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In this study we present a formula for the hydraulic head describing the mean drawdown of a three dimensional steady state pumping test in heterogeneous anisotropic porous media effectively. By modeling the hydraulic conductivity K(...) as spatial random function and using the upscaling method Coarse Graining we succeed in deriving a closed form solution hefw (r) which we understand as an extension of Thiem's formula to heterogeneous media. The solution hefw (r) does not only depend on the radial distance r but accounts also for the statistics of K(...), namely geometric mean KG, variance σ², horizontal correlation length l and anisotropy ratio e. We perform a sensitivity analysis on the parameters of hefw (r) and implement an inverse estimation strategy. Using numerical pumping tests we show the applicability of hefw (r) on the interpretation of drawdown data. This will be done for both, an ensemble of as well as for single pumping tests. Making use of the inverse estimation method we find excellent agreement of estimated parameters with initial values, in particular for the horizontal correlation length. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]