Global Ordinary Kriging
Global Ordinary Kriging Interpolation · Also known as: ordinary kriging, OK, global kriging, stationary ordinary kriging
Global Ordinary Kriging (GOK) is the canonical geostatistical interpolation method that estimates values at unsampled locations as a weighted linear combination of nearby observations. It fits a single variogram model to the entire dataset, enforcing a global stationarity assumption, and produces optimal unbiased predictions along with quantified prediction uncertainty at every interpolated point.
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When to use it
Use Global Ordinary Kriging when you have spatially referenced point data covering a study region and need smooth, uncertainty-quantified interpolated surfaces — for example, environmental monitoring, soil science, hydrology, or mining. It is appropriate when the spatial process is reasonably stationary across the domain (no strong systematic trend) and sample coverage is adequate. Do not use it when there is a clear spatial trend in the mean (use Universal Kriging instead), when the dataset is very large (computational cost grows cubically with n — use local windows or approximation methods), or when spatial structure varies markedly across sub-regions (use Local Ordinary Kriging or non-stationary models).
Strengths & limitations
- Produces the Best Linear Unbiased Predictor (BLUP) under the assumed variogram model.
- Automatically provides spatial prediction uncertainty (kriging variance) at every interpolated location.
- Respects the data exactly at sampled locations (exact interpolator) by design.
- Theoretically grounded in geostatistics with a rich literature and well-validated software implementations.
- Single global variogram is parsimonious and interpretable, facilitating communication of spatial structure.
- Stationarity assumption — constant mean and spatially uniform covariance structure — is often violated over large or heterogeneous domains.
- Computational cost scales as O(n^3) for the kriging system, making it impractical for datasets with tens of thousands of points without approximations.
- Variogram estimation and model selection introduce subjectivity; a poorly fitted variogram propagates error throughout all predictions.
- Kriging variance reflects only the model uncertainty given the variogram, not uncertainty in the variogram itself (underestimates total uncertainty).
- Performs poorly in strongly anisotropic or non-stationary fields if the global variogram does not capture local structure.
Frequently asked
What makes it 'ordinary' kriging versus other kriging variants?
Ordinary Kriging assumes the mean of the spatial process is unknown but constant. This contrasts with Simple Kriging (known constant mean), Universal Kriging (unknown spatially varying mean modelled as a polynomial trend), and Co-Kriging (which incorporates secondary covariates).
What does 'global' mean in Global Ordinary Kriging?
The term global indicates that a single variogram model is estimated from and applied to the entire dataset. All predictions share the same spatial correlation structure. This is the default OK approach; Local Ordinary Kriging fits separate variograms within moving spatial windows to allow local adaptation.
How do I choose the variogram model (spherical, exponential, Gaussian)?
Fit each candidate model by weighted least squares to the experimental variogram and compare residual sums of squares or cross-validation RMSE. The spherical and exponential models are most commonly used; the Gaussian model can produce unstable kriging systems when the nugget is near zero and should be used with caution.
Can kriging extrapolate beyond the sample area?
Technically yes, but it is inadvisable. Outside the convex hull of observations, kriging weights can become negative or very small, and the kriging variance grows quickly. Treat predictions far from data points as highly uncertain and avoid drawing strong conclusions from them.
How do I validate a kriging model?
Use leave-one-out cross-validation (jackknifing): predict each observation from the remaining points and compute RMSE and mean standardised error. Standardised errors should be near zero on average and have variance near 1 if the kriging variance is well-calibrated.
Sources
- Cressie, N. A. C. (1993). Statistics for Spatial Data (revised ed.). Wiley. ISBN: 978-0471002550
- Chiles, J.-P., & Delfiner, P. (2012). Geostatistics: Modeling Spatial Uncertainty (2nd ed.). Wiley. ISBN: 978-0470183151
How to cite this page
ScholarGate. (2026, June 3). Global Ordinary Kriging Interpolation. ScholarGate. https://scholargate.app/en/spatial-analysis/global-ordinary-kriging
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Co-krigingSpatial analysis↔ compare
- Local Ordinary KrigingSpatial analysis↔ compare
- Ordinary KrigingSpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare
- Universal KrigingSpatial analysis↔ compare