Synchronization and Causality Across Time-scales: Complex Dynamics and Extremes in El Niño/Southern Oscillation

A better understanding of dynamics in complex systems, such as the Earth's climate is one of the key challenges for contemporary science and society. A large amount of experimental data requires new mathematical and computational approaches. Natural complex systems vary on many temporal and spatial scales, often exhibiting recurring patterns and quasi-oscillatory phenomena. The statistical inference of causal interactions and synchronization between dynamical phenomena evolving on different temporal scales is of vital importance for better understanding of underlying mechanisms and a key for modeling and prediction of such systems. This study introduces and applies information theory diagnostics to phase and amplitude time series of different wavelet components of the observed data that characterizes El Niño. A suite of significant interactions between processes operating on different time scales was detected, and intermittent synchronization among different time scales has been associated with the extreme El Niño events. The mechanisms of these nonlinear interactions were further studied in conceptual low-order and state-of-the-art dynamical, as well as statistical climate models. Observed and simulated interactions exhibit substantial discrepancies, whose understanding may be the key to an improved prediction. Moreover, the statistical framework which we apply here is suitable for direct usage of inferring cross-scale interactions in nonlinear time series from complex systems such as the terrestrial magnetosphere, solar-terrestrial interactions, seismic activity or even human brain dynamics.