Table 1. Percent of observations where the largest 

 departure of the standard deviations from 

 the mean in the observations was as indi- 

 cated (871 observations in 1970). 



Deviation from mean (pet) 



Percent of Observations 



< 2 



41 



3 to 10 



52 



11 to 20 



1 



> 20 



6 



This comparison indicates the system operated consistently. The 

 field wave records used for wave direction computation (discussed later) 

 were chosen from the observations in Table 1, for which the standard 

 deviations from all gages differed by 3 percent or less from their mean 

 and for which the average significant wave height (uncompensated for 

 attenuation with depth) was above 0.61 meter. 



Fourier analysis provides a reliable procedure for obtaining the 

 periods of the most important waves. A Fourier analysis of sea-surface 

 elevation (or pressure) with time results in the distribution of energy 

 with frequency, usually referred to as the energy spectrum. The energy 

 spectrum for the record from gage 5 in each of the eight daily observa- 

 tions was computed using the Fast Fourier Transform algorithm developed 

 by Cooley and Tukey (1967). The first 1,024 seconds of the 20-minute 

 record was used in this computation. Gage 5 was chosen because of a 

 good history of performance. 



Fast Fourier Transform computations yield the contribution to the 

 v^ariance at each of a set of frequencies which are harmonics of a funda- 

 nental given by the inverse of the record duration, T. In this study, 

 the frequencies of these harmonics are referred to as spectral frequencies., 

 md the corresponding periods, given by their inverse, as spectral periods. 

 ?he energy content between 32 seconds and 3 seconds was used to normalize 

 ;he spectrum. The lower limit on period was estimated from the thickness 

 )f the water column above the pressure sensors. A summarized spectrum 

 Fig. 7) was formed by combining the energy content in 11 adjacent spec- 

 ral periods. The band width in the summarized spectrum was slightly 

 arger than 10~^ hertz (0.0107 hertz). The energy appearing at each 

 pectral period in the pressure spectrum was compensated for attenuation 

 ith depth by using the classical hydrodynaraic pressure correction: 



F(k,h) 



cosh kh 

 cosh kAz 



(1) 



here k is the wave number, h the water depth, and Az the vertical 

 istance of sensor from bottom. This resulted in a surface or compensated 



16 



