Comparing Rare-Event Algorithms and Direct Sampling for Estimating the Probability of CO₂-Driven AMOC Tipping

The Atlantic Meridional Overturning Circulation (AMOC) is a key tipping element of the climate system and can be viewed as a multistable, stochastic dynamical system subject to both external forcing and internal variability. While most modelling studies emphasize deterministic thresholds for AMOC collapse, the role of internal variability in shaping the timing, probability, and nature of transitions remains poorly constrained.

This motivates a shift toward probabilistic prediction of AMOC tipping. Transition probabilities can be estimated using direct Monte Carlo sampling with large ensembles; however, this approach is severely limited in climate applications, as simulations are computationally expensive and statistical precision improves only slowly with increasing ensemble size. Rare-event algorithms provide an efficient alternative. In particular, the Giardina–Kurchan–Tailleur–Lecomte (GKTL) and Trajectory-Adaptive Multilevel Splitting (TAMS) methods enable targeted sampling of low-probability transitions at substantially reduced computational cost.

Using the intermediate-complexity PlaSIM–LSG model, we estimate AMOC transition probabilities by comparing direct Monte Carlo sampling with GKTL and TAMS. In a 600 ppm CO₂ case study, TAMS delivers the most precise probability estimates per unit cost, outperforming both Monte Carlo and GKTL and emerging as the most reliable approach for probability estimation.

We further apply TAMS to assess the transition probability to a weak AMOC state under three SSP scenarios, revealing a strong dependence on the forcing pathway. Under the high-emissions scenario SSP5–8.5, the probability of entering the AMOC-weak state remains below 1% by 2100, increases to about 20% by 2150, and reaches roughly 95% by 2200. In contrast, lower-emission scenarios (SSP4–6.0 and SSP2–4.5) maintain substantially lower probabilities throughout. These results are consistent with recent multi-model projections, suggesting that AMOC collapse is very unlikely in the 21st century but becomes plausible in the 22nd century under sustained high forcing. Additional freshwater input from Greenland ice-sheet melt would likely further increase these probabilities and advance the transition.

Overall, when direct sampling fails to capture rare transitions, rare-event methods enable both improved probability estimation and deeper insight into the underlying physical mechanisms. GKTL is well suited for exploring multistability and multiple transitions, while TAMS provides a rigorous framework for quantifying transition probabilities. Together, these approaches help bridge the gap between theoretical concepts of multistability and their practical investigation in complex climate models.