *15* e
10
5-I
.' : .. .
5 .--~.:11 :* .
5 / i#I .
0 I
0 5 10 15 20 25
TM(SEC), BUOY DATA
Figure 11. Cross plots of the 1988 measured and Phase II hindcast Tm from WIS 79 model at the NDBC buoy 41001 location.




25
C
C
20
LU
C
10
15 (
Li0
5,

10 15
Tm (SEC] BUOY DATR

Figure 12. Cross plots of the 1988 measured and Phase WIS 87 model at the NDBC buoy 41001 location.

II hindcast Tm from




WRVE ENERGY
DENSITY(M2S)

100 50

A r

JANUARY, 1988

00
0.03 FREQUENCY (HZ)

Figure 13. Time history of January 1988 hindcast wave spectra from the WIS 79 model at the Buoy 41001 location.

II I




WAVE ENERGY
DENS ITY (M25)

JANUARYT,

0
0.15
FEQUENCT (HZ0.09 FREQUENCT (HZ) 003

Figure 14. Time history of January 1988 hindcast wave spectra from the WIS 87 model at the Buoy 41001 location.
29

100
50

M A

1988

A

A-A




AWRVE ENERGT OENSITT(MZS)

100
50
0
0.15
0.09
FREQUENCT(HZ)0"

JANUART, 1988

Figure 15. Time history of January 1988 measured wave spectra analyzed from the Buoy 41001 data.




Verification of Phase III Hindcast Results

25. The Phase III wave data were generated assuming straight and parallel bottom contours, and no additional energy sources were added in
the Phase III process. During the computations, differences in wave
characteristics caused by fluctuation in water depth (due to tides and surges) were neglected.
26. There were two basic steps in the calculation of the shallowwater wave climate (Jensen 1983). First, the given Phase II sea wave parameters (height, period, and direction) were used to construct a twodimensional (frequency and wave direction) discrete spectrum. Only the energy bands (in the direction space) that were within 90 degrees to shore normal for a given Phase III station were retained. The analysis became slightly more complex when wave sheltering was introduced. The
swell was assumed to be a unidirectional, monochromatic wave. If the
deepwater swell mean direction of wave propagation was 90 degrees to shore normal, then the data were analyzed.
27. The second step in the Phase III analysis assumed that the local
wave and swell populations were independent; thus, the analysis of the sea and swell transformations into the shallow water could be carried out separately. The transformation mechanism common to both populations were refraction, shoaling, wave breaking, and wave' sheltering (when applicable). One additional mechanism involved in the sea wave transformation was the influence due to nonlinear transfers of spectral
energy, known as wave-wave interactions. Any number of transformation mechanisms can be considered within the framework of this approach. This
means that it is easy to add or delete mechanisms from the computer analog. As shallow water wave transformation mechanisms become more clearly understood, the Phase III methodology provides an accurate basis for the generation of a shallow water wave climate.
28. The Phase III hindcast results obtained from the WIS 79 and 87 models were also saved for every four hour intervals. Tables 7, 8, 9,
and 10 present some statistics calculated for the significant wave height
and modal period, respectively, between the hindcast and measured wave data at six NDBC and eight FCDN shallow water stations. Table 11 shows the




Table 7. Summary of statistics between computed and measured values of Hs at six NDBC stations for Phase III hindcast study
station data -s,m(m) BH7,c Hs(m) CHC Hs, (m) 6Hs,c Hs,m length
ID.# (1988) NDBC WLS79* WISS7* WIS79 NVISS7 N1S79 WIS87
41008 1.0 0.0 -0.1 0.3 0.3 0.18 0.22
44006 Jan, 1.3 0.0 -0.1 0.7 0.6 0.18 0.36 44007 Feb, 1.1 0.4 0.3 0.8 0.6 0.23 0.60 44009 Mar 1.1 0.2 -0.1 0.7 0.6 0.24 0.27 44012 1.1 0.1 0.0 0.6 0.5 0.33 0.51
44013 0.6 1.2 0.5 1.4 0.7 0.11 0.40
41008 0.9 -0.3 -0.3 0.5 0.5 0.39 0.40
44007 Apr, 0.9 0.0 0.1 0.5 0.5 0.26 0.36 44009 May, 1.1 -0.2 -0.1 0.5 0.5 0.60 0.56 44012 Jun 1.0 -0.1 -0.1 0.5 0.5 0.42 0.51 44013 0.6 0.4 0.2 0.8 0.6 0.42 0.37
41008 0.9 -0.4 -0.4 0.5 0.5 0.65 0.60
44007 Jul, 0.7 -0.1 0.3 0.4 0.5 0.30 0.13 44009 Aug, 0.8 -0.2 0.1 0.4 0.3 0.42 0.21 44012 Sep 0.8 -0.3 -0.1 0.5 0.4 0.21 0.01 44013 0.4 0.3 0.5 0.5 0.6 0.23 0.01
41008 1.1 -0.4 -0.5 0.5 0.6 0.59 0.67
44007 Oct, 1.1 0.1 0.1 0.9 0.8 0.20 0.45 44009 Nov, 1.2 -0.3 -0.3 0.6 0.6 0.47 0.40 44012 Dec 1.1 -0.1 -0.1 0.5 0.5 0.46 0.53 44013 0.9 0.3 0.1 1.0 0.9 0.22 0.25
41008 1.0 -0.3 -0.4 0.5 0.5 0.54 0.57
44007 0.9 0.1 0.2 0.7 0.6 0.32 0.47
44009 Annual 1.0 -0.1 -0.1 0.5 0.5 0.47 0.39 44012 1.0 0.0 -0.1 0.5 0.5 0.39 0.50
44013 0.6 0.6 0.4 1.0 0.7 0.28 0.31
* WIS79 and WIS87 indicate the WIS 79 and 87 wave models,
respectively.
** Hs,c and Hs,m are computed and measured wave heights,
respectively.




Table 8. Summary of statistics between computed and measured values of Tm at six NDBC stations for Phase III hindcast study
station data -im(s) .Bm,c Tm,m(s) Tmc TMM TM,c Tm,m length
ID.# (1988) NDBC WIS79- WIS87* NIS79 NIS87 NfIS79 NIS87
41008 8.3 0.0 1.8 2.9 3.4 -0.25 0.40
44006 Jan, 8.0 1.4 2.0 3.4 4.3 0.15 0.37 44007 Feb, 8.5 0.4 3.0 3.1 5.0 0.22 0.19 44009 Mar 7.3 2.5 4.0 3.7 5.4 0.23 0.27 44012 7.6 2.0 3.4 3.6 5.1 0.17 0.28
44013 8.0 0.8 4.0 3.8 5.8 0.17 0.32
41008 7.9 -0.3 1.7 2.9 3.8 0.29 0.25
44007 Apr, 8.4 -0.4 0.6 2.9 3.3 0.13 0.17 44009 May, 7.8 0.1 1.5 2.3 3.5 0.22 0.21 44012 Jun 7.7 0.4 2.0 2.4 3.7 0.15 0.24 44013 8.2 -0.5 1.1 2.8 3.8 0.10 0.22
41008 7.4 -0.7 1.9 2.3 3.0 -0.09 -0.02
44007 Jul, 7.7 -1.0 1.2 2.6 3.0 -0.01 0.18 44009 Aug, 7.5 -0.7 0.0 2.3 3.1 -0.04 0.08 44012 Sep 7.6 -0.4 2.9 3.1 4.0 -0.03 0.32 44013 8.5 -2.0 0.1 3.3 3.5 0.10 0.10
41008 7.6 0.5 2.1 2.8 4.3 0.14 0.10
44007 Oct, 8.0 0.1 0.8 3.0 3.5 0.19 0.36 44009 Nov, 7.8 0.1 2.1 3.0 3.8 0.23 0.27 44012 Dec 7.0 1.1 3.3 3.1 4.9 0.21 0.23 44013 8.5 -0.6 1.0 3.2 4.0 0.26 0.31
41008 7.7 -0.2 1.9 2.7 3.7 0.15 0.15
44007 8.1 -0.2 1.4 2.9 3.8 0.18 0.25
44009 Annual 7.6 0.3 1.5 2.7 3.8 0.12 0.17 44012 7.5 1.0 2.9 3.1 4.6 0.16 0.25
44013 8.3 -0.6 1.6 3.3 4.4 0.11 0.21
* WIS79 and WIS87 indicate the WIS 79 and 87 wave models,
respectively.
** Tm,c and Tm,m are computed and measured modal periods,
respectively.




