Horizontal soil water potential heterogeneity simplifying approaches for crop water dynamics models

Soil water potential (SWP) is known to affect plant water status, and even though observations demonstrate that SWP distribution around roots may limit plant water availability, its horizontal heterogeneity within the root zone is often neglected in hydrological models. As motive, using a horizontal discretisation significantly larger than one centimetre is often essential for computing time considerations, especially for large-scale hydrodynamics models. In this paper, we simulate soil and root system hydrodynamics at the centimetre scale and evaluate approaches to upscale variables and parameters related to root water uptake (RWU) for two crop systems: a densely seeded crop with an average uniform distribution of roots in the horizontal direction (winter wheat) and a wide-row crop with lateral variations in root density(maize). In a first approach, the upscaled water potential at soil–root interfaces was assumed to equal the bulk SWP of the upscaled soil element. Using this assumption, the 3-D high-resolution model could be accurately upscaled to a 2-D model for maize and a 1-D model for wheat. The accuracy of the upscaled models generally increased with soil hydraulic conductivity, lateral homogeneity of root distribution, and low transpiration rate. The link between horizontal upscaling and an implicit assumption on soil water redistribution was demonstrated in quantitative terms, and explained upscaling accuracy. In a second approach, the soil–root interface water potential was estimated by using a constant rate analytical solution of the axisymmetric soil water flow towards individual roots. In addition to the theoretical model properties, effective properties were tested in order to account for unfulfilled assumptions of the analytical solution: non-uniform lateral root distributions and transient RWU rates. Significant improvements were however only noticed for winter wheat, for which the first approach was already satisfying. This study confirms that the use of 1-D spatial discretisation to represent soil–plant water dynamics is a worthy choice for densely seeded crops. For wide-row crops, e.g. maize, further theoretical developments that better account for horizontal SWP heterogeneity might be needed in order to properly predict soil–plant hydrodynamics in 1-D