of energy in the primary mode. The distribution is cumulative so that, for 

 the highest frequency, one can see that about 32 percent of all cases (the top 

 of bar with the broad diagonal shading which slopes upward from left to right) 

 have between 70 and 100 percent of total energy in the primary mode. 



211. Overall, it appears that roughly two- thirds of all directional 

 distributions have 90 to 100 percent of energy (the ratio of black- shaded area 

 to total area in Figure 24 as a whole) in the primary mode. This means that 

 the remaining one -third of cases, primarily at the higher frequencies, have 

 significant energy in secondary modes. In response to the question initiated 

 by the results given in Figure 23, the answer is that a significant fraction 

 of distributions are multimodal and that secondary modes are commonly as 

 energetic as primary modes. Hence, modal structure must be considered 

 important in natural directional distributions (at this site, at least). 



212. Some of the multimodality can be discounted as being caused by low 

 signal-to-noise ratio and large pressure response function. These conditions 

 occur most often at the higher frequencies. Energy at these frequencies is 

 typically low relative to the spectral peak (e.g., the frequency spectra in 

 Figures 5 and 7) so that, if there is roughly the same amount of noise at all 

 frequencies in the system, the signal-to-noise ratio will be low at the higher 

 frequencies. The pressure response function (which converts pressure to sea- 

 surface displacement via linear wave theory) for a frequency of 0.32 Hz in 8 m 

 of water is about 13. Any noise at this frequency also is amplified by a 

 factor of 13. These effects can degrade the cross -spectral estimates from 

 which the directional distributions are computed. The results can be noisy 

 distributions which might be interpreted as multimodal when, in fact, they are 

 just not known very well. 



213. However, at intermediate frequencies (0.15 to 0.20 Hz, say) there 

 is typically greater energy (see the frequency spectra in Figures 5, 6, 



and 7) , and the pressure response function is only about 2 for 8 m of water. 

 In this case, the effects of noise should be far less. Figure 23 indicates 

 that there is still significant bimodality (20 to 40 percent) at these 

 frequencies, and Figure 24 shows that more than 20 percent of all cases at 

 these frequencies have at least 30 percent of total energy in the secondary 

 mode. Hence, the conclusion remains that multimodal distributions are an 

 important feature of wave directionality at the present experiment site. 



87 



