Benchmark-based metric distances as predictors of geochemical processes and data variability: A comprehensive discussion

Understanding compositional changes is the key to investigate how complex natural systems evolve. Traditional geochemical approaches, such as univariate, bivariate, or multivariate analyses, usually focus on variability around a central composition. However, they do not provide insights into evolutionary paths or changes from benchmark states. In this work, we propose a comprehensive conceptual and methodological discussion of a holistic approach that addresses these limitations. We combine compositional data with metrics tailored to the simplex structure, specifically the robust Mahalanobis distance (MD) and perturbation analysis. Two large-scale datasets were analyzed: the Abyssal Volcanic Glasses Database (AVGD) with primitive compositions (chondrites and MORBs) as benchmarks, and the FOREGS repository of European stream and alluvial sediments, with crustal averages and diluted waters as reference states. By calculating MD from benchmark compositions and examining the frequency distribution, skewness, kurtosis, and multimodality, we identify patterns of compositional change, resilience, and potential instability. This work provides a data-driven perspective on how compositional metrics can enhance the understanding of Earth system dynamics. In particular, the proposed framework enables the detection of early-warning signals and tipping points. This offers a powerful tool for multi-scale assessment of geochemical system dynamics and resilience.