Influence of extreme events modeled by Lévy flight on Atlantic meridional overturning circulation stability

How will extreme events due to human activities and climate change affect the Atlantic meridional overturning circulation (AMOC) is a key concern in climate predictions. The stability of the thermohaline circulation with respect to extreme events, such as fresh-water oscillations, is examined using a conceptual stochastic Stommel two-compartment model. The extreme fluctuations are modeled by symmetric $\alpha$-stable Lévy motions whose pathways are cádlág functions with at most a countable number of jumps. The mean first passage time, escape probability and stochastic basin of attraction are used to perform the stability analysis of on (off) equilibrium states. Our aim is to elucidate the interplay between fresh-water forcing, $\alpha$, and the stability of metastable AMOC states. Our results argue that for a model with weak fresh-water forcing strength, the greatest threat to the stability of the on-state represents noise with low jumps and higher frequency (modeled by small values of $\alpha$) that can be seen as fresh-water inputs from glacier melting due to ocean warming caused by increased greenhouse gas emissions. On the other hand, the off-state stability is more vulnerable to agitations with moderate jumps (modeled by moderate values of $\alpha$) and frequencies that can be interpreted as a possible scenario of recovery of the Atlantic thermohaline circulation. Under the repercussion of stochastic noise, on to off transitions are more expected in the model with the strong fresh-water influx. Moreover, transitions from one metastable state to another are equiprobable when the fresh-water input induces a symmetric potential well.