Soil heterogeneity characterization using PCA (Xvariogram) - Multivariate analysis of spatial signatures for optimal sampling purposes

• Present specific matrix type consisting of variograms as input, Xvariogram.
• Explain a combination of variographic analysis and multivariate data analysis.
• Show how PCA is able to characterize a multitude of variograms simultaneously.
• Present a complete approach for characterizing scale-varying spatial heterogeneity.
• The approach is applicable for any fields with heterogeneity management needs.

This study explores how to combine variographic spatial characterization with multivariate data analysis, by showing how Principal Component Analysis (PCA) can be applied to unconventional types of data matrices, Xvariogram. This is here performed on a specific data set from an agricultural field in western Jutland, Denmark, but the data analytical approach is generic. In order to characterize the heterogeneity of a typical sandy soil, a variographic experiment along a 1-D profile is performed on 38 different minerogenic variables (geochemical elements). While the variogram is defined for one variable only, it is shown how PCA is able to characterize a multitude of variograms simultaneously, facilitating subject-matter interpretation of the fingerprints of the process(es) responsible for the spatial heterogeneity encountered. PCA scores and loadings contain information pertaining to the specific matrix type consisting of variograms, Xvariogram. Together with a companion paper, a complete approach for characterizing scale-varying spatial heterogeneity is presented with a view of developing sampling procedures for managing the intrinsic variability in natural soil and in similar systems (e.g. environmental characterization and monitoring, pollution in time and space, applied geochemistry, medical geology). Sampling in all of these contexts is shown to be much more than a ‘materials handling’ issue, by force involving the Theory of Sampling, TOS. The PCA (Xvariogram) approach can be applied for tuning in of sampling procedures and 1-D and 2-D sampling plans in soil, environmental substrates, pollution and medical geology studies with a carrying-over potential to many other application fields with similar heterogeneity management needs.