is an option to SpatialEstimate and other spatial functions that gives the noise variance level in the data.


  • SpatialNoiseLevel is also known as a nugget or variogram nugget.
  • SpatialNoiseLevel effectively describes the data measurement error.
  • SpatialNoiseLevel together with VariogramFunction is used to make local predictions of spatial values. Combining local predictions with a global trend gives the full spatial prediction function.
  • The effect on spatial prediction of specifying positive SpatialNoiseLevel is that the prediction function is no longer required to interpolate through the values at each location. In such a case, the prediction surface no longer interpolates the data, but it is a smoother approximating surface.
  • Possible settings for SpatialNoiseLevel:
  • Automaticestimate the noise level from the data
    θspecifiy the non-negative noise level of size


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Basic Examples  (2)

Add noise variance to VariogramModel:

Create prediction surface with and without spatial noise variance:

Create spatial predictor function with zero noise level:

Compute the prediction function with positive noise level:

Compare the prediction surfaces:

Scope  (1)

1D example:

Create spatial prediction function with linear trend:

If the noise variance is 0, SpatialPredict interpolates exactly:

Applications  (1)

SpatialNoiseLevel can create a smoother picture of the data:

Standard ways to visualize the data:

Spatial estimate with smoothing:

Compute estimates for random locations:

Properties & Relations  (1)

Only with zero SpatialNoiseLevel is SpatialEstimate an exact interpolator:

Compute spatial estimate for varying values of spatial noise level:

Visualize the estimates with the data:

Wolfram Research (2021), SpatialNoiseLevel, Wolfram Language function,


Wolfram Research (2021), SpatialNoiseLevel, Wolfram Language function,


Wolfram Language. 2021. "SpatialNoiseLevel." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2021). SpatialNoiseLevel. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_spatialnoiselevel, author="Wolfram Research", title="{SpatialNoiseLevel}", year="2021", howpublished="\url{}", note=[Accessed: 24-July-2024 ]}


@online{reference.wolfram_2024_spatialnoiselevel, organization={Wolfram Research}, title={SpatialNoiseLevel}, year={2021}, url={}, note=[Accessed: 24-July-2024 ]}