regressionkriging

Regression kriging is a geostatistical interpolation method that combines a regression of a target variable on auxiliary covariates with kriging of the regression residuals. It leverages both deterministic information from secondary data and the spatial autocorrelation present in residuals after removing the trend.

The method typically proceeds in two stages. First, a regression model is fitted to predict the variable of interest using covariates such as environmental, land-use, or sensor-derived variables. Second, the residuals from this regression are analyzed for spatial structure and kriged to obtain predictions at unsampled locations. The final estimate at a location is obtained by adding the regression prediction to the kriged residual: predicted value = regression-based trend + kriged residual. Variograms or covariance models for the residuals are estimated to drive the kriging step, and the uncertainty can be captured by the sum of the regression model uncertainty and the kriging variance.

Extensions of regression kriging include external drift or universal kriging, where the regression component represents a known trend (drift) linked to covariates while the residuals are treated with kriging. The approach is flexible: the regression can use linear, nonlinear, or machine learning models, and the kriging can be ordinary, universal, or cokriging with additional variables.

Applications are common in environmental science, soil mapping, hydrology, agriculture, and mining, where auxiliary data are available and spatially structured variability is present. Strengths include improved accuracy when covariates explain part of the variability and residual spatial structure is meaningful; limitations involve dependence on covariate quality, potential bias if covariates are mismeasured, and the need for careful variogram modeling.