eS aie Cath Gag Mee. Qo TP TP 82-1 Empirical Guidelines for Use of Irregular Wave Model to Estimate Nearshore Wave Height nm by Michael G. Mattie WHO! DOCUMENT =CTION TECHNICAL PAPER NO. 82-1 \COrr Moan. JULY 1982 Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING RESEARCH CENTER Kingman Building Fort Belvoir, Va. 22060 Weave Cash Gag Mee. GTP TP 82-1 Empirical Guidelines for Use of Irregular Wave Model to Estimate Nearshore Wave Height a WHO! os ae DOCUMENT =CTION TECHNICAL PAPER NO. 82-1 \COr«t! JULY 1982 Mion. SX A J \ OS SBinine 3827 Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING RESEARCH CENTER Kingman Building Fort Belvoir, Va. 22060 Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: Nattonal Technical Information Service ATTN: Operattons Division 5285 Port Royal Road Springfield, Virginia 22161 Contents of this report are not to be used for advertising, publication, or promotional purposes. Gikakio~==—~ — a official endorse rommercial product | The bnstrued as an unless so des UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO,| 3. RECIPIENT’S CATALOG NUMBER TP 82-1 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED Technical Paper 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER(s) EMPIRICAL GUIDELINES FOR USE OF IRREGULAR WAVE MODEL TO ESTIMATE NEARSHORE WAVE HEIGHT 7. AUTHOR(s) Michael G. Mattie 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of the Army Coastal Engineering Research Center (CERRE-CO) Kingman Building, Fort Belvoir, Virginia 22060 A31592 12. REPORT DATE July 1982 13. NUMBER OF PAGES 18 1S. SECURITY CLASS. (of thie report) UNCLASSIFIED 1Sa. DECLASSIFICATION/ DOWNGRADING SCHEDULE Approved for public release; distribution unlimited. CONTROLLING OFFICE NAME AND ADDRESS Department of the Army Coastal Engineering Research Center Kingman Building, Fort Belvoir, Virginia 22060 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 11. 16. DISTRIBUTION STATEMENT (of this Report) DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) SUPPLEMENTARY NOTES KEY WORDS (Continue on reverse side if necessary and identify by block number) Irregular wave model Nearshore waves Wave heights ABSTRACT (Continue am reverse side if necesaary and identify by block number) An irregular wave technique based on a method developed by Goda (1975) and the SPM method for predicting nearshore wave height are compared with wave gage measurements from the CERC Field Research Facility. The SPM method is a classical monochromatic approach, while the irregular wave technique attempts to represent the actual distribution of ocean waves. These two techniques have certain limitations and ranges of applicability. Comparisons with field data will better define the limits and proper use for these techniques. The performance of the models is evalu- ated for a variety of wave conditions and water depths. FORM DD . san 7a 1473 = EDITION OF 1 NOV 6515S OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREFACE This report presents a comparison of field wave gage measurements with nearshore wave height predictions, which were generated by two techniques: an irregular wave model (Seelig and Ahrens, 1980) based on the method of Goda (1975) and the Shore Protection Manual (SPM) method (U.S. Army, Corps of Engi- neers, Coastal Engineering Research Center, 1977). The field gage measurements were gathered at the Field Research Facility (FRF) at Duck, North Carolina. The work was carried out under the U.S. Army Coastal Engineering Research Cen- ter's (CERC) Wave Estimation for Design work unit, Coastal Flooding and Storm Protection Program, Coastal Engineering Area of Civil Works Research and Development. The report was prepared by Michael G. Mattie, Physicist, under the general supervision of Dr. C.L. Vincent, Chief, Coastal Oceanography Branch, and Mr. R.P. Savage, Chief, Research Division. The author expresses appreciation to E.F. Thompson, CERC, for the Raleigh distribution analysis and to D. Orndorff for data reduction. Technical Director of CERC was Dr. Robert W. Whalin, P.E., upon publication of this report. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. y TED E. BISHOP Colonel, Corps of Engineers Commander and Director I INTRODUCTION. VI CONTENTS CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) ....... SNAMIHOIS ANNO) IDIMIUNIEIIOIISS 6 56 9 6 5 39 oOo Sop oe DOH IDAVPICINILIE ILO OEY WANS, WSURILGIEME 5 5 gb pl 6 8 APPROACH 4 COMPARISON OF PREDICTIONS WITH MEASUREMENTS . . EVALUATION. 