Geographical models

It was shown, that the current approach of plugging in the great-circle distance directly into the covariance/variogram function does not automatically result in a valid covariance model on the sphere.

To overcome this flaw, we should use the so called Yadrenko Covariance Function (See here). Starting with a valid isotropic model in 3D, where the covariance between two points is given as a function of their distance:

cov(x1, x2) = func(dist(x1, x2))

We can construct the related yadrenko model on the sphere, that takes the great-circle distance zeta(x1, x2) with the following modification:

cov_sph(x1, x2) = func(2 * sin(zeta(x1, x2) / 2))

One should not, that 2 * sin(x / 2) is approximately x for small angles, which means, that the current approach in PyKrige is approximately correct for small angles.

[MuellerSeb]

This is now solved in GSTools and will be used in PyKrige in the future:

• https://github.com/GeoStat-Framework/GSTools/pull/113

[MuellerSeb]

@mjziebarth : I would suggest doing this within the GS-Framework 2.0 project. By increasing the major version of Pykrige and GSTools we can break backward compatibility. We can still keep v1.x of PyKrige alive, but I wouldn’t introduce a deprecation cycle there. Of course, we have to well-document this change and the behavior.