Kriging Spatial Interpolation
Also known as: geostatistical interpolation, Gaussian process regression (geostatistics), ordinary kriging, Kriging (Mekânsal Enterpolasyon)
Kriging is a geostatistical method that predicts the value of a continuous variable at unmeasured locations from nearby measurements, using the spatial correlation structure captured by a variogram. Formalised by Georges Matheron in 1963, it is the best linear unbiased predictor (BLUP) for spatial data and comes in Ordinary, Universal, and Co-Kriging forms.
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When to use it
Use kriging when you have a continuous variable measured at scattered locations with known geographic coordinates (x, y) and want to interpolate onto unmeasured points or a grid, with a reasonable sample (at least about 30 points). It assumes intrinsic (second-order) stationarity, requires a variogram model that genuinely fits the data, and may need declustering to correct sampling bias when points are clustered. It is not applicable without coordinates — there a standard regression predictor is preferred.
Strengths & limitations
- Best linear unbiased predictor (BLUP) for spatially correlated data — it exploits the measured spatial structure rather than assuming one.
- Returns a prediction variance at every location, quantifying the uncertainty of each interpolated value.
- Flexible family: Ordinary, Universal, and Co-Kriging handle constant means, spatial trends, and auxiliary correlated variables.
- Requires geographic coordinates; with no coordinates kriging cannot be applied at all.
- Quality hinges on choosing and fitting an appropriate variogram model (spherical, exponential, Gaussian, Matérn) — a poor fit gives misleading predictions.
- Assumes intrinsic stationarity, which can fail under strong trends; clustered sampling can bias the variogram unless declustering is applied.
Frequently asked
What is a variogram and why does kriging need it?
The variogram measures how much the difference between two values grows as the distance between their locations increases. It encodes the spatial correlation structure, and kriging uses a fitted variogram model to decide how much weight each nearby observation should receive.
How is kriging different from inverse-distance weighting?
Inverse-distance weighting fixes in advance how influence fades with distance, whereas kriging learns that decay from the data through the variogram and chooses weights that minimise the prediction error variance. Kriging also returns a prediction variance, which inverse-distance weighting does not.
What are Ordinary, Universal, and Co-Kriging?
Ordinary kriging assumes an unknown but constant mean over the area; universal kriging models a spatial trend in the mean; co-kriging brings in one or more correlated auxiliary variables to improve prediction of the target.
What can I do if my points are clustered?
Clustered sampling biases the empirical variogram and the predictions. Applying declustering — down-weighting densely sampled areas — corrects this bias before the variogram is fitted.
Sources
- Matheron, G. (1963). Principles of Geostatistics. Economic Geology, 58(8), 1246–1266. DOI: 10.2113/gsecongeo.58.8.1246 ↗
- Cressie, N. (1993). Statistics for Spatial Data (Revised ed.). Wiley. ISBN: 978-0471002550
How to cite this page
ScholarGate. (2026, June 1). Kriging Spatial Interpolation. ScholarGate. https://scholargate.app/en/spatial-analysis/kriging-interpolation
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.
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