A semi analytical solution for rising limb of hydrograph in 2D overland flow

In almost all of the present mathematical models, the upstream subbasins, with overland flow as the dominant type of flow, are simulated as a rectangular plane. However, the converging plane is the closest shape to an actual upstream subbasin. The intricate nature of the governing equations of the overland flow on a converging plane is the cause of prolonged absence of an analytical or semi analytical solution to define the rising limb of the resulted hydrograph. In the present research, a new geomorphologic semi analytical method was developed that tries to establish a relationship between the parallel and converging flows to reduce the complexity of the equations. The proposed method uses the principals of the Time Area method modified to apply the kinematic wave theory and then by applying a correction factor finds the actual discharge. The correction factor, which is based on the proportion of the effective drained area to the analytically calculated one, introduces the convergence effect of the flow in reducing the potentially available discharge in a parallel flow. The proposed method was applied to a case study and the result was compared with that of Woolhiserʹs numerical method that showed the reliability of the new method.