A semi-analytical model of expected areal-average infiltration under spatial heterogeneity of rainfall and soil saturated hydraulic conductivity

A semi-analytical model for the estimate of expected areal-average infiltration rate at hillslope scale is presented. It accounts for spatial heterogeneity of the saturated hydraulic conductivity, Ks, and rainfall rate, r. The Ks field is characterized by a lognormal probability density function while the rainfall rate r is represented by a uniform distribution between two extreme values. The model formulation relies upon the use of cumulative infiltration as the independent variable which is then expressed as a function of an expected time for use in practical applications. The solution is applicable for those ranges of r and Ks that allow for neglecting the infiltration of surface water running downslope into pervious soils (run-on process). The model was tested by comparisons with Monte Carlo simulations carried out for a variety of coefficients of variation of r and Ks over a clay loam soil and a sandy loam soil. The model was found to be very reliable both with coupled spatial variability of r and Ks and when only one variable is characterized by spatial heterogeneity while the other is uniform.