Linear approximation of open-channel flow routing with backwater effects

This paper proposes a new model for linear flow routing in open-channels. The proposed model, called LBLR for Linear Backwater Lag and Route, is a first order with delay model that explicitly takes into account two parameters which are usually neglected: 1) the downstream boundary condition and 2) the nonuniform flow conditions, both of which are shown to have a strong influence on the flow dynamics. The model parameters are obtained analytically from the pool characteristics (geometry, friction, discharge and downstream boundary condition). A frequency domain approach is used to compute the frequency response of the linearized Saint-Venant equations. This model is then approximated by a first order plus delay model using the moment matching method. The proposed model is shown to perform better than existing models when the flow is affected by backwater and/or by different downstream boundary conditions from the one corresponding to uniform flow.