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

  • Trung Hieu MaiEmail author
  • Andrea Schnepf
  • Harry Vereecken
  • Jan Vanderborght
Regular Article


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.


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+.


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.


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.


Water uptake Nutrient uptake Root system architecture Root soil modelling Multiscale Root system scale Single root scale Rhizosphere 



This work was funded by the German Federal Ministry of Education and Research (BMBF) in the framework of the funding initiative “Soil as a Sustainable Resource for the Bioeconomy BonaRes”, the project “BonaRes (Module A): Sustainable Subsoil Management-Soil3; subproject 3” (grant 031B0026C). The authors would like to thank Timo Koch, Katharina Heck, Bernd Flemisch and Rainer Helmig from the Department of Hydromechanics and Modelling of Hydrosystem at University of Stuttgart, Germany, for their helpful advice on technical implementation in DuMux framework and three anonymous reviewers for their valuable comments and suggestions for improving this manuscript.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Forschungszentrum Juelich GmbH, Agrosphere (IBG-3)JuelichGermany

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