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VariogramFunction

is an option to SpatialEstimate that specifies the local variation model to use.

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VariogramFunction

VariogramFunction

is an option to SpatialEstimate that specifies the local variation model to use.

Details

  • VariogramFunction together with SpatialNoiseLevel is used to make local predictions of spatial values. Combining local predictions with a global trend gives the full spatial prediction function.
  • The local variation is described using a variogram , where is a spatial field of values. When the spatial field is weakly stationary and isotropic, gamma(p_1,p_2)=gamma(TemplateBox[{{{p, _, 1}, -, {p, _, 2}}}, Norm]). A typical isotropic variogram can be described in terms of its sill, range and noise variance.
  • For full details, see the EstimatedVariogramModel page.
  • The following settings can be used:
  • Automaticautomatically compute a variogram
    "model"fit "model" variogram
    {"model",pars}use "model" with given parameters pars
    VariogramModel[…]use fully specified variogram model
  • The possible "model" values are given in VariogramModel.

Examples

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Basic Examples  (1)

Use SpatialEstimate with specified variogram function:

Wolfram Language code: data = SpatialPointData[«2»];

The data consists of rainfall observations in Switzerland:

Wolfram Language code: Show[Region[data["ObservationRegion"]], PointValuePlot[data, ColorFunction -> "Rainbow"]]

Create spatial predictor function with exponential variogram model:

Wolfram Language code: locs = data["Points"]; vals = data["Annotations"]["Rainfall"];
Wolfram Language code: spf = SpatialEstimate[locs -> vals, VariogramFunction -> "Exponential"]

Visualize the estimator values over the observation region:

Wolfram Language code: sim = RandomPoint[data["ObservationRegion"], 2000];
Wolfram Language code: PointValuePlot[sim -> spf[sim], ColorFunction -> "Rainbow", AspectRatio -> .7]

Scope  (1)

Use SpatialEstimate with fitted variogram function:

Wolfram Language code: data = SpatialPointData[«2»];

The data consists of rainfall observations in Switzerland:

Wolfram Language code: Show[Region[data["ObservationRegion"]], PointValuePlot[data, ColorFunction -> "Rainbow"]]

Fit a cubic variogram model and use it for spatial prediction:

Wolfram Language code: locs = data["Points"]; vals = data["Annotations"]["Rainfall"];
Wolfram Language code: cvf = EstimatedVariogramModel[locs -> vals, "Cubic"]
Wolfram Language code: cvf["Visualization"]

Compute the prediction functions with the fitted cubic variogram model:

Wolfram Language code: spf = SpatialEstimate[locs -> vals, VariogramFunction -> cvf]
Wolfram Language code: spf["Visualization", "Data" -> True, Method -> "3D"]

Applications  (1)

Specifying VariogramFunction in SpatialEstimate allows you to obtain a gallery of models:

Wolfram Language code: data = ResourceData["Sample Data: Swiss Rainfall"]

Visualize data:

Wolfram Language code: Show[Region[data["ObservationRegion"]], PointValuePlot[data, ColorFunction -> "Rainbow"]]

Compute estimates using specific models:

Wolfram Language code: models = {"Cubic", "Spherical", "Exponential", "Gaussian"};
Wolfram Language code: estimates = SpatialEstimate[data, VariogramFunction -> #]& /@ models;

Create a set of random points and compute the estimated values at these locations:

Wolfram Language code: pts = RandomPoint[data["ObservationRegion"], 2000]; vals = Comap[estimates, pts];

Visualize rainfall values over the whole region:

Wolfram Language code: Grid@ArrayReshape[#, {2, 2}]&@MapThread[Show[Region[data["ObservationRegion"]], PointValuePlot[pts -> #1, PlotStyle -> PointSize[0.015], ColorFunction -> "Rainbow"], PlotLabel -> #2]&, {vals, models}]
Wolfram Research (2021), VariogramFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/VariogramFunction.html.

Text

Wolfram Research (2021), VariogramFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/VariogramFunction.html.

CMS

Wolfram Language. 2021. "VariogramFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VariogramFunction.html.

APA

Wolfram Language. (2021). VariogramFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VariogramFunction.html

BibTeX

@misc{reference.wolfram_2026_variogramfunction, author="Wolfram Research", title="{VariogramFunction}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/VariogramFunction.html}", note=[Accessed: 15-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_variogramfunction, organization={Wolfram Research}, title={VariogramFunction}, year={2021}, url={https://reference.wolfram.com/language/ref/VariogramFunction.html}, note=[Accessed: 15-June-2026]}