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Figure 4.
Ocean heat transports entering Arctic region: (a) annual means and (b) standard deviations. Solid curves cor-
respond to the CCSM3 realization shown in Figure 1. Shaded dashed curves denote the ensemble mean of the statistical
model, and shaded curves denote a single realization of the statistical model. The single-realization standard deviations
in Figure 4b are computed using a 21-year sliding window.
unit variance, and f
=
exp(-1/
t
A
) » 0.61 for an assumed
autocorrelation time of
t
A
= 2 years, similar to that of the
OHT time series from CCSM3. The ensemble variance is
taken to evolve as s
n
= s
0
(
¯
n
/
H
0
) with s
0
= 0.6 W m
-2
.
This yields an ensemble standard deviation, described by
the dashed curve in Figure 4b, which corresponds reason-
ably well to the standard deviation of the CCSM3 time series
within a running 21-year window (solid curve in Figure 4b);
for comparison, a similar running standard deviation ap-
plied to the synthetic time series in Figure 4a is also shown
(shaded curve in Figure 4b).
Bitz
, 2003]. HbT and
Winton
[2006] discuss the likely role
of ice-albedo feedback in accelerating ice retreat.
To parameterize this feedback, we consider the shortwave
radiation
Q
SW
absorbed by the ocean in the Arctic region,
which is approximately equal to
Q
SW
= (1 -
a
ice
)(1 - a
ocn
)
F
SW
,
where a
ocn
is the ocean albedo,
a
ice
is the ice-covered frac-
tion, and
F
SW
is the downwelling shortwave radiation at the
surface. Penetration of solar radiation through the ice into
the ocean is neglected. Changes in
Q
SW
are dominated by
decreasing ice cover, with changes in
F
SW
, which decreases
by approximately 18% over the 21st century, playing a small
compensating role. (Such a decrease, seen also in other cur-
rent generation climate models, is associated with increased
cloudiness [
Sorteberg et al.
, 2007].) This suggests approxi-
mating changes in annually averaged ocean shortwave
absorption
Q
n
as proportional to September open water area
A
max
-
A
n
:
3.2.3. Ice-albedo feedback.
The decrease in surface albedo
as sea ice retreats in a warming climate leads to increased
surface absorption of shortwave radiation and is believed to
constitute a significant positive feedback which amplifies
polar warming relative to other regions [e.g.,
Holland and
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