Root-Water Uptake Model at Heterogeneous Soil Fields

Abstract

A new stochastic model for one-dimensional root-water uptake is developed with main emphasis on its probabilistic structure from random variations in saturated hydraulic conductivity. The resulting model has the form of a two-dimensional Fokker-Planck equation, and its applicability as a model for the probabilistic evolution of the nonlinear stochastic root-water uptake process is explored with the saturated hydraulic conductivity taken as stochastic random field. In order to perform this exploration, the generalization of a one-dimensional numerical scheme for the numerical solution of a two-dimensional Fokker-Planck equation is attempted. The proposed model has the advantage of providing a probabilistic solution to soil-water flow under root-water uptake, from which one can obtain the ensemble average behavior of the soil-water system at the scale of a heterogeneous field soil.