The semivariogram/covariance cloud allows you to examine the spatial autocorrelation between the measured sample points. In spatial autocorrelation, it is assumed that things that are close to one another are more alike. The semivariogram/covariance cloud lets you examine this relationship. To do so, a semivariogram value, which is the difference squared between the values of each pair of locations, is plotted on the y-axis relative to the distance separating each pair on the x-axis.

To view the semivariogram cloud, click the Geostatistical Analyst drop-down arrow, point to Explore Data, then click Semivariogram/Covariance Cloud. Click the Layer drop-down arrow and click ca_ozone_pts. Click the Attribute drop-down arrow and click OZONE.

Each red dot in the semivariogram/covariance cloud represents a pair of locations. Since locations that are close to each other should be more alike, in the semivariogram the close locations (far left on the x-axis) should have small semivariogram values (low on the y-axis). As the distance between the pairs of locations increases (move right on the x-axis), the semivariogram values should also increase (move up on the y-axis). However, a certain distance is reached where the cloud flattens out, indicating that the relationship between the pairs of locations beyond this distance is no longer correlated.

Looking at the semivariogram, if it appears that some data locations that are close together (near zero on the x-axis) have a higher semivariogram value (high on the y-axis) than you would expect, you should investigate these pairs of locations to see if there is a possibility that the data is inaccurate.

Click and drag the Selection pointer over these points to select them.

The pairs of sample locations that are selected in the semivariogram are highlighted on the map, and lines link the locations, indicating the pairing.

There are many reasons for the difference in data values among sample locations between the Los Angeles area and other areas. One possibility is that there are more cars in the Los Angeles area than in other areas, which will invariably produce more pollution, contributing to a higher ozone buildup in the Los Angeles area.

Besides global trends that were discussed in the previous section, there may also be directional influences affecting the data. The reasons for these directional influences may not be known, but they can be statistically quantified. These directional influences will affect the accuracy of the surface you create in the next exercise. However, once you know if one exists, Geostatistical Analyst provides tools to account for it in the surface-creation process. To explore for a directional influence in the semivariogram cloud, you can use the Search Direction tools.

Check Show search direction, then click and drag the directional pointer to any angle.

The direction the pointer is facing determines which pairs of data locations are plotted on the semivariogram. For example, if the pointer is facing an east–west direction, only the pairs of data locations that are east or west of one another will be plotted on the semivariogram. This enables you to eliminate pairs you are not interested in and to explore the directional influences on the data.

Click and drag the Selection tool along the pairs with the highest semivariogram values to select them on the plot and in the map.

You will notice that the majority of the linked locations (representing pairs of points on the map), regardless of distance, correspond to one of the sample points from the Los Angeles region. Taking more pairs of points, at any distance, into consideration shows that it is not just pairs of points from the Los Angeles region out to the coast that have high semivariogram values. Many of the pairs of data locations from the Los Angeles region to other inland areas also have high semivariogram values. This is because the values of ozone in the Los Angeles area are so much higher than anywhere else in California.

Close the dialog box.