Quasipotential analysis of tipping points for a box model of the Atlantic Meridional Overturning Circulation

A non-autonomous system can undergo a rapid change of state in response to a small or slow change in forcing, due to the presence of nonlinear processes that give rise to critical transitions or tipping points. Such transitions are thought to exist in various subsystems (tipping elements) of the Earth’s climate system. The Atlantic Meridional Overturning Circulation (AMOC) is considered a particular tipping element where models of varying complexity have shown the potential for bi-stability and tipping. Quasipotentials are a useful mathematical tool for understanding the ‘potential’ of such a system, where the potential cannot be calculated analytically, or may not exist. Quasipotentials can be used to calculate useful features such as minimum action paths and transition times, based on a purely stochastically forced system. In this work, we utilise an Ordered Line Integral Method (OLIM) of Cameron et.al. (2017) to estimate quasipotentials for a 2-dimensional AMOC box model with anisotropic noise estimated from complex model output. We also examine how the quasipotential depends on the anisotropy of the noise, calculate minimum action paths between stable states for these various scenarios, and how the quasipotential changes as an external forcing is increased. We also extend this model and the OLIM to 3-dimensions and explore different statistical features.