Infiltration Over Soils with Spatially-Correlated Hydraulic Properties

We study the problem of field-scale infiltration over soils where spatial variability of saturated hydraulic conductivity is represented by a homogeneous correlated log-normal random field. The Green-Ampt equation is used to describe infiltration at the local scale in terms of cumulative infiltration. Expressions for the ensemble mean and variance of field-scale infiltration are developed. Analytical expression is derived for the expected time it takes for a given depth of water to infiltrate into the soil. The results are compared with extensive sets of Monte-Carlo simulations for a wide variety of cases. The simulations reveal that the proposed formulations provide an adequate estimate of the field-scale infiltration, and that the variance of field-scale infiltration can be parameterized through a simple scaling relationship in terms of the correlation length of the saturated hydraulic conductivity field. Simplified expressions for the variance under asymptotic correlation lengths are also presented.