Arctic catastrophes in an idealized sea ice model

With recent observations of diminishing summer Arctic sea ice extent, the hypothesis of a “tipping point” in summer ice cover has been the focus of a number of studies. This view suggests that as summer Arctic sea ice cover retreats it will reach a critical point after which the ice–albedo effect will cause the summer ice cover to disappear altogether. We have examined the heuristic argument behind this hypothesis using an idealized, but observationally constrained, model of Arctic sea ice with representations of ice and ocean mixed layer thermodynamics, varying open water fraction, an energy balance atmosphere, and scalable CO2. We find that summer ice cover retreats toward an ice-free summer ocean at an accelerating rate in a scenario with exponentially increasing CO2. However, we find no critical CO2 concentration or “tipping point” using observationally based parameter values. We identify in the extended parameter space a bifurcation associated with multiple summer ice cover states and a cusp catastrophe, and we find that it occurs far from the physically realistic parameter regime. Our results suggest that the argument for a “tipping point” in summer Arctic ice cover brought on by ice albedo may not hold up when quantified. The reason is related to the fact that ice cover has only just begun to retreat at the time of maximum sunlight (June), and the minimum ice area occurs in September when there is very little Arctic sunlight.