Water flow within and towards plant roots – a new concurrent solution

Abstract Various analytical models that calculate the water flow either around or inside plant roots are available, but a combined analytical solution has not yet been derived. The classical solution of Landsberg and Fowkes for water flow within a root relates the second derivative of xylem water potential to the radial water influx term. This term can be linked to well-known steady state or steady rate-based solutions for computing soil water fluxes around roots. While neglecting lateral fluxes between local depletion zones around roots, we use this link to construct a system of continuous equations that combine root internal and external water flow that can be solved numerically for two boundary conditions (specified root collar water potential and zero distal influx) and one constraint (mean bulk matric flux potential). Furthermore, an iterative matrix solution for the stepwise analytical solution of homogeneous root segments is developed. Besides accounting for soil water flow iteratively, the intrinsic effect of variable axial conductance is accounted simultaneously. The reference and the iterative matrix solution are compared for different types of corn roots, soil textures and soil dryness states, which showed good correspondence. This also revealed the importance of accounting for variable axial conductance in more detail. The proposed reference solution can be used for the evaluation of different morphological and hydraulic designs of single or multiple parallel-connected roots operating in targeted soil environments. Some details of the iterative matrix solution may be adopted in analytical–numerical solutions of water flow in complex root systems.