Anisotropic Kriging

Command line

The Anisotropic Kriging operation can be directly executed by typing one of the following expressions on the command line of the Main window:

OUTMAP	=	MapKrigingAnisotropic(InputPointMap, Georef, SemiVarModel, LimDist, Angle, Ratio)
OUTMAP	=	MapKrigingAnisotropic(InputPointMap, Georef, SemiVarModel, LimDist, Angle, Ratio, 1\|0)
OUTMAP	=	MapKrigingAnisotropic(InputPointMap, Georef, SemiVarModel, LimDist, Angle, Ratio, 1\|0, min, max)
OUTMAP	=	MapKrigingAnisotropic(InputPointMap, Georef, SemiVarModel, LimDist, Angle, Ratio, 1\|0, min, max, No \| Average \| Firstval)
OUTMAP	=	MapKrigingAnisotropic(InputPointMap, Georef, SemiVarModel, LimDist, Angle, Ratio, 1\|0, min, max, Average \| Firstval, Tolerance)

where:

OUTMAP	is the name of the output raster map containing the Kriging estimates.
MapKrigingAnisotropic	is the command to start the Anisotropic Kriging operation.
InputPointMap	is the name of the input point map with a value domain. To use a value attribute column from an attribute table which is linked to an ID point map, use InputPointMap.Columnname.
Georef	is the name of an existing georeference for the output raster map.
SemiVarModel	Model(nugget, sill, range) \| Power(nugget, slope, pow) This expression defines the semi-variogram model and its parameters that should be used. You should specify the parameters for the model with the largest range or, when using the Power model, the model with the lowest slope.
Model	Spherical \| Exponential \| Gaussian \| Wave \| RatQuad \| Circular
nugget	value for the nugget, according to your semi-variogram (real value).
sill	value for the sill, according to your semi-variogram (real value).
range	value for the range, according to your semi-variogram (real value > 0).
slope	when using the Power model: value for the 'slope'. When pow is specified as 1 (i.e. thus using a linear model), then slope is the direction coefficient, i.e. Dg/Dh (real value >= 0).
pow	when using the Power model: an exponent 0 < real value < 2. When you use value 1, the Power model will become linear and the slope will be constant. If the power exponent is 2 the assumed stochastic model (�randomness�) is not always justifiable and the interpolation can become pathological.
LimDist	A value for the limiting distance: points that are further away from an output pixel than the limiting distance will not be used in the Kriging equations. Normally, this is a value smaller than the range of the semi-variogram model (0 <= real value < diagonal size of map).
Angle	Anisotropy angle in degrees clockwise from the north (-360 <= real value <= 360).
Ratio	Anisotropy ratio, i.e. the largest semi-variogram range divided by the smallest range (1 < real value <= 10).
1 \| 0	Specify whether or not an error map has to be created. The error map will contain the square root of the Kriging error variance values, i.e. standard deviations per pixel. When this parameter is not specified, no error map will be created.
1	Create an error map. The error map will obtain the same name as specified for the output Kriging map followed by the additional string _Error.
0	Do not create an error map.
min, max	Optional parameters (integer values) to specify the minimum and maximum number of points that should be taken into account per Kriging estimate/prediction, i.e. the number of points within the limiting distance of an output pixel that should be taken into account in the calculation of the output value for that pixel. When the minimum is not specified a minimum value 1 will be used. When, for an output pixel, less points than the specified minimum are found within the specified limiting distance, no Kriging is performed and the output pixel will become undefined. If the whole map contains less points than the specified minimum, an error message will appear and no output will be produced. When the maximum is not specified, value 16 will be used. When, for an output pixel, more points than the specified maximum are found within the specified limiting distance, only the specified maximum number of points that are nearest to the output pixel will be used.
No \| Average \| Firstval
	Choose how to handle possible coinciding points or duplicates. When no method is specified, Average will be used.
No	No removal of duplicates. Mind: when there are coinciding points, the Kriging system may become unsolvable and will give undefined values for the pixels for which coinciding points are found.
Average	Values of duplicates are replaced by the average (arithmetic mean); the coordinates of the first point are taken as new position.
Firstval	Values of duplicates (and their coordinates) are replaced by those of the first point.
Tolerance	Optional parameter to specify the distance within which 2 sample points are considered to coincide. When not specified, a tolerance of 0.1 m will be used.

When the definition symbol = is used, a dependent output map is created; when the assignment symbol := is used, the dependency link is immediately broken after the output map has been calculated.

Example:

The following expression:

OutAniK

MapKrigingAnisotropic(MyPoints.MyAttr, MyGeoref, Spherical(10, 70, 800), 200, 35, 1.4, 1, 6, 20, Firstval, 0.2)

performs Anisotropic Kriging:

on the attribute values in column MyAttr in an attribute table that is linked to point map MyPoints;
georeference MyGeoref will be used for the output raster maps;
a Spherical semi-variogram model will be used with a nugget of 10, a sill of 70, and a range of 800 meter;
a limiting distance will be used of 200 m;
an anisotropy angle of 35 degrees, and an anisotropy ratio of 1.4 will be used;
an output error map will be defined;
each Kriging equation will use at least 6 points and at most 20 points (min, max);
points are considered as coinciding when the distance between them is less than 0.2 m (tolerance);
for coinciding points only the value and coordinates of the first point encountered will be used.

The results of the expression are:

output raster map OutAniK containing the Kriging estimates;
output error map OutAniK_Error.

Note:

You can also use the MapKrigingUniversal(...) expressions to perform Anisotropic Kriging:

OUTMAP	=	MapKrigingUniversal(InputPointMap, Georef, SemiVarModel, LimDist, 0, Angle, Ratio [, 1\|0 [, min, max [, No \| Average \| Firstval ]]] )
OUTMAP	=	MapKrigingUniversal(InputPointMap, Georef, SemiVarModel, LimDist, 0, Angle, Ratio [, 1\|0 [, min, max [, Average \| Firstval [, Tolerance ]]]] )

where:

MapKrigingUniversal	is the command to start the Anisotropic Kriging operation.
0	Obligatory parameter to indicate Anisotropic Kriging.
Angle	Anisotropy angle in degrees clockwise from the north (-360 <= real value <= 360).
Ratio	Anisotropy ratio, i.e. the largest semi-variogram range divided by the smallest range (1 <= real value <=10) .
1 \| 0	Specify whether or not an error map has to be created. The error map will contain the square root of the Kriging error variance values, i.e. standard deviations per pixel. When this parameter is not specified, no error map will be created.
1	Create an error map. The error map will obtain the same name as specified for the output Kriging map followed by the additional string _Error.
0	Do not create an error map.
Parameters between square brackets [] are optional. For an explanation on parameters which are not described here, see above.