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.

中文翻译：

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整体关系：关于复杂地球化学河流系统动力学的新见解

大自然通常具有远非热力学平衡的特征，河流不是地球关键区域的例外。在研究溪流水的化学成分时，发现河流系统表现为复杂的系统。这意味着该组合物具有取决于整体（即，具有所有化学成分的组合物）的完整性的特性，这些特性归因于该组成元素之间无数的非线性相互作用。互连的存在表明，通过单独检查系统的各个部分，无法完全理解整体的属性。在这项工作中 我们建议通过使用CoDA（组成数据分析）方法研究河流化学的复杂性，并研究单纯形几何中微扰算子的性能。河流碳酸氢盐被认为是区域和全球生物地球化学循环和钙的重要组成部分²⁺视为大多与carbonatic岩石风化，计算扰动对于组合物的后续耦合排名数据用于增加对数比Ln的值之后（CA ²⁺ / HCO ₃ ^- ）。通过使用稳健的主成分分析以及与分布和多重分形方法相关的组成部分（热图）之间的非参数相关性来分析数值。结果表明，HCO ₃ ^- ，钙²⁺，镁²⁺和Sr ²⁺是更有弹性，因此有助于为LN的所有值（钙成分变化²⁺ / HCO ₃ ^-）相对于其他化学元素/成分而言程度较小。此外，跟踪序列变化的所有序列的互补累积分布函数以及它们各自的Q矩与缩放指数之间的非线性关系表明存在多重分形可变性，从而揭示了波动的缩放特性。