analysis) and to normalize it with the frequency spectral density at that 

 frequency S(fj,) . The result, given the symbol DCf^.^^,) , is called the 

 directional distribution function. It is defined by 



D(fn.^J = ^S^fn^ - ^^^^ 



where the 9^ are the discrete directions from the directional analysis. The 

 units of the directional distribution function are deg"^ . It is useful 

 because it has unit area, i.e., 



I D(f„,^j de = 1 (14) 



m=l 



by virtue of Equation 8 when Equation 13 is inserted in Equation 14. The 

 normalization of Equation 13 makes it possible to intercompare the directional 

 distributions from spectra with various frequency spectral densities S(f„) . 



139. Peak direction is a fundamental parameter in any directional 

 distribution. In addition to the bulk peak directions 9 pp and 9 jpg 

 defined in Part II, a peak direction denoted as ^p „ can be found from the 

 directional distribution at each frequency. It is equal to the direction of 

 the maximum of T){t^,9^) [or S(fn,^„) ] at frequency f^ . There will be a 

 peak direction for each of the N frequencies in a discrete frequency- 

 direction spectriim. 



140. Several alternatives were considered for defining directional 

 spread. A common one is called the full width at half power, defined as the 

 arc subtended by points on the shoulders of a directional distribution 

 function which have values of one-half the maximum of D(fj,,^^) for a given 

 fn . This definition of spread has been used by many authors because it is a 

 simple, meaningful parameter for unimodal distributions. However, its 

 assignment and meaning become somewhat complicated when the distribution has 

 more than one main mode, especially if the modes have comparable areas. 

 Another method is to define spread indirectly through a parameter of an 

 analytic function fitted to the data. This method was used by both Mitsuyasu 

 et al. (1975) and Donelan, Hamilton and Hui (1985) and works well if the 



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