ext_thiem_3d(rad, r_ref, cond_gmean, var, len_scale, anis=1.0, lat_ext=1.0, rate=-0.0001, h_ref=0.0, K_well='KH', prop=1.6)[source]

The extended Thiem solution in 3D.

The extended Thiem solution for steady-state flow under a pumping condition in a confined aquifer. The type curve is describing the effective drawdown in a 3D statistical framework, where the conductivity distribution is following a log-normal distribution with a gaussian correlation function and taking vertical anisotropy into account. Presented in [Zech2013].

  • rad (numpy.ndarray) – Array with all radii where the function should be evaluated

  • r_ref (float) – Reference radius with known head (see h_ref)

  • cond_gmean (float) – Geometric-mean conductivity.

  • var (float) – Variance of the log-conductivity.

  • len_scale (float) – Corralation-length of log-conductivity.

  • anis (float, optional) – Anisotropy-ratio of the vertical and horizontal corralation-lengths. Default: 1.0

  • lat_ext (float, optional) – Lateral extend of the aquifer (thickness). Default: 1.0

  • rate (float, optional) – Pumpingrate at the well. Default: -1e-4

  • h_ref (float, optional) – Reference head at the reference-radius r_ref. Default: 0.0

  • K_well (string/float, optional) – Explicit conductivity value at the well. One can choose between the harmonic mean ("KH"), the arithmetic mean ("KA") or an arbitrary float value. Default: "KH"

  • prop (float, optional) – Proportionality factor used within the upscaling procedure. Default: 1.6


head – Array with all heads at the given radii.

Return type




Zech, A. ‘’Impact of Aqifer Heterogeneity on Subsurface Flow and Salt Transport at Different Scales: from a method determine parameters of heterogeneous permeability at local scale to a large-scale model for the sedimentary basin of Thuringia.’’ PhD thesis, Friedrich-Schiller-Universität Jena, 2013


If you want to use cartesian coordiantes, just use the formula r = sqrt(x**2 + y**2)


>>> ext_thiem_3d([1,2,3], 10, 0.001, 1, 10, 1, 1, -0.001)
array([-0.48828026, -0.31472059, -0.22043022])