5.2-Accuracy of hydrodynamic models of free surface flows

Abstract

Hydrodynamic models of overland flow and channel flow are based on the shallow water-wave theory that is described by the St. Venant (SV) equations. These models are derived from either the kinematic-wave (KW) approximation, the diffusion-wave (DW) approximation or the dynamic-wave (DYW) representation of the SW equations. In the studies reported to date, different types of criteria have been established to evaluate the adequacy of the KW and DW approximations, but no explicit relations either in time or in space between these criteria and the errors resulting from these approximations have been derived yet. Furthermore, when doing hydrologic modeling, it is not evident if the KW and DW approximations are valid For the entire hydrograph or a portion thereof. In other words, most of these criteria take on fixed point-values for a given rainfall-runoff event. This paper attempts to derive, under simplified conditions, error equations for the KW or DW approximation for space-independent flows, which provide a continuous description of error in the flow-discharge hydrograph. A dimensionless parameter y is defined which reflects the effect of initial depth of flow, channel-bed slope, lateral inflow, and channel roughness. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through y. By comparing the kinematic wave and diffusion wave solutions with the dynamic wave solution, equations are derived in terms of y for the error in the kinematic wave and diffusion wave approximations.