assessing wave-power distributions along shorelines has befe'n set aside. 

 The authors feel, moreover, that the high-speed method ultimately adopted 

 for calculating wave refraction is of such basic importance to the larger 

 problem that a detailed presentation is warranted at this time. 



Earlier Studies of Wave Refraction 



The investigations of Krumbein (1944) and Munk and Traylor (1947) 

 were among the first in which steps were taken to assess the link between 

 wave refraction, the energy distribution along the shore, and beach erosion 

 or deposition. These workers constructed wave-refraction diagrams for 

 selected deep-water wave periods by hand-drawn methods, a time-consuming 

 process that at best permits only partial assessment of the effect of a 

 spectrum of waves on shore erosion. 



About ten years ago, Pierson, Neumann, and James (1953) considered 

 wave refraction effects in some detail and concluded (1953, p. 186) that 

 to use only significant height and the average "period" of the waves in 

 deep water and to refract the waves with these two numbers will lead to 

 totally unrealistic results. These authors went on to outline a method 

 (1953, p. 197) for forecasting wave heights and characteristics at a point 

 in shallow water near a coast. The method involves construction of a 

 large number of ray diagrams by graphical methods. 



Except for the great amount of work involved, the method holds 

 promise for a realistic assessment of energy distributions along a shore- 

 line, assuming the deep-water spectra can be adequately approximated. 

 Although more "practical" methods for determining wave refraction (cf. 

 Silvester, 1963) and for assessing wave energy along coasts (cf . Walsh, 

 Reid, and Bader, 1962) have been proposed, the present authors feel that 

 the adequate treatment of the problem of energy inflow must of necessity 

 include large-scale computations. The treatment of wave refraction, for 

 example, should be as thorough as that outlined by Pierson, Neumann, and 

 James (1952, p. 197), and this requires many man hours. The advent of 

 high-speed computers offers the possibility of significant reductions in 

 the time required for construction of refraction diagrams, wave spectral 

 forecasts, and resultant distributions of energy at the shore. The 

 machine methods given below for constructing refraction diagrams represent 

 a step in the attempt to develop a comprehensive computer program for the 

 routine determination of wave energy along shorelines. 



Scope of Present Study 



It will be assumed that the deep-water wave spectral periods, heights, 

 and directions are known, and that they may serve as input to a computer 

 program for determining wave refraction as part of an overall method such 



