On Solving the Flow Equation in Unsaturated Soils by Optimization: Horizontal Infiltration

Recently, integral methods have been developed that provide accurate approximations to the diffusion equation with rapidly varying diffusivity, but require in general some numerical iteration. In the present paper, a new analytical approach is developed which yields optimal approximations without any numerical iteration. The method is applied to the problem of one-dimensional horizontal infiltration of water in soils. In that case it is shown that the sorptivity is an invariant, which can be expressed in terms of the sum of two integrals involving the diffusivity. The analytical results are in excellent agreement with numerical calculations for Yolo light clay.