An integrated solution of the overland and subsurface flow along a sloping soil layer

SummaryFlow profiles of surface water passing over a vegetation-free area under a uniform rainfall are investigated by a semi-analytical approach. The ground is considered to be pervious and the soil layer of finite thickness is assumed homogeneous. The Navier–Stokes equations and Biot’s theory of poroelasticity are employed to govern the surface water flow and subsurface water flow, respectively. Since the velocity distributions appear to be still a function of the water depth, a numerical technique is necessary to find the flow profiles on the ground before solving the flow velocity and discharge. A dimensionless parameter related to soil porosity and permeability is proposed to reveal its effect on surface and subsurface water flow. The water depths at the upper boundary for surface water flow also verify the previous research. The present solutions are compared to the conventional solutions and numerical solutions to show the validation.

► Surface flow profiles over an unplanted area with rainfall were investigated analytically.
► A new dimensionless parameter denoting the soil permeability was proposed.
► The non-zero horizontal velocity at the bed surface was found to depend on the soil permeability.
► The water depth at the upper boundary depends mainly on slope, and secondly on soil permeability.
► A new idea to better understand the mechanism of surface and subsurface water flows was proposed.