warranted by the size or importance of the problem. These methods are 

 recommended only if a computer is available. A brief description of 

 these methods and references to them follows. 



Solutions to the basic equations given can be obtained by the tech- 

 niques of numerical integration. The differential equations are approxi- 

 mated 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 evalua- 

 tion 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 propa- 

 gation in various water bodies by numerous investigators. Some investi- 

 gations of this type are listed below. Mungall and Matthews (1970) devel- 

 oped a variable-boundary, numerical tidal model for a fjord inlet. The 

 problem of surge on the open coast has been treated by Miyazaki (1963), 

 Leendertse (1967), and Jelesnianski (1966, 1967, and 1970). Platzman 

 (1958) developed a model for computing the surge on Lake Michigan result- 

 ing from a moving pressure front, and also developed a dynamical wind tide 

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

 a niimerical model for computing surges in a bay system taking into account 

 flooding of adjacent low lying terrain and overtopping of low barrier 

 islands. 



b. Simplified Techniques for Determining Storm Surge . The tech- 

 niques described here for the determination of storm surge are simple, and 

 it is possible to carry out all storm surge calculations manually, using a 

 desk calculator or slide rule. In most cases, however, it is desirable to 

 employ a digital computer for the computations to reduce the effort and to 

 improve accuracy. It is sometimes possible to estimate surge with satis- 

 factory accuracy using a set of simplified equations, if the particular 

 problem is not too complex, and if the simplified technique can be verified 

 from actual prototype field data. Simpler schemes for computing storm 

 surge are obtained by including only those phenomena that appear signifi- 

 cant to the investigation; thus some of the less important terms are 

 omitted from Equations 3-50, 3-51 and 3-52. 



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

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

 ocean basins permits large tropical or extratropical storms to be situated 

 entirely over water areas allowing tremendous energy to be transferred 

 from the atmosphere to the water. Wind-induced surface currents, when 

 moving from the deep ocean to the coast, are impeded by the shoaling 

 bottom, causing an increase in water level over the Continental Shelf. 



3-96 



