The FOREGS repository: Modelling variability in stream water on a continental scale revising classical diagrams from CoDA (compositional data analysis) perspective

• Two non-orthogonal coordinates in real space represent the binary Gibbs diagram.
• Classical statistics cannot be applied when coordinates are non-orthogonal.
• Gibbs diagram was revised coherently with the compositional nature of water chemistry.
• Gibbs diagram was transformed in a powerful tool to statistically classify river chemistry.
• Stream waters from the FOREGS repository were used to improve Gibbs diagram.

The investigation of variability that characterises stream water composition is a very important item since the role of the weathering processes that have acted during geological time can be recognised. Several methods are often used to achieve this aim, starting from bivariate diagrams towards more complicated multivariate or inverse procedure approaches. In the first case, several examples are known like the Gibbs's diagram or other diagrams with molar ratios sharing a common denominator or tri-linear plots. In all cases, the basic idea is to identify compositions related to the dominance of specific geochemical processes (rock weathering, evaporation, dilution by precipitation and runoff, pollution) to be then used as reference terms to interpret the meaning of new data when located in the same framework. For this reason, the diagrams were derived from experimental data, but considering information on a very wide scale, continental or worldwide. The chemical data of the most important rivers of the world were thus often considered. In this context, the use of information about water collected in monogenetic basins, characterised by a well-defined lithology has improved the use of these tools, thus clearly characterising the chemistry of water interacting with silicates or carbonates or other type of material. However, the use of binary diagrams may be highly compromised when compositional data are analysed, due to their constrained nature and positivity. In particular, because of their construction, it is not possible to apply statistical analysis correctly on the Gibbs's diagram or on diagrams with coordinates given by molar ratios, since they represent non-orthogonal directions, thus limiting the modelling phase.In this paper, a revision of the Gibbs's diagram is presented proposing an approach coherent with the nature of compositional data, thus obtaining a simple tool to be used in a statistical sense, going beyond the descriptive approach. The chemical composition of the European stream water samples derived from the FOREGS (Forum of European Geological Surveys) repository is used to verify the proposed method, and to evidence the processes affecting the aqueous solutions on such a continent-wide scale, thus giving a convenient tool that can be also used to compare statistically the chemistry of new data.