Continuum multiscale model of root water and nutrient uptake from soil with explicit consideration of the 3D root architecture and the rhizosphere gradients

Background and aims Although modelling of water and nutrient uptake by root systems has advanced considerably in recent years, steep local gradients of nutrient concentration near the root-soil interface in the rhizosphere are still a central challenge for accurate simulation of water and nutrient uptake at the root system scale. Conventionally, mesh refinement is used to resolve these gradients. However, it results in excessive computational costs. The object of the study is to present a multiscale approach which resolves the steep gradient of nutrient concentrations at rhizosphere scale and simulates nutrient and water fluxes within the entire root zone at macroscale scale in a computationally efficient way. Methods We developed a 3D water and nutrient transport model of the root-soil system with explicit consideration of the 3D root architecture. To capture the nutrient gradients at root surfaces, 1D axisymmetric soil models at rhizosphere scale were constructed and coupled to the coarse 3D root-system-scale simulations using a mass conservative approach. The multiscale model was investigated under different scenarios for water and potassium (K + ) uptake of a single root, multiple roots, and whole 3D architecture of a Zea mays L. root system in conditions of dynamic soil water and different soil buffer capacity of K + . Results The steep gradients of K + concentrations were efficiently resolved in the multiscale simulations thanks to the 1D model at the rhizosphere scale. In comparison with the refinement method, the multiscale model achieved a significant accuracy of K + uptake prediction with a relative error below 5%. Meanwhile, the simulation at macroscale with coarse mesh could overestimate the K + uptake in one order of magnitude. Moreover, the computational cost of multiscale simulations was decreased considerably by using coarse soil mesh. Conclusions The newly developed model can describe the effect of the drying and nutrient transport in the root zone on nutrient uptake. It also allows to simulate processes in larger and complex root systems because of the considerable reduction in computational cost.