Global Kriging
Also known as: global-neighborhood kriging, full-data kriging, exhaustive kriging, non-local kriging
Global Kriging is the ordinary kriging interpolation procedure applied using all available sample points as the neighborhood — no spatial search window limits which data contribute to each prediction. It produces optimal linear unbiased predictions of an unobserved value at any target location, with associated prediction-error variances, by exploiting a fitted variogram model that encodes spatial autocorrelation across the entire dataset.
Key highlights
- Produces optimal (minimum-variance) linear unbiased predictions under stationarity assumptions.
- Uses all available spatial information without arbitrary neighborhood truncation.
- Provides prediction-error variances at every location, enabling spatially explicit uncertainty mapping.
- Theoretically well-grounded in random field theory with a rich geostatistical literature.
- Consistent and reproducible — the same variogram model yields identical results regardless of how prediction locations are ordered.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use global kriging when the dataset is small to moderate in size (typically fewer than a few hundred points), the spatial process is stationary (constant mean and variance) across the entire domain, and you need theoretically minimum-variance linear unbiased predictions. It is appropriate when no strong spatial non-stationarity is present and when computational cost is manageable. Do not use global kriging when the dataset is large (thousands of points) — the n x n matrix inversion becomes prohibitive; prefer local kriging with a search neighborhood instead. Also avoid it when the spatial process is non-stationary (use universal kriging or regression-kriging) or when multiple correlated variables are available (use co-kriging).
Strengths & limitations
- Produces optimal (minimum-variance) linear unbiased predictions under stationarity assumptions.
- Uses all available spatial information without arbitrary neighborhood truncation.
- Provides prediction-error variances at every location, enabling spatially explicit uncertainty mapping.
- Theoretically well-grounded in random field theory with a rich geostatistical literature.
- Consistent and reproducible — the same variogram model yields identical results regardless of how prediction locations are ordered.
- Computational cost scales as O(n^3) with sample size — infeasible for large datasets without approximations.
- Requires stationarity of the spatial process; violated when the mean or variance drifts across the study area.
- Prediction quality is highly sensitive to variogram model choice and fitting; poor variogram estimation propagates into biased weights.
- Cannot incorporate non-spatial covariates without extension to regression-kriging or co-kriging.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
How does global kriging differ from local kriging?
Global kriging uses all n sample points to predict each unobserved location, forming and solving one system of size n. Local kriging restricts predictions to only the nearest k points within a search radius, solving a smaller system repeatedly. Global kriging is theoretically optimal under stationarity but computationally expensive; local kriging scales to large datasets by trading some theoretical optimality for practicality.
When is global kriging preferable to ordinary kriging with a local neighborhood?
When the dataset is small enough that the full n x n covariance matrix inversion is tractable (roughly n < 500), and the spatial autocorrelation structure is genuinely stationary across the entire domain, global kriging is preferred because it avoids the arbitrary choices involved in defining a search neighborhood radius and minimum/maximum neighbor counts.
Does global kriging require the data to be normally distributed?
No — kriging is a linear predictor and achieves minimum-variance unbiasedness among linear predictors regardless of distributional assumptions. Normal distribution is needed only if you want the kriging variance to define exact probability intervals rather than just second-moment bounds.
How do I validate a global kriging model?
Use leave-one-out cross-validation (also called jackknifing): remove each sample point in turn, predict its value using the remaining points, and compare predicted to observed. Report RMSE and the standardized error mean and variance; a well-calibrated model has standardized errors near zero mean and unit variance.
Can global kriging handle datasets with trend (non-stationarity)?
Not directly. If a trend exists, global ordinary kriging will produce biased predictions. You should either remove the trend first (universal kriging / kriging with external drift) or use regression-kriging, which models the trend with covariates and kriging on residuals.
Sources
- 1.Cressie, N. A. C. (1993). Statistics for Spatial Data (revised ed.). Wiley-Interscience.ISBN 978-0471002550
- 2.Isaaks, E. H., & Srivastava, R. M. (1989). An Introduction to Applied Geostatistics. Oxford University Press.ISBN 978-0195050134
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Global Kriging. ScholarGate. https://scholargate.app/spatial-analysis/global-kriging