From hydraulic root architecture models to efficient macroscopic sink terms including perirhizal resistance: Quantifying accuracy and computational speed

Abstract. Root water uptake strongly affects soil water balance and plant development. It can be described by mechanistic models of soil-root hydraulics based on soil water content, soil and root hydraulic properties, and the dynamic development of the root architecture. Recently, novel upscaling methods have emerged, which enable the application of detailed mechanistic models on a larger scale, particularly for land surface and crop models, by using mathematical upscaling.

In this study, we explore the underlying assumptions and the mathematical fundamentals of different upscaling approaches. Our analysis rigorously investigates the errors introduced in each step during the transition from fine-scale mechanistic models, which considers the nonlinear perirhizal resistance around each root, to more macroscopic representations. Upscaling steps simplify the representation of the root architecture, the perirhizal geometry, and the soil spatial dimension and thus introduces errors compared to the full complex 3D simulations. In order to investigate the extent of these errors, we perform simulation case studies: spring barley as a representative non-row crop and maize as a representative row crop, and using three different soils.

We show that the error introduced by the upscaling steps strongly differs, depending on root architecture and soil type. Furthermore, we identify the individual steps and assumptions that lead to the most important losses in accuracy. An analysis of the trade off between model complexity and accuracy provides valuable guidance for selecting the most suitable approach for specific applications.