GSTools Quickstart

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Youtube Tutorial on GSTools

Purpose

GeoStatTools provides geostatistical tools for various purposes:

• random field generation, including periodic boundaries

• simple, ordinary, universal and external drift kriging

• conditioned field generation

• incompressible random vector field generation

• (automated) variogram estimation and fitting

• directional variogram estimation and modelling

• data normalization and transformation

• many readily provided and even user-defined covariance models

• metric spatio-temporal modelling

• plotting and exporting routines

Installation

conda

GSTools can be installed via conda on Linux, Mac, and Windows. Install the package by typing the following command in a command terminal:

conda install gstools

In case conda forge is not set up for your system yet, see the easy to follow instructions on conda forge. Using conda, the parallelized version of GSTools should be installed.

pip

GSTools can be installed via pip on Linux, Mac, and Windows. On Windows you can install WinPython to get Python and pip running. Install the package by typing the following into command in a command terminal:

pip install gstools

To get the latest development version you can install it directly from GitHub:

pip install git+git://github.com/GeoStat-Framework/GSTools.git@main

If something went wrong during installation, try the -I flag from pip.

Speeding up GSTools by parallelization

We provide two possibilities to run GSTools in parallel, often causing a massive improvement in runtime. In either case, the number of parallel threads can be set with the global variable config.NUM_THREADS. If not set, all cores are used. When using conda, the parallel version of GSTools is installed per default.

*Parallelizing Cython*

To enable the OpenMP support in Cython when using pip, you have to provide a C compiler and OpenMP. Parallel support is controlled by an environment variable GSTOOLS_BUILD_PARALLEL, that can be 0 or 1 (interpreted as 0 if not present). GSTools then needs to be installed from source:

export GSTOOLS_BUILD_PARALLEL=1
pip install --no-binary=gstools gstools

Note, that the --no-binary=gstools option forces pip to not use a wheel for GSTools.

For the development version, you can do almost the same:

export GSTOOLS_BUILD_PARALLEL=1
pip install git+git://github.com/GeoStat-Framework/GSTools.git@main

*Using GSTools-Core for parallelization and even more speed*

You can install the optional dependency GSTools-Core, which is a re-implementation of the algorithms used in GSTools. The new package uses the language Rust and it should be faster (in some cases by orders of magnitude), safer, and it will potentially completely replace the current standard implementation in Cython. Once the package GSTools-Core is available on your machine, it will be used by default. In case you want to switch back to the Cython implementation, you can set gstools.config.USE_GSTOOLS_CORE=False in your code. This also works at runtime. You can install the optional dependency e.g. by

pip install gstools[rust]

or by manually installing the package

pip install gstools-core

GSTools-Core will automatically run in parallel, without having to use provide OpenMP or a local C compiler.

Citation

If you are using GSTools in your publication please cite our paper:

Müller, S., Schüler, L., Zech, A., and Heße, F.: GSTools v1.3: a toolbox for geostatistical modelling in Python, Geosci. Model Dev., 15, 3161–3182, https://doi.org/10.5194/gmd-15-3161-2022, 2022.

You can cite the Zenodo code publication of GSTools by:

Sebastian Müller & Lennart Schüler. GeoStat-Framework/GSTools. Zenodo. https://doi.org/10.5281/zenodo.1313628

If you want to cite a specific version, have a look at the Zenodo site.

Tutorials and Examples

The documentation also includes some tutorials, showing the most important use cases of GSTools, which are

• Random Field Generation

• The Covariance Model

• Variogram Estimation

• Random Vector Field Generation

• Kriging

• Conditioned random field generation

• Field transformations

• Geographic Coordinates

• Spatio-Temporal Modelling

• Normalizing Data

• Miscellaneous examples

Spatial Random Field Generation

The core of this library is the generation of spatial random fields. These fields are generated using the randomisation method, described by Heße et al. 2014.

Examples

Gaussian Covariance Model

This is an example of how to generate a 2 dimensional spatial random field (SRF) with a Gaussian covariance model.

import gstools as gs
# structured field with a size 100x100 and a grid-size of 1x1
x = y = range(100)
model = gs.Gaussian(dim=2, var=1, len_scale=10)
srf = gs.SRF(model)
srf((x, y), mesh_type='structured')
srf.plot()

GSTools also provides support for geographic coordinates. This works perfectly well with cartopy.

import matplotlib.pyplot as plt
import cartopy.crs as ccrs
import gstools as gs
# define a structured field by latitude and longitude
lat = lon = range(-80, 81)
model = gs.Gaussian(latlon=True, len_scale=777, geo_scale=gs.KM_SCALE)
srf = gs.SRF(model, seed=12345)
field = srf.structured((lat, lon))
# Orthographic plotting with cartopy
ax = plt.subplot(projection=ccrs.Orthographic(-45, 45))
cont = ax.contourf(lon, lat, field, transform=ccrs.PlateCarree())
ax.coastlines()
ax.set_global()
plt.colorbar(cont)

A similar example but for a three dimensional field is exported to a VTK file, which can be visualized with ParaView or PyVista in Python:

import gstools as gs
# structured field with a size 100x100x100 and a grid-size of 1x1x1
x = y = z = range(100)
model = gs.Gaussian(dim=3, len_scale=[16, 8, 4], angles=(0.8, 0.4, 0.2))
srf = gs.SRF(model)
srf((x, y, z), mesh_type='structured')
srf.vtk_export('3d_field') # Save to a VTK file for ParaView

mesh = srf.to_pyvista() # Create a PyVista mesh for plotting in Python
mesh.contour(isosurfaces=8).plot()

Estimating and fitting variograms

The spatial structure of a field can be analyzed with the variogram, which contains the same information as the covariance function.

