232. A typical Ad^ , A^ grouping is shown in Figure 31, which shows 

 the composition means (solid lines) plus and minus one standard deviation 

 (dashed lines) for data with A0^ in the range 38 to 42 deg and A^ in the 

 range -0.69 to -0.36 for each of the 28 frequencies. To obtain more samples 

 in each class, the width of the directional-spread classes was increased from 

 2 to 4 deg. The odd limits on the asymmetry class arise because data were 

 grouped in even increments of the exponent function of Aj, . In this case, 

 0.5 < exp(A„) < 0.7 . Frequency and number of cases in each composite are 

 shown in the upper -right corner of each subplot. Subplots with no curves have 

 fewer than two cases (for which no standard deviation could be computed) . 



233. The most interesting aspect of Figure 31 is that the distributions 

 appear to be about the same for all frequencies when classified by just the 

 two parameters A9^ and A^^ . All rise sharply on the left and decay slowly 

 with a minor lobe of energy on the right. This result suggests that direc- 

 tional distributions can occur with similar shapes at all frequencies. The 

 same behavior was observed in graphs (not shown here) of composite distribu- 

 tions for all classes of directional spread and asymmetry. This means that 

 composite shapes can be constructed using data from all frequencies. Clas- 

 sification is then only by directional spread and asymmetry (two parameters), 

 and not by frequency. 



234. Figure 31 also shows that there is more scatter (larger standard 

 deviations) in the results for the highest frequencies, partly because there 

 are fewer cases at these frequencies. The scatter may also be due to noise 

 which becomes important at low wave energy. As discussed in Part VII, low 

 signal-to-noise ratios lead to a degradation of directional spectral es- 

 timates. To ensure that reasonably large-signal data were used in subsequent 

 composites, the set of distributions was further decimated by requiring 

 frequency spectral density to be well above signals associated with limits of 

 instrument accuracy and signal discretization. Both of these were approxi- 

 mately the equivalent of 0.005 m of water in a static water column. A value 

 of twice this, 0.01 m, was used to distinguish low-energy signals. This cut- 

 off squared times the frequency -dependent pressure response function and 

 divided by the resolution bandwidth df (= 0.00977 Hz) provided the value of 

 S(f„) below which data were excluded. At the lowest frequency, data with 

 S(f;^) < 0.01 m^/Hz were excluded. At the highest frequency, this increased to 

 the exclusion of data with S(f28) < 1.73 mVHz . Of the total 29,288 



100 



