Anisotropic Kriging can be seen as a point interpolation, which requires a point map as input and which returns a raster map with estimations and optionally an error map. Anisotropic Kriging is a variant of the Ordinary Kriging operation: Anisotropic Kriging incorporates the influence of direction dependency.
Theory:
The regionalized variable theory assumes that the variation of the variable under study is the same in all directions. If this is true, the spatial variation is isotropic and you can use the Simple or Ordinary Kriging operation. In many natural situations, however, it can be expected that there is a preferred direction to the local, spatially dependent variation. In these situations the variable displays anisotropic behavior.
If anisotropy is present, and is reflected by the same sill but different ranges in the same model, then the anisotropy is called geometric anisotropy. In other words, geometric anisotropy has variations for distance h in one direction being the same as variations for distance k*h in another direction (Burrough 1986). In case of geometric anisotropy it is possible to 'remove' it by applying an affine transformation to the distances: this is Anisotropic Kriging. When for the same variable, semi-variogram values for two perpendicular directions require different models or different sills then zonal anisotropy is present. Removal of zonal anisotropy is more complex and not supported by ILWIS.
Preparation and input parameters:
Besides an input map, you need to specify the following parameters for Anisotropic Kriging:
When you specify an angle of 0 and a ratio of 1 means there is no anisotropy. Results will then be the same as in Ordinary Kriging.
Furthermore, you need to specify a limiting distance or search radius, optionally a minimum and maximum number of points within the limiting distance that should be taken into account in the calculation of an output pixel value, and a method to deal with (almost) coinciding points. These options are the same as in Ordinary Kriging.
For more information on preparations and input parameters, see Kriging: functionality, section on preparation, or How to use Kriging.
Input map requirements:
The input point map should be a value map. When you use a point map with an ID domain which has a linked attribute table, you can also select a column with a value domain from the map's attribute table. Furthermore, you need to specify the angle and ratio of anisotropy, the semi-variogram model with the largest range (except when using the Power model), the limiting distance, etc. For explanations, see above.
When using the dialog box, there is a limitation of a maximum of 100 valid input point values within each limiting distance (search radius). This limitation is not present when using the command line.
Domain and georeference of output raster maps:
The output raster map containing the Kriging estimates or predictions uses the same value domain as the input point map or the attribute column. The value range and precision can be adjusted for the output map; it is advised to choose a wider value range for the output map than the input value range.
The georeference for the output Kriging map has to be selected or created; you can usually select an existing georeference corners.
Optionally, an output error map can be created which will contain the standard errors of the estimates, i.e. the square root of the error variance. The error map will obtain the same name as specified for the output Kriging map, followed by the string _Error. The output error map will use the same domain and the same georeference as the output Kriging map with the predictions.
Confidence interval maps:
From the combination of a Kriged output map containing the estimates and its output error map, you can create confidence interval maps by using some MapCalc statements. For more information, see How to calculate confidence interval maps.
See also:
Anisotropic Kriging : dialog box
Anisotropic Kriging : command line
Anisotropic Kriging : algorithm
Moving average : functionality
Variogram surface : functionality
Spatial correlation : functionality