3. Wave Gage Data Collection and Analysis . 



During the period 30 July 1974 to 6 May 1975, two total pressure sensors 

 were located near the bottom in an approximate 6-meter water depth, separated 

 by approximately 23 meters; the geometric characteristics of the gage instal- 

 lations are presented in Figure 15. Pressure records, which were recorded in 

 digital form approximately every 2 hours, contained 4,096 data points at 0.25 

 seconds each, resulting in a record length of 17.07 minutes. In order to cal- 

 culate P£s at breaking, the following steps were carried out: (a) Calculation 

 of the frequency-by-frequency wave direction and energy at the location of the 

 wave gages; (b) transformation of the wave spectrum to the breaker line, in- 

 cluding shoaling and refraction effects; and (c) computation of P^g at the 

 surf line. Each of these is described below. 



-► X ( normol to contours ) 

 Gage 1 



Figure 15. Characteristics of a two-gage array at Channel 

 Islands Harbor, California. 



a. Calculation of VJave Characteristics at Wave Gages . The pressure time 

 series were analyzed using a standard fast Fourier transform (FFT) program to 

 determine the coefficients. For example, the time series from gage 1 is rep- 

 resented by 



i2TTnj 



-1 — rr 

 P^(tj) = E [a^(n) - ib^(n)Je 



(10) 



in which i = /-I, and N is the total number of data points (N = 4,096) for 

 each gage. 



The FFT coefficients are defined in terms of the pressure time series as 



i2iTnj 



1 N " N 



ai(n) - ibi(n) = - Z^ Pi(tj)e (11) 



and the a^ (0) term represents the mean of the record. In calculating the FFT 

 coefficients, there are a large number of "tapers" (or windows) that may be 

 used to reduce the adverse effects of spectral leakage which arises due to 

 representing an aperiodic time series by a periodic series (Harris, 1976). 

 These tapers all have the form 



29 



