There are two conditions for which it was not possible to calculate the 

 wave directions Q(n) . These include poorly conditioned wave data, presumably 

 due to spectral leakage, and spatial aliasing due to large separation distance 

 between the two gages. If the data are poorly conditioned for determining 

 wave direction, the absolute value of the quantity within the brackets { - } in 

 equation (19) may exceed unity, a physically impossible condition since the 

 extreme values of the cosine function are ±1 . This tends to occur for the 

 extremely long waves for which the energy is small and the value of k(n) is 

 also small, the latter tending to result in large values of the bracketed 

 quantity. The percentage of energy for which this condition occurred in the 

 analysis of one year's wave data collected at Channel Islands Harbor was 

 relatively small, averaging 2 to 3 percent with a maximum of approximately 

 10 percent. The second condition is related to spatial aliasing and requires 

 that one-half the wavelength be equal to or greater than the projection of the 

 wave gage separation distance in the direction of wave propagation. Referring 

 to Figure 1 , 



L > 21 {cos[0(n) - 3]} max (20) 



which indicates that for the least adverse effects of spatial aliasing, the 

 gages should be on an alinement parallel to the dominant orientation of the 

 wave crests. As will be discussed later, in calculating P» an attempt was 

 made to account for this effect of aliasing by augmenting the calculated 

 values, illustrated as follows by 



E T0T 

 ( p £s>cm= (Wc^T- (2D 



in which the subscripts c and cm indicate calculated and calculated modi- 

 fied, respectively. E TOT an d E represent the total wave energy values 

 and the wave energy not affected by spatial aliasing or poorly conditioned 

 wave data, respectively. The total wave energy is that energy in the wave 

 spectrum below the high frequency spectral cutoff value. 



2. Transformation of Wave Spectrum to Breaker Line. 



At this stage, the wave energy and wave direction in the vicinity of the 

 gages are determined. These values are then transformed to the breaker line 

 accounting for wave refraction and shoaling. 



To determine the wave breaking depth, the onshore-directed energy flux is 

 calculated in accordance with the expression (based on Snell's law of refrac- 

 tion) and equated to an equivalent expressed in terms of wave characteristics 

 at breaking . 



N/2 

 Onshore energy flux = £ y2 [a(n) 2 + b(n) 2 ] C (n) cos 0(n) 



n-1 



(22) 



YE 2 , 



= — - c„, cos e K 



o gb b 



12 



