Resilience of the AMOC

The Atlantic Meridional Overturning Circulation (AMOC) is a crucial part of the climate system that carries warm and saline water towards the northern Atlantic and is an important component in the global meridional heat transport. However, the AMOC is a so-called tipping element: there is observational evidence that it is in a bistable regime and may thus collapse under anthropogenic greenhouse gas emissions. Bi-stability has also been found in a hierarchy of models, from a simple two-box model up to a CMIP5 global climate model (CESM1). Considering a possible upcoming tipping, it is critical to assess how likely the AMOC is to undergo a collapse under different greenhouse gas forcing scenarios. This issue is tightly related to the notion of resilience, which refers to the ability of a system to sustain a certain forcing while remaining in its original state or to return to its original state after being displaced. Studying the resilience of the AMOC requires to observe its collapse, which is very difficult due to its rarity, especially in very complex models. That is why we use a rare-event algorithm called Transition-Adaptive Multilevel Splitting (TAMS). Given a certain definition of the current-day and collapsed AMOC, TAMS pushes trajectories in the direction of a collapse at a much lower cost than Monte-Carlo simulations. This method outputs typical collapse trajectories starting from a present-day AMOC, under a certain chosen hosing flux. This process is repeated for a wide range of freshwater forcings. From those trajectories, we extract observables (e.g. the AMOC strength), which are scalar functions that are interpreted as resilience observables. By monitoring these observables, we can rank different climate change scenarios depending on the risks they impose on the AMOC. Moreover, we relate these observables to existing mathematical definitions of resilience. Finally, we determine which observables are best suited to describe the resilience of the AMOC, with a focus on those that can be measured in the field.