redundant computations of direction from the 10 three- gage arrays is an 

 indication of the degree of confidence that can be placed on the result- 

 ing directions. 



Directions were computed for a few observations (using the equation 

 below) for the representative phase difference in each spectral band, 

 where again, the sign of numerator and denominator must be considered. 



'12 



= tan' 



Quad/\^ 



A L ^°A J 



Co. 



(4) 



The subscript A in equation (4) indicates the value is for a given 

 spectral band. The cospectrum, Co, and quadrature spectrum, Quad, 

 are defined as : 



Co. = E x^X2 cos (j)22 



Quad^ = E Xj^X2 sin iii-^2 » C^) 



A 



where Xj and X2 are the spectral amplitudes from wave records 1 and 

 2, and Z indicates summation over the adjacent spectral periods com- 

 bined to make up a band. Jenkins and Watts (1968) showed that the defi- 

 nitions in equation (5) are equivalent to the more standard definitions 

 based on correlation functions. 



A computer output for runs using this approach is presented in Appen- 

 dix B. Summaries of the results of the observations at 0700 hours, 25 

 June, and 2010 hours, 28 June, are given in Table 2. The first column 

 in the table gives the period at the center of the band; the second 

 column gives the average percent energy in each band for the five gages. 

 The last 10 columns give the computed "representative" direction of each 

 band for the three-gage array. Directions are measured from the seaward 

 normal with positive values counterclockwise and negative values clock- 

 wise. The table shows that in these two observations disagreements in 

 direction of the order of 20° are obtained for the longer period peaks 

 and of 160° for the shorter period peaks. Examination of the computer 

 output in Appendix B indicates the results are typical. 



The array had been expected to yield directions to better than 20° 

 for periods between 25 and 7 seconds. Understanding of the problems 

 involved was sought by simulating the propagation through the array of 

 narrow-banded wave trains traveling in a specified direction (discussed 

 in next subsection). 



2. Simulated Data Analysis . 



In simulating the wave records for use, special consideration was 

 given to wave period and to the difficulties arising in spectral analysis, 



20 



