Methods for the Study of Rare Transitions in the Atlantic Meridional Overturning Circulation

Abstract

Tipping elements are climate subsystems that may collapse under anthropogenic forcing. It is then crucial to study the drivers and potential impacts of tipping events. Here, we focus on one tipping element whose collapse may have global consequences: the Atlantic Meridional Overturning Circulation (AMOC). The AMOC plays an important role in the meridional transport of heat and salt across the Atlantic Ocean, thereby influencing the climate of the Northern Hemisphere. Although the AMOC may be in a bistable regime, the probability that it collapses within 100 years is still poorly constrained. Rare-event algorithms are designed to efficiently sample such transitions, however rare, and estimate their probability. Here, we focus on Trajectory-Adaptive Multilevel Splitting (TAMS), which iteratively biases an ensemble simulation to bring all ensemble members to a target domain. At each iteration, trajectories far from the target are discarded and replaced by cloning and resimulating better-performing trajectories. This selection step relies on a score function, which also determines the efficiency and accuracy of TAMS. The optimal score function, or committor function, is however impossible to compute, even in small-dimensional systems. First, we compare the performance of several data-driven committor estimation schemes in a context of data scarcity. We measure for each method the quality of its committor estimate, its computational cost and the required amount of training data. Reservoir Computing (RC), a type of neural network that embeds nonlinear dynamics into a larger-dimensional space, is found to be particularly efficient in all metrics. The RC is then coupled to TAMS and applied to an AMOC model to estimate the probability that it collapses within 100 years. The RC is trained exclusively using the data sampled by TAMS, while also serving as score for TAMS. At every TAMS iteration, new data is sampled and immediately used to improve the RC performance. Moreover, we set up a transfer learning scheme: the training of the RC is iteratively shifted to model parameters where an AMOC collapse is very difficult to simulate. We show that the RC is able to adapt to changing dynamics even, for very small transition probabilities. Finally, the interpretability of the RC gives an approximate analytical expression of the learned committor. The second part of this thesis addresses the efficiency of TAMS by extending its applications. TAMS can indeed estimate many observables at no additional computational cost, which opens new possibilities for rare-event algorithms. Important quantities such as the transition time, can be tracked across every stage of the AMOC collapse to obtain insight into the transition dynamics. We use these properties to define a new indicator of resilience for stochastic systems, which does not require any prior knowledge on the system. Finally, we use TAMS to analyse the relation between the AMOC and the Amazon rainforest and quantify the probability of a tipping cascade. The distribution of AMOC strengths can be reconstructed at every stage of the transition of the Amazon rainforest to a savannah, which gives insight into the influence of the AMOC on the rainforest.