VI. DISCUSSION OF HURRICANE CARLA WAVE SPECTRA 



The spectral lines (shown as dots] and the spectral density estimates 

 averaged from the lines (shown as a line or a string of pluses) are given 

 in Figures 1 through 12. 



Close examination yields two very interesting facts. First, the peak 

 values of the spectral densities are related closely to one or two spec- 

 tral lines. Only in record 6883 is the peak related to four exceptionally 

 large lines. In the other cases it is always one or two. Second, these 

 exceptionally large spectral lines do not seem to persist. The two 

 members of record pairs (6881-1 and 6881-2; 6886-1 and 6886-2) are sepa- 

 rated from each other by only 20 minutes. Yet in both cases, exception- 

 ally large spectral lines are present in one member of the pair but not 

 in the other. 



A general examination of the spectral lines versus the spectral 

 density estimates cannot help but develop a sense of healthy skepticism 

 concerning the general reality of the fine structure in the spectral 

 density. Also, it is felt that the exceptionally large spectral lines, 

 often twice as large as the nearest other line value, must belong to 

 another population from the rest of the lines. Perhaps some sort of 

 resonant phenomenon is creating a main wave train with the rest of the 

 lines functioning as superimposed noise. 



VII. STATISTICAL VARIABILITY OF THE SPECTRAL LINES 



The spectral density was subtracted from each spectral line for 

 6^m_<305 to provide 300 residual values, R,^ , 



Rm = PCfm) - k^m) ■ (35) 



A positive and negative standard deviation for the residuals were computed 

 with the weights introduced in Table 2. Let J^ be the values of the 

 index m for which the residuals are positive while J_ are the values 

 of m for which the residuals are negative. The positive and negative 

 variance of the residuals are defined as: 



<,m- .^, ^j'^ij/ .^, ^j (36) 



,m 



= I WjR2_. / I Wj (37) 



jeJ_ jeJ_ 



where "e" means "belongs to the set of." Thus, 0^. ^ will be a moving 

 average estimate of the root-mean-square (rms) of tfte positive residuals 

 in the vicinity of the frequency f^,. A similar statement relative to 

 o_ and the negative residuals will also hold. 



18 



