Compositional changes in the chemistry of large rivers deduced by the application of the differential scaling operator (perturbation) in the simplex metric

Compositional data analysis consist of vectors whose components are the proportions or percentages of some whole. Their numerical or statistical analysis performed in the real Euclidean sample space is not sensible to capture their features in a complete way. This type of data lies in a constrained space, called simplex, where to characterize the "difference" between compositions, or changes from one composition to another, specific tools have to be defined. In this paper the use of perturbation, or group operator working in the geometry of the simplex sample space, was applied to analyze the differences in the chemical composition of the major solutes of the most important rivers of the world, ranked by runoff increase. Significant results are related to the identification of both chemostatic and not-stationary behavior for different chemical components to be linked to their geochemical cycles.