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

open allclose all

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:

Query the estimated trend:

Visualize the random field:

Create spatial prediction with an unknown quadratic trend:

Visualize the data:

Compute the spatial estimate:

Query the estimated trend:

Visualize the random field:

Create spatial prediction with a trend specified by a basis:

Visualize the data:

Compute the spatial estimate:

Query the estimated trend:

Visualize the random field:

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_2024_spatialtrendfunction, author="Wolfram Research", title="{SpatialTrendFunction}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/SpatialTrendFunction.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_spatialtrendfunction, organization={Wolfram Research}, title={SpatialTrendFunction}, year={2021}, url={https://reference.wolfram.com/language/ref/SpatialTrendFunction.html}, note=[Accessed: 21-December-2024 ]}