9 . Ps SUMMARY . 0 5 IICISRVMIUIRIS, GINRD>5 56 6 5 560 0000000580060 6 Wave gage H, (3 September, (13 September, Plot comparing Hs-pred > with Plot comparing Plot comparing Plot comparing Plot comparing measured wave FIGURES and spectra plots for three wave conditions: swell 1500), sea (13 September, 1200) and H, > 1.8 meters Zak 0) Gots maces et Isa on wae) As Bch Meare) COM em ees irregular wave technique predicted wave height, measured le oie for entire data set H with Hg_oppg for sea wave cases . s-pred Hs-pred With Hg-obs for swell wave cases Hs-pred With H,_5p, for Ho > 1.8-meter cases . predicted wave height by SPM Pore ue Hspm, with MeUeIMe, Bliigikeo 0 9 0 9 60 0 0 0 0 9 17 18 16 CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SL) UNITS OF MEASUREMENT U.S. customary units of measurement used in this report can be converted to metric (SI) units as follows: Tee. EEE Multiply by To obtain aS inches 25.4 millimeters 2.54 centimeters square inches 6.452 square centimeters cubic inches 16.39 cubic centimeters feet 30.48 centimeters 0.3048 meters square feet 0.0929 square meters cubic feet 0.0283 cubic meters yards 0.9144 meters square yards 0.836 square meters cubic yards 0.7646 cubic meters miles 1.6093 kilometers square miles 259.0 hectares knots 1.852 kilometers per hour acres 0.4047 hectares foot-pounds 1.3558 newton meters NisleIc bates Ls@iOF7 se 1073 kilograms per square centimeter ounces 28.35 grams pounds 453.6 grams 0.4536 kilograms ton, long 1.0160 metric tons ton, short 0.9072 metric tons degrees (angle) 0.01745 radians Fahrenheit degrees 5/9 Celsius degrees or Kelvins! lTo obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use formula: C = (5/9) (F -32). To obtain Kelvin (K) readings, use formula: K = (6/9) (CF =32) + 273.15. Hb Ho SYMBOLS AND DEFINITIONS stillwater depth depth of water at breaking wave wave height at breaking (breaker height) deepwater significant wave height significant wave height or average height of the highest one-third of the waves significant wave height measured by FRF gages significant wave height predicted by irregular wave model wave height predicted by SPM method variance of sea-surface elevation EMPIRICAL GUIDELINES FOR USE OF IRREGULAR WAVE MODEL TO ESTIMATE NEARSHORE WAVE HEIGHT by Michael G. Mattte I. INTRODUCTION The techniques for estimating nearshore wave height rely on theories based on one of two assumptions about the nature of waves. The assumption of mono- chromatic waves is the basis for the technique of selecting design waves dis- cussed in Section 7.12 of the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977). A second approach is to treat the waves as irregular, with wave height and period varying from one wave to the next. Seelig (1979) presents a technique for estimating near- shore significant wave height, originally suggested by Goda (1975), based on this irregular wave assumption. Seelig and Ahrens (1980) enhance this tech- nique to include wave refraction. The present report compares the predictions of the enhanced irregular wave technique with field measurements taken at CERC's Field Research Facility (FRF) at Duck, North Carolina. A range of conditions for which the technique is applicable can be defined from these comparisons. The predictions of the SPM method are also compared with the results from Seelig and Ahrens' technique and with the FRF field measurements. II. DEFINITION OF WAVE HEIGHT This report examines the quantity ocean wave height as measured by gages and as predicted by two techniques; however, the way each technique defines or computes ocean wave height differs. Therefore, it is necessary to examine the definitions to ensure that these differences are recognized in comparisons of similar physical properties of waves and that these comparisons are meaningful. The wave gage records an approximately 17-minute time series of the water surface elevation. This measurement shows waves that are irregular having a distribution of wave height and period. The time series is transformed to the frequency domain where a spectrum representation of the wave data is commonly used. The significant wave