Local Ordinary Kriging
Also known as: moving window kriging, local kriging, neighborhood kriging, LOK
Local Ordinary Kriging (LOK) is a geostatistical interpolation method that estimates values at unsampled locations using only a spatially defined moving neighborhood of nearby observations. By restricting each prediction to a local data window rather than the full dataset, LOK accommodates spatial non-stationarity, reduces computational cost, and often yields more accurate local predictions than global ordinary kriging.
Key highlights
- Adapts to local spatial non-stationarity by refitting the variogram within each moving window.
- Computationally efficient for large datasets because the kriging system is solved on a small local subset rather than the entire sample.
- Provides a kriging variance (uncertainty) map alongside predictions, enabling principled uncertainty quantification.
- Unbiased by construction: the unbiasedness constraint (weights summing to one) removes dependence on an unknown mean.
- Robust to edge effects and spatially irregular sampling density when the neighborhood is defined adaptively.
Intuition
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How it works
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When to use it
Use Local Ordinary Kriging when you have continuous georeferenced measurements (soil properties, pollutant concentrations, temperature, elevation) and need spatially varying predictions that respect local correlation structure. It is particularly valuable when the dataset is large (global kriging becomes computationally prohibitive) or when spatial stationarity cannot be assumed across the full domain. It is not appropriate when the data are sparse (fewer than ~15–20 local neighbors per window), when the spatial process has a strong trend that is better handled by universal kriging or regression-kriging, or when the variable has an inherently categorical nature.
Strengths & limitations
- Adapts to local spatial non-stationarity by refitting the variogram within each moving window.
- Computationally efficient for large datasets because the kriging system is solved on a small local subset rather than the entire sample.
- Provides a kriging variance (uncertainty) map alongside predictions, enabling principled uncertainty quantification.
- Unbiased by construction: the unbiasedness constraint (weights summing to one) removes dependence on an unknown mean.
- Robust to edge effects and spatially irregular sampling density when the neighborhood is defined adaptively.
- Variogram estimation within a small local window can be unstable when fewer than ~20 pairs of points are available, leading to unreliable weights.
- Results depend on subjective choices: neighborhood size, search strategy, and variogram model family.
- Local variogram fitting multiplied across thousands of prediction locations increases total computation relative to a single global variogram fit.
- Cannot extrapolate beyond the range of spatial dependence; predictions far from any observation converge to the local mean with high uncertainty.
Common pitfalls
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Applications
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Frequently asked
How is Local Ordinary Kriging different from global Ordinary Kriging?
Global ordinary kriging estimates one variogram from all data and solves one large kriging system. Local ordinary kriging restricts each prediction to a moving spatial neighborhood, refitting the variogram locally and solving a much smaller system. This makes LOK faster for large datasets and more flexible when spatial correlation varies across the study area.
How do I choose the neighborhood size?
A common rule of thumb is to include 16–30 nearest neighbors, or a radius equal to the practical range of the global variogram. Cross-validation (leave-one-out) comparing mean squared prediction error across candidate neighborhood sizes is the most principled approach.
Can I use LOK when my data have a spatial trend?
Not directly. LOK assumes local stationarity (no systematic trend within the window). If a trend is present, first remove it with a regression or polynomial surface and then apply kriging to the residuals (regression-kriging), or use universal kriging which explicitly models the trend.
What does the kriging variance tell me?
The kriging variance measures prediction uncertainty based on the distance to nearby observations and the variogram model — it is small near data points and grows away from them. It is not a classical confidence interval unless the data follow a Gaussian process, so cross-validation of actual coverage is recommended.
Is LOK the same as geographically weighted regression?
No. Both use spatial windows, but LOK is a geostatistical interpolator for a single regionalized variable and derives weights from a covariance (variogram) model. Geographically weighted regression is a local regression method that estimates spatially varying relationships between a response and predictors. They address different problems.
Sources
- 1.Chiles, J.-P., & Delfiner, P. (1999). Geostatistics: Modeling Spatial Uncertainty. Wiley.ISBN 978-0471083153
- 2.Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. Oxford University Press.ISBN 978-0195115383
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Cite this page
ScholarGate. (2026, June 3). Local Ordinary Kriging. ScholarGate. https://scholargate.app/spatial-analysis/local-ordinary-kriging