Unsteady, one‐dimensional flow over a plane—The rising hydrograph

The equations describing overland flow, in three nondimensional forms, are solved for the rising hydrograph by finite‐difference integration of the characteristic equations utilizing a characteristic net. A dry channel was used as an initial condition; the upstream and downstream boundary conditions were zero inflow and critical depth (or no condition for supercritical flow), respectively. A series solution is derived for flow in Zone A , the domain of determinacy of the initial conditions along t = 0. When compared with previous numerical, analytic, and experimental results, the results show that in general there is no unique dimensionless rising hydrograph for overland flow, but that for most hydrologically significant cases the kinematic wave solution gives very accurate results. A single dimensionless parameter was found to be a suitable criterion for choice between the complete equations or the kinematic wave approximation.