A simple three-dimensional macroscopic root water uptake model based on the hydraulic architecture approach

Many hydrological models including root water uptake (RWU) do not consider the dimension of root system hydraulic architecture (HA) because explicitly solving water flow in such a complex system is too much time consuming. However, they might lack process understanding when basing RWU and plant water stress predictions on functions of variables such as the root length density distribution. On the basis of analytical solutions of water flow in a simple HA, we developed an "implicit" model of the root system HA for simulation of RWU distribution (sink term of Richards' equation) and plant water stress in three-dimensional soil water flow models. The new model has three macroscopic parameters defined at the soil element scale or at the plant scale rather than for each segment of the root architecture: the standard sink distribution SSD, the root system equivalent conductance Krs and the compensatory conductance Kcomp. It clearly decouples the process of water stress from compensatory RWU and its structure is appropriate for hydraulic lift simulation. As compared to a model explicitly solving water flow in a realistic maize root system HA, the implicit model showed to be accurate for predicting RWU distribution and plant collar water potential, with one single set of parameters, in contrasted water dynamics scenarios. For these scenarios, the computing time of the implicit model was a factor 28 to 214 shorter than that of the explicit one. We also provide a new expression for the effective soil water potential sensed by plants in soils with a heterogeneous water potential distribution, which emerged from the implicit model equations. With the proposed implicit model of the root system HA, new concepts are brought which open avenues towards simple and process understanding RWU models and water stress functions operational for field scale water dynamics simulation.