LRBF meshless methods for predicting soil moisture distribution in root zone

TL;DR

This paper tackles predicting soil moisture distribution in root zones by coupling unsaturated flow with root water uptake via the Richards equation, incorporating a sink term and Gardner capillary-pressure model. A Kirchhoff transformation reduces nonlinearity, and an LRBF meshless method with implicit time stepping and Picard linearization solves the resulting system, producing sparse matrices that improve conditioning. Two macroscopic root uptake models are examined, and the approach is validated against nontrivial analytical solutions and experimental data across 1D to 3D scenarios, demonstrating high accuracy and computational efficiency. The framework supports irrigation and crop-water-management applications by accurately capturing root-zone moisture dynamics under varying surface fluxes and irrigation schemes.

Abstract

In this paper, we first propose a coupled numerical model of unsaturated flow in soils and plant root water uptake. The Richards equation and different formulations are used in the developed numerical model to describe infiltration in root zone and to investigate the impact of the plant root on the distribution of soil moisture. The Kirchhoff transformed Richards equation is used and the Gardner model is considered for capillary pressure. In our approach, we employ a meshless method based on localized radial basis functions (LRBF) to solve the resulting system of equations. The LRBF approach is an accurate and computationally efficient method that does not require mesh generation and is flexible in addressing high-dimensional problems with complex geometries. Furthermore, this method leads to a sparse matrix system, which avoids ill-conditioning issues. We implement the coupled numerical model of infiltration and plant root water uptake for one, two, and three-dimensional soils. Numerical experiments are performed using nontrivial analytical solutions and available experimental data to validate the coupled numerical model. The numerical results demonstrate the performance and ability of the proposed numerical method to predict soil moisture dynamics in root zone.

Figures (14)

• Figure 1: Schematic of vadose zone.
• Figure 2: Schematic of influence domains $\Omega^{[s]}$ for $n_s=3,~5,~\text{and}~9$.
• Figure 3: Left: measured and computed water content profile for three cases. Right: measured and computed evaporative rate. Symbols present the experimental profile, dashed lines are for exact solution and the solid lines are for approximate solution.
• Figure 4: Case 1: $\alpha=0.01~cm^{-1}$ and $R_0=0.02~h^{-1}$. Comparison of the water content and pressure head results of the approximate and exact solutions. Left: with root water uptake. Right: without root water uptake.
• Figure 5: Case 2: $\alpha=0.1~cm^{-1}$ and $R_0=0.0025~h^{-1}$. Comparison of the water content and pressure head results of the approximate and exact solutions. Left: with root water uptake. Right: without root water uptake.