ext_thiem_2d(rad, r_ref, trans_gmean, var, len_scale, rate=-0.0001, h_ref=0.0, T_well=None, prop=1.6)[source]

The extended Thiem solution in 2D.

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 2D statistical framework, where the transmissivity distribution is following a log-normal distribution with a gaussian correlation function. Presented in [Zech2013].

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

  • r_ref (float) – Radius of the reference head.

  • trans_gmean (float) – Geometric-mean transmissivity.

  • var (float) – Variance of log-transmissivity.

  • len_scale (float) – Correlation-length of log-transmissivity.

  • 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

  • T_well (float, optional) – Explicit transmissivity value at the well. Default: None

  • 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_2d([1,2,3], 10, 0.001, 1, 10, -0.001)
array([-0.53084596, -0.35363029, -0.25419375])