Regionalization (geostatistics)

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Under regionalization is understood in the geostatistics the transmission of data point to the area. Of course, this process does not only play a role in this area, which is primarily concerned with it. Rather, regionalization is of great importance wherever data are recorded selectively, i.e. randomly , and then displayed over a large area. Classic examples are hydrology , meteorology , soil science or surveying .

Procedure

Thiessen polygons

The Thiessen or Voronoi polygons offer a very simple possibility of regionalization, which can also be easily carried out by hand . The total area is divided into individual polygons without gaps using a vertical construction. As a result, every point in a polygon is closer to its reference point than any other point. The value of the reference point of a polygon is now assigned to the entire polygon.

The advantage of this procedure is the possibility to regionalize even nominal data . A major disadvantage, however, are cracks on the polygon edges.

Interpolation method

Interpolation methods calculate a value for each unknown point of the surface taking into account the known points. If all measuring points are included, one speaks of a global procedure , whereas only measuring points of a defined environment are included, a local procedure . Many interpolation methods are based on networks such as a TIN ( Triangulated Irregular Network ).

Inverse distance weighting

In the inverse distance weighting (English: Inverse Distance Weighting) receives an unknown point, a weighted average of neighboring pixel values assigned. The weight is calculated depending on the distance:

where w is the weighting or the weighting factor and d is the distance between the known and the unknown point. The greater the power k is chosen, the less the influence of more distant points.

Splines

Splines are best fit curves that are calculated on the basis of higher-order polynomials . They are relatively easy to calculate and provide very smooth boundaries. The disadvantage is that higher order polynomials can produce unrealistically high or low values.

Kriging

The best interpolation method is probably kriging . The first step here is a statistical analysis of the data ( semivariogram analysis ), in which the best possible estimator of the correlation between distance and weighting is determined. This estimator can then be used to interpolate.

Kriging generally delivers very good regionalization results. It is also advantageous to be able to calculate the residual error - you can therefore make a statement about the accuracy of the result.

Programs