Directional Variograms#

General#

With version 0.2.2, directional variograms have been introduced. A directional variogram is a variogram where point pairs are only included into the semivariance calculation if they fulfill a specified spatial relation. This relation is expressed as a search area that identifies all directional points for a given specific point. SciKit-GStat refers to this point as poi (point of interest). The implementation is done by the DirectionalVariogram class.

Understanding Search Area#

Note

The DirectionalVariogram is in general capable of handling n-dimensional coordinates. The application of directional dependency is, however, only applied to the first two dimensions.

Understanding the search area of a directional is vital for using the DirectionalVariogram class. The search area is controlled by the directional_model property which determines the shape of the search area. The extend and orientation of this area is controlled by the parameters:

As of this writing, SciKit-GStat supports three different search area shapes:

triangle (default)
circle
compass

Additionally, the shape generation is controlled by the tolerance parameter (triangle, compass) and bandwidth parameter (triangle, circle). The azimuth is used to rotate the search area into a desired direction. An azimuth of 0° is heading East of the coordinate plane. Positive values for azimuth rotate the search area clockwise, negative values counter-clockwise. The tolerance specifies how far the angle (against ‘x-axis’) between two points can be off the azimuth to be still considered as a directional point pair. Based on this definition, two points at a larger distance would generally be allowed to differ more from azimuth in terms of coordinate distance. Therefore the bandwidth defines a maximum coordinate distance, a point can have from the azimuth line. The difference between the triangle and the compass search area is that the triangle uses the bandwidth and the compass does not.

The DirectionalVariogram has a function to plot the effect of the search area. The method is called pair_field. Using random coordinates, the visualization is shown below.

In [1]: from skgstat import DirectionalVariogram

In [2]: from skgstat.plotting import backend

In [3]: import numpy as np

In [4]: import matplotlib.pyplot as plt

In [5]: plt.style.use('ggplot')

In [6]: backend('matplotlib')

In [7]: np.random.seed(42)

In [8]: coords = np.random.gamma(15, 6, (40, 2))

In [9]: np.random.seed(42)

In [10]: vals = np.random.normal(5,1, 40)

In [11]: DV = DirectionalVariogram(coords, vals,
   ....:     azimuth=0,
   ....:     tolerance=45,
   ....:     directional_model='triangle')
   ....: 

In [12]: DV.pair_field(plt.gca())
Out[12]: <Figure size 640x480 with 1 Axes>

The model can easily be changed, using the set_directional_model function:

In [13]: fig, axes = plt.subplots(1, 2, figsize=(8, 4))

In [14]: DV.set_directional_model('triangle')

In [15]: DV.pair_field(plt.gca())
Out[15]: <Figure size 800x400 with 2 Axes>

In [16]: DV.pair_field(plt.gca())
Out[16]: <Figure size 800x400 with 2 Axes>

In [17]: fig.show()

In [18]: DV.set_directional_model('compass')

In [19]: DV.pair_field(plt.gca())
Out[19]: <Figure size 800x400 with 2 Axes>

In [20]: fig.show()