dividing the positive and negative deviations by the local root-mean- 

 square positive and negative deviations respectively. 



2. A simulation procedure based on the probability behavior of the random 

 noise of the spectral line deviation was used to generate probability 

 intervals for the spectral density estimates. 



3. The simulation probability intervals were found to agree reasonably 

 well with that predicted from the chi-squared probability law. Al- 

 though the chi-squared probabilities are expected to be valid for 

 "low wave" spectral densities, it was somewhat surprising to have 

 them work for the nonlinear hurricane waves. 



4. An investigation of the above item led to the discovery that the 

 finite Fourier transform coefficients will be approximately independ- 

 ent and normally distributed for large data sets even though the water 

 level elevations are not normally distributed. This face was derived 

 from probability theory after assuming (a) m-dependence of the water 

 level elevations about mean water level, and (b) a water level proba- 

 bility density which is bounded for large y by the function 

 a|y|ng-b|y| ^^^ j-,^ ^j^jj ^ ^yg arbitrary constants). A central limit 

 theorem was derived from these assumptions which led to the finite 

 Fourier transform coefficients being asymptotically normally distrib- 

 uted and independent as the data length tended to infinity. 



5. Under the conditions of the item above, the smoothed spectral esti- 

 mates were found to be asymptotically chi-squared distributed pro- 

 viding the true spectrum is constant over the smoothing interval. If 

 the true spectrum is not constant, the spectral density estimates 

 would still be reasonably close to having chi-squared behavior 

 although there would be some deviations as evidenced by the deviations 

 of the simulation results from the chi-squared results. 



6. The wave spectral lines exhibit members which appear unusually large 

 as compared with the rest of the spectrum. The "outlier" lines 

 always appear associated with the "peak energy" part of the spectral 

 density. These unusual lines of energy might predominate the wave 

 record so that a satellite picture would show waves of those frequen- 

 cies riding on top of the rest of "noisy" wave combinations. However, 

 this is just conjecture. 



7. The outlier spectral lines mentioned above do not persist for long 

 periods of time. In the two cases where Hurricane Carla wave data 

 were available 20 minutes apart, the outliers were found in one set 

 of the data pair but not in the other. 



8. The conclusion of the study relative to reliability of directional 

 spectrum estimation is that the finite transform coefficients may be 

 taken as being serially uncorrelated and approximately normally 

 distributed with zero mean, variance Pj^N At/2, and the appropriate 



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