What is the difference between "direction" and "angles" pars in vario_estimate() function?

[flydream0428]

I have tried to estimate a directional variogram by the 'direction' and 'angles' parameters. It turns out it gives very similar results.
For 'direction', I am using,

bin_center, dir_vario_ani = gs.vario_estimate(
    pos=(x_con, y_con), 
    field=z_con, 
    direction=gs.rotated_main_axes(dim=2, angles=1/8*np.pi),
)

For 'angles', I am using,

bin_center, dir_vario_ani = gs.vario_estimate(
    pos=(x_con, y_con), 
    field=z_con, 
    angles=[1/8*np.pi, 5/8*np.pi],
)

What is the right one to use here? I have tried to read the function docstring, but I am still confused.

[MuellerSeb]

Hey there!

This is a very good question. You can use both to get the same results. In case of direction, you need to pass a vector (or multiple vectors) that points in the direction you want to estimate the variogram.

If you use angles you can describe the same directions, but in Spherical coordinates.

In your case

gs.rotated_main_axes(dim=2, angles=1/8*np.pi))

Gives two direction vectors:

1. pointing in the direction with an angle of 22,5°
2. the orthogonal direction to the first direction (112,5° or 5/8*np.pi)

This means

direction=gs.rotated_main_axes(dim=2, angles=1/8*np.pi)
# and
angles=[1/8*np.pi, 5/8*np.pi]

are describing the same directions.

Only thing to take care about is, that the angles parameter in rotated_main_axes describes the rotation angles of a covariance model (like Tait–Bryan angles in 3D) where you need d * (d - 1) / 2 angles (1D: 0, 2D: 1, 3D: 3, 4D: 6, ...) to fully describe rotation, whereas the angles parameter in vario_estimate are the mentioned spherical coordinates, where you only need (d - 1) angles (1D: 0, 2D: 1, 3D: 2, 4D: 3, ...).

In two dimension the number and the meaning of these angles coincide, therefore everything worked fine here. See the example about higher dimension to get an explanation of the rotation angles of a covariance model.

Hope that helps.
Sebastian