Using D ( m ) as a representative directional distribution function, the integral 

 function is 



/(8. " 0. ) = E O(0 ; )d6 (30) 



where the cyclic nature of the distribution function is employed if necessary. 

 Quartile directions satisfy 



/(6 25% - B m J = 0.25 (31) 



^(0 5 o% " 0^) = 0.50 (32) 



and 



'(875% - KJ = °- 75 ( 33 > 



A measure of directional spread A6 is the span of the two middle quartiles 



Ae = e 75% - e 25% (34) 



and has the specific interpretation that it is the arc subtending the central 50 per- 

 cent of the energy distribution. 



A measure of asymmetry of a distribution is the ratio of the directional width 

 of the third quartile to that of the second quartile. By taking the natural logarithm 

 of this ratio, a symmetric distribution has an asymmetry parameter A near zero, 

 and that for a skewed distribution acquires a positive or negative sign if the skew- 

 ness is toward larger or smaller angles, respectively. The asymmetry parameter is 

 thus defined as 



6 75% - 6 50% 



6 50% - 6 25% 



(35) 



Summary of Parameters 



The nine bulk parameters (H mo , f p , Q p , 6 , o, y, 6, A0, and A ) defined 

 here are useful for classifying general wind wave energy distributions. For refer- 

 ence as an index of processed data from the 1994 collection year, these parameters 

 are listed in Appendix A, and plotted as time series in Appendix B. Graphs in 

 Appendix B provide an overview of the directional wave climate at Harvest Plat- 



Chapter 4 Characterizing Parameters 



17 



