Sjmthetic wave heights average to an exceedence curve that is more nearly 

 represented by the Modified Rayleigh model than the Rayleigh model. Dramatic 

 differences from Figure 14 are seen in Figure 15, which represents a case with 

 small relative energy. In Figure 15, synthetic data differ dramatically from 

 both Rayleigh and Modified Rayleigh pdf curves. The exceedence estimate of 

 the synthetic data clearly differs from the Rayleigh model, as shown in the 

 lower part of Figure 15. Synthetic data also deviate by more than one 

 standard deviation from the Modified Rayleigh curve at low and intermediate 

 wave heights. The Modified Rayleigh model does appear to conform reasonably 

 well with synthetic data in the high-wave tail of the distribution, but this 

 may simply be a fortuitous circumstance, given the poor agreement elsewhere in 

 the distribution. 



82. To summarize, it appears that for spectra with broad ranges of 

 modal separation parameter and with a moderate range of relative modal 

 energies roughly greater than 1.0, derived wave height distributions tend to 

 be well-represented by the Modified Rayleigh model. Most distributions in 

 these ranges of parameters tend to be overpredicted by the Rayleigh model, as 

 was found for time series derived from broad-banded spectra and as have been 

 found frequently in natural observations (SPM 1984) . For large modal separa- 

 tions and small relative modal energy, synthetic data deviate strongly from 

 the Rayleigh model and deviate significantly from the Modified Rayleigh model. 

 This result suggests the need for a third model to represent wave height 

 distributions under conditions where governing spectra have wide modal 

 separations and low relative energies. It also suggests that further study be 

 performed to determine how frequently such conditions occur in nature, so as 

 to determine their relative importance. 



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