Cokriging
Also known as: co-kriging, multivariate kriging, ortak kriging
Cokriging extends kriging to use one or more correlated secondary variables to improve prediction of a primary variable. When the variable of interest is sparsely sampled but a related, cheaper-to-measure variable is densely sampled, cokriging borrows strength from the secondary variable through their cross-correlation, yielding more accurate interpolations and prediction variances than kriging the primary variable alone.
Key highlights
- Improves prediction of a sparsely sampled variable using correlated secondary data.
- Provides prediction variances, quantifying uncertainty like all kriging.
- Exploits multivariate spatial structure that univariate kriging ignores.
- Flexible: handles several secondary variables through coregionalization.
Intuition
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How it works
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When to use it
Use cokriging when the primary variable is undersampled but a correlated secondary variable is more abundantly measured, and you want to exploit that correlation for better predictions with honest uncertainty — common in soil and environmental science, mining, hydrology, and remote-sensing-assisted mapping. It pays off most when the cross-correlation is strong and the secondary variable is much more densely sampled. The costs are modelling effort and stability: fitting a valid joint variogram model (linear model of coregionalization) is more demanding than a single variogram, the system is larger and can be numerically delicate, and weak cross-correlation yields little gain over ordinary kriging. When the secondary variable is exhaustively known (e.g., a covariate raster), simpler alternatives such as kriging with external drift or regression kriging are often easier and competitive.
Strengths & limitations
- Improves prediction of a sparsely sampled variable using correlated secondary data.
- Provides prediction variances, quantifying uncertainty like all kriging.
- Exploits multivariate spatial structure that univariate kriging ignores.
- Flexible: handles several secondary variables through coregionalization.
- Requires fitting a valid joint (cross-)variogram model, which is demanding.
- Larger, sometimes numerically unstable linear systems than ordinary kriging.
- Little benefit when the cross-correlation between variables is weak.
- More data, assumptions, and expertise needed than deterministic interpolators.
Common pitfalls
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Applications
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Frequently asked
When does cokriging beat ordinary kriging?
When the primary variable is sparsely sampled, a secondary variable is more densely sampled, and the two are strongly cross-correlated. In that case the secondary data meaningfully reduce prediction error and variance. If the cross-correlation is weak or the secondary variable is as sparse as the primary, cokriging offers little advantage.
What is the cross-variogram?
It describes how the differences in the primary and secondary variables co-vary as a function of the distance between locations — the spatial analogue of cross-covariance. Cokriging needs a jointly valid set of auto- and cross-variograms (a linear model of coregionalization) so the prediction system is well-posed.
Is there a simpler alternative when I have a full covariate map?
Yes. If the secondary variable is known everywhere (e.g., an elevation or remote-sensing raster), kriging with external drift or regression kriging incorporate it more simply than full cokriging and are often equally accurate, avoiding the harder joint-variogram modelling.
Sources
- 1.Matheron, G. (1963). Principles of geostatistics. Economic Geology, 58(8), 1246–1266.
- 2.Cressie, N. A. C. (1993). Statistics for Spatial Data (Revised ed.). John Wiley & Sons.ISBN 978-0-471-00255-0
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Cite this page
ScholarGate. (2026, June 2). Cokriging. ScholarGate. https://scholargate.app/spatial-analysis/cokriging