Is Compositional Data Analysis (CoDA) a theory able to discover complex dynamics in aqueous geochemical systems?

Abstract

The study of the structure of compositional changes characterizing a geochemical system in time or space could be the key to understand its dynamics and resilience to environmental and anthropic perturbations. Variables characterizing the composition of an aqueous system (river or ground waters) constitute a multivariate system that moves as a whole due to multiple interrelationships and feed-back mechanisms. If the goal of the research is to understand how the whole moves, the Compositional Data Analysis (CoDA) theory offers the correct statistical framework since aqueous geochemical data pertaining to the simplex sample space. Cases of a compositional matrix can be ranked by using some criterium (e.g. increasing runoff or conductivity values), and the differences between subsequent rows calculated by using the perturbation operator that measures the change in the simplex geometry. The obtained perturbation matrix can be then analyzed by using robust Principal Component Analysis (robust-PCA) to discover the association between variables subjected to proportional perturbations during geochemical processes. The calculus of the robust Mahalanobis distance from the barycenter of this matrix appears to be also useful to reveal presence of intermittency in time or space. Intermittency is highly related to the fractal nature of variability representing an emergent property of self-organized complex dissipative systems since it optimizes the dissipation energy gradients and maximize entropy production. Application examples for the surficial waters of the Alps region and the Arno river basin (Tuscany, Central Italy) reveal that the methodology is powerful and able to discover complex dynamics moving on the boundary between different sample spaces, from the Euclidean one to the fractal one. The proposed approach allows us to shift the perspective to the nature of the dynamic interactions and transitions affecting a geochemical landscape revealing how variability moves and how presence of intermittency and resilient behavior affects evolution and prediction.