Channel hydrological response function considering inflow conditions and hydraulic characteristics

Abstract

To bypass the problem of numerical instability in conducting the channel routing system, the application of an impulse response function based on the linearization of Saint Venant equations has been an alternative for predicting streamflow discharge. However, the distribution type of the impulse response function proposed by Dooge et al. (1987a) is restricted during a flood, so this approach cannot adequately describe flow response in practical applications. In considering that the flow response in a natural channel is usually influenced by the shape of the cross-section, the terrain of channel bed and the discharge of the moving flood, this study focuses on improving the original unit impulse function by conducting two aspects of analysis: (1) the distribution of unit impulse response function was changed with time by adjusting the reference parameters according to the inflow condition and the hydraulic variables; (2) the outcome of this modified linear approach was thoroughly examined by comparing the simulated results with that adopting the original linear channel method and the numerical scheme based on the nonlinear Saint Venant equations. Moreover, for achieving the simulation of a whole river basin, a complete executing procedure was provided to explain the connection between the upstream inflows, lateral flows, and the linear channel response of each channel reach. A series of tests showed that the proposed method can produce approximated hydrographs in comparison with numerical simulation results owing to the flexibility of the impulse response function although the linear channel routing adopts simplified mathematical operations. A case study of a natural river basin also demonstrated the applicability of the modified channel response system.