Recent studies have shown that rhizosphere hydraulic properties may differ from those of the bulk soil. Specifically, mucilage at the root–soil interface may increase the rhizosphere water holding capacity and hydraulic conductivity during drying. The goal of this study was to point out the implications of such altered rhizosphere hydraulic properties for soil–plant water relations. We addressed this problem through modeling based on a steady‐rate approach. We calculated the water flow toward a single root assuming that the rhizosphere and bulk soil were two concentric cylinders having different hydraulic properties. Based on our previous experimental results, we assumed that the rhizosphere had higher water holding capacity and unsaturated conductivity than the bulk soil. The results showed that the water potential gradients in the rhizosphere were much smaller than in the bulk soil. The consequence is that the rhizosphere attenuated and delayed the drop in water potential in the vicinity of the root surface when the soil dried. This led to increased water availability to plants, as well as to higher effective conductivity under unsaturated conditions. The reasons were two: (i) thanks to the high unsaturated conductivity of the rhizosphere, the radius of water uptake was extended from the root to the rhizosphere surface; and (ii) thanks to the high soil water capacity of the rhizosphere, the water depletion in the bulk soil was compensated by water depletion in the rhizosphere. We conclude that under the assumed conditions, the rhizosphere works as an optimal hydraulic conductor and as a reservoir of water that can be taken up when water in the bulk soil becomes limiting.

a b s t r a c tWe identify sufficient conditions under which evolution equations for probability density functions (PDF) of random concentrations are equivalent to Fokker-Planck equations. The novelty of our approach is that it allows consistent PDF approximations by densities of computational particles governed by Itô processes in concentration-position spaces. Accurate numerical solutions are obtained with a global random walk (GRW) algorithm, stable, free of numerical diffusion, and insensitive to the increase of the total number of computational particles. The system of Itô equations is specified by drift and diffusion coefficients describing the PDF transport in the physical space, provided by up-scaling procedures, as well as by drift and mixing coefficients describing the PDF transport in concentration spaces. Mixing models can be obtained similarly to classical PDF approaches or, alternatively, from measured or simulated concentration time series. We compare their performance for a GRW-PDF numerical solution to a problem of contaminant transport in heterogeneous groundwater systems.

Abstract. Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of, for example, earth sciences. Valuable information can be extracted from these correlations, also helping to address the often encountered burden of data scarcity. Despite the value of additional data, the use of geostatistics still falls short of its potential. This problem is often connected to the lack of user-friendly software hampering the use and application of geostatistics. We therefore present GSTools, a Python-based software suite for solving a wide range of geostatistical problems. We chose Python due to its unique balance between usability, flexibility, and efficiency and due to its adoption in the scientific community. GSTools provides methods for generating random fields; it can perform kriging, variogram estimation and much more. We demonstrate its abilities by virtue of a series of example applications detailing their use.