where C = wave velocity, E's,= coefficients, and X,Y are the grid coor- 

 dinates for the arbitrary point. 



With the least-squares method of surface fitting, it is possible to 

 obtain certain matrices which are used each time the equation of a plane 

 is derived for a grid cell. These matrices have been derived in PRMAT. 

 (See Appendix C. ) That portion of the surface-fitting procedure which must 

 be carried out each time a linear equation is to be derived is given in 

 SURFCE subroutine of MAIN 1620 (Appendix D) and MAIN 7094 (Appendix E) . 



Determination of each desired ray for a given period is accomplished 

 by first specifying origin coordinates and an angle of approach. The actual 

 ray is constructed by plotting and connecting the series of successive 

 calculation points (computed by MAIN 1620, Appendix D, or MAIN 7094, Appendix 

 E) which range across the velocity grid until striking the beach or grid 

 margin, (As discussed by Griswold (1963, p. 1722) the rays may be run from 

 the shore seaward, if the construction of a refraction diagram at a point 

 is desired.) Velocity at each point is calculated as mentioned above; ray 

 curvature (FK) is calculated by using the following expression (Munk and 

 Arthur, 1952) : 



- = M.-"*(S) --A(if)] 



where A = approach angle, as defined in Appendix D. 



In order to determine Xn+1, Yn+i An+1, and FKn+l for calculation point 

 n+1 (with those similar values known for point n) , the following equations 

 (Griswold and Nagle, 1962; Griswold, 1963) are solved by an iteration 

 procedure : 



AA 



= 



(FK + FK , )D 

 n n+l 



n+l 



= 



A + AA 

 n 



A 



= 



^\ ^ \.1> /2 



\.l 



= 



X + D cos A 

 n 



\.l 



= 



Y + D sin A 

 n 



where D equals the incremented distance between points n and n+l. (See 

 MOVE subroutine of MAIN 1620, Appendix D, and of MAIN 7094, Appendix E.) 



