Sea Ice–Albedo Feedback and Nonlinear Arctic Climate Change - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 119

an examination of the polar region heat budgets for the two
models shown in Figure 2. These budgets are constructed by
regressing the fluxes on temperature in the three temperature
ranges. The slopes are then multiplied by 5°C to give a rep-
resentative flux change between the beginning and end of
the specified temperature era. Figure 2 shows that the large
increase of SAF in the MPI model at warmer temperatures
also appears in the overall shortwave budget of the region
and that there is a smaller increase in the shortwave budget
of the NCAR model. The outgoing longwave radiation has
a small damping effect on the warming of the region in both
models. The surface budget changes are quite different: the
MPI model has only small changes, while the NCAR model
has a large increase in surface forcing as the ocean supplies
increased heating. This ocean heating contributes more to
the warming of the NCAR model in the warmest tempera-
ture era than the SAF. The atmospheric heat transport con-
vergence shifts from a forcing for the warming in the coldest
temperature era to damping the warming in the two warmer
eras in both models. It is this change in atmospheric con-
vergence of heat, rather than the OlR, that does the most
to balance the forcing factors: shortwave flux in MPI and
shortwave plus surface flux in NCAR. All of the surface flux
changes are opposite to the atmosphere flux convergences in
their impacts on the warming.
To gain a sense of the regional extent of nonlinear climate
changes, we split the polar amplification into two factors:
polar to Arctic (60°N-90°N) and Arctic to global amplifica-
tions. Figure 3 (top) shows the relationship between polar
and Arctic temperatures and Figure 3 (bottom) shows Arctic
and global temperatures for the two models over the course
of the 1% per year to 4 times CO 2 runs. The warmest polar
temperature attained in the two models is about the same,
but the global temperature rise is considerably larger in the
MPI model, while the Arctic/global and polar/Arctic ampli-
fications are correspondingly smaller. The lines in Figure 3
are fits to the relationships for data with polar temperatures
less than −5°C. A deviation from this fit at warmer tempera-
tures might reflect the enhanced warming due to the dramatic
changes in sea ice cover above this temperature in both mod-

els. The relationship is mainly linear in both models, but in
the ECHAM5 model the polar temperature rises above the
reference line starting at a polar temperature of −4°C until it
is about 2°C larger and then begins to parallel the fitted line
at a polar temperature of 0°C. Apparently, the large increase
in surface albedo feedback in this range of temperatures
(discussed above) plays a role in this extra warming of the
polar region. After the ice is eliminated, the SAF drops to
zero, and further warming falls below the −4°C to 0°C ratio.
The behavior of the CCSM3 is somewhat different. At −5°C
the polar temperature rises slightly above the fitted line but
then parallels it as both regions warm further. In both cases,
the transition to seasonally ice free at a polar temperature of
−9°C does not disturb the linear relationship between warm-
ing in the two regions. The relationship between Arctic and
global temperatures (Figure 3, bottom) is quite linear in both
models indicating that the nonlinear changes in the Arctic
Ocean do not have significant impacts on the broader region
temperatures. Although the elimination of Arctic sea ice
would doubtless have enormous consequences for the local
environment, these models do not show it to be particularly
important for the larger-scale climate changes.

5. EBM INTERPRETATION OF THE TRANSITION
TO ANNuAlly ICE FREE

Now, to provide a mechanistic comparison to the GCM
behaviors of the last section, we examine polar amplification
in a simple one dimensional EBM as it experiences small
ice cap instability. Following North [1984], the temperature
equation for the EBM is

- D d

¾

dx (1- x 2 ) dT

dx + A + BT = S ( x )[1-a( T )]. (3)

Table 1 defines the notation and gives parameter values.
The value for the longwave sensitivity parameter, B, comes
from a regression of International Satellite Cloud Clima-
tology Project outgoing longwave on surface temperature
[ Marani , 1999]. The value used for the albedo jump with
temperature is the Gorodetskaya et al . [2006] value for the

Table 1. Notation and Parameter Values
Notation description

x sin(latitude)

T(x) surface temperature (°C)

A, B longwave parameters (B = 1.5 W m -2 °C −1 ; A is variable (W m −2 )

d atmospheric diffusion (= 0.36B, W m −2 )

a(T) albedo (= 0.3 if T > 0°C; = 0.52 if T < −DT M ; = (0.3(T + DT M ) − 0.52T)/DT M , otherwise)

DT M temperature range over which albedos transition linearly from ice covered to ice free

S(x) annual shortwave distribution (= 340(1 − 0.482P 2 (x)); P 2 (x) = (3x 2 − 1)/2)