This is the third of six segments that show you how to improve the ozone prediction surface.

The color scale, which represents the calculated semivariogram value, provides a direct link between the empirical semivariogram values on the graph and those on the semivariogram surface. The value of each cell in the semivariogram surface is color coded, with lower values blue and green and higher values orange and red. The average value for each cell of the semivariogram surface is plotted on the semivariogram graph. The x-axis on the semivariogram graph is the distance from the center of the cell to the center of the semivariogram surface. The semivariogram values represent dissimilarity. For this example, the semivariogram starts low at short distances (things close together are more similar) and increases as distance increases (things get more dissimilar farther apart). Notice from the semivariogram surface that dissimilarity increases more rapidly in the southwest-northeast direction than in the southeast-northwest direction. Earlier, you removed a coarse-scale trend. Now it appears that there are directional components to the autocorrelation at finer scales, so you will model that next.

A directional influence will affect the points of the semivariogram and the model that will be fit. In certain directions, things that are closer to each other may be more alike than in other directions. Geostatistical Analyst can account for directional influences, or anisotropy. Anisotropy can be caused by wind, runoff, a geological structure, or a wide variety of other processes. The directional influence can be statistically quantified and accounted for when making your map.

You can explore the dissimilarity in data points for a certain direction with the Search Direction tool. This allows you to examine directional influences on the semivariogram chart. It does not affect the output surface. The following steps show how to achieve this.

To explore the fine scale directional trends, check Show search direction. Note the reduction in the number of semivariogram values. Only those points in the direction of the search are displayed.

Click and hold the mouse pointer on the center blue line of the Search Direction tool. Change the search direction by dragging the center line. As you change the direction of the search, note how the semivariogram changes. Only the semivariogram surface values within the direction of the search are plotted on the semivariogram chart above.

To actually account for the directional influences on the semivariogram model for the surface calculations, you must calculate the anisotropical semivariogram or covariance model.

To do so, check the Anisotropy check box.

The dark red ellipse on the semivariogram surface indicates the range of the semivariogram in different directions. In this case, the major axis lies approximately in the NNW-SSE direction.

Anisotropy will now be incorporated into the model to adjust for the directional influence of autocorrelation in the output surface.

Click the Angle direction box and type an Angle direction of 249.6.

Note that the shape of the semivariogram curve increases more rapidly to its sill value. The x- and y-coordinates are in meters, so the range in this direction is approximately 74 kilometers.

Click the Angle direction box and type an Angle direction of 339.6.

The semivariogram model increases more gradually, then flattens out. The range in this direction is 190 kilometers.

The plateau that the semivariogram models reach in both these directions is the same and is known as the sill. The range is the distance at which the semivariogram model reaches its limiting value (the sill). Beyond the range, the dissimilarity between points becomes constant with increased lag distance. The lag is defined by the distance between pairs of points. Points separated by a lag distance greater than the range are spatially uncorrelated. The nugget represents measurement error and/or microscale variation (variation at spatial scales too fine to detect). It is possible to estimate the measurement error if you have multiple observations per location, or you can decompose the nugget into measurement error and microscale variation by switching to the Error Modeling tab.

Click Next.

Now you have a fitted model to describe the spatial autocorrelation, taking into account detrending and directional influences in the data. This information, along with the configuration and measurements of locations around the prediction location, is used to make a prediction. But how should man-measured locations be used for the calculations?