the basic equations when they are either equivalent to zero or are negligible, 

 but accurate solutions can be achieved only by retaining the full two- 

 dimensional characteristics of the surge problem. Various simplifications 

 (discussed later) can be made by ignoring some of the physical processes. 

 These simplifications may provide a satisfactory estimate, but it must always 

 be considered as only an approximation. 



In the past, simplified methods were used extensively to evaluate storm 

 surge because it was necessary to make all computations manually. Manual 

 solutions of the complete basic equations in two dimensions were prohibitively 

 expensive because of the enormous computational effort. With high-speed 

 computers it is possible to resolve the basic hydrodynamic relations 

 efficiently and economically. As a result of computers, several workers have 

 recently developed useful mathematical models for computing storm surge. 

 These models have substantially improved accuracy and provide a means for 

 evaluating the surge in the two horizontal dimensions. These more accurate 

 methods are not covered here, but they are highly recommended for resolving 

 storm surge problems where more exactness is warranted by the size or 

 importance of the problem. A brief description of these methods and 

 references to them follows. 



Solutions to the basic equations given can be obtained by the techniques 

 of numerical integration. The differential equations are approximated by 

 finite differences resulting in a set of equations referred to as the 

 numerical analogs. The finite-difference analogs, together with known input 

 data and properly specified boundary conditions, allow evaluation at discrete 

 points in space of both the fields of transport and water level elevations. 

 Because the equations involve a transient problem, steps in time are 

 necessary; the time interval required for these steps is restricted to a value 

 between a few seconds and a few minutes, depending on the resolution desired 

 and the maximum total water depth. Thus, solutions are obtained by a 

 repetitive process where transport values and water level elevations are 

 evaluated at all prescribed spatial positions for each time level throughout 

 the temporal range. 



These techniques have been applied to the study of long wave propagation 

 in various waterbodies by numerous investigators. Some investigations of this 

 type are listed below. Mungall and Matthews (1970) developed a variable 

 boundary, numerical tidal model for a fiord inlet. The problem of surge on 

 the open coast has been treated by Miyazaki (1963), Leendertse (1967), and 

 Jelesnianski (1966, 1967, 1970, 1972, 1974, and 1976). Platzman (1958) 

 developed a model for computing the surge on Lake Michigan resulting from a 

 moving pressure front, and also developed a dynamical wind tide model for Lake 

 Erie (Platzman, 1963). Reid and Bodine (1968) developed a numerical model for 

 computing surges in a bay system, taking into account flooding of adjacent 

 low-lying terrain and overtopping of low barrier islands. 



Subsequently, Reid et al. (1977) added embedded channels to the model to 



simulate rivers and channels in a bay area. An alternative approach to 



resolving small-scale features such as channels and barriers is provided by 

 the numerical model of Butler (1978a, 1978b, 1978c, 1979). 



(2) Storm Surge on the Open Coast . Ocean basins are large and deep 

 beyond the shallow waters of the Continental Shelf. The expanse of ocean 



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