Suitability of simplified overland flow equations

A dimensionless formulation of the acceleration terms of the Saint‐Venant equations is presented for one‐dimensional overland flows under either laminar or turbulent conditions. For stationary storms over a plane surface of uniform roughness, dimensionless analytical expressions are derived during the rising limb for the local acceleration a l * , and during equilibrium for the convective acceleration a c * and the pressure gradient a p * ((13), (14), and (15), respectively). In terms of the order of magnitude, the three acceleration terms are inversely proportional to the kinematic flow number K . At equilibrium, the pressure gradient a p * is also inversely proportional to the square of the Froude number Fr . The relative magnitude of the acceleration terms for supercritical overland flow ( a l * > a c * > a p * ) differs from subcritical overland flow ( a p * > a l * > a c * ), which in all cases contrasts with open‐channel flows ( a p * > a c * > a l * ). The kinematic wave approximation is therefore only suitable when both K and Fr are large. Improvements using the diffusive wave approximation are only possible for subcritical overland flow. Both the diffusive wave and the quasi‐steady dynamic wave approximations are not suitable for supercritical overland flow. The analysis of moving storms corroborates these findings in that the local acceleration exceeds the convective acceleration. These effects are particularly pronounced during the rising limb of overland flow hydrographs for downstream moving rainstorms.