Probabilistic prediction of tipping points in Earth system with deep learning

Abrupt transitions in the Earth system can arise from bifurcation-induced tipping, rapid forcing rates, or noise-driven excursions, making early warning inherently probabilistic. Using the Atlantic Meridional Overturning Circulation (AMOC) as a case study, we run large ensemble simulations of a calibrated AMOC model under time-varying freshwater forcing and stochastic perturbations. Even under identical forcing scenarios, only a subset of ensemble members undergoes a tipping transition, highlighting an intrinsically stochastic regime. In this setting, conventional early-warning signals based on critical slowing down (CSD, e.g., increasing lag-1 autocorrelation and variance) show limited prediction ability and are easily confounded by non-stationary forcing and noise. We develop a deep-learning (DL) indicator trained on labeled ensemble trajectories to distinguish transitioning from non-transitioning dynamics using sliding windows of time series, thereby capturing high-order temporal statistics beyond traditional early-warning indicators. In application, the model outputs trajectory-specific probabilities of tipping in real time, enabling probabilistic warnings ahead of tipping. Across a range of freshwater forcing pathways and noise amplitudes, the DL indicator provides earlier and more robust probabilistic forecasts than CSD indicators and supports a probabilistic interpretation of safe operating boundaries. The framework is transferable to other Earth system components where tipping risk must be assessed under uncertainty from stochastics and forcing.