247. For directional spreads greater than 34 deg, the character of the 

 observed distributions seems to differ from the model curves. The composite 

 data appear to evolve relatively flat distributions in the ranges of their 

 maximum values, high curvature at the ends of these ranges, and tail distribu- 

 tions that appear less dependent on directional spread than the model dis- 

 tributions. It is difficult to assert with much confidence that this indicat- 

 ed behavior is true. There are few observations at the larger spreads (only 

 six at the largest); and data confidence, as indicated by the standard devia- 

 tion curves, is not high. Flat regions strongly indicated for the largest 

 spreads are not as wide for slightly smaller spreads where there are more 

 observations and therefore higher confidence. 



248. Note that the reference to flat regions means the somewhat sinuous 

 curves at the peaks of the broad distributions. As explained earlier, the 

 IMLE method can result in small lobes of energy which deviate from true 

 distributions, especially where distributions are flat. It could well be that 

 deviations of observations from the fitted model curves are, in these cases, 

 simply an artifact of the data processing algorithm. If this is so, model 

 curves can be considered to approximate the data reasonably well at the larger 

 directional spreads. A proper way to state this is that the model curves are 

 within one standard deviation of the data mean curves (with a few exceptional 

 points) but that the standard deviations are large, approaching 30 percent of 

 mean values in some locations. 



249. These results suggest that the model proposed by Longuet-Higgins , 

 Cartwright, and Smith (1963) can give a reasonable characterization of the 

 symmetric directional distributions found in the present data set. However, 

 since the symmetric observations account for only one-quarter to one-half of 

 all observations, the model is not complete. Furthermore, the simple shape of 

 the model does not lend itself to representation of the asymmetric classes of 

 data which account for the other one-half to three-quarters of the observation 

 set. This means that further research is necessary to find a class of 

 mathematical functions with which to characterize these observations. It 

 appears that a reasonable starting point in such research would be an exten- 

 sion or modification of the tested model, subject to the constraint that it 

 revert to the form given by Equation 31 for symmetric distributions of narrow- 

 to- intermediate spreads. 



121 



