(or a combination of both terms). Other discussions of flow conditions and the sensitivity to the various terms of the flow equations are given in Miller and Cunge (1975), Morris and Woolhiser (1980), and Henderson (1963).

It is stressed that the ultimate objective of this paper is to develop a two-dimensional diffusion model for use in estimating flood plain evolution such as occurs due to drainage system deficiencies. Prior to finalizing such a model, the requirement of including the inertia terms in the unsteady flow equations needs to be ascertained. The strategy used to check on this requirement is to evaluate the accuracy in predicted flood depths produced from a one-dimensional diffusion model with respect to the one-dimensional U.S.G.S K-634 dam-break model which includes all of the inertia term components.

One-Dimensional Analysis

Study Approach

In order to evaluate the accuracy of the one-dimensional diffusion model (equation 22) in the prediction of flood depths, the U.S.G.S. fully dynamic flow model K-634 (Land, 1980a,b) is used to determine channel flood depths for comparison purposes. The K-634 model solves the coupled flow equations of continuity and momentum by an implicit finite difference approach and is considered to be a highly accurate model for many unsteady flow problems. The study approach is to compare predicted: (1) flood depths, and (2) discharge hydrographs from both the K-634 and the diffusion hydrodynamic model (equation 22) for various channel slopes and inflow hydrographs.

It should be noted that different initial conditions are used for these two models. The U.S.G.S. K-634 model requires a base flow to start the simulation; therefore, the initial depth of water cannot be zero. Next, the normal depth assumption is used to generate an initial water depth before the simulation starts. These two steps are not required by the DHM.

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