Transform 22

Introductory example

%matplotlib widget
import matplotlib.pyplot as plt
# turn of warnings
import warnings

Let us start with a short example of a self defined model (Of course, we provide a lot of predefined models gstools.covmodel, but they all work the same way). Therefore we reimplement the Gaussian covariance model by defining just the "normalized" correlation function:

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))

Here the parameter h stands for the normalized range r / len_scale. Now we can instantiate this model:

model = Gau(dim=2, var=2.0, len_scale=10)
ax = model.plot()
model.plot("covariance", ax=ax)
model.plot("correlation", ax=ax)

This is almost identical to the already provided Gaussian model. There, a scaling factor is implemented so the len_scale coincides with the integral scale:

gau_model = gs.Gaussian(dim=2, var=2.0, len_scale=10)
ax = gau_model.plot(ax=ax)


We already used some parameters, which every covariance models has. The basic ones are:

  • dim : dimension of the model
  • var : variance of the model (on top of the subscale variance)
  • len_scale : length scale of the model
  • nugget : nugget (subscale variance) of the model

These are the common parameters used to characterize a covariance model and are therefore used by every model in GSTools. You can also access and reset them:

print("old model:", model)
model.dim = 3
model.var = 1
model.len_scale = 15
model.nugget = 0.1
print("new model:", model)
old model: Gau(dim=2, var=2.0, len_scale=10.0, nugget=0.0)
new model: Gau(dim=3, var=1.0, len_scale=15.0, nugget=0.1)


  • The sill of the variogram is calculated by sill = variance + nugget So we treat the variance as everything above the nugget, which is sometimes called partial sill.
  • A covariance model can also have additional parameters.