profile. Keulegan (1945) studied the ratio of trough depth h^ to bar crest 

 depth hj, . He found an average value for h^/h^. of 1.69 for laboratory 

 beaches and 1.65 for field beaches. Shepard (1950) found much lower ratios at 

 the Scripps pier, with a mean value of 1.16 (referenced to mean sea level). 

 The smaller value determined by Shepard is expected, since the tidal range is 

 relatively large (order of 2 ra) along the southern coast of California. 

 Changing water level, combined with random and longer period waves in the 

 southern California Bight, would act to smooth the profile. 



250. In the present study, this ratio was calculated for 26 CE and 

 CRIEPI cases and ranged between 1.26 to 2.16, with an average of 1.74 and 

 standard deviation of 0.26. The ratio was calculated as an average for all 

 profiles surveyed during a case and showed little change in time for most 

 cases. However, for some cases the very first profile survey showed a 

 markedly different value of ht/h^ , typically much lower than the average, 

 and these spurious values were excluded from the calculation of the average. 



251. The ratio of trough depth to crest depth showed an inverse depen- 

 dence on the wave period, as illustrated in Figure 19. The wave period 

 accounted for 60 percent of the variation in the data using a regression 

 relationship between \/h^ and the wave period. Expressed as an empirical 

 power law in terms of wave steepness, regression analysis gave 



2.50 



(11) 



252. Equation 11 had a coefficient of determination of 55 percent, 

 slightly less than that found using only the wave period, but from a general 

 point of view it is more attractive to use as a predictive relationship. 

 Keulegan (1948) did not report a dependence on wave steepness. 



253. Qualitative examination of the scattered data indicated that the 

 ratio hj^/h(. tended to increase with grain size for bars formed on erosional 

 profiles, but decreased with grain size for bars formed on accretionary 

 profiles. In erosional cases in general the profile for coarser grain sizes 

 showed a steeper shoreward bar slope, allowing for a larger vertical distance 

 between the bar crest and trough bottom. The breakpoint bar formed on an 



89 



