Multiscale mathematical modelling of water and solute movement in plant systems

Abstract

This thesis deals with multiscale mathematical modelling of water and solute movement in soil systems, with particular focus on the soil structures that are formed by agricultural practices. The first mathematical model is developed to describe water movement in a generalised ridge and furrow soil system, which is coupled to dynamic surface water infiltration due to ponding. The model is based on a non-linear Darcy-Richards’ equation in pressure formulation to describe variably saturated soil. This model is then extended and coupled to an advective-diffusion equation for solute movement. Using the mathematical model, we compare water and solute movement in two soil structures: a ridge and furrow soil and a flat field soil. We highlight scenarios that increase the risk of solute leaching in both flat field and ridged soils. We also discuss the key factors affecting solute leaching in these systems. We then focus on the water dynamics in the regions of soil that contain crops. Using the Darcy-Richards’ equation for water movement, we apply multiple scale asymptotic homogenisation to derive an approximate set of equations that captures water movement around crops. We find the approximate equations to be more computationally efficient by a factor of O(10²) when compared to the full equations. Extending this idea, we develop a mathematical model that captures crop growth and its effect on solute movement. The growth and development of the crops is dependent on the cumulative uptake of nutrients available to the plant. The soil is modelled as a poroelastic material that is able to deform due to crop growth. Special attention is paid to the reduction in void space, change in local volumetric water content and the impact on solute movement as the crops increase in size. Multiple scale asymptotic homogenisation is used to derive a set of approximate equations that describe macroscale nutrient movement and crop growth in the soil. This approach increases computational efficient by a factor of O(10³) while maintaining a percentage error of ^<∼ 2%.

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ORCID for Tiina Roose: orcid.org/0000-0001-8710-1063

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