ArcGIS Tutorial: Composition of geostatistical models

The geostatistical (kriging) model consists of several components: examining the data (distribution, trend, direction composition, and outliers), calculating empirical semivariogram or covariance values, fitting the model based on empirical values, generating a kriging equation matrix, and solving it to obtain the predicted value and its associated error for each position in the output surface ( Uncertainties).

　　Calculate Empirical Semivariogram

As with most interpolation methods, Kriging is based on the similarity of things that are closer to each other (this is quantified as spatial autocorrelation). Empirical Semivariogram is a way to explore this relationship. Points that are close to each other at distances are smaller than the point pairs that are farther away from each other. In the empirical Semivariogram, you can examine the scope that makes this assumption possible.

　　

　　Fit model

Fit is achieved by using a point definition to provide the best fit model (Blue line in). This means finding a line so that the weighted squared difference between each point and the line is as small as possible. This is called weighted least squares fitting. This model quantifies spatial autocorrelation in the data.

　　

　　Create a matrix

The kriging equation is contained in matrices and vectors that depend on the spatial autocorrelation of the measurement sampling location and the prediction location. Spatial autocorrelation values are derived from the Semivariogram model. Matrices and vectors determine the kriging weights assigned to each measured value in the search neighborhood.

　　Make predictions

Based on the kriging weights of the measured values, the software calculates the predicted values for locations that contain unknown values.

　　

ArcGIS Tutorial: Composition of geostatistical models