Geoscience Reference
In-Depth Information
Figure 7.
Time series of 20th and 21st century (a) September ice extent
A
n
and (b) mean March ice thickness
T
n
, as in
Figure 1, but generated by equations (6) - (8) with the CCSM3 time series of ocean heat transport shown in Figure 4a as
input. The gray bands represent an abrupt transition according to the same criterion as in Figure 1.
surface albedo effect. The modeled feedbacks and the way
in which the system responds to an increase in OHT are il-
lustrated schematically in Figure 8; here the key nonlinearity
resulting from the inverse dependence of summer open wa-
ter area on the previous winter's ice thickness as discussed
in 3.2.1 is represented by the thick arrow.
In obtaining the above expressions major simplifications
have been made, and clearly such a representation does not
capture all the complexity of the Arctic climate system as
simulated by CCSM3. Nonetheless, by considering in iso-
lation a small number of processes thought to be relevant
to sea ice abrupt transitions, further insights into this phe-
nomenon can potentially be gained, and the possible range
of behaviors, under differing climatic conditions and in
different models, can plausibly be explored. As an initial
step, equilibrium solutions to these equations are examined
next.
(6) and (8). Such nonlinearity can potentially give rise to
multiple equilibria.
Equilibria of (6) - (8) can be obtained as a function of
H
by setting
T
n
and
A
n
to constant equilibrium values
T
e
and
A
e
.
Substituting (8) into (7) and (7) into (6) then leads to
(
T
*
/
T
e
)(
M
(
s
)
0
+
M
(
b
)
é
ë
0
+
wH
)
1 + (
T
*
/
T
e
)
wH
/ 2
T
e
(
H
) =
F
-
wH
-
wbA
max
,
(9a)
A
e
(
H
) =
A
max
1 - (
T
*
/
T
e
)(
M
(
s
)
+
M
(
b
)
é
ë
0
+
wH
/ 2)
1 + (
T
*
/
T
e
)
wH
/ 2
0
,
(9b)
in instances where (8) yields
M
£
T
e
/
T
*
. When forcing is
sufficiently strong that
M
=
T
e
/
T
*
according to (8), the equi-
librium solution is
T
e
(
H
) =
max
[
F
−
wH
−
wbA
max
,
0
]
,
(10a)
3.3. Equilibrium Solutions
A
e
(
H
) =
0
.
(10b)
For
H
>
w
-1
F
-
bA
max
this equilibrium solution implies zero
winter ice thickness, i.e., a perennially ice-free Arctic, as is
approached under quadrupling of CO
2
in CCSM3 [
Winton
,
2006].
Equations (6) - (8) describing Arctic sea ice evolution con-
tain nonlinearities arising from the inverse dependence of
open water production efficiency on
T
n
in (7) and from clip-
ping to prevent unphysical negative values of
T
n
and
A
n
in
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