Areal infiltration modeling over soils with spatially-correlated hydraulic conductivities

We study the problem of field-scale infiltration over soils where spatial variability of saturated hydraulic conductivity is represented by a homogeneous correlated lognormal random field. The Green-Ampt equation was used to describe infiltration at the local scale. Cumulative infiltration, F, was initially used as the independent variable to develop expressions for the ensemble mean and variance of field-scale infiltration under both constant and time-dependent rainfall rates. Analytical expression was derived for the expected time it takes for a given areal depth of water to infiltrate into the soil. Approximate expressions based on a series expansion and a parameterization of the local cumulative infiltration were also presented for describing the ensemble- averaged field-scale infiltration. These results were compared with extensive sets of Monte Carlo simulations for a wide variety of cases. The simulations revealed that the proposed formulations provide an adequate estimate of field-scale infiltration, and that the variance of field-scale infiltration could 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 were also presented.