SpatialTrendFunction

SpatialTrendFunction

is an option to SpatialEstimate that specifies what global trend model to use for data.

Details

  • SpatialTrendFunction specifies the family of global trends to fit to data. The global trend is a part of the spatial prediction model, where the remaining parts come from local variation and noise.
  • The following settings can be used:
  • Automaticautomatically determine trend model
    na polynomial with total degree n (universal kriging)
    {{f1,f2,},{x,y,}}estimate the model β0+β1f1+β2f2+ with the basis functions fi in the variables x,y, as in LinearModelFit (universal kriging)

Examples

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Basic Examples  (1)

The following data consists of the location of 84 weather stations in Illinois and the temperature measured at noon on September 1, 2021:

Visualize the values at locations:

Create spatial prediction with linear global trend:

Generate random locations in the region defined by the weather stations:

Compute the prediction values and visualize:

Scope  (3)

Create spatial prediction with an unknown constant trend:

Visualize the data:

Compute the spatial estimate:

Visualize the random field:

Query the estimated trend:

Create spatial prediction with an unknown quadratic trend:

Visualize the data:

Compute the spatial estimate:

Query the estimated trend:

Create spatial prediction with a trend specified by a basis:

Visualize the data:

Compute the spatial estimate:

Properties & Relations  (2)

For large spatial noise levels, the spatial estimator converges to the trend function:

Compute SpatialEstimate for increasing values of noise level for specified polynomial trend order:

Visualize:

The method for estimating the trend will change depending on whether we supply the variogram:

Compute spatial estimate with a given variogram model:

Compute spatial estimate with the variogram being estimated automatically:

Compare the estimated trend functions:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2022_spatialtrendfunction, author="Wolfram Research", title="{SpatialTrendFunction}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/SpatialTrendFunction.html}", note=[Accessed: 07-October-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_spatialtrendfunction, organization={Wolfram Research}, title={SpatialTrendFunction}, year={2021}, url={https://reference.wolfram.com/language/ref/SpatialTrendFunction.html}, note=[Accessed: 07-October-2022 ]}