Abstract
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 stream waters is investigated, it emerges that riverine systems behave as complex systems. This means that the compositions have properties that depend on the integrity of the whole (i.e., the composition with all the chemical constituents), properties that arise thanks to the innumerable nonlinear interactions between the elements of the composition. The presence of interconnections indicates that the properties 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 in the simplex geometry. With riverine bicarbonate considered as a key component of regional and global biogeochemical cycles and Ca2+ considered as mostly related to the weathering of carbonatic rocks, perturbations were calculated for subsequent couples of compositions after ranking the data for increasing values of the log-ratio ln(Ca2+/HCO3−). Numerical values were analyzed by using robust 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 the values 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 the compositional change and the nonlinear relationship between the Q-th moment versus the scaling exponents for each of them indicate the presence of multifractal variability, thus revealing scaling properties of the fluctuations.
Highlights
The relations between the whole and its parts have fascinated human beings throughout time, starting from the observation of nature to mathematical studies [1].Part–whole relations are fundamental to governing the dynamics of a complex system and to moving from linear to nonlinear regimes
With riverine bicarbonate considered as a key component of regional and global biogeochemical cycles and Ca2+ considered as mostly related to the weathering of carbonatic rocks, perturbations were calculated for subsequent couples of compositions after ranking the data for increasing values of the log-ratio ln(Ca2+ /HCO3 − )
Numerical values were analyzed by using robust principal component analysis and non-parametric correlations between compositional parts associated with distributional and multifractal methods
Summary
The relations between the whole and its parts have fascinated human beings throughout time, starting from the observation of nature (e.g., spirals of seashells, the form of flowers, proportions of the human body) to mathematical studies (e.g., the Fibonacci series, where the ratio of two subsequent terms tends to a constant irrational value equal to 1.618, the golden section, inversely proportional to 0.618) [1]. Part–whole relations are fundamental to governing the dynamics of a complex system and to moving from linear to nonlinear regimes This occurs since the whole is given by the sum of the constituting parts, but it is affected by the nature of their complex interactions [2,3]. Our interest focused on the first approach and, in particular, on the use of the perturbation operator The latter is one of the basic tools required to give to the simplex a vector space structure, an operator having a strategic role in monitoring changes [4,10]. The research question is whether the perturbation operator is able to give us information about the dynamic of compositional changes and to indicate similarity among chemical elements under this perspective, offering a new geochemical tool of investigation
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