EMPIRICAL GUIDELINES FOR USE OF IRREGULAR 

 WAVE MODEL TO ESTIMATE NEARSHORE WAVE HEIGHT 



by 



Michael G. Mattie 



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, H s , 

 is equal to four times the square root of the variance of the sea-surface eleva- 

 tion, H s = 4o. 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, 4o 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, 

 H s , measured in this study were calculated from the variance as 4a. 



The irregular wave model used for prediction of nearshore wave height in 

 this report calculates the distribution of wave heights. However, a single 



