Fast Approach for Unsteady Flow Routing in Complex River Networks Based on Performance Graphs

Abstract

This paper presents a new model for unsteady flow routing through dendritic and looped river networks based on performance graphs. The model builds on the application of a hydraulic performance graph (HPG) to unsteady flow routing introduced in a previous study and adopts the volume performance graph (VPG) introduced in another study. The HPG of a channel reach graphically summarizes the dynamic relation between the flow through and the stages at the ends of the reach under gradually varied flow (GVF) conditions, and the VPG summarizes the corresponding storage. Both the HPG and VPG are unique to a channel reach with a given geometry and roughness and can be computed decoupled from unsteady boundary conditions by solving the GVF equation for all feasible conditions in the reach. Hence, in the proposed approach, the performance graphs can be used for different boundary conditions without the need to recompute them. Previous models based on the performance graph concept were formulated for routing through single channels or channels in series. The new approach expands on the use of HPG/VPGs and adds the use of rating performance graphs for unsteady flow routing in dentritic and looped networks. The applicability of the proposed model to subcritical unsteady flow routing is exemplified through a looped network, and its simulation results are contrasted with those from the well-known unsteady Hydrologic Engineering Centers River Analysis System model. The results show that the present extension of application of the HPG/VPGs appears to inherit the robustness of the HPG routing approach in a previous study. The unsteady flow model based on performance graphs presented in this paper can be extended to include supercritical flows.