Software Open Access

GeoStat-Framework/GSTools: v1.3.0-rc2 'Pure Pink' 2. Release Candidate

Sebastian Müller; Lennart Schüler

Bane Sullivan
Research group(s)
Falk Heße; Alraune Zech
Sabine Attinger

Release Notes

A big step forward for GSTools. We now support geographical coordinates, directional variograms, auto-binning, arbitrary dimensions, normalizers and trends and much much more.


You can install GSTools with conda:

conda install -c conda-forge gstools

or with pip:

pip install gstools


The documentation can be found at:

What's new?


Geographical Coordinates Support (#113)

  • added boolean init parameter latlon to indicate a geographic model. When given, spatial dimension is fixed to dim=3, anis and angles will be ignored, since anisotropy is not well-defined on a sphere.
  • add property field_dim to indicate the dimension of the resulting field. Will be 2 if latlon=True
  • added yadrenko variogram, covariance and correlation method, since the geographic models are derived from standard models in 3D by plugging in the chordal distance of two points on a sphere derived from there great-circle distance zeta:
    • vario_yadrenko: given by variogram(2 * np.sin(zeta / 2))
    • cov_yadrenko: given by covariance(2 * np.sin(zeta / 2))
    • cor_yadrenko: given by correlation(2 * np.sin(zeta / 2))
  • added plotting routines for yadrenko methods described above
  • the isometrize and anisometrize methods will convert latlon tuples (given in degree) to points on the unit-sphere in 3D and vice versa
  • representation of geographical models don't display the dim, anis and angles parameters, but latlon=True
  • fit_variogram will expect an estimated variogram with great-circle distances given in radians
  • Variogram estimation
    • latlon switch implemented in estimate_vario routine
    • will return a variogram estimated by the great-circle distance (haversine formula) given in radians
  • Field
    • added plotting routines for latlon fields
    • no vector fields possible on latlon fields
    • corretly handle pos tuple for latlon fields

Krige Unification (#97)

  • Swiss Army Knife for kriging: The Krige class now provides everything in one place
  • "Kriging the mean" is now possible with the switch only_mean in the call routine
  • Simple/Ordinary/Universal/ExtDrift/Detrended are only shortcuts to Krige with limited input parameter list
  • We now use the covariance function to build up the kriging matrix (instead of variogram)
  • An unbiased switch was added to enable simple kriging (where the unbiased condition is not given)
  • An exact switch was added to allow smother results, if a nugget is present in the model
  • An cond_err parameter was added, where measurement error variances can be given for each conditional point
  • pseudo-inverse matrix is now used to solve the kriging system (can be disabled by the new switch pseudo_inv), this is equal to solving the system with least-squares and prevents numerical errors
  • added options fit_normalizer and fit_variogram to automatically fit normalizer and variogram to given data

Directional Variograms and Auto-binning (#87, #106, #131)

  • new routine name vario_estimate instead of vario_estimate_unstructured (old kept for legacy code) for simplicity
  • new routine name vario_estimate_axis instead of vario_estimate_structured (old kept for legacy code) for simplicity
  • vario_estimate
    • added simple automatic binning routine to determine bins from given data (one third of box diameter as max bin distance, sturges rule for number of bins)
    • allow to pass multiple fields for joint variogram estimation (e.g. for daily precipitation) on same mesh
    • no_data option added to allow missing values
    • masked fields
      • user can now pass a masked array (or a list of masked arrays) to deselect data points.
      • in addition, a mask keyword was added to provide an external mask
    • directional variograms
      • diretional variograms can now be estimated
      • either provide a list of direction vectors or angles for directions (spherical coordinates)
      • can be controlled by given angle tolerance and (optional) bandwidth
      • prepared for nD
    • structured fields (pos tuple describes axes) can now be passed to estimate an isotropic or directional variogram
    • distance calculation in cython routines in now independent of dimension
  • vario_estimate_axis
    • estimation along array axis now possible in arbitrary dimensions
    • no_data option added to allow missing values (sovles #83)
    • axis can be given by name ("x", "y", "z") or axis number (0, 1, 2, 3, ...)

