Robust Kriging
Robust Kriging Spatial Interpolation · Also known as: robust spatial kriging, outlier-resistant kriging, resistant kriging, robust geostatistical interpolation
Robust Kriging is a geostatistical interpolation method that extends classical kriging by replacing sensitive variogram estimation with outlier-resistant alternatives, most notably the Cressie-Hawkins robust estimator. It produces spatially interpolated predictions that are not distorted by anomalous or extreme observations in the data.
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When to use it
Use Robust Kriging when you have continuous georeferenced data suspected of containing outliers, measurement errors, or heavy-tailed distributions that could distort classical variogram estimation — for example, geochemical surveys, environmental pollution mapping, or ecological field data. It is also appropriate when the classical variogram shows erratic behaviour or unusually high nugget effects that may reflect data contamination rather than genuine nugget variance. Do not use it when data are well-behaved and Gaussian, where classical ordinary kriging is equally valid and simpler; and do not apply it when outliers are genuinely meaningful extreme events that should influence the interpolation.
Strengths & limitations
- The Cressie-Hawkins variogram estimator is substantially less sensitive to isolated extreme values than the classical method-of-moments estimator.
- Produces more reliable spatial predictions in geochemical, pollution, and ecological datasets where contamination or measurement error is common.
- Preserves all benefits of classical kriging — optimal linear unbiased prediction, spatial uncertainty quantification — while gaining robustness.
- Widely implemented in standard geostatistical software (gstat in R, gslib, SGeMS), making it practically accessible.
- Allows contaminated datasets to be used without requiring complete removal of outliers, retaining valuable spatial information.
- The robust variogram estimator is still not fully resistant to multiple clustered outliers or masking effects in heavily contaminated datasets.
- Fitting the theoretical variogram to robust empirical estimates still requires subjective decisions (model choice, lag binning) that can affect results.
- Does not address spatial non-stationarity; if the mean or variance changes systematically across the study area, robust kriging alone is insufficient.
- Computationally more involved than classical kriging for large datasets with many lag classes.
- Robustness is gained at the variogram estimation stage only; if outliers are pervasive the kriging step itself is not fully protected.
Frequently asked
What is the key difference between robust kriging and ordinary kriging?
The difference lies in the variogram estimation step. Ordinary kriging uses the classical method-of-moments estimator, which is strongly affected by outliers. Robust kriging uses an outlier-resistant estimator (most commonly the Cressie-Hawkins estimator) to obtain a more reliable variogram, upon which the same kriging prediction equations are then applied.
Does robust kriging remove or ignore outliers?
No. Robust kriging downweights the influence of outliers during variogram estimation but uses all observations in the final prediction step. The outliers remain in the dataset and contribute to the prediction, but their distorting effect on the variogram — and hence on spatial weights — is reduced.
When should I prefer robust kriging over log-transforming my data?
Log transformation stabilises variance for strictly positive skewed data and then allows classical kriging on the transformed scale. Robust kriging is preferable when data contain true outliers (not just skewness), when zero values are present (log is undefined), or when back-transforming to the original scale introduces bias. Both approaches can be combined.
Which software supports robust kriging?
The gstat package in R implements the Cressie-Hawkins robust variogram estimator. GSLIB and SGeMS also offer robust variogram options. Python users can use PyKrige or gstools with custom robust estimators.
How many data points do I need for robust kriging?
As a rule of thumb, at least 100 observations are recommended to obtain stable variogram estimates, and each lag distance class should contain at least 30 observation pairs. With fewer data the robust estimator itself becomes unstable, and simple ordinary kriging with careful outlier inspection may be more practical.
Sources
- Cressie, N., & Hawkins, D. M. (1980). Robust estimation of the variogram: I. Journal of the International Association for Mathematical Geology, 12(2), 115–125. DOI: 10.1007/BF01035243 ↗
- 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). Robust Kriging Spatial Interpolation. ScholarGate. https://scholargate.app/en/spatial-analysis/robust-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