Overland flow and groundwater flow from a steady rainfall of finite duration

The buildup and decay of a laminar or turbulent flow over a sloping plane is treated by the kinematic-wave method, neglecting the slope of the water surface relative to the slope of the plane. The relationships developed show certain distinct differences from those postulated in the unit hydrograph method. However, a comparison of the results of calculations with published experimental measurements shows quite good agreement. The problem is extended to include the case of groundwater flow through a porous medium overlying a sloping impermeable stratum, where water is supplied by infiltration from the ground surface above. Here the depth of water may be appreciable, so that the actual slope of the water surface influences the gravity flow significantly, leading to a nonlinear diffusion problem. Solutions of this problem for the buildup and decay phases are compared with those obtained by the kinematic-wave method, and significant differences are noted for the latter phase. Further, the physical boundary condition at the upper edge of the slope changes at a critical precipitation rate, the depth of water being either finite or zero there depending upon whether the rate is greater than or less than the critical value.