Point statistics

Point statistics may help to get an impression of the nature of your point data prior to for instance a point interpolation, and to find necessary input parameters for a Kriging operation.

For point statistics a point map is required in which:

the points themselves are values (point map with a value domain), for instance concentration values, or
the points have an identifier (point map with a Class or ID domain) and values are stored in a column of the attribute table that is linked to the map.

The output of the Spatial correlation, Cross Variogram and the Pattern analysis operations is a table. By displaying the output table, you can also display graphs, especially semi-variograms. The output of the Variogram surface operation is a plot-like raster map.

Operations to calculate point statistics:

Spatial correlation: calculates spatial autocorrelation (as Moran's I), spatial variance (as Geary's c) and semi-variogram values g(h) for point values that are at certain distances towards each other in a point map.

Regarding spatial autocorrelation and spatial variance is the user encouraged to compare his or her data set with a data set consisting of the same point locations, with a set of attribute values, approximately in the same range as the measured variable, but created at random (using one of the RND functions in Table Calculation). If the correlation/variance graphs are very much the same for the measured data and the random data, no autocorrelation exists between the data points. Hence, point interpolation is not useful.

By calculating semi-variogram values, you can display a semi-variogram. By modelling the semi-variogram, you can find the necessary input parameters, such as a model (spherical, exponential, etc.) and sill, range, and nugget values, for a Kriging operation.

Variogram surface: calculates a surface of semi-variogram values where each cell (pixel) in the surface represents a directional distance class. The output surface, a raster map with a special kind of georeference, may help you to visualize possible anisotropy of your data and to determine the direction of the anisotropy axis. As input, you can use a point map or a raster map.

Subsequently, you can calculate directional semi-variograms by using the directional method in the Spatial correlation operation. From the output table of Spatial correlation, you can prepare a semi-variogram model and investigate the range of the variable in the semi-variogram model both in the direction of anisotropy as well as in the direction perpendicular to it. Then, you are ready to perform Anisotropic Kriging.

Cross Variogram: calculates experimental semi-variogram values for two variables and cross-variogram values for the combination of both variables. As input for the Cross Variogram operation, you can use a point map with a linked attribute table containing at least two value attribute columns. The Cross Variogram operation is a multivariate form of the Spatial correlation operation.

From the output table of the Cross Variogram operation, you can create semi-variogram models for both variables and a cross-variogram model for the combination of the variables. All three models serve as input for the CoKriging operation. CoKriging calculates estimates or predictions for a poorly sampled variable (the predictand) with help of a well-sampled variable (the covariable). The variables should be highly correlated (positive or negative).

Pattern analysis: a tool to obtain information on the spatial distribution of points in a point map. The output table contains six columns with the probabilities of finding 1 point (Prob1Pnt) within a certain distance from any point in your input map, then 2 points (Prob2Pnt), 3 points (Prob3Pnt), etc. Another column (ProbAllPnt) contains the sum of Prob1Pnt, Prob2Pnt, ..., Prob(n-1), in which n is the number of points in the input map.

By inspecting the graphs of distances against probabilities, you may recognize distribution patterns of your points like random, clustered, regular, paired etc.