Sea Ice–Albedo Feedback and Nonlinear Arctic Climate Change - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 122

radiative effectiveness of Northern hemisphere sea ice: the
impact on planetary albedo of the change from total to zero
sea ice cover. This was determined using the Earth Radiation
Budget Experiment shortwave measurements and HadISST1
sea ice concentration data. After setting these two param-
eters, the atmospheric diffusivity, D, is adjusted to give a
reasonable planetary range of surface temperatures.
Most EBM studies explore climate sensitivity by varying
the solar constant. Here, we are interested in exploring the
relationship between temperature change at the pole (T( x =
1)) and the global mean temperature change ( ò 0 T ( x ) dx ) as
climate warms. To this end, it is desirable to force in a man-
ner that does not affect this relationship. So here we force
climate in a meridionally uniform way by varying A, reduc-
ing A induces warming. Thus, we can think of A as a forcing
for global mean temperature since
ò 0 T ( x ) dx = ( ò 0 (1 - a) Sdx - A ) / B .
With this forcing, all polar amplification is due to ice-
albedo feedback, the only spatially variable feedback in the
system.
Initially, we configure the EBM with a step jump in albedo
at 0°C (ΔT M = 0°C). North [1984] used −10°C as the location
of the step change. This lower value presumably represents
the temperature needed to retain terrestrial snow through
the summertime. Sea ice has a source (seawater freezing)
that decreases with increased temperature but is positive
while there are periods of below-freezing temperatures. This
added source is a factor aiding the persistence of summer
sea ice cover at higher annual temperatures than terrestrial
snow.
Plate 5 shows the polar and global temperatures for the
MPI ECHAM5 experiment discussed in the previous section
(green) and the EBM with a step albedo jump (blue) and
with the same jump smoothed over a transition zone of 5°C
(red). The EBM changes have been forced by varying A in
(3), while the GCM changes are forced by CO 2 increase, of
course. The CO 2 forcing itself is generally somewhat reduced
in the Arctic [ Winton , 2006]. Nonetheless, the GCM line is
the steepest at each polar temperature, so the polar amplifi-
cation is always larger for the GCM than for the EBM. This
is consistent with the findings of a number of studies that
factors beside the surface albedo feedback contribute sig-
nificantly to polar amplification of climate change [ Alexeev ,
2003; Holland and Bitz , 2003; Hall , 2004; Winton , 2006].
Further evidence of this can be seen in the MPI ECHAM5
curve where significant polar amplification remains even
after the sea ice has been eliminated. The EBM does not
represent these additional factors and so has smaller polar
amplifications.

The EBM with a step albedo change has a discontinuity
in polar and global temperatures where the small ice cap in-
stability is encountered, and both warm abruptly with the
removal of the reflective ice cap. The light blue dashed line
spans this jump, and its slope defines a polar amplification
across the instability. In the cooler part of the curve, to the
left of this jump, the pole is always below freezing tempera-
ture so the local shortwave absorption does not change. The
amplification of polar temperature change over global in this
part of the curve, about 1.8, is due to the influence of in-
creased absorption of shortwave energy at the ice edge, as
the ice retreats poleward, conveyed to the pole by atmos-
pheric transport. North [1984] shows that, as the instability
is approached, the pole feels nearly as much warming impact
from the ice retreat as the ice edge itself.
On the basis of the fact that the ice cap covers about 6% of
the hemisphere before its elimination, we might expect the
polar amplification across the jump to be about 16, since this
increased absorption is the cause of both temperature jumps.
The actual polar amplification is much less because atmo-
spheric heating at the pole, which has been increasing to that
point, collapses with the ice cap, countering its local impact
to a large degree (Plate 6). After the ice cap collapse, there
is no ice-albedo feedback, and polar and global temperatures
rise in a one-to-one relationship. The sequence of changes in
the polar energy budget encountered as the climate warms
leads to a medium/high/none sequence of polar amplifica-
tions in the EBM.
The global and polar temperatures for the MPI ECHAM5
show a three-slope regime behavior similar to that of the
EBM. However, the GCM does not show any discontinuity
in these temperatures. This may be partly due to the GCM,
unlike the EBM, not being fully equilibrated at each point in
time and hence able to fill the “forbidden zone” with transient
temperatures. However, taking note that the ECHAM5 sensi-
tivity of polar albedo to temperature is steep but far from step-
like (Plate 4, bottom), we explore the possibility that having
the albedo changes occur over a finite range of temperatures
stabilizes the transition while retaining enhanced polar sen-
sitivity because of increased surface albedo feedback. EBM
runs show that the multiple equilibria remain, with a reduced
ΔT across the jump, for a ramp range of ΔT M = 4°C but is
eliminated when for ΔT M = 5°C. The plot for the polar am-
plification in the stabilized case (Plate 5, red line) shows that
a continuous section of enhanced polar amplification fills the
region occupied by the jump in the step albedo EBM. The
enhanced sensitivity in this region is caused by the reduced
overall (negative) feedback due to a positive, but subcritical,
local ice-albedo feedback. Plate 6 shows that the diffusive
term, operating as a negative feedback, provides less heating
to the pole, opposing the enhanced shortwave absorption.