Analysis of a Diffusion Model for Plant Root Growth and an Application to Plant Soil-Water Uptake

This paper considers the problem of modeling crop root growth and soil-water uptake. The development of the plant root is modeled with a nonlinear diffusion equation. Root growth data for corn are used to evaluate the suitability of the model and to estimate the root diffusivity, which is interpreted in terms of plant and soil parameters. The flow of soil-water is assumed to satisfy Darcy's law. Soil-water uptake by the root system is accounted for in the model by a volumetric sink term. The usefulness of the model is discussed and demonstrated by numerical simulations that demonstrate the sensitivity of the soil-water uptake model to the root distribution.