Extreme events in multiscale systems: theory and applications

Many geophysical systems show emergent phenomena and extreme events at different scales, with signatures of chaos at large scales and an apparently random behavior at small scales. Despite the intrinsic morphological and/or physical difference between geophysical extremes, they all originate as temporary deviations from the typical trajectories of the large scale geophysical flows, resulting in dynamical patterns and structures. This motivated to bring together statistics (extreme value theory) and dynamics (dynamical system theory) to provide a new definition of extremes as rare recurrences in the phase space of physical systems. This means to explore the instantaneous properties of the geometrical object hosting the frequency and probability of all physical states attainable by the system, namely the so-called attractor, to inform us on the predictability, persistence and synchronization of physical states.

 

Here we present a recently proposed formalism to explore the active number of degrees of freedom and the predictability horizon of multiscale complex systems showing non-hyperbolic chaos, randomness, state-dependent persistence and predictability. We briefly discuss the newly introduced framework in comparison with classical approaches, based on generalized fractal dimensions, Lyapunov exponents, and Renyi entropies. Finally, we demonstrate the suitability of this novel formalism to trace the instantaneous scale-dependent and state-dependent features of climate and geophysical extremes, pointing out how the predictability horizon, the persistence and synchronization of geophysical systems’ states is a matter of scales.