directional distributions available (1,046 frequency-direction spectra 

 multiplied by 28 frequencies per spectrum), only about half (14,218 distribu- 

 tions) remained after this discrimination procedure. However, some assurance 

 was obtained that noisy (low-resolution) data were eliminated, and some 

 compensation was gained by being able to group data from all frequencies. 



235. Directional distributions were grouped a third time and composite 

 curves constructed. Thirteen classes of directional spread parameter A^ 

 were used, ranging from 10 to 62 deg in 4-deg arcs. The frequency subscript 

 n is dropped because samples from all frequencies are grouped together. 

 Twelve classes of asymmetry were used. Because of the way asymmetry is 

 defined in Equation 18, a distribution with one value of asymmetry which is 

 positive should be the mirror image of a distribution with the same magnitude 

 of asymmetry but which is negative. Hence, the 12 asymmetry classes were in 

 terms of the magnitude of asymmetry |A| , ranging from 0.0 to 1.2 in bands of 

 0.1 . A distribution with negative asymmetry was reversed about the central 

 (0-deg) direction after being shifted by the centering angle 6 and before 

 being summed in the composite. All composite curves are thus computed as if 

 they had positive asymmetry, but a count is kept of the number of positive and 

 negative contributions. 



Resulting Shapes 



236. Results are illustrated in Figures 32 to 44. One figure is shown 

 for each of the 13 classes of directional spread. The total number of cases 

 is 14,218 . The largest number of cases contributing to any one class is 708 

 (in Figure 37, 30 deg < A^ < 34 deg, for the class with lowest asymmetry, 0.0 

 < |A| < 0.1 ). Classes with fewer than two cases are not graphed, as no 

 standard deviation could be computed. 



237. All classes are shown to illustrate the range of shapes dis- 

 covered, the transition of shapes between spread and asymmetry classes, the 

 nature of the structure which gives rise to asymmetric distributions, and, 

 through the case counts, the relative importance of each class. Classes with 

 the smallest asymmetries (0.0<|A|<0.1 , in the upper- left subplot of each 

 figure) have shapes most nearly like the symmetric models. This special 

 subgroup is called the symmetric class of distributions. Asymmetry occurs in 

 the remaining distributions as the result of a lobe of energy which appears to 



102 



