Binning empirical semivariograms
As you can see from the landscape of locations and the semivariogram cloud shown in Creating the empirical semivariogram, plotting each pair of locations quickly becomes unmanageable. There are so many points that the plot becomes congested and little can be interpreted from it. To reduce the number of points in the empirical semivariogram, the pairs of locations will be grouped based on their distance from one another. This grouping process is known as binning.
Binning is a two-stage process.
Stage one
First, form pairs of points, and second, group the pairs so that they have a common distance and direction. In the landscape scene of 12 locations, you can see the pairing of all the locations with one location, the red point. Similar colors for the links between pairs indicate similar bin distances.
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This process continues for all possible pairs. You can see that, in the pairing process, the number of pairs increases rapidly with the addition of each location. This is why, for each bin, only the average distance and semivariance for all the pairs in that bin are plotted as a single point on the semivariogram.
Stage two
In the second stage of the binning process, pairs are grouped based on common distances and directions. Imagine a graph so each point has a common origin. This property makes the empirical semivariogram symmetric.
For each bin, you form the squared difference from the values for all pairs of locations that are linked, and these are then averaged and multiplied by 0.5 to give one empirical semivariogram value per bin. In Geostatistical Analyst, you can control the lag size and number of lags. The empirical semivariogram value in each bin is color coded and is called the semivariogram surface.