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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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