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.

Over the last decades, groundwater resources at global level have suffered a significant deterioration due to nitrate pollution, mainly related to the input of agricultural fertilizers, manure, sewage, and untreated urban and industrial effluents. The most impacted waters are those forming surface and shallow reservoirs, which usually play a key role in supplying waters to civil, agricultural, and industrial activities. The terminal portion of the Metauro River plain, located in central Italy along the Adriatic Sea coastline, hosts a strategic phreatic aquifer that, along with the surface water of the Metauro River, supplies water to the local population (i.e., about 60,000 people). This shallow coastal aquifer experiences a long-lasting story of nitrate contamination since the 1970s when the increase in the use of agricultural fertilizers contributed to very high levels of pollution (NO₃⁻ > 100 mg/L). This fact prompted the local authorities to carry out remediation actions that involve a pumping system to inject the NO₃⁻-poor waters from the Metauro River course directly into the shallow aquifer. The present work was aimed at defining the contamination of nitrates in this important water resource. The main geochemical characteristics and the temporal evolution of NO₃⁻ concentrations (between 2009 and 2020), in the shallow coastal aquifer of the Metauro River plain, were analyzed by means of classical geochemical analyses and multivariate methods accounting for the compositional nature of the data, to assess the efficiency of the in-situ remediation over time.

In geochemical data analysis, assessing the potential of new techniques to identify compositional time–space changes is of great interest for monitoring purposes. This work aims to evaluate, in the light of the compositional data analysis perspective, the performance of different statistical indices in tracing the evolution of a geochemical composition and the relationships among its parts. To reach this goal, source-to-sink chemical changes in water and stream sediment composition of the Tiber river (central Italy) are analyzed using three indices: (i) the cumulative sum of unclosed perturbation factors of each composition (row sum) with respect to a reference composition; (ii) the robust Mahalanobis distance, describing the compositional differences from the same reference and, (iii) the geometric mean of each composition as a measure able to capture the interactions among the parts. The results highlight the major compositional changes downriver, allowing to explore geochemical footprints’ propagation and their natural or anthropogenic origin. The tested indices are consistent in most cases, particularly if high-variability species are treated separately and low values are rare. Under this latter condition, the geometric mean of the composition shows a close connection with the cumulative sum of unclosed perturbation factors. This indicates that both indices inherit the complex history of the changes, well capturing the interactions among the parts under the influence of environmental drivers. With this awareness, the application of these methods in monitoring and applied geochemical studies could offer new insights into the inner workings of river systems and their resilience to environmental pressures.