S Sea surface variance spectral density 



S^,^ Discrete spectral density at k''^ frequency of time series x 



S 1, Discrete spectral density at k"'^ frequency of time series y 



t Element n of a sequence of N discrete times 



u Bin index for histogram of wave heights 



Uxk Uniform random deviate at k"^^ frequency of time series x 



U k Uniform random deviate at k"'' frequency of time series y 



X Dummy integration variable; a time series 



Xn Element n of discrete time series x 



X^ Discrete Fourier transform element k of time series x 



y A time series 



y Element n of discrete time series y 



Y^ Discrete Fourier transform element k of time series y 



Zy_ Discrete Fourier transform element k of complex time series 

 X + iy 



a Parameter of Modified Rayleigh pdf 



r Gamma function 



Af Discrete increment of frequency 



AH Discrete increment of wave height 



At Discrete time step 



€ Frequency spectral width parameter 



<j> i^ Phase of sinusoidal component k of time series x 



A3 



