Convective-diffusive model of two-dimensional root growth and proliferation

Simulations of crop productivity and environmental quality depend strongly on the root activity model used. Flexible, generic root system models are needed that can easily be coupled to various process-based soil models and can easily be modified to test various hypotheses about how roots respond to their environment. In this paper, we develop a convective-diffusive model of root growth and proliferation, and use it to test some of these hypotheses with data on the growth of roots on potted chrysanthemum cuttings. The proliferation of roots is viewed as a result of a diffusion-like gradient-driven propagation in all directions and convection-like propagation downwards caused by geotropism. The finite element method was used to solve the boundary problem for the convective-diffusive equation. To test hypotheses, we wrote modules in a way that caused a test parameter to be zero, should the hypothesis be rejected. These modules were added or removed to test each hypothesis in turn and in various combinations. The model explained 92% of the variation in the experimental data of Chen and Lieth (1993) on root growth of potted chrysanthemum cuttings. For this dataset the following hypotheses were accepted: (1) root diffusivity (colonization of new soil) did not depend on root density, (2) there was no geotropic trend in root development, (3) potential root growth increased linearly with root density, (4) there were (at least) two classes of roots with different rates of growth and proliferation, and (5) potential root growth rate decreased with distance fl om the plant stem base.