depth values. Where these charts did not offer coverage, depths were 

 picked off charts 1222 and 1227. Smoothed contours of the depth values 

 at grid points appear on Figure 2. 



Deep-water starting points and directions for the 52 wave rays of 

 the example are given in Tables 1 and 2, and are shown plotted on Figure 

 3. An example of the coding of the wave-ray and wave- velocity input data 

 is given under the heading "INPUT" in Appendix D, 



Computer Operations 



Programs Used . For each wave period selected for the investigation, 

 a table of depths and their associated wave velocities is prepared. This 

 is accomplished by solving the following equation (U. S. Army, Corps of 

 Engineers, 1942; U. S. Navy, Hydrographic Office, 1944; Mason, 1950) by 

 an iteration process: 



r _ gT 2nd 

 C - — tanh Ytc) 



where C = wave velocity, g = acceleration due to gravity, T = wave period, 

 and d = water depth. This equation has been programmed, and a sample 

 depth-velocity table has been prepared for T = 4 seconds. (See OOMPV in 

 Appendix A. ) 



As in other wave refraction studies (Pocinki, 1950; Pierson, 1951; 

 Pierson, Neumann, and James, 1953), it is assumed that wave velocity is a 

 function only of water depth and wave period, as expressed by the above 

 equation. Various factors such as bottom friction, percolation, reflection, 

 currents, and winds are considered as having no effect on the refracting 

 waves. 



Given the absolute value of a water depth, it is possible to check 

 the appropriate table, which has been previously prepared, for the 

 associated wave velocity. Preparation of an entire velocity grid for 

 each wave period to be studied is then carried out. This procedure has 

 also been programmed, and a portion (from X = to X = 19, and from 

 Y = to Y = 2) of the depth grid described abbve has been derived for 

 T = 4 seconds. (See DISTV in Appendix B.) 



The procedure for determining the wave-velocity value at an 

 arbitrary point in a grid cell involves fitting a plane to the velocity 

 values at the four grid intersections that bound the grid cell in question. 

 This linear surface is fit by the least-squares method, using an equation 

 of the form: 



C = El + E2X + E3Y 



