Influence of extreme events modeled by Lévy flight on global thermohaline circulation stability

Abstract

Abstract. How will extreme events due to human activities and climate change affect the oceanic thermohaline circulation is a key concern in climate predictions. The stability of the thermohaline circulation with respect to extreme events, such as fresh-water oscillations, greenhouse gas accumulations and collapse of the Atlantic meridional overturning circulation, is examined using a conceptual stochastic Stommel two-compartment model. The extreme fluctuations are modeled by symmetric α-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 results argue that for 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 that can be seen as civilization-induced greenhouse gas accumulation. On the other hand, the off-state stability is more vulnerable to the agitations with moderate jumps and frequencies which can be interpreted as wind- driven circulations towards higher latitudes. Under the repercussion of stochastic noise, on to off transitions are more expected in the model if the fresh-water influx is strong. Moreover, transitions from one metastable state to another are equiprobable when the fresh-water input induces a symmetric potential well.

Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package

“…For instance, it has been proposed that this might have been of relevance for climate system states on a millennial time scale during the last glacial period as was observed in icecores [57]. Also, transitions triggered by extreme events emerging from Lévy-distributions in other nonlinear cli-mate system components such as the Amazon rainforest or the thermohaline circulation have been investigated, as well as transitions in gene expression processes in molecular biology [58][59][60].…”

Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package

“…For instance, it has been proposed that this might have been of relevance for climate system states on a millennial time scale during the last glacial period as was observed in ice-cores [57]. Also, transitions triggered by extreme events emerging from Lévy-distributions in other nonlinear climate system components such as the Amazon rainforest or the thermohaline circulation have been investigated, as well as transitions in gene expression processes in molecular biology [58,59,60].…”

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

“…In the natural world, there are different types of random noises, such as the well-known white noise, the Lévy jump noise which considers the motivation that the continuity of solutions may be inevitably under severe environmental perturbations, such as earthquakes, floods, volcanic eruptions, SARS, influenza [21][22][23], and a jump process should be introduced to prevent and control diseases, and so on. Mathematically, several authors [24][25][26][27] used the Lévy process to describe the phenomena that cause a big jump to occur occasionally.…”