Modelling Compositional Change: The Example of Chemical Weathering of Granitoid Rocks

Perturbation on the simplex is an operation which can be used to numerically describe changes in the composition of, for example, soils, sediments, or rocks. The combination of perturbation and power transformation provides a strong tool for analyzing compositional linear processes in the simplex. When the process is constrained in the sense of a well-known starting (or final) composition, noncentred principal component analysis can be used to estimate the leading perturbation vector of the process. Applying these mathematical tools to chemical major element data from a weathering profile developed on granitoid rocks allows us to model the compositional changes associated with the process of chemical weathering. The comparison of these results with the compositional linear trend defined by erosional products of several of the world's major drainage systems yields close similarities. The latter observation allows for a mathematical formulation of a global mean weathering trend within the system Al₂O₃–CaO– Na₂O– K₂O. We further demonstrate the usefulness of the approach for validating processes behind individual trends and for combining the effects of different processes which modify the composition of soils, sediments, and rocks. Alternatives to the Chemical Index of Alteration (CIA) are discussed to obtain a translation-invariant scale for the process of chemical weathering.