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Interpolation[Kriging]

  

SetVariogram

  

set the variogram of the Kriging object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SetVariogram(k, var)

Parameters

k

-

a Kriging object

var

-

a variogram, specified by name (Spherical, Exponential, Gaussian, Wave, RationalQuadratic or Circular) or as a function call with three positive numerical arguments

Description

• 

The SetVariogram command sets the variogram associated with the given Kriging object.

• 

This variogram is used in the Kriging interpolation process to determine the weights for various points. For example, it is used when you interpolate at a given point. The variogram gives the variance of the difference between field values at two locations at a given distance.

• 

If the variogram is specified as a name only, then the parameters will be estimated by the FitVariogramParameters command.

• 

A Kriging object by default has its variogram set to the Spherical model with parameters determined by FitVariogramParameters, and it will keep this default until SetVariogram is called.

• 

The variogram has three parameters: the nugget, sill, and range.

– 

The nugget is the limit of the variogram as the distance approaches zero, and corresponds to a base level of uncertainty and variation. The nugget must be nonnegative.

– 

The sill is the maximum variance achieved for any distance. The sill must be greater than or equal to the nugget; so in particular, it must be nonnegative.

– 

The (effective) range is the distance at which the variogram reaches 95% of the sill, or for some variograms, the distance where the sill is reached. More precisely, it is a distance a so that if ah, then γh deviates from the sill by less than 5%. Points at a distance greater than the range are not used to compute interpolated values. The range must be positive.

Examples

The available variogram models are as follows. Each is a family of functions of h, the distance, with parameters c__n, c__s, and a corresponding to the nugget, sill, and range, respectively. After defining each variogram model, you see a graph of the variogram with parameters c__n=0.5, c__s=5, and a=4, displayed for h from 0 to 6. Dashed lines indicate the nugget, sill, and range, and a gray rectangle indicates the bounds between which the variogram is guaranteed to lie at distances greater than the range. After this graph, you see a heat map of a sample generated with GenerateSpatialData according to the same variogram over a square with sides of length 6.

The Sphericalc__n,c__s,a model has the following equation.

γh=c__n+c__sc__n3h2ah32a3hac__sotherwise

heatmap

The Exponentialc__n,c__s,a model has the following equation.

γh=c__n+c__sc__n1ⅇ3ha

heatmap

The Gaussianc__n,c__s,a model has the following equation.

γh=c__n+c__sc__n1ⅇ3h2a2

heatmap

The Wavec__n,c__s,a model has the following equation.

γh=c__n+c__sc__n1sin20haa20h

heatmap

The RationalQuadraticc__n,c__s,a model has the following equation.

γh=c__n+19c__sc__nh2a21+19h2a2

heatmap

The Circularc__n,c__s,a model has the following equation.

γh=c__n+c__sc__n12arccoshaπ+2h1h2a2πah<ac__sotherwise

heatmap

withInterpolation&colon;

We generate some values that have the specified variogram.

points,dataKriging:-GenerateSpatialDataSpherical1&comma;10&comma;1

(1)

kKrigingpoints&comma;data

kKrⅈgⅈng ⅈnt&ExponentialE;rpolatⅈon obȷ&ExponentialE;ct wⅈth 30 sampl&ExponentialE; poⅈntsVarⅈogram: Sph&ExponentialE;rⅈcal(1.94850490681975,21.5388709430209,.52789833)

(2)

Setting the variogram explicitly is not required, as a variogram with estimated parameters is set by default. However, it leads to better results if the correct variogram is set.

SetVariogramk&comma;Spherical1&comma;10&comma;1

Krⅈgⅈng ⅈnt&ExponentialE;rpolatⅈon obȷ&ExponentialE;ct wⅈth 30 sampl&ExponentialE; poⅈntsVarⅈogram: Sph&ExponentialE;rⅈcal(1,10,1)

(3)

ComputeGridk&comma;0..1&comma;0..1&comma;0.1&comma;output=plot

Compatibility

• 

The Interpolation[Kriging][SetVariogram] command was introduced in Maple 2018.

• 

For more information on Maple 2018 changes, see Updates in Maple 2018.

See Also

ComputeGrid

Constructor

DisplayVariogram

Interpolating at a point

Kriging