instance, if either of the two gages with the smallest spacing is lost, 

 results for high-frequency waves are severely compromised. In this case, no 

 analysis was performed. If these two are not lost, then considerable direc- 

 tional information can be obtained with as few as five gages. 



105. For the data set discussed in this report, there were never fewer 

 than six functioning gages; most of the time there were eight. To estimate 

 the effects of this, tests were performed with subsets of gages in two 

 collections where all gages were operational. The tests indicated that the 

 general features of the frequency-direction spectra were reasonably well 

 represented by all the gage subsets used in the first year of collection. 

 Some of the finer details of the spectra were changed in amplitude or in 

 directional position so that, in refined studies of spectral structure, the 

 pattern of operating gages needs to be considered. 



106. To keep track of the set of operating gages, a parameter called 

 the gage pattern was created for each collection. It is a nine-place charac- 

 ter string which represents the linear array gages in order of placement. In 

 each place in the string is an identifying number if the gage is functioning 

 or a minus (-) sign if the gage was not used in analysis. This parameter is 

 archived along with analysis results for future reference. In this report, 

 all results are used where six or more gages were functioning, making optimum 

 use of data obtained and providing a reasonably faithful first look at direc- 

 tional spectral structure. 



Directional Spectral Estimation 



107. For the gages in a collection that are retained for analysis after 

 error checking, the next step is estimation of the directional distribution of 

 energy. The computation is done in four parts: (a) Fourier transformation of 

 time series to the frequency domain, (b) conversion of pressure spectra to sea 

 surface variance spectra, (c) computation of cross spectra between all gage 

 pairs for each frequency, and (d) estimation of a directional distribution 

 that corresponds to the spatial variation in cross -spectral density for each 

 frequency. 



Fourier transformation 



108. Fourier transformation is done by conventional methods. The 

 16,384-point time series for each gage is divided into 15 half -overlapping 



41 



