Covariance models on the surface of a sphere: when does it matter?

Jaehong Jeong, Mikyoung Jun

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


There is a growing interest in developing covariance functions for processes on the surface of a sphere because of the wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle distance, isotropic and positive definite functions in a Euclidean space can be used as covariance functions on the surface of a sphere. This approach, however, may result in physically unrealistic distortion on the sphere especially for large distances. We consider several classes of parametric covariance functions on the surface of a sphere, defined with either the great circle distance or the Euclidean distance, and investigate their impact upon spatial prediction. We fit several isotropic covariance models to simulated data as well as real data from National Center for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis on the sphere. We demonstrate that covariance functions originally defined with the Euclidean distance may not be adequate for some global data.
Original languageEnglish (US)
Pages (from-to)167-182
Number of pages16
Issue number1
StatePublished - Jun 10 2015
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-03-31
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Mikyoung Jun's research was supported by NSF grant DMS-1208421. This publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The NCEP/NCAR reanalysis data used in this work was provided by the NOAA/ESRL PSD, Boulder, Colorado, USA. The authors would like to thank Peter Guttorp for the discussion about this problem and Ramalingam Saravanan for suggesting to look at geopotential height data. We also thank David Bolin and Håvard Rue for their help to generate an oscillating Matérn models from the R-INLA package.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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