g = 3ac + b (D-6) 



-k X 

 is assigned as the multiplicand of 1 - exp 1 , the boundary conditions 



are satisfied and the shoreface function becomes 



(l - exp-'^l^) 



To fit a curve to the shoreface of the 49 profiles, and to evaluate 

 the characteristics of -k x, the inshore sector, 300 meters (1,000 feet) 

 ^ X £ c, was used because it was relatively smooth. The shoreface pro- 

 file in the nearshore region, x < 300 meters, was not considered because 

 it is relatively unsteady and is frequently complicated by offshore bars. 

 Because of shape irregularities, the region between c and 3c is not 

 particularly useful in evaluating the goodness of fit of a mathematically 

 generated curve to the actual shoreface profile. Since it is desirable 

 that c, a boundary parameter, be used, and because the landward profile 

 between x = 300 meters and x = c is evaluated, the function may be re- 

 written as 



Zs = g (l - exp c ) (D-8) 



in which f is the exponent defining concavity. Using a computer, 

 values of f from 0.01 to 5.00 were evaluated by trial-and-error 

 comparisons of the actual upper shoreface profile [App. C) and the 

 computed (eq . D-8) upper shoreface profile. The f value was assigned 

 corresponding to the smallest residual value R (in square meters) where 



I {h - ny 



^-2.-1; 



t -^-^ -!- ^ (D-9) 



i c - 300 



in which z. is the calculated depth at x- using an f value, and 

 z^ is the actual depth value at x^; p is the number of distance 

 stations between x = 300 meters and x = c. The y^-l values reference 

 distance from shore. R is, therefore, a distance-weighted scale which 

 references the mean variation of the elevation interval squared between 

 the actual upper shoreface depth and the value calculated according to 

 equation (D-8). The values of f for the 49 profiles are listed in 

 Table 1. The f value chosen varies inversely with the concavity index, 

 I, defined as 



I = ^^ (D-10) 



g/3c 



89 



