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100,000-year timescale. These oscillations feature relatively
abrupt onsets and collapses of sea ice cover that occur on
timescales of a few decades, minute compared to the oscilla-
tion period. The model behaved similarly when extended to
incorporate seasonal and orbital forcing [
Gildor and Tziper-
man
, 2000], as well as greater resolution in latitude [
Sayag
et al.
, 2004]. Although these studies did not show explic-
itly that multiple sea ice equilibria exist under fixed climatic
forcing, this is strongly implied by the abrupt “switching” or
threshold behavior for sea ice in their solutions.
To achieve varying degrees of simplification, each of
these studies emphasized particular aspects of sea ice and its
relation to climate, as summarized in Table 1; typically, the
simpler formulations yield analytical determinations of equi-
libria, whereas for the more complex ones equilibria were
determined numerically. However, one aspect common to
all these studies that have found multiple sea ice equilibria
is the increase in surface shortwave absorption that results
from decreased albedo as ice cover thins or retreats.
In section 3 we describe an attempt to represent the behav-
ior of Arctic sea ice in a complex climate model through a
set of equations sufficiently simple that their equilibria can
be obtained analytically.
cation structure is analyzed section in 3.3, where it is found
that multiple equilibria can exist provided changes in ocean
shortwave absorption due to ice-albedo feedback are suffi-
ciently strong. Numerical solutions of the simplified equa-
tions are compared with CCSM3 behavior in section 3.4;
additional solutions exhibiting vacillations between stable
equilibria and hysteresis effects are also briefly considered.
Finally, the predictability of simulated sea ice abrupt transi-
tions is examined in section 3.5.
3.1. Background
In light of the retreat of Arctic sea ice at a rate approaching
10% per decade in recent years [e.g.,
Stroeve et al
., 2005],
possibly attributable to anthropogenically induced climatic
warming [
Overpeck et al.
, 2005], it is clearly of interest to
examine climate model projections of future Arctic sea ice
trends. Recently,
Holland et al.
[2006a] (hereinafter referred
to as HbT) described such projections from version 3 of the
Community Climate System Model (CCSM3), which sim-
ulates with reasonable fidelity the observed sea ice extent
and trends in the late 20th and early 21st centuries. They
considered an ensemble of seven simulations employing the
Special Report on Emissions Scenarios (SRES) A1b forc-
ing scenario [
Intergovernmental Panel on Climate Change
,
2001] and found in each that the future Arctic summer sea
ice extent undergoes sudden and substantial decreases at
rates far exceeding those already observed. These events,
which they termed “abrupt transitions,” occur as early as
2015 and lead to a nearly ice-free summertime Arctic Ocean
3. ANAlySIS OF AbRUPT ARCTIC SEA ICE
TRANSITIONS IN CCSM3
After explaining the motivation for this study in section
3.1, simple nonlinear equations describing Arctic sea ice ev-
olution in CCSM3 are formulated in section 3.2. Their bifur-
Table 1.
Studies of Multiple Sea Ice Equilibria
a
North
[1984]
Thorndike
[1992]
Flato and
Brown
[1996]
Taylor and
Feltham
[2005]
Björk and
Söderkvist
[2002]
Gildor and
Tziperman
[2001]
This Study
Domain
planetary
local
local
local
local
planetary
Arctic
SW heating
•
•
•
•
•
•
•
Albedo changes
•
•
•
•
•
•
•
Radiative cooling
•
•
•
◦
•
•
-
SW penetration
-
-
•
•
-
-
-
Atmospheric heat
transport
•
-
-
-
•
•
-
Ocean heat transport
-
•
-
-
-
•
•
Seasonality
-
•
•
-
•
-
•
Partial ice cover
•
-
-
-
•
•
•
Ice thickness
-
•
•
•
•
-
•
Ice dynamics/export
-
-
-
-
•
-
-
Snow cover
-
-
•
-
•
-
-
Analytical solutions
•
◦
-
•
-
-
•
a
Symbols represent the following: • indicates considered; ◦ indicates partial or incomplete; and - indicates not considered.
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