common approach is to compute spectral statistics which are often based 

 on moments of the spectrum, where the nth spectral moment, m^^, is 

 defined as 



% 



oo 



fs(f) f^df CI) 



where f is the frequency and S(f) the spectral energy at frequency f. 

 This approach is used in many cases because it is the only tractable way 

 to deal with large numbers of spectra. However, some of these spectral 

 statistical parameters have disadvantages which will be discussed later. 

 A relatively new and promising approach to spectral parameterization 

 involves the use of eigenfunctions (Vincent and Resio, 1977). 



Another approach to the problem of how to characterize and summarize 

 ocean wave spectra has been used in conjunction with ship-response pre- 

 diction. Hoffman (1974) organized deepwater spectra into 10 groups 

 from a site in the North Atlantic according to significant height. For 

 each group, the mean and standard deviation of spectral energy in each 

 band were computed. The average energy of the one-third highest and 

 one-third lowest values in each band was also computed. The importance 

 of accounting for variability of spectral shape when predicting ship- 

 bending moment responses was demonstrated. 



An averaging procedure for summarizing deepwater spectra from a site 

 in the North Atlantic was also used by Gospodnetic and Miles (1974). 

 Spectra were grouped according to both significant wave height and 

 average wave period. The average spectra were made dimensionless to 

 facilitate comparison of spectral shapes. Although most of the varia- 

 tions were removed by using the dimensionless format, it was concluded 

 that even the dimensionless spectra vary systemmatically with both height 

 and period. 



In very shallow water, spectral characteristics would be expected to 

 have a pronounced systematic relationship to both significant height and 

 dominant spectral period, although the relationship would be somewhat 

 obscured when major secondary wave trains exist. Wave height is impor- 

 tant because high waves lead to wave breaking in shallow water. Thus, 

 any reasonable attempt to compute average spectra at a shallow-water 

 location must include stratification of the spectra according to wave 

 height or energy. 



The extent of wave shoaling is specified by the relative water depth, 

 d/Lp, which is directly related to the dominant wave period. Waves in 

 very shallow water assume a nonsinusoidal profile which gives rise to 

 spectra with peaks at multiples of the dominant frequency. An example 

 of the profile and spectrum for several cnoidal wave cases is shown in 

 Figure 2; another example is an aerial photo spectrum pair in McClenan 

 and Harris (1975, p. 63-64). Because of such systematic effects on the 

 shallow-water spectrum, spectra should also be stratified by d/Lp or 

 by a characteristic wave period. 



23 



