Sea Ice–Albedo Feedback and Nonlinear Arctic Climate Change - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 112

[ Marani , 1999]) into (2), we get a critical transition tem-
perature range of about 25°C. This value indicates instability
of the transition to a sea ice-free climate because the an-
nual mean temperature over the perennial sea ice today is
about −18°C, and the perennial ice-free zone just beyond
the maximum ice edge is at about 0°C. Since ice in this tem-
perature range is producing the satellite-observed planetary
albedo drop, the average slope of the albedo/temperature
curve on the way to ice-free conditions exceeds the critical
slope, and so the critical slope would have to be exceeded at
some point, producing instability. However, this conclusion
depends upon the assumption that heating from atmospheric
transport remains fixed.
But it is unlikely that atmospheric heat transport would
not respond to changes in shortwave absorption. The region
north of 70°N receives more energy from the atmospheric
transport than it absorbs from the Sun, and together they
make up nearly all of the OLR; the surface flux is small [ Ser-
reze and Barry , 2005]. Since atmospheric heat transport is a
big player in Arctic climate, it would not likely stand on the
sidelines letting OlR completely balance a large change in
absorbed shortwave radiation. Indeed, it is probable that the
Arctic heat convergence is as high as it is because it is coun-
tering the smallness of Arctic shortwave absorption, which
is about 1/3 of the global mean [ Serreze and Barry , 2005].
horizontal temperature diffusion is a simple method of
representing heat transport in an EBM. However, adding
diffusive heat transport to the EBM does not eliminate un-
stable transitions in all cases. Instead, these diffusive trans-
port models can exhibit an unstable loss of a finite patch of
polar ice as forcing is increased. The instability is called the
SICI and in some ways is a companion to the large ice cap
instability whereby the globe becomes ice covered after the
ice reaches a critical maximum extent. The ice edge lies in a
temperature boundary zone having a length scale determined
by the diffusivity and longwave damping parameters [ North ,
1984]. Both instabilities occur when this zone impinges on
a boundary, either the equator or the pole. The instability
can be removed by reducing the albedo ramp slope, but the
main point here is that the instability can occur in spite of
down-gradient (warm to cold) transport. At least in some
configurations, the instability is also robust to the inclusion
of a seasonal insolation cycle [ Lin and North , 1990].
Furthermore, we expect that the transport changes in re-
sponse to CO 2 increase will have a significant up-gradient
component. In the atmosphere this comes about because
warmer air allows for an increase in the latent heat transport.
Held and Soden [2006] show that increased latent transport
drives an increase in heat transport to the polar regions, in
spite of enhanced warming there, in both equilibrium and
transient CO 2 increase experiments. Additionally, Holland

and Bitz [2003] have shown that the ocean also transports
more heat into the Arctic, even as the heat transport is being
reduced at lower latitudes in association with the weakened
meridional overturning circulation. Thus, it is not clear that
heat transport can be relied upon to stabilize Arctic climate
by exerting a cooling influence on the region as it warms at
a larger-than-global rate.
When evaluating the linearity of polar climate, it will
be useful to note the well-established fact that the global
temperature response to forcing is linear. This was clearly
shown for the Goddard Institute for Space Studies model by
Hansen et al . [2005], who calculated forcing efficacy, the
ratio of global temperature change to forcing magnitudes
for various forcing types and magnitudes. The efficacy was
constant over a large range of magnitudes including the last
Glacial Maximum and the anthropogenic future.
We can make use of the global linearity as follows:
since global temperature change is linear in forcing, if po-
lar temperature change is linearly related to it, then polar
temperature change must also be linear. The ratio of polar
to global temperature change is called the polar amplifica-
tion. It is typically larger than one for a number of reasons
including the ice-albedo feedback. If the polar amplification
is also constant, then polar climate change is linear. If there
is a nonlinear relationship between polar and global tem-
perature, a nonconstant polar amplification, then the polar
change must be nonlinear. unstable behavior is a subcate-
gory of nonlinear behavior. If the relationship between polar
and global temperature is nonlinear and shows a temperature
discontinuity, we have evidence of an unstable polar climate
change.

3. ARCTIC lINEARITy IN 21ST CENTuRy
ExPERIMENTS

Now we turn to the GCMs to see whether the projected
21st century polar climate change exhibits nonlinearity.
Since Arctic climate is quite variable, it will be useful to do
some averaging to bring out the forced signal. First, to form
ΔT P , the change in polar surface air temperature, we aver-
age over the “half-cap” polar region north of 80°N between
90°E and 270°E in the coldest part of the Arctic Ocean. In
the remainder of this paper this region is referred to as the
polar region. Next we take 5-year averages, and we also av-
erage over the separate runs of the individual models made
available in the AR4 experiment archive; thus each point
represents an average over 15 to 35 years, depending upon
the model's ensemble size. Plate 2 shows the results for five
models that supplied multiple runs to the archive for the Spe-
cial Report on Emissions Scenario (SRES) A1B experiment.
In spite of differences in global warming, polar warming,