where y^ = distance to the point of breaking 



a = constant to allow sediment transport above mean water line (MWL) 

 (swash transport or transport in region of wave setup) to be 

 represented 



c = a constant establishing the width of the curve (to be determined) 



3 f" 



■^ — ^ (causes / q (y) dy = 1.0) 



: V, J ^ 



c y, 







Based on Fulford's (1982) results and considering a to be proportional 

 to the breaking height divided by the beach slope, the constant of propor- 

 tionality was determined to be unity; i.e., a = ht)/(3h/ay). Using equation 

 (22) and a digitized version of the curve shown in Figure 4, a nonlinear least 

 squares regression was carried out to determine the value of c. A Taylor's 

 series expansion of the form 



f"^ "■ ^ (c,y) = f''(c,y) + fl AC (23) 



where k and k + 1 represent the number of the iteration carried out. Least 

 squares regression minimizes the square of the difference between observed 

 and predicted values with respect to a change in the parameter being 

 computed, or 



3 

 3(AC) 



I ks - ^^'(^'^^ ^ i ''^'\= ° (24] 

 n=l ; 



where fQBS i^epresents the observed values, which in this case is 

 qx(y)oBS- Carrying out the differentiation indicated and manipulating 

 terms, ac can be solved in terms of known quantities. 



An iterative procedure was then used by updating the values of 

 f'^(c,y), 3f/3c, and c until an acceptably small change in c results. For 

 the data herein, the value of c was determined to be 1.25. The final form of 

 sediment transport of a y location in the surf zone results for a shoreline 

 with straight and parallel contours, as 



q (y) = 3^ (, . a)2 e - ^^y ' ^^/(l-25 y,)^' (25) 



(1.25)-^(y^)-^ 



20 



