Most probable transition path to an ice-free state in a model for Arctic energy balance

We investigate the most probable transition path from a perennially ice-covered state to an ice-free Arctic state, using a piecewise-smooth periodically forced energy balance model for the yearly evolution of energy in the Arctic introduced by Eisenman and Wettlaufer. Although a summertime ice-free state is widely expected to occur if current climate change trends persist, the time frame and pathway by which the Arctic may transition to an ice-free state remains in debate. Using the Freidlin-Wentzell theory of large deviations with an appropriate rate functional for piecewise-smooth systems, we characterize noise-induced transitions in the energy balance model framed as a stochastic differential equation. We derive the most probable transition path using gradient flow applied to a mollified system and validate our qualitative results using Monte Carlo simulations. These simulations show that transitions typically begin during the first half of the year with an average duration of approximately 19.5 years. We further derive an effective quasi-potential to estimate the expected escape time from the metastable states to the switching manifold. Our results provide insight into Arctic sea ice loss mechanisms, as well as a case study for how transition paths may be characterized in piecewise-smooth systems.