topic Re: K-Bessel Semivariogram Equation in ArcGIS GeoStatistical Analyst Questions

K-Bessel Semivariogram Equation

MatthewPoppleton — Tue, 16 Jul 2024 21:29:27 GMT

I completed an analysis using EBK with the "Power" semivariogram model and the "K-Bessel Detrended" semivariogram model.

The equation for power (γ(h)= Nugget + b|h|α) can be found in "What is empirical Bayesian kriging?", but the K-Bessel equation is not included. If understand correctly, the detrended model should would be the same equation as K-Bessel but with a first-order trend removal.

Can anyone provide the equation for the K-Bessel semivariogram model, or suggest where I might be able to find this referenced? I'm not sure if K-Bessel would be an equation I could can reference elsewhere in literature or if it would be specific to this version of ArcGIS Pro EBK.

I did find an answer to a similar question by @EricKrause from 2012 that references ArcGIS 9 Documentation, and includes a K-Bessel equation on page 257. Would this be the same model?

Re: K-Bessel Semivariogram Equation

EricKrause — Fri, 19 Jul 2024 14:15:37 GMT

Hi @MatthewPoppleton,

Yes, that equation from the ArcGIS 9 documentation is the formula for the K-Bessel semivariogram that is used for all instances of K-Bessel in Geostatistical Analyst. As you said, the detrended version performs a first-order trend removal, then applies the K-Bessel formula to the detrended values.

Also, the K-Bessel semivariogram is often called the "Matern" semivariogram in other geostatistical literature. You might be able to find more information searching for that keyword instead.

-Eric

Re: K-Bessel Semivariogram Equation

MatthewPoppleton — Mon, 22 Jul 2024 17:24:47 GMT

Thank you so much for the clarification, really appreciate the help!

Cheers,

Matthew