curve near its terminus that appears out of context when compared to the 

 adjacent wave rays. This is due to a combination of (1) a poor "fit" by 

 the linear-interpolation surface at this point, and (2) poor grid control 

 (i.e., poor representation of depth values recorded on the initial depth 

 grid). Suggestions for elimination of these factors are discussed in the 

 section "Grid Considerations." 



PROGRAM DEVELOPMENT 



The computer programs presented in the appendices have by no means 

 been refined to the fullest extent. At the moment the following factors 

 may be considered of most importance to their continued development: (1) 

 improvement of the surface-fitting scheme for wave velocity interpolation,. 

 (2) improvement of the method of ray-curvature approximation, (3) addition 

 of a provision for changes in grid scale and incremented distance as a ray 

 moves shoreward, (4) refinement of ray-plotting techniques, and (5) testing 

 of the revised program at a suitable place in nature. 



Interpolation Surfaces 



"Forced-cubic" Interpolation Surface. First mentioned by way of 

 review is the surface-fitting scheme for interpolation of wave velocity 

 used in the Griswold-Mehr program. Their scheme involves fitting a cubic 

 surface that (1) passes exactly through the velocity values at the grid 

 intersections of the given grid cell, and (2) is the cubic surface of 

 best fit (by the least-squares method) to the velocity values at the 

 eight grid intersections closest to and surrounding the four grid inter- 

 sections of the given cell. This cubic surface is called a "forced-cubic" 

 surface because it is "forced" to pass through the four innermost velocity 

 values. Because it permits the taking of first and second derivatives for 

 use in wave intensity calculations, as explained by Griswold (1963, p. 1720) 

 it was the first surface-fitting program used in this study. 



An example of the results of its use appears in Figure 9C. It is 

 obvious from the figure that this method of interpolation is invalid. The 

 forced feature of the surface creates undesired ridges and/or troughs in 

 the velocity surface. Thus, depending upon the location of a given calcu- 

 lation point in a grid cell, the ray can be deflected erratically from a 

 "normal" path. Results such as those exemplified in Figure 9C necessitated 

 a search for an interpolation surface that could adequately portray the 

 general trend of wave velocity change in a given cell. 



Quadratic-interpolation Surface . The Griswold^ehr program was 

 altered by insertion of a quadratic surface of best fit (by the least- 

 squares method) subroutine for preparation of the interpolation surface. 

 In order to derive a quadratic surface, at least six data points are 

 necessary. It was decided to use the velocity values at the closest 12 

 grid intersections. The results (Figure 9B) , however, did not yield a 



