ArcGIS Tutorial: Fitting models based on empirical Semivariogram

Semivariogram/Covariance modeling is a key step between spatial description and spatial prediction. The primary application of geostatistical is to predict attribute values (kriging) at the location of the sample.

Empirical Semivariogram and covariance provide information about the spatial autocorrelation of a DataSet. However, information about all possible directions and distances is not provided. Therefore, to ensure that the kriging variance of kriging predictions is positive, it is necessary to fit the model (that is, continuous function or curve) based on the empirical Semivariogram/covariance method.

　　Different views of empirical semivariogram/covariance values

The Geostatistical Wizard provides three different views of the empirical Semivariogram value. You can use any number (one, two, or all three) views to help you fit the model to your data. The default view shows the experienced Semivariogram/covariance values that have been discarded and have been averaged.

　　

Dropped values are displayed as red dots, which are generated by using a square cell with a width of one step to close the empirical semivariogram/covariance together (grouped). The average point is shown as a blue cross symbol, which is generated by grouping empirical semivariogram/covariance in a circular partition. The drop point shows a local change in the Semivariogram/covariance value, while the mean shows a smooth change of the Semivariogram/covariance value. In many cases, it is easier to fit the model based on the average because they provide a relatively concise view of the spatial autocorrelation in the data, and the average will show a smoother change in the Semivariogram value than the drop point.

The display point control can be set to discarded and averaged (as shown), discarded, or averaged (as shown).

　　

　　

In addition, you can add lines to the diagram. These lines are local polynomial that are fitted based on discarded empirical semivariogram/covariance values. If the show Search direction option is set to True, only local polynomial that is fitted to the empirical semivariogram/covariance surface in the mid-axis spline with the show Search direction tool is displayed, as shown in:

　　

The Semivariogram/covariance model that is fitted based on empirical data should:

• The center of the cloud passing through the dropped values (red dots).
• Cross the position as close as possible to the average (Blue Cross symbol).
• Go through the position as close as possible to the line (the Green Line).

Keep in mind that even if the model does not fully fit the empirical data, your knowledge of the phenomenon can determine the shape and nugget of the model, as well as the variation value, the bias abutment value, and the anisotropy value (recall that the empirical data is only a sample of the real-world phenomenon model to be built, and does not represent all the spatial and statistical aspects of the

Different types of semivariogram/covariance models

Geostatistical Analyst provides the following functions for building the empirical Semivariogram model:

• Round
• Spherical
• Four Ball
• Five Ball
• Index
• Gaussian
• Rational two-time equation
• Hole effect
• K-bessel
• J-bessel
• Stability of

The selected model affects predictions for unknown values, especially when the shape of the curve approaching the origin is significantly different. The steeper the curve near the origin, the greater the impact of the nearest adjacent element on the prediction.

This will make the output surface less smooth. Each model is used to more accurately fit different kinds of phenomena.

Shows two common models ("exponential" and "Gaussian") and identifies the difference between functions:

　　

　　

ArcGIS Tutorial: Fitting models based on empirical Semivariogram