Relative vs. absolute statistical analysis of compositions: A comparative study of surface waters of a Mediterranean river

Most hydrogeological research includes some sort of statistical study, which is generally conducted on the raw measures of chemical variables, though there are several theoretical and practical studies warning against this practice. Arguments refer mainly to the positive character of this type of data, and to the fact that they carry only information about the relative abundance of each component on the whole, what makes techniques based on correlation, like the widely used Principal Component Analysis (PCA), loose their meaning. The solution proposed by Aitchison (1982, Journal of the Royal Statistical Society, Series B 44(2), 139–177)—based on working with log-ratios of observations—is equivalent to define a new distance between compositions and to adapt usual statistical techniques to it. To illustrate its effect, our study compares the performance of the biplot—a PCA graphical technique—according to the usual Euclidean and to the Aitchison distance. The study is conducted on a set of 14 molarities measured monthly through the years 1997–1999 at 30 different stations along the Llobregat River and its tributaries (Barcelona, NE Spain). Ordinary analysis, implicitly based on an Euclidean distance, presents some deficiencies, mainly because it only captures major ion variations and the inferred relationship between them actually depends on other non-relevant variables, such as water mass. An analysis based on compositional distances captures variations of all the ions; it is robust against the inclusion of non-relevant variables in the analysis; and it offers a way to build factors expressed as equilibrium equations. In our case, two promising factors are extracted, showing the different anthropogenic and geological pollution sources of the rivers.