The Best Linear Unbiased Estimator
Ordinary kriging, named after South African mining engineer Danie Krige, is mathematically the optimal way to interpolate spatially correlated data. Given a set of sample values and a variogram model describing their spatial correlation, kriging computes weights for each sample that minimize the estimation variance while ensuring the estimate is unbiased. The result is a smooth surface that passes through (or near) the sample points and gracefully reverts to the global mean in areas far from data.
How Kriging Weights Work
Unlike simple methods like inverse distance weighting, kriging weights are determined by solving a system of linear equations derived from the variogram. Samples close to the estimation point get more weight, but kriging also accounts for redundancy — if two samples are close to each other, they share information and each gets less weight than it would alone. Kriging weights can even be negative, a feature that prevents bias from clustered data and accounts for the screening effect where a nearby sample blocks the influence of a more distant one.
The Kriging Variance Map
One of kriging's greatest strengths is that it produces not just estimates but also a map of estimation uncertainty. The kriging variance at each location depends only on the geometry of nearby samples and the variogram — not on the actual measured values. This variance map shows exactly where the estimate is reliable and where additional sampling would be most beneficial. In this simulation, color intensity shows estimated values while transparency reveals kriging variance — faded areas have high uncertainty.
Applications Across Disciplines
Kriging originated in mining to estimate ore grades for resource classification and mine planning. Today it is used in petroleum engineering for reservoir characterization, in environmental science for contamination mapping, in meteorology for temperature and rainfall interpolation, in precision agriculture for soil nutrient mapping, and in epidemiology for disease rate smoothing. The unifying principle is always the same: exploit spatial correlation to make better predictions than any non-spatial method can achieve.