distributions at frequencies near 0.10 Hz survive this decimation, but only 

 about 10 percent of the highest frequency cases are retained. 



227. In an initial attempt to classify the distributions, the direc- 

 tional spread parameter A^„ alone was used. Classification was done for 

 each frequency f^ separately. This approach would result in the simplest 

 possible classification in that the directional distributions could all be 

 defined by specifying a single parameter, directional spread. Determining the 

 adequacy of this approach is important because at least two investigations of 

 directional distribution have characterized results with a single parameter. 

 Mitsuyasu et al . (1975) used the function proposed by Longuet-Higgins , 

 Cartwright, and Smith (1963) of the form 



D(f,e) = G(s) \coslid - e^)\^^ (31) 



where s is the single parameter (which can vary with f ) , 6^ is the 

 distribution peak direction, and G(s) is a coefficient given by 



2^= r^(s+l) 

 ^^^^ = 360 deg r(2s+l) ^^^^ 



where F is the gamma function (see Abramowitz and Stegun 1970) . The 

 coefficient G(s) satisfies requirement of unit area under D(f,^) . The 

 definition given here differs slightly from that given by Mitsuyasu et al . 

 (1975) in that it has been converted to units of deg"-"- to conform to the 

 system of units used in this report. Their definition is in units of ra- 

 dians"'^. Donelan, Hamilton, and Hui (1985) proposed a function of the form 



D(f,^) a sech^[fii9 - ej] (33) 



The free parameter in this function is /3 which may depend on frequency. A 

 coefficient is needed on the right side of Equation 33 to give unit area under 

 D(f,S). Each of these models is a function, symmetric about S^ , which 

 depends on a single parameter. It would be most fortunate if the data in the 

 present set fit one of these models. 



228. To test this hypothesis, data were grouped by 2 -deg increments of 

 A^j, , shifted along the direction axis by the angle 8^ , and averaged. 



96 



