Using the criteria established above, data summarized in Table 1 indicate 

 that in all cases either the finite-depth form or the f~ limit appears to 

 fit the spectra better than the deepwater form. This is because f consist- 

 ently explains less variance in these regressions than in the regressions 

 against the deepwater form. In a regression analysis under an assumption of 

 normally distributed variates, the hypothesis of zero correlation is rejected 

 for the number of frequency components from f to 2fp if the regression 

 coefficient is greater than 0.632 at a 5 percent level of significance. This 

 translates to a value of 40 percent for the values in Table 2. Table 1 indi- 

 cates that the average R for the regressions in the deepwater form are 

 always greater than 40 percent, suggesting that there is correlation with f. 

 The average finite-depth form value is less than 40 percent for all but two 

 (655 and 615) of the gages, suggesting a tendency for no correlation with f . 

 The shallow-water limit results suggest zero correlation except for gages XERB, 

 655, and 615. Table 2 indicates that the slopes are, in general, lower as 

 well. Plots of f^E(f) and f^E(f) show that the spectra appear to more 

 closely follow a f~^ slope (Fig. 2). 



The results of the regression analysis for the gages at depths greater 

 than 9 meters appear to be more closely fit by a f~ form than the results 

 at 9 meters and at shallower gages. The observed spectra at the shallower 

 gages tend to be less than the proposed upper limit. It is thought that 

 refraction, bottom friction, and massive breaking must dominate the spectra 

 in and around the peak, suppressing the values below the proposed limiting 

 value. This would indicate that in very shallow water, the proposed form may 

 be conservative. Plots of storm spectra at different gage sites are compared 

 to the limiting form in Figure 3. 



The variation of the equilibrium coefficient a computed over the range 

 fp to 2fp varies based on gage and time (as represented by sea and swell 

 conditions), with a for the sea conditions being larger. Additionally, 

 there appeared to be a tendency for a to increase slightly from deep to 

 shallow water. On occasion a calculated at the peak of the spectrum exceeded 

 the value of 0.0081. However, when' the a value at the peak was compared to 

 the a value averaged over the frequencies from f to 2f , it was evident 

 that the average value was much less than the value at the peak. 



The field evidence from a variety of sources supports the conclusion that 

 the maximum energy densities above the peak frequency of the spectrum can be 

 approximated by equation (4), which in the shallow-water limit approaches 

 equation (9). Evidence from Ou (1980) and the data in this report suggest 

 that the coefficient a may not be a universal constant. There is also 

 evidence that once very shallow depths are reached, other mechanisms can 

 dominate spectral shape in the vicinity of the peak; the deviation, however, 

 is such that equation (4) appears to be an overestimate. 



IV. FORMULATION OF DEPTH-LIMITED SIGNIFICANT WAVE HEIGHT, H£ 



Since equation (4) provides an estimate of the upper limit on energy 

 density in water depth h as a function of frequency and wave generation 

 condition as expressed by the coefficient a, it is possible to estimate the 

 upper bound on the depth-limited wave energy, Ejj, if a low-frequency cutoff 

 value, f^, is known. Ej^ can simply be estimated by 



12 



