Both Op and e are designed to fit the concept of a single-peaked 

 spectrum, but multipeaked ocean wave spectra are commonly observed. The 

 suitability of spectral parameters for representing multipeaked field 

 wave spectra has received little attention in the literature, although 

 Ochi and Hubble (1976) have developed a computationally complicated tech- 

 nique for parameterizing field spectra with two major peaks. 



Since Qp seems to be a potentially inqjortant and useful parameter, 

 it was computed for each of the spectra considered in this report. Qp 

 was based on the part of the spectrum between 0.03 and 0.2 hertz for 

 staff and accelerometer-buoy gages, between 0.03 and 0.33 hertz for the 

 Great Lakes pressure gages, and between 0.03 and 0.31 hertz for the Pt. 

 Mugu pressure gage. 



c. Parameters of Distribution Function of Sea-Surface Elevation . 

 The distribution function for instantaneous sea-surface elevations pro- 

 vides useful insight on shallow-water spectra and spectral parameters. 

 It also provides probabilities associated with instantaneous surface 

 elevations above the mean. 



The distribution function of sea-surface elevations can conveniently 

 be parameterized by its moments defined as: 



N 

 q^ = Z rf} p(n.) (6) 



•n i=i ^ 



where 



q^ = nth moment of the distribution function of sea-surface 

 elevations 



N = number of intervals in the distribution function 



ri . = sea-surface elevation associated with the ith interval 

 in the distribution function 



p(ri ) = probability associated with n- 



i ^ 



The zeroth and first moments, q^ and q, , are equivalent to the mean 

 and variance of the distribution function, q. and q are often re- 

 ferred to as the skewness and kurtosis of the distribution function. 



The distribution function of sea-surface elevations is often assiamed 

 to be Gaussian. When normalized, the Gaussian distribution function has 

 a mean of zero, a variance of one, a skewness of zero, and a kurtosis of 

 three. 



Steep waves in shallow water assume a decidedly nonsinusoidal pro- 

 file with broad, flat troughs and narrow, high crests. The distribution 

 of sea-surface elevations measured at a point is obviously non-Gaussian. 



29 