height, which is defined as the average of the one- third highest waves, is then calculated as a statistical quantity from the spectrum. This calculation is possible because the integral of the spectrum over all frequencies is the variance of the measured time series. Longuet- Higgins (1952) showed that if the individual waves in a set of waves follow a Rayleigh distribution for the heights, then the significant wave height, Hg, is equal to four times the square root of the variance of the sea-surface eleva- tion, Hy, = 40. This assumption of a Rayleigh distribution is well established for moderate to deep water. However, it may not always be the case in very shallow water near wave breaking conditions. When this assumption does not hold, 40 will only be a measure of the standard deviation of the sea surface, but will not necessarily equal the significant wave height. The wave heights, Hg, measured in this study were calculated from the variance as 4o. The irregular wave model used for prediction of nearshore wave height in this report calculates the distribution of wave heights. However, a single wave period is assumed in the calculations. Given a deepwater significant wave height and wave period, this model then assumes a Rayleigh wave height distri- bution. At points in shallower water depths, this distribution is modified. At each calculation point closer to shore the waves that break are removed from the distribution. Determining whether a particular wave height breaks depends on water depth and other factors (Goda, 1975). The significant wave height at shallow-water points is then calculated from the modified distributions prob- ability density function. At points closer to shore there is no assumption of a particular wave height distribution but rather the distribution is modified according to processes included in the model. The SPM method makes a further simplification relative to the irregular wave model. It assumes a sinusoidal wave of a single period and wave height. As an initial input to this technique, when the deepwater spectrum is available, the period is set equal to the period for the peak of the wave spectrum and the wave height equal to the significant wave height. These are reasonable choices only if the spectrum has only one narrow peak. III. APPROACH Seelig (1979) generated design curves for wave height prediction using the computer program GODAS (Seelig, 1978). For this study a modified GODAS program, which includes refraction, was used to predict the wave height at the FRF pier wave gage locations. The field measurements were made with several Baylor staff gages mounted on the pier and one waverider buoy located 2.8 kilometers offshore in a water depth of approximately 16.8 meters. The significant wave height and peak period from the waverider buoy data were used as the deepwater wave inputs to this wave height prediction program. The water depths at the several Baylor gages were taken from weekly leadline soundings made along the pier, which were corrected for the tide. An offshore bar is often present at the FRF. For the Baylor gage locations shoreward of the bar where the water depth was greater than at the bar crest, the depth at the bar crest was used as the input to the program. Seelig (1979) recommends this approach when using the technique where an offshore bar is present. The final input is the wave direction, which was measured from radar imagery taken either simultaneously with or within an hour of the gage measure- ments. During the period September 1978 to March 1979, a total of 21 cases were chosen for study. As required by the irregular wave technique, single wave train situations were selected. The data set included a variety of wave periods (4 to 13 seconds) and significant wave heights (0.9 to 2.7 meters). IV. COMPARISON OF PREDICTIONS WITH MEASUREMENTS Preliminary comparisons of the irregular wave model predictions with the measured significant wave height showed that an analysis of the results should be segmented into three types of wave conditions: swell waves (waves propaga- ting into FRF area which were generated offshore and are no longer receiving energy input from local wind), sea waves (waves still being generated by local wind), and deepwater significant wave height, Ho, greater than 1.8 meters. Figure 