What Is the Trajectory of Arctic Sea Ice? - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 171

What Is the Trajectory of Arctic Sea Ice?

Harry L. Stern and Ronald W. Lindsay

Polar Science Center, Applied Physics Laboratory, University of Washington, Seattle, Washington, USA

Cecilia M. Bitz and Paul Hezel

Department of Atmospheric Sciences, University of Washington, Seattle, Washington, USA

We consider the trajectory in phase space of the Arctic sea ice thickness
distribution, in which each dimension or component is the time series of sea ice
area for a given ice thickness bin. We analyze the trajectory as determined by
output from an ice-ocean model, finding that the first two principal components
account for 98% of the variance. Simplifying the ice thickness distribution into
thin ice, thick ice, and open water, we construct a simple empirical linear model
that converges to a stable annual cycle from any initial state. When we include a
quadratic nonlinearity to simulate a crude ice-albedo feedback, the model exhibits
two stable states, one with perennial ice and one with ice-free summers, resembling
the projections of some climate models for the late 21st century. We discuss the
interplay between external forcing, internal dynamics, and “tipping points” in the
decline of Arctic sea ice.

1. InTRODUCTIOn The sea ice thickness distribution g(h) over some region R

gives the fractional area of R covered by ice of thickness h.
It is the fundamental description of the Arctic sea ice cover
[ Thorndike et al. , 1975]. The processes controlling g(h) are
ice growth, melt, divergence, ridging, and import/export
(into or out of R). Models that simulate the evolution of g(h)
often use discrete bins of ice thickness. Let g k represent the
fractional area covered by ice with thickness in the range
h k < h < h k+1 , for k = 1 to n, where n is the number of bins.
The area with h < h 1 is considered open water. The sum of
the fractional areas g 1 + … + g n is the total ice concentration.
now consider (g 1 , …, g n ) as a point in n-dimensional space.
As time progresses, the point moves in the n space, tracing
out a trajectory. That is what we mean by the trajectory of
Arctic sea ice. A point on the trajectory gives the ice thick-
ness distribution at a particular time. Each component g k (t)
is a time series of the fractional ice area in thickness bin
k. The region R over which this description applies may be
chosen to be as small as one model grid cell or as large as the
entire Arctic Ocean.

Significant changes in the Arctic sea ice, ocean, atmo-
sphere, ice sheets, and freshwater cycle over the past few
decades are well documented [ Intergovernmental Panel on
Climate Change , 2007]. Several recent articles refer to the
“trajectories” of these components, in which the word trajec-
tory is used in a figurative sense [e.g., Overpeck et al. , 2005;
Peterson et al. , 2006]. The literal meaning of a trajectory is
a path in physical space or phase space. In this work we con-
sider the trajectory of sea ice in the ice thickness phase space.
We then analyze that trajectory as determined by model sea
ice thickness distributions. Our use of the word trajectory
does not refer to the physical motion of ice floes.