Drought Flow from Hillslope

Hillslope subsurface drainage is one of the key elements in the hydrology of upland watersheds. This explains or simulates the simple rainfall-runoff response to precipitation and the hydrology under drought conditions. The purpose of this study is the derivation of the solution of the nonlinear partial differential equation to given drought conditions and its comparison with the experimental results. To analyze drought flows, subsurface drainage from a hillslope above a sloping impermeable layer is theoretically and experimentally studied. The resultant governing equation is a nonlinear diffusion equation, which is difficult to solve analytically. The approximate solution obtained by the method of variation is in good agreement with the experimental results. The linearized solution of the nonlinear diffusion equation is also compared with the nonlinear solution. Finally, the effect of the slope angle of an impermeable layer and the applicability of Darcyʹs law to hillslope subsurface flow are discussed.