1 shows examples of each condition. The September wave spectrum shows a prominent swell wave train. The plot of wave height versus location for the Hg (ft) Hg (ft) T=105 6 Hg= 3.94 ft (1.2m) X Predicted 5 A Measured us 3 Sept.1978 1500 hr 500 700 900 1100 1300 1500 1700 1900 2100 Location on Pier (ft) 8 T=4.52s 7 H =5.56 ft (1.7m) A Measured 6 X Predicted 13 Sept.1978 |200hr “500 700 900 1100 1300 !500 1700 1900 2100 Location on Pier (ft) 9 8 * —— 6 Hg= 8.44 ft (2.6m) cs) + Predicted A Measured 4 13 Sept.1978 21/00hr 3 2 600 700 900 1100 1300 1500 1700 1900 2100 Location along Pier (ft) —> Figure 1. Wave gage H, and spectra plots for three wave conditions: swell (3 September, 1500), sea (13 September, 1200) and o > L.8 meters (13 September, 2100). H Energy Density (m/s) Energy Density (m?/s) Energy Density (m*/s) 2.0 S @ So b 2.0 6.0 48 3.6 0.! 0.1 @----Gage 620 Wave Ht--1.2 m,Wave Per.--9s 9/3/78 1520 br 0.2 0.3 Freq (1/s) e----Gage 620 0.2 Wave Ht-- 1.6 m, Wave Per.--4s 0.4 9/13/78 1220 br 0.3 Freq (I/s) o----Gage 620 0.2 Wave Ht--2.5m,Wave Per.--7 3 9/13/78 2120 br 0.3 Freq (I/s ) 0.4 0.4 0.5 0.5 0.5 0.6 0.6 0.6 predicted and measured results shows an overestimation of the significant wave height, H,, by this prediction technique. For 13 September at 1200 a devel- oping sea is dominant and the comparison shows good agreement. However, at 2100 the same day the seas had grown to more than 2.4 meters and the irregular wave technique overpredicts H, for the deeper water and underpredicts for the relatively shallower water depths. A more quantitative description of these trends can be obtained through analysis of all the data for each of these cases. The entire data set for the irregular wave technique is shown in Figure 2. The ordinate is the ratio of the predicted significant wave height, Hs_pred> to measured significant wave height, Hg_op5- This ratio would be equal to one for perfect agreement between the model and measured results. The ratio of the water depth to measured Hg 5p, is plotted along the abscissa. The SPM method (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977) pre- dicts that the ratio of breaker depth to breaker wave height is between 1.5 and 1.2 for the conditions encountered for these field measurements. The scatter in the data shown in Figure 2 is of the same magnitude as seen by Goda (1975), Fig. 12) in data from Sakota Port. Subsets of the data are plotted in Figures 3, 4, and 5, which show the results for the three wave categories: sea, swell, and H)p > 1.8 meters. An analysis of these plots leads to the following conclusions on the performance of the irregular wave prediction technique for estimating H,: (a) At or below the breaker limit (i.e., d/Hg < 1.5) the model underpredicts Hg, by as much as 40 percent. (b) For sea conditions (i.e., waves are still in the stage of generation by local wind) and H, < 1.8 meters, there is good agree- ment between predicted and measured results. The predicted H, is on the average 13 percent greater than the measured Hg. The ratio Hs-pred/Hs-ops has mean 1.13 with a standard deviation of 0.14. For alil eyesllanle Cages OF ells Eye GW, apy > Zo (c) For swell waves where d/Hs-obs > 2 there is significant over- prediction by the model. The predicted Hg, exceeds the measured Hg by as much as 150 percent with the average on the order of 50 percent. The best agreement was for the measurements made at the Baylor farthest offshore in about 7.6 meters of water. The ratio Hs_pred/Hs-obs has mean of 1.5 with a standard deviation of 0.38. (d) For Ho > 1.8 meters, the model performance is mixed. For observations at the Baylor gage in the deepest water (V 7.6 meters) the model shows good agreement with the gage measurements. For the other locations, there is a tread where the model performance de- creases as d/H,_5,, increases. At d/Hs_op5 ~ 1.5 the agreement is good. As Hs-obs increases the overprediction of Hs by the model increases rapidly until at d/Hg_opg5 = 4.0 the model is over- predicting by about 80 percent. To determine how the SPM method compares to the field data, the SPM method, given the deepwater wave height Hg and wave direction, can be used to predict the wave height at points close to shore (decreased water depth). This method applies the linear wave theory for refraction and shoaling to obtain wave 2.6 2.4 Cue S-obs Hs-pred/y Figure 2. with measured He sobs 4 =Seo O = Swell A=Sea at 1900 8 = Swell at 1900 Baylor Baylor A Se0 at 620 = Swell ot 620 Baylor Baylor Q=Sea Ho>!.8m Q=Swell Ho>Il.8m a underprediction Hsobs Plot comparing irregular wave technique predicted wave height, for entire data set. S-obs H5- pred / 4 2.2 2.0 Figure 3. 