Mathematical Modelling of Plant Root Water Uptake under Heterogeneous Soil Conditions

Abstract

This paper introduces a nonlinear mathematics model of plant root water uptake in heterogeneous soil based on the coupled soil–plant hydrodynamics. The process of variably saturated water flow and moisture extraction mechanisms is described by Richards' partial differential equation integrated with spatially distributed root uptake sink functions. Discretization for numerical approximation is used on adaptive heterogeneous grids: finite difference and finite element discretization schemes. The model includes the variability in hydraulic conductivity, soil water retention relationships, and uptake dynamics that are dependent on stress. The iterative Newton–Raphson formulations are used to study the stability and convergence for the nonlinear coupled system. Numerical modelling shows that under different boundary conditions, the moisture distribution, the hydraulic gradient and the ability of the root zone to extract water from the soil are markedly influenced by the degree of soil heterogeneity.Moisture distribution, hydraulic gradient and root-zone extraction efficiency vary significantly as a function of soil heterogeneity under different boundary conditions, as demonstrated by numerical modelling. The proposed framework enhances the prediction of irrigation and sustainable agriculture water management.