where i = V^T and x is now defined as the principal direction of propa- 

 gation. Here, the velocity potential describes only the forward scattered 

 wave field. The assumption made above, concerning the relative magnitude of 

 the diffractive effects, changes the character of the governing equation from 

 elliptic to parabolic. Very efficient computational techniques exist for 

 solving this type of equation. Candel (1979), Radder (1979), Lozano and Liu 

 (1980), Tsay and Liu (1982), Berkhoff, Booy, and Radder (1982), Booij (1981), 

 and Kirby (1983) all applied this approach to study the problem of wave propa- 

 gation over complex bathymetries using finite difference solution techniques. 



10. The "parabolic approximation" method, as it is called, has the fol- 

 lowing disadvantage. It requires that one grid coordinate be approximately 

 parallel to the predominant wave direction. This requirement can conceivably 

 result in erroneous solutions to problems involving complex bathymetries where 

 a dominant wave direction may not be clearly defined. Booij (1981) examined 

 errors associated with the application of different parabolic approximations 

 to solve the problem of oblique wave incidence over a horizontal bottom. To 

 date, nothing has been documented concerning errors which may result from 

 using this method to model wave incidence over arbitrary bathymetry. This di- 

 rectional restriction also implies that more than one grid system may be re- 

 quired in order to simulate a wide range of incident wave directions. The 

 parabolic approximation method is a powerful tool for predicting linear wave 

 transformations, but, it does have some deficiencies. These unaddressed prob- 

 lems currently preclude its incorporation into the regional modeling system, 

 as it is envisioned. 



11. The model presented in this report, RCPWAVE, is an alternative ap- 

 proach for solving the open coast wave propagation problem. It addresses both 

 processes, refraction and diffraction, and can be applied on a regional basis 

 quite economically. The model also contains an algorithm which estimates wave 

 conditions inside the surf zone. This wave breaking model is an extension of 

 the work of Dally, Dean, and Dalrymple (1984) to two horizontal dimensions. 

 Kirby (1983) implemented their one-dimensional breaking model into his para- 

 bolic approximation model. Any short-wave propagation model integrated into 

 the regional system must address the problem of wave transformation within the 

 surf zone where many of the physical processes interact and move sediment. 



