Ordinary Kriging
Ordinary Kriging Spatial Interpolation · Also known as: OK, kriging interpolation, geostatistical interpolation, BLUE spatial predictor
Ordinary Kriging (OK) is the standard geostatistical method for interpolating a continuous spatial variable at unsampled locations. It derives optimal, unbiased weights from the spatial covariance structure of the data, making it the Best Linear Unbiased Predictor (BLUP) under stationarity assumptions. Unlike simpler distance-based methods, it also provides a prediction uncertainty (kriging variance) at every interpolated point.
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When to use it
Use Ordinary Kriging when you have spatially referenced continuous data (e.g., soil contaminant concentrations, groundwater heads, temperature fields) and want the best unbiased interpolation with uncertainty quantification. It is appropriate when the mean is unknown but approximately constant across the study area (second-order stationarity). Do not use OK when the mean shows a clear spatial trend — use Universal Kriging instead. Avoid it with very small samples (fewer than ~30 points), highly anisotropic fields that are hard to model, or data that violate stationarity without transformation.
Strengths & limitations
- Produces the Best Linear Unbiased Predictor (BLUP) under Gaussian, stationary conditions.
- Automatically provides a kriging variance (prediction uncertainty) at every interpolated location.
- Weights are data-driven, derived from the actual spatial dependence structure rather than arbitrary distance decay functions.
- Exact interpolator: predicted values honour the observed data at sampled locations.
- Well-supported in widely used open-source tools (R gstat, Python pykrige, ArcGIS Geostatistical Analyst).
- Requires a reliable variogram model; poor variogram fitting propagates errors into all predictions.
- Assumes spatial stationarity (constant mean, covariance depends only on distance), which is often violated in practice.
- Kriging variance reflects only sample configuration and the variogram model — it can underestimate true uncertainty if the model is wrong.
- Computationally intensive for very large datasets (O(n3) system solving), though local kriging neighbourhoods mitigate this.
- Does not incorporate secondary variables or covariates; use Co-Kriging or Regression Kriging for that.
Frequently asked
What is the difference between Ordinary Kriging and Inverse Distance Weighting?
Inverse Distance Weighting (IDW) assigns weights purely based on geometric distance, with no statistical foundation. Ordinary Kriging derives weights from the variogram — the actual spatial dependence of the data — making it statistically optimal under the assumed model. OK also provides uncertainty estimates; IDW does not.
How do I choose a variogram model (spherical, exponential, Gaussian)?
Fit candidate models to the empirical variogram and compare them using cross-validation (leave-one-out RMSE and mean error). In practice, the spherical and exponential models are most common; the Gaussian model implies very smooth fields and can be numerically unstable. Visual fit to the empirical variogram provides a first guide, but CV statistics should drive the final choice.
When should I use Universal Kriging instead of Ordinary Kriging?
When the mean of the variable shows a systematic spatial trend (e.g., elevation increasing from west to east), the stationarity assumption of OK is violated. Universal Kriging (Kriging with a trend) explicitly models this trend as a deterministic function of coordinates, then kriging is applied to the residuals.
What does the nugget effect represent?
The nugget is the variogram value at zero lag. It captures measurement error and spatial variation at scales smaller than the minimum sample spacing. A large nugget relative to the sill (total variance) indicates weak spatial structure and leads to predictions that revert quickly toward the global mean.
Can Ordinary Kriging handle very large datasets?
Naively, solving the kriging system is O(n3) in the number of observations, which becomes prohibitive beyond a few thousand points. Practical solutions include using a local search neighbourhood (only the nearest k points contribute), or switching to Fixed Rank Kriging or other approximate methods designed for large n.
Sources
- Matheron, G. (1963). Principles of geostatistics. Economic Geology, 58(8), 1246-1266. DOI: 10.2113/gsecongeo.58.8.1246 ↗
- Cressie, N. A. C. (1993). Statistics for Spatial Data (Revised ed.). Wiley-Interscience. ISBN: 978-0471002550
How to cite this page
ScholarGate. (2026, June 3). Ordinary Kriging Spatial Interpolation. ScholarGate. https://scholargate.app/en/spatial-analysis/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
- Geographically Weighted RegressionSpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare
- Universal KrigingSpatial analysis↔ compare