Global Co-Kriging
Global Co-Kriging Spatial Interpolation · Also known as: global cokriging, co-kriging, cokriging, multivariate kriging
Global Co-Kriging is a multivariate geostatistical interpolation method that estimates an unsampled primary variable by exploiting its spatial cross-correlation with one or more secondary variables. Unlike local (moving-window) approaches, it fits a single set of variogram and cross-variogram models to the entire study domain and solves one global cokriging system for each prediction location.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use Global Co-Kriging when you have a spatially sparse primary variable (e.g., soil pollutant, ore grade) and a correlated secondary variable sampled more densely (e.g., remote-sensing reflectance, elevation, a cheap proxy measurement), and when the cross-correlation structure is stationary or approximately stationary across the entire study area. It is the right choice when a coherent, domain-wide variogram model is scientifically justifiable and when prediction consistency across the map matters more than hyper-local flexibility. Avoid it when cross-correlation is strongly non-stationary (e.g., varies dramatically between sub-regions) — in that case local co-kriging or geographically weighted approaches are preferable. Also avoid it when secondary variables are very weakly correlated with the primary (cross-variogram is near zero), as the added complexity then yields no benefit over ordinary kriging.
Strengths & limitations
- Exploits cross-correlation between variables to reduce prediction variance compared to univariate kriging.
- A single globally fitted covariance model ensures consistent, interpretable spatial relationships across the entire domain.
- Provides exact interpolation at observed primary data locations (zero prediction error at sample points).
- Produces co-kriging variance maps that quantify uncertainty, supporting risk-aware decision making.
- Theoretically optimal (BLUP) under second-order stationarity and a correctly specified linear model of coregionalization.
- Requires fitting a valid linear model of coregionalization, which is complex and subjective — poorly fitted cross-variograms can degrade performance.
- Assumes cross-correlation is stationary across the domain; violated in heterogeneous landscapes, leading to biased predictions.
- Computationally expensive: the co-kriging system matrix grows with the total number of primary and secondary observations.
- Data requirements are high — the secondary variable must be genuinely correlated with the primary; otherwise it adds noise and complexity.
- Interpretation of weights is less intuitive than ordinary kriging, especially when multiple secondary variables are included.
Frequently asked
How is Global Co-Kriging different from Ordinary Kriging?
Ordinary kriging uses only the primary variable and its direct variogram. Co-kriging additionally incorporates one or more secondary variables and their cross-variograms with the primary. This allows the secondary data — often cheaper or denser — to improve estimation of the primary variable wherever cross-correlation is strong.
What is the linear model of coregionalization (LMC) and why is it required?
The LMC is a mathematical constraint that ensures the joint covariance matrix of all variables is positive-definite (a requirement for the co-kriging system to have a unique solution). It decomposes all direct and cross-variograms as positive linear combinations of the same set of basic variogram structures. Without a valid LMC, the co-kriging system can produce negative kriging variances, which are physically meaningless.
When does the 'global' label matter — isn't all co-kriging global by default?
In practice, co-kriging can be applied with a locally adaptive strategy (using only observations within a moving neighborhood window and possibly re-fitting the model locally), analogous to local kriging. 'Global' explicitly means a single variogram and cross-variogram model is estimated from all data and applied domain-wide. This is the classical and most common implementation, but the distinction matters when comparing to local or geographically weighted alternatives.
What if my secondary variable is only weakly correlated with the primary?
Weak cross-correlation means the co-kriging weights assigned to secondary observations will be near zero, and the method degenerates toward ordinary kriging. In this case, adding the secondary variable introduces model complexity without accuracy gains. A cross-variogram near the zero line or a correlation below 0.4–0.5 in magnitude typically signals that co-kriging will not outperform ordinary kriging.
How do I validate a Global Co-Kriging model?
Use leave-one-out cross-validation (jack-knife) on the primary variable: remove each observation in turn, predict it from the remaining data, and compare predicted versus observed values. Key diagnostics are mean error (bias), mean squared error, and the standardized mean squared error (should be close to 1 if kriging variances are well calibrated). Compare these metrics against ordinary kriging to confirm the benefit of including secondary data.
Sources
- Myers, D. E. (1982). Matrix formulation of co-kriging. Journal of the International Association for Mathematical Geology, 14(3), 249–257. DOI: 10.1007/BF01032887 ↗
- Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. Oxford University Press. ISBN: 9780195115383
How to cite this page
ScholarGate. (2026, June 3). Global Co-Kriging Spatial Interpolation. ScholarGate. https://scholargate.app/en/spatial-analysis/global-co-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
- Ordinary KrigingSpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare
- Universal KrigingSpatial analysis↔ compare