GSTools provides support for geographic coordinates given by:
lat: specifies the north–south position of a point on the Earth’s surface
lon: specifies the east–west position of a point on the Earth’s surface
If you want to use this feature for field generation or Kriging, you
have to set up a geographical covariance Model by setting
in your desired model (see
import numpy as np import gstools as gs model = gs.Gaussian(latlon=True, var=2, len_scale=np.pi / 16)
By doing so, the model will use the associated Yadrenko model on a sphere
The len_scale is given in radians to scale the arc-length.
In order to have a more meaningful length scale, one can use the
import gstools as gs model = gs.Gaussian(latlon=True, var=2, len_scale=500, rescale=gs.EARTH_RADIUS)
len_scale can be interpreted as given in km.
A Yadrenko model is derived from a valid isotropic covariance model in 3D by the following relation:
Where is the great-circle distance.
lon are given in degree, whereas the great-circle distance
is given in radians.
Note, that is the chordal distance of two points on a sphere, which means we simply think of the earth surface as a sphere, that is cut out of the surrounding three dimensional space, when using the Yadrenko model.