Estimate of areal average infiltration through an equivalent saturated hydraulic conductivity

A simple semi-empirical model for areal average infiltration at slope scale is proposed. It involves the estimate of an equivalent saturated hydraulic conductivity, Kse, which enables us to reduce infiltration into a randomly varying field of saturated hydraulic conductivity, Ks, to a deterministic problem. The quantity Kse is linked with rainfall duration scaled by the time to ponding associated with the average value of Ks. The model has been formulated in a preliminar version for a coefficient of variation of Ks equal to one and incorporates the infiltration of overland flow into saturated and unsaturated areas located downslope. Its validation was performed by a comparison with a coupled numerical solution of the nonlinear kinematic wave equation for overland flow and a Green-Ampt type equation for local infiltration. The proposed model appears to reproduce reasonably well the total volume of overland flow for different rainfall patterns and for fine-textured and sandy loam soils.