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Hydrodynamic models employed for computing flood discharges 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. This paper attempts to derive, under simplified conditions, error equations for the KW and DW approximations for space-independent as well as for time-independent flows, which provide a continuous description of error in the flow-discharge hydrograph. For space-independent flows, a dimensionless parameter gamma is defined which reflects the effect of initial depth of flow, channel-bed slope, lateral inflow, and channel roughness. For time-independent flows, the dimensionless parameter is the product of the kinematic wave number and the square of the Froude number. The kinematic wave, diffusion wave end dynamic wave solutions are parameterized through these parameters. By comparing the kinematic wave and diffusion wave solutions with the dynamic wave solution, equations are derived in terms of these parameters for the error in the kinematic wave and diffusion wave approximations. (MM).