Velocity Hydrograph Routing to Enable Discharge Estimation at a Channel Section

Recent developments in hydrometric practices enable the measurements of continuous maximum surface velocity of flow passing at a river section and the corresponding water level using a combined surface velocity and water level sensors installed across river bridges. These measurements enable continuous discharge estimation at these river section by employing the well-studied entropy methods. However, the cost of equipping these combined radars at many gauging stations of a river may be prohibitive. But the use of standalone water level radars at many stations may not be cost-wise prohibitive. Taking into consideration of this aspect, the current study proposes a novel method of routing the upstream estimated velocity hydrograph to a desired downstream station of a river reach, which is equipped with a water level sensor, and using the routed velocity hydrograph and the water levels measured at that station, one can estimate the corresponding discharge hydrograph. The proposed study establishes the equation governing the velocity hydrograph propagation in a channel reach which is of the same form as that of the weak-diffusive wave equations governing the discharge and flow depth hydrographs propagation. The derived velocity routing equation is of the same form as the Muskingum routing equation. The parameters of the routing method are estimated using the channel and velocity characteristics of the propagating velocity hydrograph. The proposed velocity routing method is tested by routing the hypothetical velocity hydrographs arrived at by routing a given hypothetical discharge hydrograph defined by Pearson Type-III mathematical function at the inlet of 25 uniform trapezoidal channel reaches each characterised by a unique combination of bed slope and Manning’s roughness characteristics. The benchmark solutions were arrived using the HEC-RAS model. The routed velocity hydrographs enable the close reproduction of the corresponding estimated benchmark velocity hydrographs and, thus, proving the appropriateness of the proposed velocity hydrograph routing method.