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

A new ensemble averaged kinematic wave equation is derived for the flow routing problem in large channel networks. The derivation is done by ensemble averaging the second-order Taylor series expansion of the point scale kinematic wave equation around the mean value of the parameters of the concerned equation. Utilizing this ensemble averaged kinematic wave equation, ensemble averaged solution for the same ordered channels (according to Strahler-Horton ordering) are obtained. Instead of solving each channel flow 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. For channel orders that do not form an ensemble of adequate size, the standard solution method is followed. Using this methodology, the computational load and parameter data requirement are reduced substantially. Besides the obtained economy in computations and data requirement, this methodology also provides excellent results when compared to numerical solutions of the flows within the actual, detailed channel network.