Thompson's (1980) findings, it appears that multimodal processes are common in 

 nature so that one is obligated to investigate wave height distributions in 

 them. 



Purpose of Study 



7. The intent of the study reported here is to conduct a preliminary 

 examination of wave height distributions that arise in multimodal processes. 

 Only bimodal processes are considered here in order to keep the investigation 

 simple. To maintain maximum control of experiment conditions, time series 

 from which to analyze extrema are artificially produced linear sums of 

 sinusoidal components. This procedure makes the study somewhat idealized, but 

 avoids some of the vagaries associated with field data. Amplitudes and 

 frequencies of component wave signals are established through a spectral 

 definition. Phases of component signals are selected at random. 



8. Statistical distributions of artificially generated wave heights are 

 compared with two distribution models. The first is the Rayleigh model dis- 

 cussed above. The second model is the deepwater asymptotic form of the so- 

 called Beta-Rayleigh distribution introduced by Hughes and Borgman (1987) . 

 This second model is a two-parameter function that collapses to the Rayleigh 

 model for a specific ratio of its parameters. In general, it is less restric- 

 tive than the Rayleigh model (because it has two parameters instead of just 

 one) and is called the Modified Rayleigh model. It is included in this 

 analysis because an analysis by Long (in preparation) indicates that it 

 represents observations better than either the Rayleigh model or the full 

 Beta-Rayleigh model for waves having a variety of directional distributions in 

 intermediate and shallow water. The hypothesis posed here is that the 

 Modified Rayleigh pdf may represent adequately distributions that deviate 

 significantly from Rayleigh distributions due to either broad-bandedness or 

 multimodality . 



Scope of Investigation 



9. Mathematical descriptions of the models used in this study are given 

 in Part II. Part III describes the way in which test data are generated. 

 Part IV discusses an analysis of unimodal processes. This analysis is 

 necessary because it is not clear how many components distributed over what 

 bandwidths are necessary to approximate reasonably a Rayleigh process. Such 



