# Tutorial 2: The Covariance Model¶

One of the core-features of GSTools is the powerful CovModel class, which allows you to easily define arbitrary covariance models by yourself. The resulting models provide a bunch of nice features to explore the covariance models.

A covariance model is used to characterize the semi-variogram, denoted by , of a spatial random field. In GSTools, we use the following form for an isotropic and stationary field: Where:

• is the so called correlation function depending on the distance • is the variance
• is the nugget (subscale variance)

Note

We are not limited to isotropic models. GSTools supports anisotropy ratios for length scales in orthogonal transversal directions like:

• (main direction)
• (1. transversal direction)
• (2. transversal direction)

These main directions can also be rotated. Just have a look at the corresponding examples.

## Provided Covariance Models¶

The following standard covariance models are provided by GSTools

 Gaussian([dim, var, len_scale, nugget, …]) The Gaussian covariance model. Exponential([dim, var, len_scale, nugget, …]) The Exponential covariance model. Matern([dim, var, len_scale, nugget, anis, …]) The Matérn covariance model. Stable([dim, var, len_scale, nugget, anis, …]) The stable covariance model. Rational([dim, var, len_scale, nugget, …]) The rational quadratic covariance model. Linear([dim, var, len_scale, nugget, anis, …]) The bounded linear covariance model. Circular([dim, var, len_scale, nugget, …]) The circular covariance model. Spherical([dim, var, len_scale, nugget, …]) The Spherical covariance model. Intersection([dim, var, len_scale, nugget, …]) The Intersection covariance model.

As a special feature, we also provide truncated power law (TPL) covariance models

 TPLGaussian([dim, var, len_scale, nugget, …]) Truncated-Power-Law with Gaussian modes. TPLExponential([dim, var, len_scale, …]) Truncated-Power-Law with Exponential modes. TPLStable([dim, var, len_scale, nugget, …]) Truncated-Power-Law with Stable modes.