Part-whole relations: New insights about the dynamics of complex geochemical riverine systems

Nature is often characterized by systems that are far from thermodynamic equilibrium,and rivers are not an exception for the Earth's critical zone. When the chemical composition of streamwaters is investigated, it emerges that riverine systems behave as complex systems. This means thatthe compositions have properties that depend on the integrity of the whole (i.e., the composition withall the chemical constituents), properties that arise thanks to the innumerable nonlinear interactionsbetween the elements of the composition. The presence of interconnections indicates that theproperties of the whole cannot be fully understood by examining the parts of the system in isolation.In this work, we propose investigating the complexity of riverine chemistry by using the CoDA(Compositional Data Analysis) methodology and the performance of the perturbation operator inthe simplex geometry. With riverine bicarbonate considered as a key component of regional andglobal biogeochemical cycles and Ca2+ considered as mostly related to the weathering of carbonaticrocks, perturbations were calculated for subsequent couples of compositions after ranking the datafor increasing values of the log-ratio ln(Ca2+/HCO3-). Numerical values were analyzed by usingrobust principal component analysis and non-parametric correlations between compositional parts(heat map) associated with distributional and multifractal methods. The results indicate that HCO3-,Ca2+, Mg2+ and Sr2+ are more resilient, thus contributing to compositional changes for all thevalues of ln(Ca2+/HCO3-) to a lesser degree with respect to the other chemical elements/components.Moreover, the complementary cumulative distribution function of all the sequences tracing thecompositional change and the nonlinear relationship between the Q-th moment versus the scalingexponents for each of them indicate the presence of multifractal variability, thus revealing scalingproperties of the fluctuations.