Distributed approximation of open-channel flow routing accounting for backwater effects

In this article, we propose a new model, called LBLR for Linear Backwater Lag-and-Route, which approximates the Saint-Venant equations linearized around a non-uniform flow in a finite channel (with a downstream boundary condition). A classical frequency approach is used to build the distributed Saint-Venant transfer function providing the discharge at any point in the channel in the Laplace domain with respect to the upstream discharge. The moment matching method is used to match a second-order-with-delay model on the theoretical distributed Saint-Venant transfer function. Model parameters are then expressed analytically as functions of the pool characteristics. The proposed model efficiently accounts for the effects of downstream boundary condition on the channel dynamics.