Hillslope infiltration: Planar slopes

Abstract

The solution of the full nonlinear unsaturated flow equation is given for a problem of infiltration (and associated subsurface flows) into a planar hillslope of a homogeneous isotropic soil with uniform initial moisture content. The solution uses the assumption that, at some distance below the slope crest, a spatial equilibrium is approached with the moisture content (and other properties) independent of downslope coordinate x* and dependent only on the normal coordinate z* and time t. The analysis is found to be generally applicable beyond a small distance from the slope crest (or from a point of slope change). For slope angles less than 30°, infiltration normal to the slope differs relatively little from infiltration from a horizontal surface. Interesting aspects of the solution include a time‐independent total horizontal flow into the slope and a time‐dependent downslope total flow component which behaves as t1/2 at small t and as t at large t. Previously, hillslope flows in these directions have been discussed in terms of soil anisotropy and layering, but these flows in a homogeneous isotropic soil are simple physical consequences of capillarity and gravity. The analysis applies with minor modification to two simple types of hillslope anisotropy: (1) anisotropy parallel to the slope and (2) horizontal anisotropy. Type 1 yields a complicated time dependence of the horizontal flow, and type 2 affects downslope flow similarly. These flow directions will commonly reverse during the course of the infiltration process.