ACCURACY OF KINEMATIC WAVE AND DIFFUSION WAVE APPROXIMATIONS FOR SPACE INDEPENDENT FLOWS

Hydrodynamic models of overland flow and channel flow are based on the shallow water wave theory described by the St Venant (SV) equations. These models are derived from either the kinematic wave (KW) approximation, the diffusion wave approximation (DW), or the dynamic wave (DYW) representation of the SV equations. In studies reported to date, different 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 yet been derived. Furthermore, when carrying out hydrological modelling, it is not evident if the KW and the DW approximations are valid for the entire hydrograph or a portion thereof. In other words, 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 approximations for space independent flows, which provide a continuous description of error in the flow discharge hydrograph. The KW, DW and DYW solutions are parameterized through a dimensionless parameter gamma which reflects the effect of the initial depth of flow, channel bed slope, lateral inflow and channel roughness. By comparing the kinematic wave and diffusion wave solutions with the dynamic wave solution, equations are derived in terms of gamma for the error in the kinematic wave and diffusion wave approximations. The error equations turn out to be the Riccati equation.