Table 9. Summary of statistics between computed and measured values of Hs at eight FCDN stations for Phase III hindcast study
station data 7s,m(m) BHc HS,m(m) CHSc HSm(m) 81$,c Hsa
length
ID.# (1988) NDBC WS79* WIS87* WlS79 VIIS87 y11s79 WIS87
Miami Beach 0.5 0.2 0.3 0.4 0.4 0.66 0.78
West Palm Beach 0.6 0.2 0.2 0.4 0.4 0.61 0.60
Vero Beach Jan, 0.8 0.1 0.1 0.4 0.4 0.14 0.56
Marineland Feb, 0.9 0.1 -0.1 0.5 0.4 0.18 0.39
Jacksonville Mar 0.7 0.2 0.0 0.5 0.4 0.16 0.44
King's Bay #4 1.0 -0.1 -0.2 0.3 0.3 0.46 0.44
King's Bay #5 0.9 0.1 -0.1 0.6 0.5 0.12 0.34
Miami Beach 0.3 0.0 0.2 0.2 0.3 0.82 0.77
West Palm Beach 0.5 0.0 0.2 0.3 0.3 0.76 0.81
Vero Beach Apr, 0.5 0.1 0.2 0.3 0.4 0.75 0.77
Marineland May, 0.7 -0.2 -0.2 0.4 0.5 0.35 0.23
Jacksonville Jun 0.6 -0.1 -0.2 0.4 0.4 0.16 0.20
King's Bay #4 0.6 0.0 0.0 0.4 0.4 0.08 0.03
King's Bay #5 0.7 0.0 -0.1 0.4 0.4 0.16 0.21
West Palm Beach 0.3 0.0 0.1 0.2 0.2 0.85 0.85
Vero Beach 0.3 0.1 0.2 0.2 0.3 0.72 0.60
Cape Canaveral Jul, 0.4 0.0 -0.1 0.2 0.1 0.65 0.76 Marineland Aug, 0.6 -0.1 -0.1 0.3 0.3 0.56 0.57
Jacksonville Sep 0.7 -0.1 -0.2 0.3 0.3 0.78 0.79
King's Bay #4 0.7 -0.2 -0.2 0.4 0.4 0.55 0.44
King's Bay #5 0.7 -0.1 -0.1 0.3 0.4 0.60 0.45
West Palm Beach 0.6 0.0 0.0 0.3 0.3 0.66 0.65
Vero Beach 0.4 0.3 0.3 0.4 0.4 0.60 0.51
Cape Canaveral Oct, 0.6 0.1 0.1 0.3 0.3 0.50 0.45 Marineland Nov, 0.9 -0.2 -0.3 0.5 0.5 0.61 0.61
Jacksonville Dec 0.8 -0.1 -0.2 0.3 0.4 0.57 0.57
King's Bay #4 0.7 0.0. -0.1 0.5 0.5 0.16 0.17
King's Bay #5 0.7 0.1 0.0 0.5 0.5 0.13 0.16
Miami Beach 0.4 0.1 0.3 0.3 0.4 0.76 0.80
West Palm Beach 0.5 0.1 0.2 0.3 0.3 0.73 0.74
Vero Beach 0.5 0.1 0.2 0.3 0.4 0.66 0.66
Cape Canaveral Annual 0.5 0.0 0.0 0.2 0.2 0.60 0.59 Marineland 0.8 -0.1 -0.2 0.4 0.4 0.44 0.48
Jacksonville 0.7 0.0 -0.1 0.4 0.3 0.47 0.56
King's Bay #4 0.7 -0.1 -0.2 0.4 0.4 0.41 0.43
King's Bay #5 0.7 0.0 -0.1 0.4 0.4 0.37 0.45
* WIS79 and WIS87 indicate the WIS 79 and 87 models, respectively.
** Hs,c and Hs,m are computed and measured wave heights,
respectively.




Table 10. Summary of statistics between computed and measured values of Tm at eight FCDN stations for Phase III hindcast study
station data n,m(s) Bm, Tmm(s) C Tm,c Tm,m(m) 6Tm,c Tmn
length
ID.# (1988) NDBC NIS79 fISS'7/ WYS79 NIS87 N11S79 YIS87
Miami Beach 6.2 1.5 2.1 3.8 5.0 -0.17 -0.07
West Palm Beach 7.5 0.7 2.0 3.1 4.7 0.06 0.15
Vero Beach Jan, 7.6 1.5 3.2 3.4 4.8 -0.01 0.32
Marineland Feb, 8.1 0.9 2.0 3.1 4.3 0.20 0.37
Jacksonville Mar 8.2 1.1 1.6 3.4 4.6 0.02 0.25
King's Bay #4 8.3 1.1 2.8 3.4 6.5 -0.05 -0.31
King's Bay #5 8.0 1.0 2.0 3.0 4.7 0.10 0.14
Miami Beach 6.0 0.3 2.8 6.1 7.3 -0.03 0.03
West Palm Beach 8.3 1.1 1.5 2.4 3.5 0.21 0.33
Vero Beach Apr, 7.9 -0.5 1.2 2.2 3.4 0.46 0.46
Marineland May, 8.7 -1.0 1.0 2.7 3.3 0.20 0.16
Jacksonville Jun 8.2 -0.8 1.6 2.5 3.6 0.30 0.09
King's Bay #4 8.9 -1.5 1.0 3.7 4.6 0.10 -0.03
King's Bay #5 8.8 -1.1 1.0 3.3 3.9 0.17 0.05
West Palm Beach 7.5 -1.0 1.9 2.3 3.0 0.08 0.23
Vero Beach 7.3 -0.8 2.0 2.2 2.9 -0.20 0.25
Cape Canaveral Jul, 8.1 -1.6 2.9 2.4 3.5 0.20 0.10 Marineland Aug, 8.0 -1.4 1.3 2.3 2.2 0.04 0.26
Jacksonville Sep 7.6 -1.0 1.5 2.2 2.5 -0.13 0.17
King's Bay #4 7.8 -1.0 1.6 2.3 2.6 -0.01 0.08
King's Bay #5 7.3 -0.4 2.0 2.1 3.1 0.04 0.08
West Palm Beach 7.6 -0.4 0.6 2.5 3.7 0.33 0.23
Vero Beach 6.9 1.0 2.9 2.5 4.8 0.28 0.03
Cape Canaveral Oct, 7.8 0.6 2.6 2.7 5.2 0.43 0.30 Marineland Nov, 7.9 0.1 2.0 2.7 4.4 0.14 0.14
Jacksonville Dec 7.7 0.3 2.1 2.6 4.1 0.23 0.16
King's Bay #4 7.8 0.3 1.7 2.7 4.0 0.19 0.13
King's Bay #5 7.8 0.3 1.7 2.7 4.0 0.21 0.10
Miami Beach 6.1 0.9 2.5 5.1 6.3 -0.05 0.01
West Palm Beach 7.6 -0.2 1.6 2.6 3.8 0.16 0.24
Vero Beach 7.5 0.0 2.3 2.9 3.8 0.07 0.33
Cape Canaveral Annual 8.0 -0.6 3.0 2.6 4.4 0.27 0.25 Marineland 8.2 -0.4 1.6 2.7 3.6 0.15 0.24
Jacksonville 7.9 -0.2 1.7 2.6 3.6 0.15 0.17
King's Bay #4 8.0 -0.6 1.5 2.8 3.5 0.11 0.17
King's Bay #5 8.0 -0.2 1.6 2.8 3.7 0.17 0.20
* WIS79 and WIS87 indicate the WIS 79 and 87 models, respectively.
** Tm,c and Tm,m are computed and measured modal periods,
respectively.




