the coast and the 180-meter contour were digitized from an overlay 

 of bathymetric charts for the regions concerned. The smooth curve is 

 the result of applying the numerical spline interpolation routine to 

 these points. In reading the discrete positions, both the coastline 

 and the 180-meter isobath have been smoothed subjectively to suppress 

 variations with scale lengths less than the grid scale ultimately 

 employed in the surge calculations. For example, narrow entrances 

 to bays are replaced by a fictitious coastline across the entrance, 

 and the cusp- shaped features are smoothed. 



A method was adopted which minimizes the amount of computer time 

 required to solve equations (9) and (10) by hastening the convergence 

 of the iterative procedure. The method consisted of increasing N 

 at selected iteration intervals. The iterative procedure used to 

 determine the transformation coefficients was terminated if the con- 

 vergence criterion was satisfied or if the available computer storage 

 was exceeded because of increasing N , The convergence criterion 

 was a mean variance of less than 1 square kilometer between the 

 transform-generated curves and that specified. However, for develop- 

 ment purposes, the iterative procedure for the western and central 

 gulf coast and lower east coast areas was continued beyond this 

 criterion to obtain a better fit, 



It is convenient to discuss the mapping of the western and central 

 gulf coast regions at the end of this section since additional testing 

 of the solution to the mapping equations was performed with these 

 areas. Figure 4 shows the shelf region for the eastern gulf coast 

 where the Mississippi Delta is shown as the shaded area. Considera- 

 tion of the numerical time step for the surge algorithm was the prin- 

 ciple reason why the coastline to be mapped did not follow the delta. 

 The reduction in the time step if the actual coastline had been 

 followed would, probably, have been at least tenfold with respect to 

 the one used in the simulation of the storm surge induced by Hurri- 

 cane Camille (Section V) . Since the delta, or really the levee 

 adjacent to the Mississippi River, has a controlling influence on 

 the circulation and surge caused by the hurricane, this geographical 

 feature was included in the surge model as a wall protruding from the 

 coast. The fit of the transform-generated coast and seaward boundary 

 curves with respect to that specified after 1, 20, 40, 80, and 160 

 iterations is shown in Figures 7 through 11, respectively. The suc- 

 cessively better agreement of the mapped curves with respect to that 

 specified is obvious from the convergence table for the gulf coast 

 region of Atchafalaya Bay to Apalachee Bay (Table 1) . The table 

 shows the variance and convergence behavior of selected transforma- 

 tion coefficients as the iteration and N increases. The coast 

 variance in X , the third column of Table 1, is calculated by: 



M 



j^y I |x c (A 1 cc j ,e)) - x 1 ^.^)! 2 (3i) 



j=i 



25 



