The Extended Thiem's solution: Including the impact of heterogeneity


Corresponding author: A. Zech, Department of Computational Hydrosystems, UFZ Helmholtz Centre for Environmental Research, Permoserstr. 15, DE-04318 Leipzig, Germany. (


[1] 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 math formula 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 math formula, namely geometric mean KG, variance σ2, horizontal correlation length 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.