Table 11. Summary of root-mean-square error between computed and measured values of Tfor Phase III hindcast study

* *
station data c ea(deg)
length
ID.# (1988) WIS79* WIS87*
Buoy 41008 43.3 41.4
Buoy 44006 Jan, Feb, Mar 47.8 43.1
King's Bay #4 43.2 42.2
King's Bay #5 43.8 42.9
Buoy 41008 37.6 36.9
King's Bay #4 Apr, May, Jun 37.8 33.1
King's Bay #5 36.6 33.1
Buoy 41008 25.1 20.7
King's Bay #4 Jul, Aug, Sep 30.3 24.2
King's Bay #5 34.1 31.0
Buoy 41008 38.6 36.2
King's Bay #4 Oct, Nov, Dec 33.5 31.3
King's Bay #5 39.1 36.4
Buoy 41008 33.9 31.3
King's Bay #4 Annual 30.3 25.6
King's Bay #5 34.0 31.2
t7T97 A T.TTS7 i di t h I 794 "?n 0

aiL
respectively.

1,.

n1 ca e tI e an 7 wave models,

** ~c and --m are computed and measured mean
respectively.

wave directions,




root-mean-square error values between the hindcast and measured mean wave directions. The measured wave direction information was obtained from the NDBC pitch-and-roll buoys and FCDN directional wave gages. Again, the statistics were calculated based upon three-month and annual intervals for the 1988 data. A summary of the figures showing the comparison of hindcast and measured significant wave heights and modal periods versus time at six NDBC and eight FCDN stations is given in Appendix D.
29. It is shown in Tables 7, 8, 9 and 10 that similar statistics computed for significant wave heights of the Phase III results are obtained from the WIS 79 and 87 models. The bias of the mean of
significant wave height and the root-mean-square error of the hindcast significant wave heights are generally small compared to those from the Phase I and II wave hindcast studies. The correlation-coefficients of the hindcast and measured significant wave heights were again large but smaller than those obtained in the Phase I and II studies. Meanwhile, the statistics computed for modal periods show that the bias of the mean modal periods and the root-mean-square error of the modal periods obtained by the WIS 79 model are generally small and smaller than those obtained by the WIS 87 model. The positive bias of the mean modal period is again observed from WIS 87 model results as shown in Tables 8 and 10. The
positive bias may again be caused by over estimation of swells in the WIS 87 model. Similar to the Phases I and II study results, the correlation between the measured and Phase III hindcast wave periods from both the WIS 79 and 87 models is poor. According to the statistics calculated from the Phase III model results, WIS 79 and 87 models produced similar significant wave heights but WIS 79 model gave better modal periods than WIS 87 model.
30. The root-mean-square errors of the mean wave direction from both WIS 79 and 87 Phase III model results are large, ranging from 20.7 to 47.8 degrees. Large root-mean-square errors of hindcast wave direction seem to suggest that the shallow water waves may not be properly generated in the present shallow water wave model. An improved shallow water model which considers general shallow water effects, such as wave-bottom interaction on arbitrary bottom topography, wave breaking due to depth limitation, percolation and bottom friction, etc., should be used to calculate the shallow water waves in the future study.




Model Characteristics

31. The performances of the deepvater WIS 79 and 87 models were investigated in the fetch-limited and duration-limited cases under
hypothetical conditions that winds of constant speed are blowing to the offshore direction normal to a straight shoreline. The wind speeds utilized here for the model performance study are 20, 30, 40, 50, and 60 knots. Figures 16 and 17 show the growth rates of significant wave heights and the corresponding modal periods generated from the WIS 79 and 87 models under the fetch-limited and duration-limited conditions, respectively.
32. In the fetch-limited cases, the significant wave heights computed from the WIS 79 model are similar to these computed from the WIS 87 model for waves generated under the 20, 30 and 40 knot winds, but smaller for waves generated under the 50 and 60 knot .winds. The growth rates of
significant wave heights from the WIS 79 and 87 models are seen to reach a saturation condition, that is, when the wave heights cease to grow for
longer fetch or duration, in a short fetch distance for small winds. For examples, the growth of significant wave heights reaches the saturation condition in a distance of 200 km for 20 knot winds, and in a distance of
400 km for 30 knot winds. The growth rates of modal periods as a function of fetch from the two models are similar and remain unchanged after the waves reach to the saturation condition.
33. In the duration-limited cases, the significant wave heights computed from the WIS 87 and WIS 79 models are similar for duration that is smaller than 20 hours. The growth rates of significant wave heights from both models are seen to reach saturation condition in a short time period after waves are generated from models for about 30 hours. After
reaching to the saturation condition, the significant wave heights computed from the WIS 79 model are seen to be higher than the WIS 87 model for waves generated under the 20, 30, 40 and 50 knot winds, but smaller for waves generated under the 60 knot winds. The growth rates of modal periods as a function of duration from both models are similar and remain unchanged after waves reach the final saturation condition.




0 100 200 300 '00
FETCH (KILOMETER)

18
15
12 Tn (SEC)
9

S0 600

0 100 200 300 q00
FETCH (KILOMETER)

Figure 16. Growth rates of H. and Tm from WIS 79 and 87 models in fetch-limited condition.




WIS MODEL
(79) (87)
- >- -4
-0- -*-0- -3-v- -y-

20 30
DURATION (HOUR)

165-

TN (SEC)
12
8
4t

40 50 60

0 10 20 30
DURATION (HOUR)

40 50 60

Figure 17. Growth rates of H. and Tm from WIS 79 and 87 models in duration-limited condition.

WIND
(KNOTS)
60 so
50
140
30 20

20 -

12 -




Summary and Conclusions

34. Hindcast waves from two deepwater wave models developed for the Wave Information Study (WIS) project at the U.S. Army Engineer Waterways Experiment Station's (WES) Coastal Engineering Research Center (CERC) were compared with the measured Atlantic coast water waves for the entire 1988 period. The two deepwater wave models are, as identified by the years when they were developed, the WIS 79 model and the WIS 87 model. The verification of the hindcast results from the two models includes the comparison of computed and measured waves in three hindcast phases in various water depths: (I) Phase I -- numerical hindcast of deepwater waves in the Atlantic Ocean, (2) Phase II -- transformation of the Phase I hindcast waves into intermediate waters around the U.S Atlantic coast, and
(3) Phase III -- transformation of the Phaie II hindcast waves into shallow water. The Phases I and II hindcast results were obtained from the WIS 79 and 87 models. The Phase III results were obtained from a shallow water wave model which utilized the Phase II waves as the boundary condition. The wave parameters that are utilized in comparison are the significant wave height, the modal period, and the mean wave directions.
35. The measured wave information that were used in verification of the hindcast waves were the U.S Atlantic coast buoy data from the National Data Buoy Center (NDBC) and shallow water wave gage data from a Florida's Coastal Data Network (FCDN). The wind information which served as input to wave models in this study were the 1000 mb level wind field data prepared by the U.S. National Meteorological Center (NMC). The NMC wind information were mainly computed based upon the pressure field but were also blended in the observed wind data corrected to the 1000 mb level. The NMC data sets which cover most part of the Atlantic Ocean and include winter storm and hurricane events are considered as the best wind input information currently available for wave model input.
36. In this report, the verification of the 1988 hindcast waves was carried out in three-month and annual interval bases. Several conclusions relating to the current study are summarized as follows:
(1) Similar conclusions are drawn from the calculated statistics for the hindcast waves from the Phases I and II results. Strong




