as proposed by Pierson, Neumann, and James (1953). Examples of the 

 machine refraction of six separate combinations of wave period and 

 direction off Virginia Beach, Virginia, are given to illustrate the 

 method of refracting wave rays. The assumptions and methodology used 

 in constructing the wave rays are fully treated, and suggestions for im- 

 proving and amplifying the program are then presented. 



METHOD 



Previous Work 



The presently acceptable method for constructing wave-ray diagrams 

 involves the hand method of graphical construction first proposed by 

 Arthur, Munk, and Isaacs (1952) and later repeated in Pierson, Neumann, 

 and James (1953) and U. S. Army, Corps of Engineers (1961) Technical 

 Report No. 4, of the Beach Erosion Board. This procedure for graphical 

 construction of wave rays involves the use of Snell's Law, 



sm ty 



1 - 



sin 0^2 S 



where for two successive points on a ray, 1 and 2, C = wave velocity, and 

 a = angle between the wave crest and the bottom contours. In the hand- 

 refracting methods, Snell's Law requires the assumption that between points 

 1 and 2 there exist straight and parallel contours. The computer program 

 for-^onstruction of wave rays (that is to be described later) involves the 

 fitting of interpolative surfaces to points of a wave-velocity grid. This 

 program, although requiring certain assumptions of its own, avoids the 

 assumption of straight and parallel contours between successive points on 

 a ray. With this program an expression for ray curvature is solved quite 

 independently of the use of Snell's Law. 



The authors' introduction to the possibilities of computer programs 

 for the numerical construction of wave rays was gained originally through 

 discussions with Lieutenant Gale M. Griswold, then of the U. S. Navy 

 Weather Research Facility, Norfolk, Virginia. Ideas on the subject had 

 appeared in mimeographed reports (Mehr, 1961, 1962a, 1962b; Griswold and 

 Nagle, 1962) and a published paper (Griswold, 1963). A computer program, 

 although not actually operational, was provided by Griswold for develop- 

 ment in this study. (This program will be referred to henceforth as the 

 Griswold-Mehr program. ) 



Construction of Wave Rays 



Selection of Input . The first step in wave-ray determination begins 

 with the construction of a grid of depth values for the area of interest. 



