one side of the distribution peak. As shown in Figures 32 to 44, it is on the 

 left, but the negative contributions, reflected in these figures, have a lobe 

 on the right. It is not pronounced in the two groups with smallest spread 

 (Figures 32 and 33) because the arcs bounding the second and third quarters of 

 the energy (the ratio of which leads to the asymmetry parameter) are very 

 small. The effect of asymmetry in these two figures is visible as a more 

 gradual decay of the distribution on the left side as compared to the right 

 side . 



238. This effect becomes slightly more pronounced in the next two 

 spread groups (Figures 34 and 35), especially at higher asymmetries (bottom 

 two rows of each figure). Here, there is a suggestion of a distinct change in 

 the decay rates to the left of the distribution peaks. A better-defined lobe 

 of energy becomes apparent throughout the next four spread groups (Figures 36, 

 37, 38, and 39). Seen as a small secondary maximum in the distributions, it 

 is strongest at high asymmetries. It becomes more pronounced at lower 

 asymmetries as spread increases (i.e., in the sequential progression from 

 Figure 36 to 39). As a group, this set of four figures represents the most 

 common directional distributions. Based on case count, about 66 percent of 

 the low-noise, unimodal distributions are represented in these figures. The 

 range of spread parameter included in this set is 26 deg < A^ < 42 deg , 

 consistent with the peak in distribution of spread parameter found in Parts VI 

 and VIII. Figures 36 to 39 illustrate that asymmetry, as a subdivision beyond 

 spread, is an important classifier of directional distributions. 



239. In the next two spread-parameter groups (Figures 40 and 41), the 

 side lobe becomes even more pronounced. It appears in the lowest-asymmetry 

 class (upper- left subplot) as a distinct increase in curvature at the shoul- 

 ders of the distribution curves. It also becomes apparent that asymmetry 

 cannot be ignored. If, in the interest of modeling, the symmetric distribu- 

 tion (upper-left subplot) is forced to represent the remainder of the classes 

 in each of the two groups shown in Figures 40 and 41, two important errors 

 occur. First, if the symmetric distribution is centered at the peaks of the 

 remaining distributions, the overall energy distribution would be shifted by 

 about 20 deg. This is a typical angular difference between the middle of the 

 energy distributions (0 deg in the plots) and the distribution peaks. This 

 angle is about the same size as one direction bin used in much of the Wave 

 Information Study (WIS) results (Ragsdale 1983) . A shift in energy direction 



116 



