APPENDIX D 



METHODOLOGY AND PROGRAM LISTING OF COMPUTER PROGRAM WHICH 

 CONVERTS BATHYMETRIC DATA INTO MONOTONICALLY DECREASING DEPTH CONTOURS 



In order to simulate prototype shorelines (and in this case to help 

 verify the numerical model via Channel Islands Harbor data), the (x, y, z) 

 data points must be transformed into a form suitable for use in the model 

 (i.e., bars can not be present). First, the bathymetric data have to be put 

 into a form with fixed longshore and offshore spacings (i.e., ax and Ay equal 

 constants). This can be accomplished using one of the many available canned 

 programs which do the interpolation. The problem is then one of finding the 

 most suitable value of the constant, A, in the equation h = Ay2/3. 

 However, as is usually the case, the exact location of the shoreline (h = 0) 

 is unknown. In addition, one requires the added constraint is required that 

 the volumes of sediment (or conversely, the water above the profiles) 

 balance. The problem is solved using LaGrange Multipliers and the Newton 

 Raphson technique for non linear equations. 



The equation to be minimized is 



IMAX IMAX 



F(A.ydeli, ydel^, ... ydelj^^^ = .f. .^.^^^meas. ." ^ pred. / (D-1) 



where A is the scale parameter in the equilibrium beach profile, ydel . are the 

 locations of the shoreline for the IMAX profiles, h is the interpilated 

 depth from the survey, and h . is the depth predictea by the equation 



1 J J 



The constraint equation is as follows 



IMAX ( y ^ 

 g(A,ydeli, ... ydelj^^x^ = Vp^^^ = S^ ax|^^/^ 



A(y - ydel.)^/^ dy 



IMAX ^ ./, 



= .2^ I AxA(y, -ydel. ) 5/3^ V^^^3 (D-3) 



where Vp^ed is the predicted volume of water above the profile to the 

 reference datum, V^jeas ^^ the measured volume computed from the survey, ax 

 is the longshore distance between onshore-offshore profiles, and yf is the 

 distance offshore to the last point on each of the measured profiles (it was 

 a constant after the interpolation routine was used). 



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