Sea Ice–Albedo Feedback and Nonlinear Arctic Climate Change - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 113

and polar amplification, all of the models show a very linear
relationship between polar and global temperature change.
From this close relationship, it is clear that simulated 21st
century polar climate change is very linear. While linear,
the polar temperature changes are quite large in some of the
models, comparable to the magnitude of the larger warmings
at Greenland during the dansgaard-Oeschger cycles [ Alley ,
2000].
Plate 3 shows the relationship between polar region effec-
tive albedo and surface temperature. The effective albedo is
the long-term ratio of surface-up to surface-down shortwave
flux. Effective albedo can be shown to be the time-averaged
albedo weighted with the surface downward shortwave flux.
This weighting is especially important in the Arctic where
the insolation has a very large seasonal cycle. In general,
the albedo and temperature have close linear relationships.
Four of the five models become ice free during September in
the polar region over the course of the 21st century without
disturbing this relationship. In terms of the EBM discussion
of the last section, the simulated Arctic climate changes are
linear because the albedo/temperature relationship stays en-
tirely within a subcritical linear ramp region during the 21st
century.
The National Center for Atmospheric Research (NCAR)
Community Climate System Model, version 3 (CCSM3),
which spans the largest range of temperatures and albedos,
shows some gentle downward arcing in its albedo/tempera-
ture relationship (Plate 3). Since this arcing is not apparent
in the polar amplification plot, other feedbacks must be com-
pensating for its slightly nonlinear impact. An examination
of a similar plot for the planetary albedo (not shown) does
not show this arcing behavior, so the compensation may oc-
cur between atmospheric and surface shortwave terms.
Holland et al . [2006] have noted that there are abrupt de-
clines in September Arctic sea ice cover in the individual
ensemble members of the NCAR CCSM3 SRES A1B ex-
periments. Part of the steepness of the ice cover decline
must be related to an acceleration of global warming in the
early 21st century under SRES A1B forcing. holland et al.
report that the annual mean ice cover in the NCAR CCSM3
is linearly related to global mean temperature, a result earlier
found in the Uk Met Office HadCM3 model by Gregory et
al . [2002], but that September ice cover is not so related.
Therefore another factor must be involved in these sharp de-
clines. They note that ice cover responds more sensitively
to melting when it is thin. Part of the acceleration of the ice
cover decline and its increase in variability are likely due to
this increased sensitivity. It is to be expected that a binary
variable such as ice cover will show some degree of non-
linearity when confined spatial and temporal averaging is
done. The abrupt September ice cover declines are perhaps

best characterized as a nonlinear response to linear climate
dynamics.

4. ARCTIC NONLINEARITy IN ANNUALLy SEA
ICE-FREE ExPERIMENTS

From Plate 3 we note that, even with the complete loss of
September ice in most of the models, effective albedo has a
long way yet to fall to approach open water values of about
0.1. Furthermore, following their linear trends, the models
would achieve this albedo at temperatures well above freez-
ing, between 11°C and 29°C. The curves would therefore
likely experience considerable steepening under further
warming, potentially inducing nonlinear climate changes.
We can only be sure of establishing the presence or absence
of nonlinear behaviors associated with ice-albedo feedback
in experiments that warm to the point of complete ice re-
moval. Beyond this point, there can be no further reductions
in polar ocean surface albedo. The presence or absence of
sea ice is easily determined by examining air temperatures in
the coldest month and annual effective surface albedos (the
ratio of annual surface-up to annual surface-down shortwave
fluxes). If the coldest month temperature is at freezing and
the effective albedo is near an open ocean value (about 0.1),
then we can be assured that there is little sea ice in the par-
ticular region in either summer or winter. Seventy-nine runs
of four standard experiments (1% per year CO 2 increase to
doubling, 1% per year CO 2 increase to quadrupling, SRES
A1B, and SRES A2) were examined for annually ice-free
conditions in their polar regions (80°N-90°N, 90°E-270°E)
based on these criteria. Of these, only two, had years with
February polar region temperatures at freezing temperature
and annual surface albedos below 0.15. Thus, it is quite un-
common for a model's Arctic Ocean to become sea ice-free
year-round in these climate change experiments. By contrast,
it is common in these runs for the Arctic sea ice to disappear
in September; about half of the runs had Septembers with
surface albedos less than 0.15. Unlike Thorndike 's [1992]
“toy” model, the seasonally ice-free state is apparently quite
stable in GCMs.
The two runs which lose their Arctic sea ice year-round
are the 1% per year CO 2 increase to quadrupling experi-
ments of the Max Planck Institute (MPI) ECHAM5 and the
NCAR CCSM3. Eleven other models supplying data for this
experiment did not lose all Arctic sea ice. Of the four forc-
ing scenarios, the quadrupling experiment attains the highest
forcing level, over 7 W m −2 . Both models are run for nearly
300 years, well past the time of quadrupling at year 140. The
atmospheric CO 2 is held constant after quadrupling, but tem-
peratures are generally still rising in the models as the ocean
heat uptake declines [ Stouffer , 2004].