Atmospheric noise removes sea-ice tipping points in a simple stochastic model

The albedo contrast between sea ice and open ocean introduces a strong positive feedback in the surface energy balance of polar regions. Classical low-order models show that this feedback robustly produces multiple equilibria: the system can exist in either a cold, ice-covered state or a warm, ice-free state with the same external forcing.  The resulting hysteresis implies that polar regions will lose sea ice abruptly and irreversibly as external forcing increases. However, this tipping-point behavior is not observed in full-complexity climate models: in experiments where global radiative forcing is gradually ramped up until sea ice disappears, ice loss is indeed found to be relatively abrupt; but when the forcing is subsequently ramped down, sea ice reappears at the same rate, showing no sign of hysteresis or irreversibility. How do we reconcile this discrepancy between simple and complex models?

Here, I show that this reconciliation can be achieved by introducing atmospheric weather noise into the simple model. The polar ocean is modelled as a collection of points subject to local stochastic forcing, introduced as an additive white noise in the  energy balance model. This leads to a Fokker-Planck equation describing the probability distribution function (PDF) of ice thickness over the ocean basin, including a zero-thickness (ice free) class. For realistic values of noise amplitude estimated from reanalysis data, the PDF is bimodal when the global forcing supports multiple equilibria of the energy balance equation, with modes centered on the corresponding ice-free and ice covered equilibria. When global forcing is ramped up or down over long (~1000 year) timescales, the PDF evolves reversibly, showing relatively abrupt but reversible loss/recovery of sea ice. However, if the ramping timescale is shorter (~100 years), some residual irreversibility is still present. In conclusion, taking stochastic atmospheric fluctuations into account provides a promising avenue for resolving a long-standing problem in climate science.