The low frequency energy in Figure 9 is due to uncompensated plane 

 motion. While the accelerometer cancels high frequency vertical plane motion, 

 it cannot compensate for lower frequency components, nor can it account for roll- 

 ing and pitching motions, all of which introduce ficticious wave energy to the 

 apparent spectrum. It seems clear, based on Section 3.3, that these random motions 

 of the aircraft do not materially affect the statistical character of the data in the 

 frequency range that is here being described. This is further substantiated by the 

 characteristic occurrence of the extremely deep "valley" in the spectrum near 

 w = 2 rad/sec. Since the extraneous plane motion was due to random atmospheric 

 turbulence, and because of the physical size of the plane, it seems most unlikely 

 that the ficticious wave energy should rise again for w > 2.0 rad/sec. The low 

 point of the valley is almost always within the noise level of the analysis. 



In light of the preceding remarks, it was a relatively simple matter to 

 construct a numerical filter that had the desired properties. The filter effectively 

 discriminated only against disturbances with frequencies lower than 2.5 rad/sec, 

 and therefore, the statistical character of phenomena with greater frequencies re- 

 mained unaltered. 



5.3 Statistical Tests 



Once the data had been filtered, it was possible to apply various statistical 

 tests in order to determine the most advantageous length of record for spectral analysis. 

 The method was to break the entire record (extending from near the coast out almost 

 190 nm) into approximately one mile sections and then compare the statistics of a 

 selected section with its neighbors. In this way it was possible to determine how 

 many one mile sections could be considered as coming from the same population, and 

 hence, the maximum permissible length of record that could be considered as being 

 at least weakly homogeneous. Homogeneity thus means that the average properties 

 of each of the segments of sea surface, making up the length of record to be analyzed, 

 must be practically the same. The reader is reminded that the conditions for station- 

 arity have been obtained in Section 2.0. 



By the very nature of the filtering process, the mean of each section of 

 data was set to zero. The 2nd, 3rd, and 4th moments about the mean were left to 

 provide the needed Information. No tests could be found that allowed comparisons 

 of 3rd and 4th moments, and so it was not possible to determine "complete" homo- 

 geneity limits. V/ith the second moment, variance, however, it was possible to set 

 upper bounds for the condition of "weak homogeneity" . In this respect, the 3rd and 

 4th moments were useful in the sense of providing consistency to the analysis. 



Two methods of comparing variances were used: Cochran's Test and Bartlett's 



22 



