ArcGIS Tutorial: Choosing a step size

The selection of step size has an important effect on the empirical semivariogram. For example, if the step size is too large, the short-range autocorrelation may be masked. If the step size is too small, there may be many empty bar elements, and the sample in the bin element is too small to obtain a typical average of the bar element.

When a sample is on a sample grid, the grid spacing is usually an accurate representation of the step size. However, if your data is obtained using an irregular or random sampling scheme, the appropriate step size selection is not as simple. One rule of thumb is to use the step number multiplied by the step size, which should be about half the maximum distance between all points. Also, if the variable threads of the fitted Semivariogram model is very small for the empirical Semivariogram, the step size can be reduced. Conversely, if the variable threads of the fitted Semivariogram is large for the empirical Semivariogram, the step size can be increased.

Another way to determine the step size is to use the average nearest neighbor tool to determine the average distance between a point and the nearest neighbor. This provides a very good step size, because all steps will contain at least a few pairs of points. The average nearest neighbor tool is located under the Analytic mode toolset in the spatial Statistics Toolbox. An example of the use of this tool is shown below.

　　

You only need to specify the input feature class. The distance method is automatically set to Euclidean distance.

　　

The result of the tool's run (background geoprocessing option enabled) appears in the results window. The nnobserved is the average distance between the nearest points and can be used as the step size for Semivariogram/covariance modeling. However, if the dataset contains clustering points/samples, it is recommended to use a smaller step size value to obtain a more accurate nugget estimate for the Semivariogram/covariance model.

　　

ArcGIS Tutorial: Choosing a step size