Channel-flow response function considering the downstream tidal effect and hydraulic characteristics

Abstract

The channel impulse response function derived from the linearized Saint Venant equations has been widely applied to predict the streamflow discharge. Huang and Lee (2020) indicated that the distribution type of the impulse response function proposed by Dooge et al. (1987a) was restricted because of the constant reference parameters, therefore, they introduced the time-varying reference parameters according to the upstream inflow condition to reinforce the flexibility of adjusting the impulse response function. However, this model, called channel hydrological response function (CHARFU), was merely applicable to a channel under the assumption of a downstream open boundary. This study intended to apply the other impulse response function which was derived from the downstream disturbance and combine this function with the one derived from the upstream input to extend the model applicability in various channel states. To consider the temporal change of the downstream boundary condition, the time-varying reference parameters were also introduced in the function according to the tidal level at the estuary. A routing procedure that explained the integration of the two impulse responses for both upstream and downstream inputs was proposed as well for the runoff simulation of the entire river basin. A series of tests showed that the proposed model could even yield similar hydrographs with the comparative cases that applied the numerical model based on the Saint Venant equations owing to the revision of reference parameters. A practical case of a river basin was also provided to demonstrate the effectiveness of the proposed model to reflect the influence of the downstream tidal level on the simulated hydrograph. Although the proposed linear channel routing method still can not be applied to simulate a channel reach with flow transitions such as a sharp change of water surface elevation due to the assumption of gradually varied flow in the linearized governing equations, it can be more stable than a finite difference model and avoids the latter's occasional numerical oscillations, especially when applied to a shallow channel with an irregular bed.