ArcGIS Tutorial: Checking for spatial autocorrelation and direction changes

By exploring the data, you will be better able to understand the spatial autocorrelation between measured values. This understanding helps to make better decisions when choosing a spatial prediction model.

　　Spatial autocorrelation

You can explore the spatial autocorrelation of your data by examining different sample location pairs. You create a semivariogram cloud by measuring the distance between two locations and plotting the squared difference between the values in those locations. The x-axis represents the distance between locations, and the y-axis represents the squared difference between the values at those locations. Each point in the semivariogram represents a position pair, not a single location on the map.

If there is a spatial dependency, the closer point pair (the leftmost side of the x-axis) should have a small difference (smaller values on the y-axis). As the distances between the points become larger (the points move to the right on the x-axis), the square of the difference should also be increased (moving upward on the y-axis). Usually, the squared difference will remain the same after a certain distance. A position that exceeds this distance is considered irrelevant.

The basic assumption of geostatistical method is that the square of the difference should be similar for any two positions which are close to each other's distance and direction. This kind of relationship is called stationarity.

Spatial autocorrelation may depend only on the distance between two locations, which is called isotropic. However, when considering different orientations, the same autocorrelation value may appear for different distances. Another understanding is that for longer distances, things are more similar in some directions than in other directions. This directional effect exists in both semivariogram and covariance, which is called anisotropy.

It is important to find the anisotropy because the differences in direction are detected in autocorrelation, which can be considered in a semivariogram or covariance model. This, in turn, will have an impact on geostatistical forecasts.

　　Explore spatial structures with the semivariogram/covariance cloud tool

The Semivariogram/Covariance cloud tool can be used to study the autocorrelation of datasets. Next, let's consider the ozone data set. Note: In, you can select all position pairs at a certain distance, by erasing all points at that distance in the Semivariogram cloud.

　　

　　Finding directional effects using the Semivariogram/covariance cloud tool

In the previous example, the Semivariogram/covariance cloud tool was used to view the global autocorrelation of the data. However, when viewing the semivariogram surface, there may be directional differences in the values of the Semivariogram. When you click Show Search direction and set the angle and bandwidth (as shown in), you will see a very similar value in the same position as the semivariogram, since the value of the semi-variant function is relatively small.

　　

If you change the direction of the link (as shown), you will see that some of the linked locations have very different values, which makes the semivariogram values large. This indicates that, in general, the location of the north-east direction is 125000 meters apart than in the northwest direction of the position of the greater difference. Recall that when changes in one direction change faster than in the other direction, this phenomenon is called anisotropy. When you use the Geostatistical Analyst Wizard to interpolate a surface, you can use a Semivariogram model that takes into account the anisotropy.

　　

ArcGIS Tutorial: Checking for spatial autocorrelation and direction changes