Multiple Equilibria and Abrupt Transitions in Arctic Summer Sea Ice Extent

An application of bifurcation theory to the stability of Arctic sea ice cover is described. After reviewing past such efforts, a simple mathematical representation is developed of processes identified as contributing essentially to abrupt decreases in 21st century Arctic summer sea ice extent in climate model simulations of the Community Climate System Model, version 3 (CCSM3). The resulting nonlinear equations admit abrupt sea ice transitions resembling those in CCSM3 and also plausibly represent further gross aspects of simulated Arctic sea ice evolution such as the accelerating decline in summer ice extent in the late 20th and early 21st centuries. Equilibrium solutions to these equations feature multiple equilibria in a physically relevant parameter regime. This enables abrupt changes to be triggered by infinitesimal changes in forcing in the vicinity of the bifurcation or, alternatively, by finite perturbations some distance from the bifurcation, although numerical experiments suggest that abrupt transitions in CCSM3 may arise mainly from the increasing sensitivity of sea ice to fluctuations in ocean heat transport as ice thickness and extent diminish. A caveat is that behavior following a complete seasonal loss of ice cover is sensitive to aspects of the parameterization of ocean shortwave absorption.