Multiple Equilibria and Abrupt Transitions in Arctic Summer Sea Ice Extent - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 155

heat transport, have been set to CCSM3-relevant values.
Only the coefficient F representing baseline climatic forcing
of ice growth in the absence of ocean heat transport and the
open water shortwave absorption remain to be specified.
To fix F , we apply as input the actual CCSM3 time series
for H n in Figure 4a and adjust F to provide a qualitatively
reasonable match between output T n and A n and the actual
CCSM3 time series in Figures 1a and 1b. A value of F =
3.2 m yields the time series in Figure 7, which shows (1)
a slight, gradual decrease in A n and T n throughout most of
the 20th century; (2) a modest but more sudden decrease in
both quantities near 2000, followed by 2 decades or so that
feature fluctuations but no further decrease; (3) an abrupt
transition centered near 2027, during which A n decreases by
more than 50% in less than a decade; (4) minimal summer
ice cover after 2040 or so, with a brief but minor recovery
near 2065, and (5) winter ice thicknesses of less than 1 m in
the late 21st century, with a local maximum coinciding with
the minor recovery in summer extent around 2065. There
are also some notable differences between the CCSM3 and
synthetic time series; in particular, winter thickness and
summer extent are significantly underestimated throughout
much of the 20th century. (A contributing factor for this
discrepancy is the overestimation of open water formation
efficiency for T n greater than 3 m or so that is apparent in
Figure 3.) In addition, the CCSM3 time series exhibit sig-
nificantly more high-frequency variability, which may arise
from atmospheric influences, such as the Arctic Oscillation,
that modulate ice export and summer ice extent [e.g., Rigor
and Wallace , 2004; Lindsay and Zhang , 2005] but are not
included in the simple representation considered here.

Figure 6. Symbols denote accumulated annual melt M versus an-
nual mean ocean heat transport H for the Arctic region, low-pass
filtered by a sliding 21-year window, from CCSM3 simulation.
Solid curve represents melt as parameterized by equation (8), using
low-pass filtered CCSM3 ocean heat transport H and March ice
thickness T as input.

the tendency for overestimation of melting implied by (8).
The albedo effect is instead viewed as warming the ocean
mixed layer in ice-free regions, thus delaying the onset of
seasonal ice growth, as suggested by its role in suppressing
ice growth in (6).
3.2.5. Calibration to CCSM3 . In addition to the time-
dependent winter ice thickness T n and summer ice extent A n ,
both predicted, and OHT forcing H n specified as input, equa-
tions (6) - (8) contain several time-independent coefficients
(Table 2). Two of these, the maximum Arctic regional ice
extent A max and the factor w relating thickness of ice melted
to a given heat input, are physical constants. Several oth-
ers, including the ocean shortwave absorption parameter b ,
surface melt M ( s ) and basal melt M 0 ( b ) in the absence of ocean

3.2.6. Summary. Equations (6) - (8) describe evolution of
annual values T n and A n of Arctic sea ice winter thickness
and summer extent under changes in forcing, considered
to result from time dependence of ocean heat transport and
changing ocean shortwave absorption associated with the

Table 2. Parameters in Equations (6) - (8) Describing Artic Sea Ice Evolution
Parameter Description CCSM3 Value

F baseline winter ice thickness 3.2 m

b ocean shortwave absorption parameter

2 ´ 10 -12 W m -4

T* open water formation efficiency coefficient 0.8

M (0)
s

annual surface ice melt 0.4 m

baseline annual basal ice melt 0.2 m

M (0 b

σ 0 ocean heat transport variability 0.6 W m -2

A max ocean area in Arctic region a 7.23 x 10 6 km 2

w ice thickness melted by 1 W m -2 in 1 year a 0.104 m

a Physical parameters; values are model-independent.