Rui A. P. Perdigão (Portugal) 1,2
1 - Climate Change Impacts, Adaptation and Modelling group (CCIAM), CE3C, Universidade de Lisboa; 2 - Meteoceanics Interdisciplinary Centre for Complex System Science
Predictability of Complex Systems is a challenge on its own even under well-defined structural stochastic-dynamic conditions where the laws of motion and system symmetries are known. However, the edifice of complexity can be severely disrupted by internal and external factors. This leads to structural collapse and memory loss, precluding the ability of traditional stochastic-dynamic and information-theoretical metrics to provide reliable information about the system evolution.
Such disruptive transformation is under way in the Earth System under Climate Change. For this reason, unveiling predictability beyond structural collapse and memory loss is not only a fundamental problem in mathematical physics, but also one of critical importance to environmental modelling and decision support.
This contribution begins by bringing relief to the long-standing myth that statistically independent processes cannot share any information, with statistical memory loss and structural dynamic collapse believed to dictate the end of predictability. Here we unveil hidden information disproving the myth.
In order to bring out and characterise that hidden information in complex systems, generalised information measures are hereby formulated in terms of fundamental dynamic interactions following recent advances in theoretical physics (Perdigão 2018, doi:10.3390/e20010026). This generalizes information theory to far from equilibrium non-ergodic coevolution, where there is hidden dynamic codependence and the traditional stochastic-dynamic and information-theoretical frameworks no longer hold.
With these theoretical developments at hand, elusive predictability is hereby found and explicitly quantified even beyond post-critical spatiotemporal memory loss, long after nonlinear statistical information is lost. The collapse of dynamic regimes and nonlinear memory in far-from-equilibrium non-ergodic dynamics no longer impedes system understanding and robust prediction.
In methodological terms, a new framework is hereby formulated for data analysis and dynamic model design of catastrophically disrupted complex systems, including the formulation of rigorous solutions for the prediction of unprecedented critical emergence. This enables decision support in anticipation of events that until now were deemed unpredictable (black swans). Examples are provided eliciting predictability of emerging regimes, transitions and extremes in ocean-atmospheric and hydro-meteorological dynamics, unveiling hidden information beyond post-critical nonlinear memory loss.
Fundamentally, the findings open new avenues in nonlinear statistics, nonlinear dynamics and information theory, where fundamental physics comes into play to shed light into the mysteries of complexity. Operationally, the findings open new avenues in the robust prediction and dynamic risk assessment of unprecedented criticality including emerging extremes in environmental processes under structurally disruptive climate change, along with the robust assessment of the associated uncertainties for improved decision support.