correlation was found between the hindcast and measured significant wave heights. The bias of the mean value of significant wave height and the root-mean-square-error of the significant wave height from WIS 87 model are generally smaller than those from WIS 79 model. On the other hand, the correlation was poor between the hindcast and measured modal periods. The bias of the mean of modal period and the root-mean-square error of the modal period from the WIS 79 model are generally smaller than those from the WIS 87 model.
(2) The statistics of significant wave height of the Phase III results are similar to those obtained from WIS 79 and 87 models. The bias of the mean of significant wave heights and the root-mean-square error of the hindcast significant wave height from the Phase III results are generally small compared with those from the Phase I and II studies. The correlation computed for the hindcast and measured significant wave heights is again large but smaller than those from the Phase I and II results. The statistics computed for modal period show that the bias of the mean modal periods and the root-mean-square error of the modal period from WIS 79 model are smaller than those from WIS 87 model. The correlation was again found to be poor between the hindcast and measured periods from both WIS 79 and 87 Phase III results.
(3) Based on the computed statistics for year 1988 in Phases I, II and III studies, the WIS 87 model yields slightly better results in significant wave height but slightly worse in modal period than the WIS 79 model. Both wave models tend to overestimate the significant wave height for large waves and underestimate the significant wave height for small waves. The former case could be caused by using NMC wind speed data at a 1000 mb level, which is higher than the surface wind at sea level, as the input to wave model. The WIS 79 model was affected more than the WIS 87 model since the computed statistics showed larger biases of the mean of significant wave height from the WIS 79 model.
(4) The root-mean-square errors calculated for the mean wave directions from the WIS 79 and 87 models in the Phase III study are similar; both are, however, large. This large root-mean-square error of the hindcast wave direction indicates that currently applied shallow water wave model, which generates waves assuming straight and parallel bottom contours, may not properly estimate the shallow water waves. A more




advanced shallow water model which is valid for arbitrary bottom topography and considers general shallow water effects, such as the wavebottom interaction, percolation and bottom friction, etc., should be explored for hindcast of shallow water waves in the future study.
(5) It is noticed from all three hindcast phase studies that almost all the calculated biases for the mean modal periods obtained by the WIS
87 model are positive. This positive bias is thought to result from overestimating the swell component in the model.
(6) Investigation of model characteristics under the idealized winds
with constant speed blowing seaward normal to a straight shoreline displays that when the wind speed is of either 20, 30 or 40 knots the WIS 79 and 87 models predict similar significant wave heights in the fetchlimited case or in the duration-limited case if duration is smaller than about 20 hours. However, the WIS 79 model predicts higher significant wave heights than the WIS 87 model in the duration-limited case as the waves reach to saturation condition when the wind speed is equal to either 20, 30 or 40 knots. The results are not surprising since the WIS 79 model indeed tends to overestimate the significant wave heights more than the
WIS 87 model in wave hindcasting in the Atlantic Ocean where moderate winds of 20, 30, and 40 knots in long duration are commonly observed above the sea surface.
43




REFERENCES
I. Brooks, R. M., and W. D. Corson, 1984. "Summary of Archived Atlantic Coast Wave Information Study Pressure, Wind, Wave, and Water Level Data," WIS Report 13, U. S. Army Engineer Waterways Experiment Station, Hydraulics Laboratory, Vicksburg, Mississippi.
2. Corson, W. D., and D. T. Resio, 1981. "Comparisons of Hindcast and Measured Deepwater, Significant Wave Heights," WIS Report 3, U. S. Army Engineer Waterways Experiment Station, Hydraulics Laboratory, Vicksburg, Mississippi.
3. Corson, W. D., D. T. Resio, R. M. Brooks, B. A. Ebersole, R. E. Jensen,
D. S. Ragsdale, and B. A. Tracy, 1982. "Atlantic Coast Hindcast, Phase II Wave Information," WIS Report 6, U. S. Army Engineer Waterways Experiment Station, Hydraulics Laboratory, Vicksburg, Mississippi.
4. Jensen, R. E., 1983. "Atlantic Coast Hindcast, Shallow-Water, Significant Wave Information," WIS Report 9, U. S. Army Engineer Waterways Experiment Station, Hydraulics Laboratory, Vicksburg, Mississippi.
5. Resio, D. T., C. L. Vincent, and W. D. Corson, 1982. "Objective Specification of Atlantic Ocean Windfields from Historical Data," Wave Information Study (WIS) Report 4, U. S. Army Engineer Waterways Experiment Station, Hydraulics Laboratory, Vicksburg, Mississippi.
6. Wang, H., S. Schofield, L. Lin, and S. Malakar, 1990. "Wave Statistics along Florida Coast -- A Compilation of Data, 1984--1989," Tech. Report UFL/COEL-CDN-90/01, Dept. of Coastal and Oceanographic Engrg., University of Florida, Gainesville, Florida.




APPENDIX A: COMPARISON OF 1988 TIME HISTORY OF NMC AND NDBC WIND DATA
A-I




N
HWINO */
E I. I.. **
JAN FEB MAR
(1988)
50
STATION: NDBC BUOT *41001 NOBC DATA
40 6 = 0.78. Gas=7.9 (KT) NMC DATA
U10o 30
J*
(KNOT)
* *. .*
20 ,. "*
4 .. :.
10
JAN FEB MAR
(1988)
Figure Al. Comparison of Jan-Mar, 1988 NMC and NDBC wind data at buoy
41001 location.

A-2




N
G3WINO ,
H I
S
EI
APR MAY JUN
(19881
50
STATION: NOBC BUOY *41001 NOBC DARTA
40 -6 = 0.73, ems=5.9 (KT) NMC DATA
U10o 30 (KNOT)
20
10 ; 0' ~
APR MAY JUN
(1988)
Figure A2. Comparison of Apr-Jun, 1988 NMC and NDBC wind data at buoy
41001 location.




H
GWIN
W3
SuN : 4. 1,
E I-_ .:" ;' t
soo
JUL RUG SEP
(1988)
50
STATION: NOBC BUOT *41001 NOBC DAORTR
6 =0.63, Ems=I.2 (KT) NMC OATR
40
U10o 30 (KNOT)
20
10
0
JUL RUG SEP
(1988)
4,
Figure A3. Comparison of Jul-Sep, 1988 NMC and NDBC wind data at buoy
41001 location.




N .
8WIND li
W ;
- I
E (1988) ;'
OCT NOV DEC
(1988)
50
STATION: NOBC BUOY *41001 NDBC DATA
0 6 = 0.72. ems=4.9 (KT) NMC ORDATA
40
(KNOT) "
Ut 0 g I
OCT NOV DEC
(1988)
I
Figure A4. Comparison of Oct-Dec, 1988 NMC and NDBC wind data at buoy
41001 location.




OWINO a .**
S .
E ," IJAN FEB MAR
(19881]
so
STATION: NOBC BUOY *41002 NOBC ODATR
40 6 = 0.74. Rs =7.0 (KT) NMC DATA
U0o 30- (KNOT)
.20 *
2 .* **je **.
10
01.
JAN FEB MAR
(1988)
Figure A5. Comparison of Jan-Mar, 1988 NMC and NDBC wind data at buoy
41002 location.

