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Abstract

Key components of the Earth system can undergo abrupt transitions when the magnitude or rate of external forcing exceeds critical thresholds. In this study, we use the example of the Atlantic Meridional Overturning Circulation (AMOC) to demonstrate the challenges associated with anticipating such transitions when the complex system is susceptible to bifurcation-induced, rate-induced, and noise-induced tipping. Using a calibrated AMOC model, we conduct large ensemble simulations and show that transition behavior is inherently stochastic: under identical freshwater forcing scenarios, some ensemble members exhibit transitions while others do not. In this stochastic regime, traditional early warning indicators based on critical slowing down are unreliable in predicting impending transitions. To address this limitation, we develop a deep learning (DL)-based approach that identifies higher-order statistical differences between transitioning and non-transitioning trajectories within the ensemble realizations. This method enables the real-time prediction of transition probabilities for individual trajectories prior to the onset of tipping. Our results show that the DL-based indicator provides effective early warnings in a system where transitions can be induced by bifurcations, critical forcing rates, and noise. These findings underscore the probabilistic safe operating boundary and the potential in identifying early warning indicators for abrupt transitions of complex systems under uncertainty.