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.

Reduced complexity models for probabilistic forecasting of infiltration rates

“…The rationale for, and implications of, neglecting the horizontal component of flow velocity can be found in [9,26,16] and other studies reviewed in the introduction. This assumption obviates the need to solve a three-dimensional flow problem, replacing the latter with a collection of N one-dimensional flow problems to be solved in homogeneous soil columns with random but constant hydraulic parameters.…”

“…Stochastic analyses of the Richards equation with the Dagan-Bresler parameterization can be found in [26,44]. Their counterparts based on the Green-Ampt equation were found to yield accurate predictions of infiltration into heterogeneous soils [6] and have been adopted in a number of subsequent investigations, e.g., [16,19,20,42].…”

Influence of root resistivity on plant water uptake mechanism, Part II: analytical solutions for low/moderate soil-root conductivity ratio

“…Raats (1976) presented several analytical solutions for special cases of the flow equation with water extraction. Often to attain an analytical solution to flow problem and to simplify its mathematical derivation the RWU is assumed to be an exponential function of rooting depth (Rubin and Or 1993;Coelho and Or 1996;Basha 2000;Schoups and Hopmans 2002;Yuan and Lu 2005). However, due to the strong nonlinearity of the problem, most investigations apply various numerical and empirical models for analyzing dynamics of water propagation through the root zone (e.g.…”

Use of Descriptive Statistical Indicators for Aggregating Environmental Data in Multi-Scale European Databases

“…In literature, upscaling is defined as the process that replaces a heterogeneous domain with a homogeneous one in such a manner that both domains produce the same response under some upscaled boundary conditions (Rubin, 1993). The difficulty in upscaling stems from the inherent spatial variability of soil properties and their often nonlinear dependence on state variables.…”