Areal infiltration modeling over soils with spatially correlated hydraulicconductivities

We study the problem of field-scale infiltration over soils where spatial v ariability of saturated hydraulic conductivity is represented by a homogene ous correlated lognormal random field. The Green-Ampt equation was used to describe infiltration at the local scale. Cumulative infiltration, F, was i nitially used as the independent variable to develop expressions for the en semble mean and variance of field-scale infiltration under both constant an d 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 paramet erization of the local cumulative infiltration were also presented for desc ribing the ensemble-averaged field-scale infiltration. These results were c ompared with extensive sets of Monte Carlo simulations for a wide variety o f cases. The simulations revealed that the proposed formulations provide an adequate estimate of field-scale infiltration, and that the variance of fi eld-scale infiltration could be parameterized through a simple scaling rela tionship in terms of the correlation length of the saturated hydraulic cond uctivity field. Simplified expressions for the variance under asymptotic co rrelation lengths were also presented.