where the subscript 2 indicates this two-wave model and Hj.^3 is the RMS wave 

 height, determined from a set of observed wave heights through the equation 



Hrn,s - [n X ^ J 



(6) 



In Equation 6, N is the number of observed waves and H^ is the height of 

 the n"^^ wave. It is useful to treat mathematical models in dimensionless 

 form, where practicable. The only parameter in Equation 5 is Hj.^^ . Hence, 

 the pdf can be made dimensionless in the form 



P2 



Urj 



'b ■ itsr 



-^ < 72 



(7) 







H, 



> 72 



The exceedence probability corresponding to this pdf is found by integrating 

 Equation 7 in accordance with Equation 3. The result, in dimensionless form, 

 is 



it}' 



1 - — sin 



1 JL 

 72 H,„ 



H 



< 72 



(8) 







^^ < 72 



15. The two -wave model is useful for testing synthetic data generation. 

 When used with two wave trains of arbitrarily different frequencies, synthetic 

 wave heights should approximate this statistical distribution, becoming 

 asymptotically identical as the two frequencies become nearer to (but not the 

 same as) each other. For these conditions to hold, synthetic time series must 

 be long enough to include sufficient cycles of the beat period to obtain a 

 meaningful sample of wave heights. 



Rayleigh Model 



16. As described by Longuet-Higgins (1952), the Rayleigh pdf is defined 

 by the equation 



Pr(H) 



m -(H/H,„j' 



H^ 



(9) 