Better Variogram fitting (#78, #145)

  • fixing sill possible now
  • loss is now selectable for smoother handling of outliers
  • r2 score can now be returned to get an impression of the goodness of fitting
  • weights can be passed
  • instead of deselecting parameters, one can also give fix values for each parameter
  • default init guess for len_scale is now mean of given bin-centers
  • default init guess for var and nugget is now mean of given variogram values

CovModel update (#109, #122)

  • add new rescale argument and attribute to the CovModel class to be able to rescale the len_scale (usefull for unit conversion or rescaling len_scale to coincide with the integral_scale like it's the case with the Gaussian model) See: #90, GeoStat-Framework/PyKrige#119
  • added new len_rescaled attribute to the CovModel class, which is the rescaled len_scale: len_rescaled = len_scale / rescale
  • new method default_rescale to provide default rescale factor (can be overridden)
  • remove doctest calls
  • docstring updates in CovModel and derived models
  • updated all models to use the cor routine and make use of the rescale argument (See: #90)
  • TPL models got a separate base class to not repeat code
  • added new models (See: #88):
    • HyperSpherical: (Replaces the old Intersection model) Derived from the intersection of hyper-spheres in arbitrary dimensions. Coincides with the linear model in 1D, the circular model in 2D and the classical spherical model in 3D
    • SuperSpherical: like the HyperSpherical, but the shape parameter derived from dimension can be set by the user. Coincides with the HyperSpherical model by default
    • JBessel: a hole model valid in all dimensions. The shape parameter controls the dimension it was derived from. For nu=0.5 this model coincides with the well known wave hole model.
    • TPLSimple: a simple truncated power law controlled by a shape parameter nu. Coincides with the truncated linear model for nu=1
    • Cubic: to be compatible with scikit-gstat in the future
  • string representation of the CovModel class is now using a float precision (CovModel._prec=3) to truncate longish output
  • dimension validity check: raise a warning, if given model is not valid in the desired dimension (See: #86)

Normalizer, Trend and Mean (#124)

  • new normalize submodule containing power-transforms for data to gain normality
  • Base-Class: Normalizer providing basic functionality including maximum likelihood fitting
  • added: LogNormal, BoxCox, BoxCoxShift, YeoJohnson, Modulus and Manly
  • normalizer, trend and mean can be passed to SRF, Krige and variogram estimation routines
    • A trend can be a callable function, that represents a trend in input data. For example a linear decrease of temperature with height.
    • The normalizer will be applied after the data was detrended, i.e. the trend was substracted from the data, in order to gain normality.
    • The mean is now interpreted as the mean of the normalized data. The user could also provide a callable mean, but it is mostly meant to be constant.

Arbitrary dimensions (#112)

  • allow arbitrary dimensions in all routines (CovModel, Krige, SRF, variogram)
  • anisotropy and rotation following a generalization of tait-bryan angles
  • CovModel provides isometrize and anisometrize routines to convert points

New Class for Conditioned Random Fields (#130)

  • CondSRF replaces the conditioning feature of the SRF class, which was cumbersome and limited to Ordinary and Simple kriging
  • CondSRF behaves similar to the SRF class, but instead of a covariance model, it takes a kriging class as input. With this kriging class, all conditioning related settings are defined.


  • Python 3.9 Support #107
  • add routines to format struct. pos tuple by given dim or shape
  • add routine to format struct. pos tuple by given shape (variogram helper)
  • remove subpackage
  • support meshio>=4.0 and add as dependency
  • PyVista mesh support #59
  • added EARTH_RADIUS as constant providing earths radius in km (can be used to rescale models)
  • add routines latlon2pos and pos2latlon to convert lat-lon coordinates to points on unit-sphere and vice versa
  • a lot of new examples and tutorials
  • RandMeth class got a switch to select the sampling strategy
  • plotter for n-D fields added #141
  • antialias for contour plots of 2D fields #141
  • building from source is now configured with pyproject.toml to care about build dependencies, see #154


  • drop support for Python 3.5 #146
  • added a finit limit for shape-parameters in some CovModels #147
  • drop usage of pos2xyz and xyz2pos
  • remove structured option from generators (structured pos need to be converted first)
  • explicitly assert dim=2,3 when generating vector fields
  • simplify pre_pos routine to save pos tuple and reformat it an unstructured tuple
  • simplify field shaping
  • simplify plotting routines
  • only the "unstructured" keyword is recognized everywhere, everything else is interpreted as "structured" (e.g. "rectilinear")
  • use GitHub-Actions instead of TravisCI
  • parallel build now controlled by env-var GSTOOLS_BUILD_PARALLEL=1, see #154
  • install extra target for [dev] dropped, can be reproduced by pip install gstools[test, doc], see #154


  • typo in keyword argument for vario_estimate_structured #80
  • isotropic rotation of SRF was not possible #100
  • CovModel.opt_arg now sorted #103
  • check if weights are given as a string (numpy comparison error) #111

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