Similarly, the autocorrelation between wave periods is 



12 



R^(x)=y^ti 



I T(j) T(j - T) 



J-T 



I t2(j) I t2(j) 

 j=T+l j = l 



(31) 



where R^^Ct) is the autocorrelation between wave periods and T( j ) the dif- 

 ference between period of the j ' th wave and the mean period for the record. 



Wave amplitude is defined as the absolute value of the elevation differ- 

 ence between a crest or trough and the mean elevation for the record. An 

 autocorrelation between amplitude can also be computed as 



2J 



I A(j) A(j - t) 



Rl(.)=i=^p 



I A2(j) ^l ' A2(j) 



j=T+l j = l 



(32) 



where ^^(t) is the autocorrelation between wave amplitudes and A( j ) the 

 difference between j ' th amplitude and the mean amplitude for the record. 



c. Squared Time Seri es . Another approach to the study of wave grouping 

 involves the analysis of the squared time series 



- ,r2 



y(nAt) = y^(nAt) , n = 1, 2, 3, ..., N 



(33) 



The squared time series, y(nAt), can be subjected to the standard FFT analysis 

 with no data window. The spectrum obtained from y(nAt) for a Columbia Light 

 record is shown in Figure 15. Wave groups, produced by interference between 

 nearby frequencies in the original time series, appear as very low frequency 

 energy in the spectrum of the squared time series. A potential difficulty 

 with this approach arises because higher apparent frequencies are created in 

 squaring the time series. Energy at very high frequencies can, through 

 aliasing, distort the low-frequency part of the spectrum of the squared time 

 series. 



A better definition of important very low frequencies and their associated 

 amplitudes and phases can be obtained by MRS analysis. This approach was used 

 for added insight in one case. 



V. RESULTS 



1 . Component Am pl itudes and Phases . 



The MRS analysis has been applied to selected time series from the three 

 field sites. A summary of the analyses is given in Table 3, including record 

 length, number of constituents retained from MRS analysis, percent variance in 

 the time series explained by the constituents, percent variance explained by 

 the first 10 constituents, and number of constituents at second harmonic fre- 

 quencies. The MRS was more effective at explaining variance in the Columbia 

 Light and South Pass records than in the South Haven records. At least one 

 second harmonic constituent was selected in every Columbia Light analysis. 



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