Advancing the understanding of extreme events through the lens of dynamical system theory

Since Lorenz's pioneering work, dynamical systems theory has provided a powerful framework for studying complex systems. Among these, the study of their instantaneous properties is particularly significant for understanding short-lived yet impactful extreme events. Here, we propose an analogues-based index to measure the instantaneous predictability of dynamical systems over different forecasting horizons. We demonstrate its application in both classical dynamical systems and the Euro-Atlantic sector atmospheric circulation. Furthermore, recognizing that the onset of extreme events often involves processes operating across different scales, we introduce a novel framework that enables the exploration of scale-dependent dynamical properties. Given the flexible and generalizable nature of these methods, we believe they open new research avenues for studying extreme events from a dynamical systems perspective and will serve as valuable tools for deepening our understanding of extreme events.