All covariance models can be used to fit given variogram data by a simple interface.

Examples

This is an example of how to estimate the variogram of a 2 dimensional unstructured field and estimate the parameters of the covariance model again.

import numpy as np
import gstools as gs
# generate a synthetic field with an exponential model
x = np.random.RandomState(19970221).rand(1000) * 100.
y = np.random.RandomState(20011012).rand(1000) * 100.
model = gs.Exponential(dim=2, var=2, len_scale=8)
srf = gs.SRF(model, mean=0, seed=19970221)
field = srf((x, y))
# estimate the variogram of the field
bin_center, gamma = gs.vario_estimate((x, y), field)
# fit the variogram with a stable model. (no nugget fitted)
fit_model = gs.Stable(dim=2)
fit_model.fit_variogram(bin_center, gamma, nugget=False)
# output
ax = fit_model.plot(x_max=max(bin_center))
ax.scatter(bin_center, gamma)
print(fit_model)

Which gives:

Stable(dim=2, var=1.85, len_scale=7.42, nugget=0.0, anis=[1.0], angles=[0.0], alpha=1.09)

Kriging and Conditioned Random Fields

An important part of geostatistics is Kriging and conditioning spatial random fields to measurements. With conditioned random fields, an ensemble of field realizations with their variability depending on the proximity of the measurements can be generated.

Example

For better visualization, we will condition a 1d field to a few “measurements”, generate 100 realizations and plot them:

import numpy as np
import matplotlib.pyplot as plt
import gstools as gs

# conditions
cond_pos = [0.3, 1.9, 1.1, 3.3, 4.7]
cond_val = [0.47, 0.56, 0.74, 1.47, 1.74]

# conditioned spatial random field class
model = gs.Gaussian(dim=1, var=0.5, len_scale=2)
krige = gs.krige.Ordinary(model, cond_pos, cond_val)
cond_srf = gs.CondSRF(krige)
# same output positions for all ensemble members
grid_pos = np.linspace(0.0, 15.0, 151)
cond_srf.set_pos(grid_pos)

# seeded ensemble generation
seed = gs.random.MasterRNG(20170519)
for i in range(100):
    field = cond_srf(seed=seed(), store=f"field_{i}")
    plt.plot(grid_pos, field, color="k", alpha=0.1)
plt.scatter(cond_pos, cond_val, color="k")
plt.show()

User defined covariance models

One of the core-features of GSTools is the powerful CovModel class, which allows to easy define covariance models by the user.

Example

Here we re-implement the Gaussian covariance model by defining just the correlation function, which takes a non-dimensional distance h = r/l

import numpy as np
import gstools as gs
# use CovModel as the base-class
class Gau(gs.CovModel):
    def cor(self, h):
        return np.exp(-h**2)

And that’s it! With Gau you now have a fully working covariance model, which you could use for field generation or variogram fitting as shown above.

Incompressible Vector Field Generation

Using the original Kraichnan method, incompressible random spatial vector fields can be generated.

Example

import numpy as np
import gstools as gs
x = np.arange(100)
y = np.arange(100)
model = gs.Gaussian(dim=2, var=1, len_scale=10)
srf = gs.SRF(model, generator='VectorField', seed=19841203)
srf((x, y), mesh_type='structured')
srf.plot()

yielding

VTK/PyVista Export

After you have created a field, you may want to save it to file, so we provide a handy VTK export routine using the vtk_export() or you could create a VTK/PyVista dataset for use in Python with to to_pyvista() method:

import gstools as gs
x = y = range(100)
model = gs.Gaussian(dim=2, var=1, len_scale=10)
srf = gs.SRF(model)
srf((x, y), mesh_type='structured')
srf.vtk_export("field") # Saves to a VTK file
mesh = srf.to_pyvista() # Create a VTK/PyVista dataset in memory
mesh.plot()

Which gives a RectilinearGrid VTK file field.vtr or creates a PyVista mesh in memory for immediate 3D plotting in Python.

Requirements

• NumPy >= 1.20.0

• SciPy >= 1.1.0

• hankel >= 1.0.0

• emcee >= 3.0.0

• pyevtk >= 1.1.1

• meshio >= 5.1.0

Optional

• GSTools-Core >= 0.2.0

• matplotlib

• pyvista

Contact

You can contact us via info@geostat-framework.org.

License

LGPLv3