spectrum. Surface root-mean-square (rms) values were obtained from the 

 compensated energy at each spectral period. 



Since 1972, four simultaneous 20-minute records from each of the 

 three gages included in the time-shared recording sequence are processed 

 daily. More records are processed during special studies. The records 

 processed from gages 1, 2, and 3 of the Pt. Mugu array start about 0100, 

 0700, 1300, and 1900 hours (P.s.t.)- The significant wave height, the 

 distribution function, the first five moments of the distribution, and 

 the pressure spectra are computed for these records in a study of wave 

 record variability. These records are not analyzed for wave direction. 



1. Computation of Wave Direction . 



For a long-crested sinusoidal wave with frequency o^, propagating 

 in direction a^ (Fig- 8) , the phase difference between locations 1 and 

 2 with coordinates (X]^,y]^) and (X2,y2) respectively, is given by: 



"^12 " ^^[(^1 - ^2) ^°^ ^fh + (yi " ^2) 2i" "'ml ' (2) 



where k^ = 27t/L^ is the wave number associated with frequency a^, 

 and L^ is the wavelength. The subscript is used to indicate the 

 possible presence of different wave trains with different frequencies 

 and directions . 



The addition of the wave profile, rig, at a third noncolinear loca- 

 tion allows solving for the sine and cosine of af^. Thus, a unique solu- 

 tion for the wave direction is obtained from the following equation when 

 the signs of numerator and denominator are considered. (see App. A.): 



aci. = tan' 



"[(x^ 



- ^3^ ^2 - 



t-1 



- x^) 3'i3]/d' 



_[(yi 



- 72) *13 - 



Cxi 



- 73) ^12]/D_ 



(3) 



where $-^3 is the phase difference between the third and first locations 

 and D is a function of gage separation. 



Phase differences between locations for each different wave period 

 are the only lonknowns in the right-hand side of equation (3) - Estimates 

 of a representative phase difference between gage pairs for bands of 

 constant frequency width are easily computed from cross -spectra of the 

 wave (pressure) records. These spectra give, for each band, average 

 values of the covariance of the wave records along two perpendicular 

 directions. 



Substitution of these representative values of phase difference into 

 equation (3) affords an expedient and economic means of obtaining esti- 

 mates of a "representative" wave direction for each of the spectral 

 bands, provided the results are of engineering use. The agreement among 



