PART IV: UNIMODAL TESTS 



Test Conditions 



55. A total of 53 cases were examined for the unimodal tests. Table 1 

 lists the parameters used in the tests. The primary variables were the 

 bandwidth Af and the number of spectral lines N . In all cases, the center 

 frequency was f^, = 0.1 Hz , the characteristic spectrum-based wave height was 

 Hjjio = 2.0 m , and the number of runs for obtaining statistical averages was 

 20. Note that spectral component wave amplitudes were found by dividing total 

 signal variance (equal to the square of jH^q) evenly among all N compo- 

 nents. Note also that there is an upper limit to the number of component 

 waves for a given spectral bandwidth because of the finite raw bandwidth 

 imposed by the discrete Fourier technique used to create the time series. 

 Hence, the narrowest case (Af/f^ = 0.05) was limited to 164 bands, but the 

 broadest case (Af/f^ =1.5) had 5,243 bands. 



56. Test criteria were the percentage differences of h'^'^°°' , h'^'"' , 

 H'^'^' , and H*^'^' from the synthetic results with those from the test 

 models. Computations followed the pattern shown here for the comparison of 

 synthetic data with the Rayleigh model estimate of the average of the highest 

 1 percent of waves 



p[(l/100) _ ]_[(1/100) 



% Difference = — udlioo) x 100% (71) 



Comparison with the Modified Rayleigh model entails replacing H^^'^°°^ with 

 Hmr°°^ in Equation 71. Replacement of the highest 1 -percent averages with the 

 highest 10-percent averages H^^'^°^ , H^^'"^ , and H^'"' allows comparison 

 among data and models for this statistic, and so on. 



Test Results 



57. Results of such comparisons are shown in Figures 3 and 4. Figure 3 

 shows synthetic data results compared with Rayleigh model statistics for the 

 four wave height averages mentioned above. Percentage differences are shown 

 as displacements on ordinate axes. Abscissa displacements are the numbers of 

 component waves N . Symbols denote synthetic data of constant Af/f^ . The 



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