PART IX: SHAPES OF DIRECTIONAL DISTRIBUTIONS 



223. Up to this point, the directional characteristics of the present 

 observation set have been described with parameters derived from the 

 frequency-direction energy distributions. Of paramount importance are the 

 shapes of the distributions themselves. These are required for accurate 

 definitions in physical and numerical models. They are also critical for the 

 advancement of wave theory, which must account for observed distribution 

 shapes if such shapes are different from what has been proposed in the past. 

 Furthermore, if observed frequency-direction spectra can be characterized by a 

 simple class of functions, then these functions can be used as elementary 

 building blocks to construct or characterize any, even the most complex, 

 observed sea states. 



Data Reduction 



224. This section describes a basic first examination of the shapes of 

 naturally occurring directional distribution functions. A rational first 

 assumption is that the observed distributions identified as unimodal represent 

 the most basic units of directional structure. It can be assiamed, then, that 

 multimodal distributions are simply a collection of superimposed unimodal 

 distributions having different energy level and directional positioning 

 parameters. Hence, attention is focused on the shapes of unimodal distribu- 

 tions . 



225. The data examined are the set of directional distribution func- 

 tions D(fj,,^n,) defined by Equation 13. Since these are the frequency- 

 direction spectral densities SCf^,^^) divided by the frequency spectral 

 densities S(fjj) , the first step in data reduction has taken place. That is, 

 the effect of variable total energy has been removed. Since the normalization 

 is unique at each frequency, the resulting distributions must be considered on 

 a frequency-by- frequency basis, at least initially. The potential data set 

 consists of 1,046 directional distributions for each of 28 frequencies. 



226. The number of cases is reduced by requiring acceptable distribu- 

 tions to be unimodal. This results in a different number of samples at each 

 frequency, as indicated in Figure 23. For instance, almost all the 



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