Local- and field-scale infiltration into vertically non-uniform soils with spatially-variable surface hydraulic conductivities

We studied the problem of local- and field-scale infiltration over a particular class of heterogeneous soils. At the local scale, the soils are described as being vertically non-uniform, with the saturated hydraulic conductivity continuously decreasing with depth according to a power law function. Analogous to the Green–Ampt model, analytical expressions are first developed for local-scale infiltration using a sharp front approximation, and model results are compared with numerical solutions of the Richards equation. These results show that saturation does not occur from below in soils with such vertical non-uniformity, thereby allowing for the use of a sharp front approximation. Because of vertical non-uniformity, ponding conditions are achieved locally even for rainfall rates less than the surface saturated hydraulic conductivity. Furthermore, infiltration rates asymptotically approach zero at long times. To determine field-scale infiltration properties, the spatial variability in the surface saturated hydraulic conductivity is represented by a log-normal random field. Using cumulative infiltration as the independent variable, expressions are developed for the ensemble mean of field-scale infiltration and the expected time for a given depth of water to infiltrate over the field. Surface horizontal heterogeneity is found to control fieldscale infiltration at small times, whereas local vertical non-uniformity exerts a strong control at long times.