Factorial kriging analysis: a useful tool for exploring the structure of multivariate spatial soil information

Most studies of relations between soil properties fail to take account of their regionalized nature because of the lack of appropriate methods. This paper describes a geostatistical technique, factorial kriging analysis, that bridges the gap between classical multivariate analysis and a univariate geostatistical approach. The basic feature of the method is the fitting of a linear model of coregionalization, i.e. all experimental simple and cross-variograms are modelled with a linear combination of basic variogram functions. A particular variance-covariance matrix, the coregionalization matrix, can then be associated with each spatial scale defined by the range of the basic variogram function. Each coregionalization matrix describes relationships between variables at a given spatial scale. A principal component analysis of these matrices produces a set of components, the regionalized factors, that reflect the main features of the multivariate information for each spatial scale and whose scores are estimated by cokriging. The technique is described and illustrated with three case studies based on a simulated data set and soil survey data. The results are compared with those of the principal component analysis of the variance-covariance matrix and the variogram matrices.