ext_thiem_tpl(rad, r_ref, cond_gmean, len_scale, hurst, var=None, c=1.0, dim=2.0, lat_ext=1.0, rate=-0.0001, h_ref=0.0, K_well='KH', prop=1.6)[source]

The extended Thiem solution for truncated power-law fields.

The extended Theis solution for steady flow under a pumping condition in a confined aquifer. The type curve is describing the effective drawdown in a d-dimensional statistical framework, where the conductivity distribution is following a log-normal distribution with a truncated power-law correlation function build on superposition of gaussian modes.

  • 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. You can also treat this as transmissivity by leaving ‘lat_ext=1’.

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

  • hurst (float) – Hurst coefficient of the TPL model. Should be in (0, 1).

  • var (float) – Variance of the log-conductivity. If var is given, c will be calculated accordingly. Default: None

  • c (float, optional) – Intensity of variation in the TPL model. Is overwritten if var is given. Default: 1.0

  • dim (float, optional) – Dimension of space. Default: 2.0

  • lat_ext (float, optional) –

    Lateral extend of the aquifer:

    • sqare-root of cross-section in 1D

    • thickness in 2D

    • meaningless in 3D

    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 (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 and time-points.

Return type



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