SUITABILITY OF SIMPLIFIED OVERLAND-FLOW EQUATIONS

A dimensionless formulation of the acceleration terms of the Saint-Ven ant equations is presented for one-dimensional overland flows under ei ther laminar or turbulent conditions. For stationary storms over a pla ne surface of uniform roughness, dimensionless analytical expressions are derived during the rising limb for the local acceleration a(l), a nd during equilibrium for the convective acceleration a(c) and the pr essure gradient a(p) ((13), (14), and (15), respectively). In terms o f the order of magnitude, the three acceleration terms are inversely p roportional to the kinematic flow number K. At equilibrium, the pressu re 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 subc ritical overland flow (a(p) > a(l)* > a(c)*), which in all cases cont rasts with open-channel flows (a(p) > a(c)* > a(l)*). The kinematic w ave approximation is therefore only suitable when both K and Fr are la rge. Improvements using the diffusive wave approximation are only poss ible for subcritical overland flow. Both the diffusive wave and the qu asi-steady dynamic wave approximations are not suitable for supercriti cal overland flow. The analysis of moving storms corroborates these fi ndings in that the local acceleration exceeds the convective accelerat ion. These effects are particularly pronounced during the rising limb of overland flow hydrographs for downstream moving rainstorms.