are both accepted. Two of the seven records have maximum outlier ratios 

 less than 5.3. This is 28 percent which is remarkably close to the 22 

 percent derived above. 



The second measure of extremeness is the value of the SNR as based on 

 a and a_ computed without the outliers present. Other than noting 

 that a three-sigma bound is often used in reliability to indicate unusual 

 extremeness, no attempt will be made to interpret these results at this 

 point in the research. 



One nonstatistical observation may be more significant than all the 

 statistical computations. This is the twofold fact that (a) the outliers 

 always seem to fall in the maximum energy frequency range, and (b) the 

 outlier lines are exceptionally separated from their neighbors, i.e., 

 there is not a smooth transition with lots of small lines, some moderately 

 large lines, and a few very large lines. It is more like two separate 

 populations with no moderate range values between the two. This situation 

 occurs in statistics in "gross error" or outlier questions. However, 

 there is really insufficient statistical data to draw any firm conclusions. 



From an oceanographic viewpoint, the one or several outlier spectral 

 lines might well dominate the waves present so that an aerial photo would 

 show waves of that frequency proceeding in their particular direction. 

 This is, of course, just conjecture since aerial photos for Hurricane 

 Carla at that space-time location are not available. The other spectral 

 lines present might be contributing noise and making the waves highly 

 short-crested. 



The spectral line outliers may be some sort of resonant phenomena 

 within the storm waves whereby energy tends to be concentrated on certain 

 frequencies. Again, this is beyond the present research and is only 

 noted in passing. 



In the situations where several outlier lines are present in the 

 record, an investigation was made as to whether there could really be only 

 one wave train present with the other lines showing up as leakage due to 

 purely mathematical manipulations. Appendix B gives a derivation of the 

 FFT leakage for a single cosine wave. It is shown that, at least in a 

 gross sense, the leakage is delineated by the following formulas. Let 

 the wave profile be given by: 



2TTmQn 



N 



) , (67) 



where m is not necessarily an integer. The approximate FFT spectral 

 lines, if 20 _< m„ + m << N, are given by the formula: 



a^NAt r sin-rrCmo - m) 



(68) 



-,^ , « a2NAt fsm^tmo - m) y 



80 