A-6




N
8WIND t
H
S
APR
50
STATION: NOBC BUOY *41002
0 6 = 0.62. 6ms= 5.5 (KT)
Uo SO .
U10 30
(KNOT) :
20 . .
10
APR
Figure A6. Comparison of Apr-Jun,
41002 location.

MAY JUN
(1988)

MAY JUN
(1988)

1988 NMC and NDBC wind data at buoy




E .
8HINO
NH
E "I
JUL RUG SEP
(1988)
50
STATION: NOBC BUOYT #1002 NOBC DATA
0 6 0.53. 6ns=3.7 (KT) NMC ODATR
t0
Ut10 30
(KNOT)
20 :.
2 0 1, -,.
01
JUL RUG SEP
(19881
/
Figure A7. Comparison of Jul-Sep, 1988 NMC and NDBC wind data at buoy
41002 location.

A-8




N 8MIN0
W
S
E
50
STR
40 6= UIo 30(KNOT)
20 10 A
0
Figure A8.

OCT NOV DEC
(1988)

OCT NOV OEC
(1988]

Comparison of Oct-Dec, 1988 NMC and NDBC wind data at buoy 41002 location.




N ..
-'I
GMINO *
E 1 *1 *I
"".
SS
E
JUL AUG SEP
(1988)
50
STATION: NOBC BUOT *41009 NOBC DAORTA
S6=0.57, 6ans=3.7(KT) NMC DATA
40
U10o 30
(KNOT)
20 i
10
0.|
JUL AUG SEP
(1988)
Figure A9. Comparison of Jul-Sep, 1988 NMC and NDBC wind data at buoy
41009 location.

A-10




N 8WINO
H
S E

OCT NOV OEC
(1988)

Uto 30(KNOT)
0 "
OCT NOV
(1988)
f
Figure AI0. Comparison of Oct-Dec, 1988 NMC and NDBC
41009 location.

DEC

wind data at buoy

A-11




N
OWING*
H
S
E s -'' t"
JAN FEB MAR
(1988)
50
STATION: NOBC BUOY *44004 NOBC DATA
0 =0.64, Sems=8.2 (KT) NMC DATA
40
U10 30
(KNOT)
20~
1 0 Z ..
s *-* ..,.
4 .' .* .1~
. .-;, .
0- I ." :
JAN FEB MAR
(1988)
I
Figure All. Comparison of Jan-Mar, 1988 NMC and NDBC wind data at buoy
44004 location.

A-12




N
N 5 i
GWINO
S
E
APR MAT JUN
(1988)
50
STATION: NOBC BUOT *4q004 NDBC DATA
60 = 0.73. 6ems= 6.1 (KT) NMC AORTA
U10 30
(KNOT) .
20
0 1. A ** ** .
RPR MAY JUN
(1988)
f
Figure A12. Comparison of Apr-Jun, 1988 NMC and NDBC wind data at buoy
44004 location.

A-13




H
wN
S. -___*
JUL AUG SEP
(1988)
so
STATION: NOBC BUOTY 44004 NOBC DATA
O 6=0.61. 6Es=4.3 (KT) NHC DATA
U10o 30
(KNOT)
20
0
JUL AUG SEP
(1988)
f
Figure A13. Comparison of Jul-Sep, 1988 NMC and NDBC wind data at buoy
44004 location.

A-14




N
E 4W
HN '
..*
s ':' ; *
OCT NOV DEC
(1988)
50
STATION: NOBC BUOT *4004 NDBC DATA
0 6 = 0.67, ERs=5.9 (KT) NMC DATA
Uto 30 -.
(KNOT) "* *
20 - .1 "- .: "1 ** *.
i0 I *f ,
0 it" "
OCT NOV DEC
(1988)
f
Figure A14. Comparison of Oct-Dec, 1988 NMC and NDBC wind data at buoy
44004 location.

A-15




N 8HINO
S E

JAN FEB MAR
(1988)

U10
(KNOT)

JAN FEB MAR
(1988)

Figure A15. Comparison of Jan-Mar, 1988 NMC and NDBC
44008 location.

wind data at buoy

A-16




N
GWINO : .
* U *
S
. 5 *
* I **
E *
APR MAY JUN
(1988)
50
STATION: NOBC BUOT *44008 NOBC DATA
S-6 = 0.77, Ers=5.0 (KT) NMC DATA
U10 30
(KNOT) "
20 .. ,
10 0
* ** ( : .* -.. *
APR MAYT JUN
(1988)
/
Figure A16. Comparison of Apr-Jun, 1988 NMC and NDBC wind data at buoy
44008 location.
A-17




i ir ....
"-I. .. .' -.
WIN" ".
S ,
HIN0* .* :
E ** I I I ( 4 *
JUL AUG SEP
(1988)
50
STATION: NDBC BUOY *44008 NOBC DATA
40 6 0.69. Em s=4.1 (KT) NMC DATA
U1o 30
(KNOT)
20 -: '
10 **
JUL AUG SEP
(1988)
Figure A17. Comparison of Jul-Sep, 1988 NMC and NDBC wind data at buoy
44008 location.

A-18




N
J~ ~ W "
8WIND
W
E
OCT NOV DEC
(1988)
50
STATION: NOBC BUOY *4008 NOBC DATA
8 =0.73, ems=5.4 (KT) NMC ODATA
0
U o 3 0 . q .. " .J
(K OT :. ." *.
OCT NOV DEC
(1988)
Figure A18. Comparison of Oct-Dec, 1988 NMC and NDBC wind data at buoy
44008 location.

A-19




N
8WINO
S
E 7 I f I. *
JAN FEB MAR
(1988)
50
STATION: NDBC BUOT *qqO11 NOBC DATA
60 =0.70. Gems=10 (KT) NMC DATA
U10 30
(KNOT)
20 ,'~~
10 :
01*; 1
JAN FEB MAR
(1988)
Figure A19. Comparison of Jan-Mar, 1988 NMC and NDBC wind data at buoy
44011 location.

A-20




s : :j.
I
S :
APR MAY JUN
(1988)
50
so1
STATION: NOBC BUOY *4q011 NOBC DATA
0 =0.65. Sn s=6.2 (KT NMC DATA
Uto 30
(KNOT)
20
10
a. t ..
APR MAY JUN
(1988)
/
Figure A20. Comparison of Apr-Jun, 1988 NMC and NDBC wind data at buoy
44011 location.

A-21




E 4
N
8 IND .
' .1
t *
E ..** 7', '
JUL RUG SEP
(1988)
50
STATION: NOBC BUOT *44011 NOBC DATA
0 -6=0.60. Ems=6.1 (KT) NHC DATA
40
U 30
(KNOT)
20 -
10
08
JUL AUG SEP
(1988)
Figure A21. Comparison of Jul-Sep, 1988 NMC and NDBC wind data at buoy
44011 location.

A-22




WIN
W1
S~ ~ I i :"
E __ _ _ S .:
OCT NOV DEC
(1988)
50
STATION: NOBC BUOT *44011 NOBC DATA
6 = 0.72. ems=7.6 (KT) NMC ODATA
U10o 30(KNOT)
* .
20 ~*
20 .
10 a ; s, '*
.: *.. ..:*, :
OCT NOV DEC
(1988)
Figure A22. Comparison of Oct-Dec, 1988 NMC and NDBC wind data at buoy
44011 location.

