Rhizosphere models are typically 1D radial symmetric with the root as a boundary condition and root hairs as a reaction term (source/sink term). This rhizosphere representation comprises a model reduction for solute transport from 3D to 1D, which upscales the geometry of the root hairs. Further reduction is common in root architectural models, representing the root as point-sinks in a numerical mesh. We validated whether upscaling root hair geometry results in model-errors for nutrient uptake. We compared three levels of rhizosphere model reduction with varying geometric representation: (1) a 3D model with diffusion around root hairs, solved with a finite element method; (2) a 1D radial model with root hairs as sink term; (3) the root as point-sink. We investigated four different cases: short-thick-coarse, long-thick-coarse, short-thin-dense, and long-thin-dense root hairs. Each case was investigated for ammonium and phosphorus. In most cases, 1D and 3D solutions are close together, indicating that the 1D model reduction is valid. The 1D simulations deviate from 3D for slowly diffusing phosphorus taken up by long, thick, coarse root hairs; however, this is an extreme scenario and shows a theoretical limit. Further reducing the root to a point sink only estimates uptake for the ammonium scenario, which has fast diffusion. The root point sink is sensitive to the mesh resolution. Representing root hairs or roots by sink terms works for small radii or fast diffusing solutes. The 1D radial models can give valid and computationally fast results, but further reduction can lead to errors.
Kuppe et al. (Thu,) studied this question.