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Figure 2. Time series of mean ice thickness north of 70°N in CCSM3 experiments (see Table 2).
in CMIP3, which used T85 resolution, are much better. In
addition, the transient forcing during the 20th century leads
to a somewhat thinner Arctic by the end of the 20th cen-
tury compared to the fixed forcing 1990s control. In spite
of the biases in Plate 2a, the experiments are, nonetheless,
useful for evaluating general relationships among ice-albedo
feedback, the mean state, and the response to anthropogenic
forcing.
The change in sea ice thickness that results from doubling
CO 2 with freely varying albedo is shown in Plate 2b, and
the change with fixed albedo is shown in Plate 2c. It is clear
that the pattern of thickness change is a strong function of
the control thickness. As in the across-model analysis with
the CMIP3 models, the thickness changes most where ice is
thickest in the control. Although the overall magnitude of
change is less without ice-albedo feedback, the functional
dependence on the control thickness appears broadly the
same.
The influence of ice-albedo feedback can be made more
explicit by dividing the two thickness change maps in Plates
2b and 2c, as shown in Plate 3a. In the parlance of feedback
analysis from electrical engineering, this quantity is called
the “gain”:
(3)
G ' h ' h 0 ,
where D h is the thickness change in the normal perturbed
case and D h o is the thickness change from the same pertur-
bation but in the absence of some feedback (or feedbacks),
which here is the ice-albedo feedback. D h o can also be
thought of as the thickness change of a “reference system”
[ Roe and Baker , 2007], which comprises all the feedbacks in
the system except the feedback that gives rise to the gain.
The gain from ice-albedo feedback ranges from about 1.1
to 1.5 in most of the Arctic, with an average of 1.26 north
of 70°N. The gain tends to be larger near the location of the
ice edge in summer, at the interface of the perennial and sea-
sonal ice. The gain also appears somewhat noisy in spite of
the long time periods that were used to compute the means.
A feedback factor f can also be defined such that
' h o
1 f
' h
(4)
where f is related to G by f 1 G 1 . Plate 3b shows f
for CCSM3. Where G ! 1, the feedback factor is positive,
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