Extension of the Cylindrical Root Model for Water Uptake to Non‐Regular Root Distributions

Core Ideas An equivalent cylinder radius PDF can be derived from a soil to root distance PDF. Simple analytical solutions for random and clustered root systems were obtained. The obtained equations were validated with 2D simulations of soil water flow. The water flow toward a single root is efficiently solved in cylindrical coordinates using the matrix flux potential. The upscaling of single root fluxes to whole root systems is commonly based on the assumption of regularly distributed and parallel aligned roots. To provide more accurate solutions for randomly distributed roots, the point to root distance probability density function (PDF) is transformed to an equivalent cylinder size PDF ( f C ), which is used for upscaling steady‐state and steady‐rate cylindrical root models while simple analytical solutions are derived. The regular root distribution assumption leads to large overestimations (∼50%) of root water uptake for randomly distributed roots. Several numerical comparisons with simulations of the two‐dimensional (2D) Richards equation for five different soil textures and five root densities show the good performance of the derived solutions under both limiting and non‐limiting soil hydraulic conditions. Moreover, an explicit analytical solution is given for negative‐binomial clustered roots. Under this specific assumption, the solution can be transformed to an equivalent random solution with a modified root length density. Simulation of root water uptake of different 2D root maps generated by a Poisson cluster process shows the effectiveness of the derived approximation for clustered roots.