Modeling infiltration in hysteretic soils

Abstract

Existing vertical infiltration models either assume a constant infilatration rate at the soil surface and a unique set of soil-water functional relationships (hysteresis is neglected), or use empirical expressions which disregard physical laws. In this article a method for analyzing vertical infiltration in hysteretic soils subject to the random variations of point rainfall in watersheds and a procedure for solving the resulting stochastic partial differential equation is presented. The effect of the time random variability in point rainfall produces a water content process in the upper soil layer which can be modeled as a shot noise process. The hysteretic loops resulting from the natural wetting and drying cycles generate a correlated random soil-water diffusivity process, D. The modeling problem reduces to the solution of the infiltration equation subject to a shot noise boundary condition and a colored noise soil-water diffusivity. A new semi-group solution of this evolution equation is obtained and expressions for sample functions, the mean and the variance of the water content in space and time are derived. A computational procedure for each of the components of the stochastic solution is presented, and suggestions for the reduction of the predicted variance are given. It is hoped that the present methodology will provide the modeler with a better tool to model infiltration in natural soils subject to the uncertainties associated with the rainfall regime and the hysteresis in the soil, and to encourage the use of physically based models for infiltration rather than empirical equations.