A-23




APPENDIX B: COMPARISON OF 1988 TIME HISTORY OF PHASE I MEASURED AND HINDCAST WAVE DATA




PHASE I WAVE STUOT RESULTS

STATION: NOBC BUOY *41001
6 =0.31. EnNs= 2.2(S)

* NOBC DATA
-BY HIS 79 MODEL

20 6 =0.47. es=3.q (S) --BY HIS 87 MODEL
15 11
I I
(SEC) o
51
0
JAN FEB MAR
(1988)
10
STATION: NOBC BUOY 41001 NBC DATA
6 =0.72. Sms=1.32(M) HIS 79 MODEL
8 6 = 0.73. enms=1.23(MI -- HIS 87 MODEL
6
Hs
II
(M) 4
0 1
JAN FEB MAR
(1988)
STATION: NDBC BUOY *ql00Il NOBC DATA
-BY HIS 79 MODEL E --BY HIS 87 MODEL
HAVE
I
N I I I IIt v' '
iAl if lI
E 11L
JAN FEB MAR
(1988)
Figure Bl. Comparison of Jan-Mar, 1988 Phase I hindcast and measured
wave data at buoy 41001 location.




PHASE I WAVE STUOTDY RESULTS

5TRTION: NOBC BUOT *41001
6 = 0.74. 6ms= 1.6 (S)

* NOBC DATA
--BYT HIS 79 MODEL

20 6 -0.66. E.s=4.8 (S) --BT HIS 87 MODEL
15 r1 ( 'I / l I| {II
15
0I F1A
(SEC) 10 AllI I'~
0
APR MAY JUN
(1988)
10
STATION: NOBC BUOT *41001 NDBC DATA
6 = 0.61. 6gm=0.63(M) --BY HIS 79 MODEL
8 6 =0.62. Ems=0.-59(M) --BY HIS 87 MODEL
6
Hs
2
0
APR MAY JUN
(1988)
STATION: NOBC BUOY *41001 NOBC DATA
--BY HIS 79 MODEL E --BT WIS 87 MODEL
N i I ,
8WAVE I
W
N jI
II ,
S
E
, I
APR MAY JUN
(1988)
Figure B2. Comparison of Apr-Jun, 1988 Phase I hindcast and measured
wave data at buoy 41001 location.




PHASE I HAVE STUDY RESULTS

STATION: NDBC BUOYT *41001
6 =-0.0q. e ms= 3.o0 (S)

* NDBC DATA
-BY HIS 79 MODEL

20- 6 =0.16. eus= 3.6 (S) --BT HIS 87 MODEL
(SEC) 10i _15 U
01
JUL AUG SEP
(1988)
10
STATION: NOBC BUOT *41001 NOBC DATA
6=0.68. Ems=0.70(M) -BY HIS 79 MODEL
8 6=0.68. Ems=O.SS(M) --BY HIS 87 MODEL
6
Hs
2
0 .
JUL RUG SEP
(1988)
STATION: NDBC BUOY *41001 NDBC DATA
-BT HIS 79 MODEL E --BY HIS 87 MODEL
S
E I
JUL RUG SEP
(1988)
Figure B3. Comparison of Jul-Sep, 1988 Phase I hindcast and measured
wave data at buoy 41001 location.




PHASE I WAVE STUOTDY RESULTS

STATION: NOBC BUOTY *41001
6 =0.25, E Ns= 2.2 (S) 6 =0.22. ems=3.9 (S)

* NOBC DATA
-BY HIS 79 MODEL
--BY HIS 87 MODEL

25 20 15 TN (SEC) 10
5
0 10 8 6

OCT NOV DEC
(19881

OCT NOV DEC
(19881

Figure B4. Comparison of Oct-Dec, 1988 Phase I hindcast and measured
wave data at buoy 41001 location.

B-5

OCT NOV DEC
(19881

E
N
ONAVE
S
E




PHASE I WAVE STUDY RESULTS

STATION: NDBC BUOT *41002
6 = 0.13. 6 ms=2.3(S]

* NDBC DATA
-BY HIS 79 MODEL

20 6 = 0. 42. ERns=3.2 (5) --BY HIS 87 MODEL
15 $II
0 o
kN .I I I I r* I I L,
JAN FEB MAR
(1988)
10
STATION: NOBC BUOT *1002 NDBC DATA
6=0.66. Smns=I.11I(M] -BY HIS 79 MODEL
8- 6 = 0.71. EnRs=O.97(M) --BT HIS 87 MODEL
6
Hs
(M) q .
2
0 I I
JAN FEB MAR
(1988]
STATION: NDBC BUOT #41002 NDBC DATA
-BY HIS 79 MODEL
E --BY HIS 87 MODEL
HAVE I I II
EiI
JAN FEB MAR
(1988)
Figure B5. Comparison of Jan-Mar, 1988 Phase I hindcast and measured
wave data at buoy 41002 location.

B-6




PHASE I WAVE STUDY RESULTS 25
STATION: NOBC BUTOY *41002 NDBC DATA
6 = 0.46. ews=2.2 (S) --BY HIS 79 MODEL
20 6 = 0.34. 6es=4.2 (S) --BT HIS 87 MODEL
(S E C I 1 0 ~1 1 I,
I0 1I t .I
0
APR MAY JUN
(19881
10
STATION: NOBC BUOT *41002 NDBC DATA
6 = 0.73. E ns =0.75(M) -BY HIS 79 MODEL
8 6 =0.75. Is=0.70(M) --BY HIS 87 MODEL
6
Hs
2
0
APR MAY JUN
(1988)
STATION: NOBC BUOT *41002 NOBC DATA
--BT HIS 79 MODEL
E --BT HIS 87 MODEL
Ni
V I I I
II 4 1Ii
II "' ll II T i I II
S I
E "_ I -- "11 _ IP/I
APR MAT JUN
(19881
Figure B6. Comparison of Apr-Jun, 1988 Phase I hindcast and measured
wave data at buoy 41002 location.




PHRSE I WAVE STUOTDY RESULTS

STATION: NOBC BUOT *41002
6 = -O.O04. Es= 3.2 (S) 20 6 =-0.13., s = 3.2 (S)

JUL AUG SEP
(1988]

JUL RUG SEP
(1988)

JUL RUG SEP
(1988)

Figure B7. Comparison of Jul-Sep, 1988 Phase I hindcast and measured
wave data at buoy 41002 location.

B-8

* NOBC DATA
-BY HIS 79 MODEL
--BY HIS 87 MODEL

TM (SEC)

E
N
8WHAVE
N W
S E




PHASE I WAVE STUDY RESULTS

STATION: NOBC BUOY w41002
6 = 0.t1,. 6ms=2.3 (S) 6 = 0.30. E s=40. (5)

* NOBC DATA
-BY HIS 79 MODEL
--BYT HIS 87 MODEL

tu. i I_ r i J
I I
01
OCT NOV DEC
(1988)
10
STATION: NOBC BUOY *41002 NDBC DATA
6 =0.76. ms=O.63(M) --BY HIS 79 MODEL
8 6 0.77. rns=0.61(M) --BT HIS 87 MODEL
6
Hs
2M I. '
2 "
0 I I
OCT NOV DEC
(1988)
STATION: NOBC BUOY 41002 NDBC DATA
-BY HIS 79 MODEL
E --BY HIS 87 MODEL
NI
if~ It
HAVE I
H II 1
E L
OCT NOV DEC
(1988]
Figure B8. Comparison of Oct-Dec, 1988 Phase I hindcast and measured
wave data at buoy 41002 location.

B-9




PHASE I WAVE STUDY RESULTS

STATION: NOBC BUOY *44004
6 = 0.20. Sns=2.8 (S)

* NDBC DATA
-BY HIS 79 MODEL

20 6= 0.25. Enas= 5.2 (S) --BY HIS 87 MODEL
jle rlI,
15 1Ii- r J r 1 I I '
0 .II
0 1
JAN FEB MAR
(1988)
10
STATION: NDBC BUOY *44004 NDBC DATA
6 =0.53. Sms=1.541(M) -BY HIS 79 MODEL
8 6 =0.59. E= 1.20 (M) --BY HIS 87 MODEL
6 '
II
Hs 4I
0 I
JAN FEB MAR
(1988)
STATION: NOBC BUOT *qoo NOBC DATA
-BY WIS 79 MODEL
E --BY HIS 87 MODEL
L I '\ I
sW V k II I I I I I
HAVE i
l I
E .. 'I
JAN FEB MAR
(1988]
Figure B9. Comparison of Jan-Mar, 1988 Phase I hindcast and measured
wave data at buoy 44004 location.

