This provided a composite mean (and standard deviation) distribution for the 

 spread class and frequency considered. The angle J^ is defined by Equation 

 19. It has the important property that it aligns the directions bounding the 

 central half of the energy in each distribution rather than the distribution 

 peaks. Since it is an integral property (relying on all data in a distribu- 

 tion), it is more stable than a single point (the peak value) in a distribu- 

 tion. Variations of the peaks or tails of the distributions will become 

 obvious in the composite distribution, the test of adequacy of the classifica- 

 tion scheme. 



229. For distributions with small spreads, the scheme works reasonably 

 well, as illustrated in Figure 29, which represents a composition of data with 

 frequency 0.054 Hz and directional spread in the range 20 to 22 deg. Figure 

 29a shows the mean (solid line) plus and minus one standard deviation (dashed 

 lines) of the set of 29 cases with distributions shown in the spaghetti plot 

 of Figure 29b. The composite is well defined, is reasonably symmetric, has no 

 severe outlier points in Figure 29b; and the standard deviation varies, at 

 most, by about 10 percent of the distribution maximum. 



230. However, with intermediate and high directional spreads, it 

 becomes evident that the distributions do not collapse well to a single 

 representative composite. This is illustrated in Figure 30, which shows the 

 data from 80 cases at frequency 0.103 Hz and directional spread in the range 

 40 to 42 deg. Mean and standard deviation curves are shown in Figure 30a. 

 Here, the standard deviation shows significant fluctuations in the vicinity of 

 the composite peak. The most obvious discrepancy is that the distribution 

 peaks in Figure 30b do not coincide but rather scatter as much as 30 deg on 

 either side of the central direction (0 deg) . Since all samples have been 

 aligned at the directional spread boundaries, the differences must be that the 

 distributions are asymmetric. 



231. This result suggests that a more refined classification of the 

 distributions is necessary. The additional parameter chosen for this was the 

 asymmetry parameter A„ defined by Equation 18. It gives an indication of 

 how rapidly a distribution rises on one side relative to the other. The data 

 were regrouped within classes of directional spread A^„ , asymmetry A^^ , 

 and averaged as before. This was done separately for data from each frequency 



97 



