A linear-interpolation scheme (using the least-squares 

 method) is used in determination of wave velocity at a given 

 point along a ray. Ray curvature is then calculated at this 

 point and an iteration procedure is solved to obtain the 

 position of the next point. The ray terminates at the shore 

 or grid border. 



An example of usage of the programs is presented in which 

 52 rays for waves of 4- and 6-second period, from six different 

 deep-water origin points, are brought into the Atlantic shore- 

 line of the City of Virginia Beach, Virginia. 



The procedure outlined is in the developmental stage, 

 and suggestions for improvements are given that should offer 

 a quick, accurate, and objective method of constructing wave 

 rays. 



INTRODUCTION 



Background of Project 



An ultimate understanding of the changes in topography of a given 

 shoreline will be derived from a considerably fuller knowledge of the 

 input and transformation of energy along the strand than is currently 

 available. Because by far the greatest amount of energy expended in the 

 beach-ocean-atmosphere system is associated with breaking waves in the 

 surf zone, it becomes of the greatest importance to evaluate the long- 

 term distribution of wave energy along the shoreline. This energy dis- 

 tribution depends mainly upon the energy of the original deep-water waves, 

 as modified by refraction when the waves move shoreward through shallow 

 water. 



It was with these general considerations in mind that the authors 

 embarked upon a study of wave refraction at Virginia Beach, Virginia, 

 where previous studies (cf. U. S. Congress, 1953; Harrison and Wagner, 

 1964) suggested the desirability of determining wave power distributions. 

 The authors were armed with an "operational" computer program said to be 

 capable of rapid and accurate calculation of wave-ray paths. As in the 

 case of many "operational" computer programs (cf. the cogent comments of 

 Adams, 1964), the authors soon discovered that they were either in diffi- 

 culty simply trying to make the program operate, or that they were not in 

 agreement with certain of the logical steps involved. It soon became 

 apparent that the entire method needed to be reviewed and revised. 



The emphasis here on development of a numerical method for calcu- 

 lation of wave refraction does not mean that the long-range goal of 



