(4) Cospectra and quad-spectra of the gages are computed using 

 the following relationships (note in computer program index, I is 

 used for frequency counter, n) : 



Cospectra = C12(I) = F1R( I)*F2R(I) + F1I( I)*F2I( I) 

 Quad-spectra = Q12(I) = F1R(I)*F2I( I) - F2R(1)*FU( I) 



in which FIR and F1I are the real and imaginary parts of complex 

 transforms of time series 1: F2R and F2I are the real and imagi- 

 nary parts of complex transforms of time series 2. 



(5) Wave angle is calculated in accordance with equation (19). 



9 (n) = = — U- U • arctan <&§<2>] 

 ' arcosine I k(n)£ C12(n)J 



where k(n) is the wave number calculated via linear wave theory, I 

 the spacing of gages, and 3 the difference in alinement of gages 

 and shoreline in Figure 1 . 



Due to energy leakage problems in spectra, impossible wave angles 

 can result [wave angles with (l/k(n)X. arctan Q12(n)/C12(n)) greater 

 than 1.0]. When this happens, energy is lumped into a separate 

 category for later scaling up of the longshore energy flux. 



(6) The high frequency cutoff in this particular program has been 

 set at 2.09 radians per second, which corresponds to a period of 3 

 seconds or NYFR = 342. This value can be reset in the main program 

 by adjustment of NYFR where 



NAt 

 NYFR = 



T HF 



and N is the number of data points in time series , At the spacing 

 in time of data points, and Tup the high frequency cutoff period. 

 The spatial aliasing frequency is computed in subroutine HFC. 



Energy between the spatial aliasing frequency and the high fre- 

 quency cutoff is put into a special category and used to scale up the 

 final longshore energy flux. 



(7) Each frequency contribution to the onshore energy flux is 

 calculated for the gage site location as follows: 



Onshore energy flux = 2y |F (n)| 2 C (n) cos [0(n)] 



20 



