Stochastic modeling of unsaturated flow in heterogeneous soils with water uptake by plant roots: The Parallel Columns Model

Abstract

The effects of spatial variations in soil hydraulic properties and in water uptake by plant roots on the spatial distribution of matric potential (ψ) and saturation (S) were investigated. A stochastic‐analytic model for one‐dimensional steady state unsaturated flow including water uptake by plant roots was developed and tested. The model is based on the small‐perturbation approximation in two soil parameters characterizing the unsaturated hydraulic conductivity and water retention, and a plantrooting depth parameter. The soil is considered as made of decoupled soil columns with different properties. The model provides closed‐form expressions for the spatial moments of soil water matric potential and saturation using statistical information on the soil properties and plant attributes as input. The proposed model favorably compared with Monte Carlo simulations using synthetically generated random fields of soil properties and plant‐rooting depth. The results indicate that (1) there is a region above the water table where the variances of ψ and S undergo a sharp decrease from their stationary values to zero at the water table; (2) for a small enough steady surface flux this transitional region can occupy the entire unsaturated zone; (3) water uptake by plant roots skews both the means and the variance profiles of ψ and S such that they may never attain stationarity; and (4) the saturation variance profile is extremely sensitive to variations in ψ due to the nonlinear relationship between ψ and S.