Kriging is a powerful statistical interpolation method named after South African mining engineer Danie Krige. It is used to predict unknown values at unsampled locations based on known data points. Unlike simple interpolation methods, Kriging provides both predictions and uncertainty estimates, making it invaluable for spatial data analysis in fields like geology, environmental science, and mining.
Kriging operates on three key principles. First, spatial autocorrelation assumes that nearby points are more similar than distant ones. Second, optimal weighting assigns higher weights to closer points and lower weights to farther points based on the spatial correlation structure. Third, uncertainty quantification provides error estimates along with predictions, giving us confidence intervals for our interpolated values.
The variogram is the mathematical foundation of Kriging. It describes how the variance between data points increases with distance. The variogram has three key parameters: the nugget represents measurement error or micro-scale variation, the sill is the maximum variance reached at large distances, and the range is the distance at which points become spatially uncorrelated. Understanding these parameters is crucial for accurate Kriging interpolation.