cokriged

Cokriged is related to cokriging, a multivariate geostatistical estimation technique used to improve predictions of a primary variable by incorporating one or more secondary variables that are spatially related. In cokriging, the goal is to estimate the value of a target property at unsampled locations using observations of the target and auxiliary properties from nearby points, exploiting both auto- and cross-variable spatial correlations.

The method extends kriging by modeling not only the variogram of the primary variable but also cross-variograms between the primary and secondary variables, as well as among the secondary variables themselves. The estimation is performed by solving a system of cokriging equations to find the weights that minimize estimation variance while preserving unbiasedness. The resulting estimator is a linear combination of all available observations, weighted according to the modeled spatial structure.

A common framework for ensuring a coherent multivariate covariance structure is the linear model of coregionalization (LMC), which parameterizes cross-variograms and auto-variograms in a way that yields a valid, nonnegative definite covariance model. Cokriging can be implemented in various forms, including ordinary, simple, and universal cokriging, depending on detrending and mean assumptions.

Applications of cokriged span geology, hydrology, environmental science, and mining. It is particularly advantageous when secondary variables are informative about the primary variable and are sampled more densely or more cheaply, providing additional spatial information that reduces estimation error. Limitations include the need for reliable cross-covariance models and increased computational effort, along with sensitivity to non-stationarity and potential model misspecification.