B-10




PHASE I WAVE STUDY RESULTS

STATION: NDBC BUOY *400
6 =0.42. G6s=2.0 (S)

* NOBC DATA
-BY HIS 79 MODEL

20- 6 =0.17. 6Rms=3.8 (S) --BY HIS 87 MODEL
- 11
15 r I I
( loI I P,0
APR MAY JUN
(19881
10
STATION: NOBC BUOY *4004 NDBC DATA
6 = 0.73. Sws=0.79( -BY HIS 79 MODEL
8 6 = 0.77. 6ws=0.63(M) --BT HIS 87 MODEL
6
Hs
(M)
0
APR MAY JUN
(19881
STATION: NDBC BUOY *44004 NOBC DATA
-BT HIS 79 MODEL E --BT HIS 87 MODEL
N
S
SII,
E NY I I
APR MAY JUN
(19881
Figure B10. Comparison of Apr-Jun, 1988 Phase I hindcast and measured
wave data at buoy 44004 location.

B-11




PHASE I WAVE STUDY RESULTS

STATION: NDBC BUOTY *4tOOo
8 = 0.07, Ems= 2.7(S) 6 = 0.1. Enns=3.6 (S)

* NOBC DATA
-BY HIS 79 MODEL
--BY HIS 87 MODEL

JUL RUG SEP
(1988)

JUL RUG SEP
(1988)

JUL AUG SEP
(19881

Figure BI1. Comparison of Jul-Sep, 1988 Phase I hindcast and measured
wave data at buoy 44004 location.

B-12

TN
(SEC)

E
N
E




PHASE I WAVE STUDY RESULTS

STATION: NOBC BUOY *4qq004
6 = 0.25. Ems=2.3 (S)

* NOBC DATA
-BY HIS 79 MODEL

20 = 0.14. es=4.5(s) --BY HIS 87 MODEL
ri ii1fri
it *t ,r I * ,* 4 -,
T m,
01
OCT NOV DEC
(1988)
10
STATION: NOBC BUOT *44004 NOBC DATA
6 = 0.78. ms= 0.80 (M) -BY HIS 79 MODEL
8 6 = 0.79. ms = 0.80 (M) --8 HIS 87 MODEL
*.*
6
Ms .#
(M)
0l I I
OCT NOV DEC
(19881
STATION: NDBC BUOT qo4400o NOBC DATA
-BY HIS 79 MODEL ,E .--BY HIS 87 MODEL
E ^
N 1
OWAVE \qI
E I
OCT NOV DEC
(19881
Figure B12. Comparison of Oct-Dec, 1988 Phase I hindcast and measured
wave data at buoy 44004 location.

B-13




PHASE I WAVE STUDY RESULTS 25
STATION: NOBC BUOTY *44008 NOBC DATA
6 = 0.17. Ems=2.6 (S) -BY HIS 79 MODEL
20 6 = 0.42. Ens=4.B (S) --BY HIS 87 MODEL
15 rI t .
0 I
Tm j j / ;,i! l i /t ', I I
list
(SEC) lo ,,i=T k,.ri rll .., itP-- i., I -Li& lL~ica! Iu -, i ,
5
0
JAN FEB MAR
(1988)1
10
STATION: NDBC BUOY *400O8 NDBC DATA
6 = 0.46, sus=1.89(M) -BY HIS 79 MODEL
8 6 =0.51. SEis=1.53(M) --BY HIS 87 MODEL
6
Hs
' ,'
2
- V
01
JAN FEB MAR
(19881
STATION: NDBC BUOY *4OO008 NDBC DATA
-BY HIS 79 MODEL
E --ST HIS 87 MODEL
N IA1 k
8WAVE
N I ii !
II I II I I i I
H l II I I I I
- II I'\
VE II I
S ii I
I
JAN FEB MAR
(1988)
Figure B13. Comparison of Jan-Mar, 1988 Phase I hindcast and measured
wave data at buoy 44008 location.

B-14




PHASE I WAVE STUDY RESULTS

STATION: NOBC BUOY *.4008
6 = 0.. ems = I 8 (S) 6 = 0.21, 6ms=3.5 (S)

* NOBC DATA
-BY HIS 79 MODEL
--BY HIS 87 MODEL

15 1 PT 0 t1
(SEC) 0I 5 I I
0 I
APR MAY JUN
(1988)
10
STATION: NOBC BUOY *44008 NOBC DATA
6 =0.78. Ems=0.88(M) -BY HIS 79 MODEL
8 6 =0.78. Em =0.68(M) --BY HIS 87 MODEL
6
Hs
(M)
2 A
0
APR MAY JUN
(1988)
STATION: NDBC BUOY *4008 NDBC DATA
-BY HIS 79 MODEL E --BY HIS 87 MODEL
N II I I
8HAVE I
W I III
S I 1!I I
E rl
APR MAT JUN
(1988)
Figure B14. Comparison of Apr-Jun, 1988 Phase I hindcast and measured
wave data at buoy 44008 location.

B-15




PHASE I WAVE STUOY RESULTS 25
STATION: NOBC BUOT *44008 NOBC DATA
6 =0.09. EmSs=2.9 (S) --BT HIS 79 MODEL
20 6=0.19. es=3.4 i(S) --BY HIS 87 MODEL
15 .
(SEC)
58
0
JUL AUG SEP
(19881
10
STATION: NDBC BUOTY =44008 NDBC DATA
6 =0.62. Sms=0.52(M) -BYT HIS 79 MODEL
86 =0.61. Ems=0.47(M) --BY HIS 87 MODEL
6
Hs
(M)
2""
0
JUL RUG SEP
(1988)
STATION: NDBC BUOY *44008 NDBC DATA
-BY HIS 79 MODEL E --BT HIS 87 MODEL
WAVE
W !I /
S
JUL AUG SEP
(19881
Figure B15. Comparison of Jul-Sep, 1988 Phase I hindcast and measured
wave data at buoy 44008 location.

B-16




PHASE I WAVE STUOTDY RESULTS

STATION: NDBC BUOYT *44008
6 = 0.27. 6a, s=2.3 (S) 6 = 0.22. S ,s= 4.3 (S)

* NOBC DATA
-BY WIS 79 MODEL
--BY HIS 87 MODEL

OCT NOV DEC
(1988)

Tm (SEC) (
C
( i(
Hs
(M) L
()
E N
6HAVE
H
W
S E

OCT NOV DEC
(19881

Figure B16. Comparison of Oct-Dec, 1988 Phase I hindcast and measured
wave data at buoy 44008 location.

B-17

OCT NOV DEC
(1988)




PHASE I WAVE STUOTDY RESULTS

STATION: NOBC BUOY 044011
6 = 0.16. es= 2.4 (S)

* NDBC DATA
-BY HIS 79 MODEL

20 6 = 0.10. ens=5.0 (S) --BY HIS 87 MODEL
fI Ij
'aIHI$ I- a *:* r
0
JAN FEB MAR
(1988)
10
STATION: NOBC BUOY *44011 NDBC DATA
6 =0.68. Ems= 1.66(M) -BY HIS 79 MODEL
8 61' 0.73. m= 1.26(M) --BY HIS 87 MODEL
6(9)
Hs
(M) 4 5 "
2 i**. V t
JAN FEB MAR
(1988)
STATION: NOBC BUOY *q4011 NOBC DATA
-BT HIS 79 MODEL
E --BY WIS 87 MODEL
JA FEB MAR
tit
GWAVE 11 1If
i -I; I I
W
Ii II i I, I I
ii t I lI I
E I; 1 II
_ _ _ _____1 I_
JAN FEB MAR
(19881
Figure B317. Comparison of Jan-Mar, 1988 Phase I hindcast and measured
wave data at buoy 44011 location.

