A hybrid analytical-numerical method for solving water flow equations in root hydraulic architectures

Abstract

Abstract In this manuscript, we propose a new method to calculate water flow and xylem water potential distribution in hydraulic architectures (such as root systems) of any complexity. It is based on the extension of the water flow equation analytical resolution of Landsberg and Fowkes for single roots. It consists in splitting the root systems in zones of homogeneous or homogeneously changing properties and deriving the xylem potential and water flow under any given boundary conditions (plant transpiration or collar potential, and potential at soil-root interfaces) without assuming a uniform xylem potential within each zone. The method combines analytical solutions of water flow within the segmented zones with the numerical solution of flow connectivity for the whole root system. We demonstrate that the proposed solution is the asymptote of the exclusively numerical solution for infinitesimal root segment lengths (and infinite segment number). As water uptake locations and magnitudes predicted by the latter solution for finite segmentation lengths deviate from the exact solution, and are computationally more intensive, we conclude that the new methodology should always be privileged for future applications. The proposed solution can be easily coupled to soil modules (as already done with existing solutions) and further implemented in functional-structural plant models to predict water flow in the soil-plant atmosphere continuum with a better accuracy than current models. Finally the new solution may be used to calculate more accurately plant scale macroscopic parameters for crop models.