4 =Sea 4 Hs obs Plot comparing Hs_pred with Hg_ops = Sea at 1900 Boylor = Seo ot 620 Baylor for sea wave cases. 2.6 O = Swell 8 = Swell at 190 2.4 Boiler 9 Swell at 620 Baylor ne O = Swell Ho>!.8m S-obs Hs -pred/,, dy Deane Figure 4. Plot comparing Hs-pred With Hz5ps for swell wave cases. 2.4 4 = Sea ee pecnaiLoee Be BOF =Sea at 620 Ly) Xs Baylor @=Sea Hy >!.8m 2.0 0=Swell Hj >1.8m S-obs H5- pred /y Hs obs Figure 5. Plot comparing Hgsg-preq with H SoS for H, > 1.8-meter cases. height predictions. It is not a spectrum method. Rather, this model assumes a single frequency sinusoidal wave where the usual procedure, when measured deepwater wave spectra are available, is to set the amplitude equal to Ho /2 and the period equal to the significant wave period. In this study, instead of applying the SPM equations to predict the wave height, the easier to use tech- nique presented by McClenan (1975) was employed. The McClenan technique uti- lizes a monogram which was constructed from the SPM equations and gives the same results. The inputs to the monogram technique are the period, the deep- water wave height, the deepwater wave angle, and the depths of interest. Figure 6 shows the comparison of the wave heights predicted by this technique with the measured H,. There are no comparisons in the figure for d/Me=oharcnc because the SPM method is applicable only for water depths greater than the breaker limit (dp/Hp =~ Iho 3) o An examination of Figure 6 shows that the same segregation of the data into swell, sea, and H)/3 > 1.8 meters, as in the previous comparison for the irregu- lar wave technique, is appropriate for linear wave technique predictions. In general, the following similar trends in the predictions are seen: (a) For swell waves there is significant overprediction. The mean value of Hgpy/Hsobs is 1.59 with a standard deviation of ORS)5 (b) There is good agreement for the Baylor gage located in the 7.6-meter water depth. The mean is 1.04 with a standard deviation of 0.08. (c) For sea with H, < 1.8 meters, the agreement between the model and measurements is better than for swell but still overpre- dicting. The mean is 1.25 with a standard deviation of 0.17. (d) For Hy, > 1.8 meters, again the results are mixed. The prediction agrees with the measurement for the Baylor gage in the 7.6-meter depth. The model overpredicts for the other gages. The mean of Hspy/Hs_opg is 1.51 with a standard deviation of 0.34. In general, in evaluating each of the two models from the comparison with the gage measurements, it can be seen that the predictions of the irregular wave-based model were about 10 percent better than those for the McClenan-SPM model based on monochromatic waves. In addition the irregular wave model can be used in much shallower water, while the monochromatic wave model is not applicable in water shallower than the breaker depth. V. EVALUATION As indicated in the previous section, there are wide variations between the model estimates and the field measurements of wave height. Two factors that contribute to these variations are the bathymetry and the way the wave heights are calculated. Bathymetric surveys at the FRF show that there is a depression near the end of the pier. This causes some wave energy to be refracted away from the gages, resulting in lower wave height measurements. The prediction techniques 15 A = Sea O = Swell 2.6 ia} A =Sea at 1900 B = Swell at 1900 Baylor Baylor a = Seo at 620 = Swell at 620 Baylor Baylor Q@=Sea Hp>!.8m Q=Swell Ho>!.8m S-obs Hoom/y S-obs Plot comparing predicted wave height by SPM technique, Hgpy, Figure 6. with measured wave height, Hg_opg- assume that the bottom contours are straight and decreasing. To estimate the magnitude of the effect of refraction due to this depression, a spectral re- fraction model was run for both the existing bathymetry at the FRF and a smoothed bathymetry (depression removed) for deepwater wave conditions selected from the set of data