used in the present tests. The relative energy ratio varies from 0.25 to 4.0 

 following a geometric progression. 



89. Results of this part indicate that for spectra with broad ranges of 

 modal separation parameter and with a ratio of low- frequency modal energy to 

 high-frequency modal energy roughly greater than 1.0, derived wave height 

 distributions tend to be well-represented by the Modified Rayleigh model. The 

 Rayleigh model tends to overpredict all the wave height averages for these 

 parametric ranges in much the same way 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 separations and small high- 

 frequency modal energy relative to low- frequency 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. 



90. The two key findings in this study are, first, that spectra that 

 are not narrow-banded or are bimodal with moderate-to-wide modal separations 

 tend to have wave height distributions that are overpredicted by the Rayleigh 

 wave height model, which may account for the common observation that the 

 Rayleigh distribution is conservative for engineering design. Second, the 

 Modified Rayleigh wave height model has a much better capability of charac- 

 terizing distributions from broad-banded or multimodal wave fields. Further 

 research is required to determine the parameters of the Modified Rayleigh 

 model in terms of spectral parameters. Finally, these conclusions need to be 

 tested with natural data to ensure that the artifice of synthesis has not 

 biased the results. 



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