Geoscience Reference
In-Depth Information
Multiple Equilibria and Abrupt Transitions
in Arctic Summer Sea Ice Extent
William J. Merryfield
Canadian Centre for Climate Modeling and Analysis, Environment Canada, Victoria, British Columbia, Canada
Marika M. Holland
National Center for Atmospheric Research, Boulder, Colorado, USA
Adam H. Monahan
School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada
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.
The objective is to illuminate the essential processes and not to embellish
them or mix them up with others which are less important. The many
simplifications also make it possible to see how the various processes
interact, but also make it difficult to assess the quantitative validity of the
argument. If the ideas have value, it will be because they serve to develop
intuition.
Thorndike [1992]
1. INTRODUCTION
A central question in the study of climate variations is
whether climate response is smooth, in the sense of being
proportional to small changes in a forcing parameter, or
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