"""
Working with lat-lon random fields
----------------------------------

In this example, we demonstrate how to generate a random field on
geographical coordinates.

First we setup a model, with ``latlon=True``, to get the associated
Yadrenko model.

In addition, we will use the earth radius provided by :any:`EARTH_RADIUS`,
to have a meaningful length scale in km.

To generate the field, we simply pass ``(lat, lon)`` as the position tuple
to the :any:`SRF` class.
"""
import gstools as gs

model = gs.Gaussian(latlon=True, var=1, len_scale=777, rescale=gs.EARTH_RADIUS)

lat = lon = range(-80, 81)
srf = gs.SRF(model, seed=1234)
field = srf.structured((lat, lon))
srf.plot()

###############################################################################
# This was easy as always! Now we can use this field to estimate the empirical
# variogram in order to prove, that the generated field has the correct
# geo-statistical properties.
# The :any:`vario_estimate` routine also provides a ``latlon`` switch to
# indicate, that the given field is defined on geographical variables.
#
# As we will see, everthing went well... phew!

bin_edges = [0.01 * i for i in range(30)]
bin_center, emp_vario = gs.vario_estimate(
    (lat, lon),
    field,
    bin_edges,
    latlon=True,
    mesh_type="structured",
    sampling_size=2000,
    sampling_seed=12345,
)

ax = model.plot("vario_yadrenko", x_max=0.3)
model.fit_variogram(bin_center, emp_vario, nugget=False)
model.plot("vario_yadrenko", ax=ax, label="fitted", x_max=0.3)
ax.scatter(bin_center, emp_vario, color="k")
print(model)

###############################################################################
# .. note::
#
#    Note, that the estimated variogram coincides with the yadrenko variogram,
#    which means it depends on the great-circle distance given in radians.
#
#    Keep that in mind when defining bins: The range is at most
#    :math:`\pi\approx 3.14`, which corresponds to the half globe.