Ensemble-Averaged Flow Routing in Channel Networks: Kinematic Wave Equation

Abstract

A new ensemble-averaged kinematic wave equation is derived for the flow routing problem in channel networks. This derivation is performed by ensemble averaging the second-order Taylor series expansion of the point scale kinematic wave equation around the mean value of the equation’s parameters. Utilizing this ensemble-averaged kinematic wave equation, the ensemble-averaged solution for the same ordered channels (according to the Strahler–Horton ordering) are obtained. Instead of solving the flow at each channel one by one, the ensemble-averaged solution is computed for the ensemble of channels that are of the same order within the channel network. Ensemble averaging is only applied to the channel orders that include a sufficient number of channels to form an ensemble of adequate size. Using this methodology, the computational load, parameter data requirements, and time/effort required to set up the model are reduced substantially. Besides the obtained economy in computations, data requirements and effort to set up the model, this methodology also provides satisfactory results when compared to the numerical solutions of the flows within the actual, detailed channel network.