An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 2 – Simulating surface water flows with different water wave models

Abstract

The complete Saint Venant equations/2-D shallow water equations (dynamic wave equations) and the kinematic wave or diffusion wave approximations were implemented for 1-D channel network flow and 2-D overland flow in a watershed model, WASH123D. Careful choice of numerical methods is needed even for the simple kinematic wave model. Motha and Wigham (1995) reported numerical oscillation in Galerkin finite element of kinematic wave overland flow. Since the kinematic wave equation is of pure advection, the backward method of characteristics is used for kinematic wave model. A characteristic based finite element method is chosen for the hyperbolic- type dynamic wave model. And the Galerkin finite element method is used to solve the diffusion wave model. Diffusion wave and kinematic wave approximations are found in many overland runoff routing models. The error in these models has been characterized for some cases of overland flow over simple geometry (e.g. Ponce 1978; Singh 2000 and Parlange 1990). However, the nature and propagation of these approximation errors under more complex 2-D flow conditions are not well known. These issues are evaluated within WASH123D by comparison of simulation results on several example problems. The accuracy of the three wave models for 1-D channel flow was evaluated with several non-trivial (trans- critical flow; varied bottom slopes with frictions and non-prismatic cross-section) benchmark problems (MacDonnell et al., 1997). The test examples for 2-D overland flow include: (1) a simple rainfall-runoff process on a single plane with constant rainfall excess that has a kinematic analytical solution under steep slope condition. A range of bottom slopes (mild, average and steep slope) are numerically solved by the three wave models and compared; (2) Iwagaki (1955) overland flow experiments on a cascade of three planes with shock waves; (3) overland flow in a hypothetical wetland (infiltration bed). The applicability of dynamic-wave, diffusion-wave and kinematic-wave models to real watershed modeling is discussed with simulation results from these numerical experiments. It was concluded that kinematic wave model could lead to significant errors in most applications. On the other hand, diffusion wave model is adequate for modeling overland flow in most natural watersheds. The complete dynamic wave equations are required in low-terrain areas such as flood plains or wetlands and many transient fast flow situations.