analyzed for this study. The results show that for the Baylor gages, where the models overpredict, the correction to measured wave height for this refraction would be less than 10 percent. This is much less than the overprediction of the models, which is about 50 percent. For the Baylor gages in the shallowest water depth, where the irregular wave model tends to underpredict, the refraction correction increases the measured wave height from 10 to 50 percent, which makes the disagreement between the irregular wave model and the measurement even greater. The second factor, which may contribute to the differences between predic- tion and observation, is the assumption of a Rayleigh distribution in the cal- culation of significant wave height for the measured data. If the wave heights do not have a Rayleigh distribution then the measured 40 will not be equal to the average of the one-third highest waves. To get an estimate of how large an error results from using the 40 statistic for the measured H,, the individual wave heights were counted for selected time series from the data set. From this count, the average of the one-third higher waves was obtained. The dis- tributions, which were obtained, showed that the wave heights for the most part were very nearly Rayleigh distributed. The 40 values for Hg differed from that obtained by counting waves by less than 10 percent; for a majority of cases the differences were less than 5 percent. Correction of the measured wave heights for errors due to using 40 for significant wave height does not significantly affect the results of the comparisons between wave measurements and the model predictions. For most cases this correction tends to increase the discrepancy between measurement and irregular wave model prediction. The comparisons showed that the irregular wave model is better than the SPM-McClenan technique for predicting nearshore wave conditions. The irregular wave model is more representative of the physics of the wave processes, and it can be used shoreward of the SPM-defined wave breaking point, which assumes a single sinusoidal wave. It also gives results which, on the whole, are in better agreement with measurements than the SPM-McClenan technique. However, the com— parisons of the irregular wave model results with the gage measurements show large differences. In general, as the waves enter shallow water the model over- predicts. This indicates that there are significant dissipative effects that are not being accounted for by the model. In very shallow water, the model often underpredicts in the region in or near the surf zone. A hypothesis for this underprediction is that the extra measured wave energy is due to waves that have broken and re-formed, a process that is not included in the irregular wave model. VI. SUMMARY Comparisons of nearshore significant wave heights as estimated by an irreg- ular wave procedure and by the SPM-McClenan technique with gage measurements show that the irregular wave model is an improvement over the SPM-McClenan technique. Yet for many cases there remain large differences between the model predictions and gage measurements. Therefore, care should be taken when using the model, especially in very shallow water where the model often underpredicts for cases of high deepwater waves. lt LITERATURE CITED GODA, Y., ‘Irregular Wave Deformation in the Surf Zone," Coastal Engtneering tn Japan, Vol. 18, 1975, pp. 13-26. LONGUET-HIGGINS, M.S., "On The Statistical Distribution of the Heights of Sea Waves," Journal of Marine Research, Vol. I1, No. 3, 1952, pp. 254-266. McCLENAN, C.M., "Simplified Method for Estimating Refraction and Shoaling Effects on Ocean Waves,'' TM-59, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Nov. 1975. SEELIG, W.N., "Documentation of the Computer Program GODAS (720X1R1CBO) ,"' Memo- randum for Record (CERRE-CS), U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Nov. 1978. SEELIG, W.N., "Estimating Nearshore Significant Wave Height for Irregular Waves," CETA 79-5, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Oct. 1979. SEELIG, W.N., and AHRENS, J.P., "Estimating Nearshore Conditions for Irregular Waves," TP 80-3, U.S. Army, Coastal Engineering Research Center, Fort Belvoir, Va., June 1980. 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