Introducing minimum spatial cross-correlation kriging as a new estimation method of heavy metal contents in soils

- Theory of minimum spatial cross-correlation kriging (MSCK) is presented in details.
- Spatial cross-correlations of the MSC factors are close to zero.
- MSC method is more effective than PCA in producing orthogonal factors.
- Principal component kriging shows better results than MSCK and cokriging.

In earth sciences, estimation of heavy metal concentration at unknown locations is one of the most challenging problems. In multivariate cases, cokriging has been the traditional approach to solve the problem. Cokriging (CK) has some disadvantages such as modeling a number of auto and cross-variograms together to avoid facing unsolvable equation systems. In this study, minimum spatial cross-correlation kriging (MSCK) is introduced as an alternative method to cokriging (CK) approach. This method transforms spatially correlated variables into spatially uncorrelated factors, then estimates each factor separately and back-transforms the estimation results into the original data space. Jura data set is used to compare the performance of the new developed method to those of CK and principal component kriging (PCK). Performance comparison shows that although CK is a theoretically better estimation method, it does not outperform MSCK and PCK in all cases. Related to the methods based on factor estimation, improvement in spatial orthogonality does not lead to better performance.