B-18




PHASE I WAVE STUOTDY RESULTS

0 1 I
APR MAY JUN
(19881
10
STATION: NOBC BUOY *44011 NOBC DRTR
6 =0.61. emns=0.70(M) -BY HIS 79 MODEL
8 6 =0.56. Smns=0.66(M) --BY HIS 87 MODEL
6 4
Hs o
(HI \ 1 "i
2 II
0 1
APR MAY JUN
(1988)
STATION: NDBC BUOY *qqO11 NDBC DATA
-BY HIS 79 MODEL
E --BY HWIS 87 MODEL
N I I
HAV II
S II
FI I I I I I 1 1
APR MAY JUN
(1988)
Figure B18. Comparison of Apr-Jun, 1988 Phase I hindcast and measured
wave data at buoy 44011 location.

B-19




PHASE I WAVE STUDY RESULTS

STATION: NOBC BUOTY 44011
5 =0.16. Ens = 2.5 (S) 6=0.17. Emns= 3.5(S)

* NDBC DATA
-BY HIS 79 MODEL
--BY HIS 87 MODEL

E N
GHAVE
H
S E

JUL RUG SEP
(19881

JUL RUG SEP
(19881

JUL RUG SEP
(19881

Figure B19. Comparison of Jul-Sep, 1988 Phase I hindcast and measured
wave data at buoy 44011 location.

B-20

1
Tn (SEC) 1
1




PHASE I WAVE STUDY RESULTS

NOV
(1988)

OCT NOV DEC
(1988)

OCT NOV DEC
(1988)

Figure B20. Comparison of Oct-Dec, 1988 Phase I hindcast and measured
wave data at buoy 44011 location.

B-21

TN (SEC)

E
N
HAVE
H
W
S E

I







APPENDIX C: COMPARISON OF 1988 TIME HISTORY OF PHASE II MEASURED AND HINDCAST WAVE DATA




PHASE II WAVE STUDY RESULTS

STATION: NOBC BUOY *41001
6 = 0.21. E ns=2.4 (S) S= 0.33. Ens=3.5 (S)
1R
- r1 iI

* NDBC DATR
-BY HIS 79 MODEL
--BT HIS 87 MODEL
I1

JAN FEB MAR
(1988)

JAN FEB MAR
(19881

Figure CI. Comparison of Jan-Mar, 1988 Phase II hindcast and measured
wave data at buoy 41001 location.

T(
(SEC)

9HAVE
W




PHASE II WAVE STUOT RESULTS
BUOY *41001 NOBC DATA
Is= 1.7 (S) -BY HIS 79 MODEL
"s=5.4 (S) --BY HIS 87 MODEL

APR MAY JUN
(1988)

APR MAY JUN
(1988)

APR MAY JUN
(1988)

Figure C2. Comparison of Apr-Jun, 1988 Phase II hindcast and measured
wave data at buoy 41001 location.

Tn
(SEC)

E
N 8HAVE
W
S E




PHASE II WAVE STUOTDY RESULTS

STATION: NOBC BUOY *41001
6 = 0.13. E6s = 2.7 (S) 6 =0.16. ERmS=3.3 (S)

* NDBC DATA
-BY HIS 79 MODEL
--BY HIS 87 MODEL

JUL AUG SEP
(1988)

JUL AUG SEP
(1988)

JUL AUG SEP
(1988)

Figure C3. Comparison of Jul-Sep, 1988 Phase II hindcast and measured
wave data at buoy 41001 location.

Tn
(SEC)

E
N
HAVE
H
S E




PHASE II WAVE STUOT RESULTS

STATION: NOBC BUOY *41001
6 = 0.32. 6rms= 2.1 (S) S= 18. En mms= 4.1 (S)

* NOBC DARTR
-BY HIS 79 MODEL
--BT HIS 87 MODEL
II Ii
1
,, F!l .bu" .

OCT NOV DEC
(1988)

OCT NOV DEC
[1988)

OCT NOV DEC
(1988)

Figure C4. Comparison of Oct-Dec, 1988 Phase II hindcast and measured
wave data at buoy 41001 location.

TP
(SEC)

E
N
8HAYE
W
S E




PHASE II WAVE STUDY RESULTS

STATION: NOBC BUOT z41002
6 =0.13. 6mts=2.5(S)

* NDBC DATA
-BY HIS 79 MODEL

20 6 =0.42. S s=3. 1 (S) --BT HIS 87 MODEL
I ~
15 11 rl
.I.'- '
(SEC) 10 """
5 "" -' "* '
0
JAN FEB MAR
(1988)
10
STATION: NDBC BUOY *41002 NDBC DATA
6 = 0.61. SRns=1.31(M) -BY HIS 79 MODEL
8 6 =0.64. Enms=0.92(M) --BY HIS 87 MODEL
6
I ~ 'II!
Hs .
0
JRN FEB MAR
(1988)
STATION: NOBC BUOY *41002 NOBC DRTR
-BY HIS 79 MODEL
E --BT HIS 87 MODEL
Ni
HAVE 1 1
I I I
E I I
JAN FEB MAR
(1988)
Figure C5. Comparison of Jan-Mar, 1988 Phase II hindcast and measured
wave data at buoy 41002 location.




PHASE II WAVE STUDY RESULTS

STATION: NOBC BUOY "41002
6 = 0.43. Se s=2.2 (S)
- 6 = 0.26. eRSs= 4.2 (S)

* NOBC DATA
-BY HIS 79 MODEL
--BT HIS 87 MODEL

APR MAY JUN
(1988)

TN
(SEC) 0
5
0 10
8
6 Hs
(M)
E N HAVE
N
S E

APR MAT JUN
(19881

Figure C6. Comparison of Apr-Jun, 1988 Phase II hindcast and measured
wave data at buoy 41002 location.

C-7

PPR MAT JUN
(1988)




PHASE II WAVE STUDY RESULTS

STATION: NOBC BUOY *41002
6 =-0.29. 6s =3.5(S) 6 = 0.22. 6ems=2. 4 (S)

* NDBC DATA
-BY HIS 79 MODEL
--BY HIS 87 MODEL

15 r
TS
(SEC)10 I
5
JUL AUG SEP
(1988)
10
STATION: NDBC BUOY *41002 NOBC DATA
6 =0.64. ems=0.53(M) -BY HIS 79 MODEL
8 6 = 0.63. Es=0.25(M) --BY HIS 87 MODEL
6
Hs
(M) 14
2 r
0
JUL AUG SEP
(1988)
STATION: NDBC BUOY *41002 NOBC DATA
-BY HIS 79 MODEL E --BY HIS 87 MODEL
S
E ______________ ________________________JUL RUG SEP
(1988)
Figure C7. Comparison of Jul-Sep, 1988 Phase II hindcast and measured
wave data at buoy 41002 location.




TN (SEC)

E
N 8HAVE
H
S E

PHASE II WAVE STUYT RESULTS BUOY *41002 NDBC DRTA
s= 2. (3) -BY HIS 79 MODEL
1s=4.2(S) --BY HIS 87 MODEL

OCT NOV DEC
(1988)

OCT NOV DEC
(1988)

OCT NOV DEC
(1988]

Figure C8. Comparison of Oct-Dec, 1988 Phase II hindcast and measured
wave data at buoy 41002 location.

C-9