78. A remarkable improvement over the results shown in Figure 10 is the 

 comparison of the same synthetic data with the Modified Rayliegh model as 

 shown in Figure 11. This improved comparison could be expected for two 

 reasons. One reason is that the Modified Rayleigh model is a two-parameter 

 model and is therefore much more highly adaptable than the Rayleigh model. 

 The second reason is that the effective broadening of the spectra by medium- 

 to-large modal separations and medium- to- large energy ratios is rather like 

 the broad unimodal cases for which the Modified Rayleigh model worked excep- 

 tionally well, as shown in Figure 4. 



79. However, bimodal cases with large modal separations and small 

 energy ratios were not entirely well-fitted by the Modified Rayleigh model. 

 There is some improvement over the Rayleigh model as can be seen by comparing 

 Figures 10 and 11 (they are plotted at the same scale) , but this improvement 

 is likely due to the improved adaptability of the Modified Rayleigh model 

 rather than any inherent ability to represent the underlying process. This 

 result suggests that for wide modal separations and small energy ratios , there 

 is another, as yet undefined, distribution which better represents these 

 processes . 



80. Some examples will clarify the above arguments. Figures 12, 13, 

 14, and 15 show pdf and exceedence curves for time series derived from bimodal 

 spectra with small, intermediate, and two cases of large modal separation. 

 Figure 12 represents a case where modal separation is small ( = 0.10) and 

 energy ratio is also small ( = 0.25). In this case, the synthetic data lie 

 very close to the Rayleigh curve, and the Modified Rayleigh model is very near 

 the Rayleigh model asymptotic shape. Hence, under these conditions, the 

 process is well -modeled by the Rayleigh pdf. Figure 13 represents a case with 

 the same energy ratio as in Figure 12, but with an intermediate modal 

 separation ( = 0.60). The effective spectral broadening is apparent, espe- 

 cially in the exceedence curves. Synthetic data and Modified Rayleigh results 

 agree very closely, and both differ from the Rayleigh model on the high-wave 

 tail of the distribution. This behavior is very much like that shown in 

 Figure 9, representing broad-banded, unimodal spectra. 



81. Figures 14 and 15 depict results from cases where the governing 

 bimodal spectra have the largest separation parameter ( = 1.33), but extremes 

 of relative energy parameter ( = 4.0 and 0.25, respectively). Figure 14 

 represents a case that follows the pattern of large relative modal energy. 



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