Unsaturated flow in spatially variable fields: 1. Derivation of models of infiltration and redistribution

Models of water flow in the upper soil layer of spatially variable fields are developed. Field variability is assumed to take place in the horizontal plane. The saturated hydraulic conductivity is assumed to be a random variable of lognormal distribution, and head suction and moisture content are related to it by simple analytical relationships. The aim of the study is to derive the expectation and variances of the moisture content, suction heads, hydraulic conductivity, and water flux as functions of depth and time for infiltration and redistribution. Toward this aim a simplified solution of vertical flow in a homogeneous column, based on the concept of moving front, is developed. The statistical procedure for using this solution in a spatially variable field is outlined.