Geoscience Reference
In-Depth Information
2. With the creation of more open water in july, the ice-
albedo feedback may be exerting more influence. The frac-
tion of open water in july goes from 0.19 (1966) to 0.27
(2005) to 0.51 (2044). That is an increase of 42% in the first
39-year period and 89% in the second 39-year period. With
more open water in july, more solar radiation is absorbed by
the ocean, leading to more melting of thin ice and the crea-
tion of more open water.
These processes can also be understood in terms of open
water formation efficiency (OWFE) [
Holland
et al.
, 2006b;
Merryfield
et al.
, this volume], which is the change in open
water fraction per meter of ice melt, over the course of the
melt season (May to September). OWfE increases dramati-
cally in CCSM3 simulations as the mean winter ice thick-
ness decreases; that is, it becomes much easier to create
open water for a given amount of melt if one starts with
thinner ice. The strength of the OWfE depends on the ice
thickness distribution, i.e., on the internal model dynamics.
The ice-free summers in CCSM3 toward the end of the 21st
century are undoubtedly due to both the trend in forcing and
the internal model dynamics, but the relative contributions
of these factors are unknown.
What role might internal dynamics play in the transition
to an ice-free Arctic summer?
Flato and Brown
[1996]
constructed a one-dimensional thermodynamic model to
study landfast sea ice. The model successfully reproduced
seasonal and interannual variability of ice thickness at two
locations in the Canadian Arctic for which data were avail-
able. The model was also shown to have two stable states:
thin seasonal ice and thick perennial ice. A relatively modest
change in climate was sufficient to cause the model to jump
from the thick perennial state to the thin seasonal state. An
unstable equilibrium existed between the two stable states
(as is always the case) which arose because of the contrast
in albedo between thick ice and thin ice/open water.
Merry-
ield
et al.
[this volume] studied the phenomenon of abrupt
sea ice reductions in CCSM3 (as documented by
Holland
et
al.
[2006b]) by constructing a simplified physical model of
the essential processes with just two dependent variables:
winter sea ice thickness and summer sea ice extent. They
found that pulses of ocean heat transport into the Arctic,
along with increased sensitivity of summer sea ice to de-
clining ice extent, were the likely causes of the abrupt drops
in summer sea ice. Their nonlinear model also exhibited
multiple stable states in a physically relevant parameter re-
gime. These examples suggest that internal dynamics could
play a role in guiding the trajectory of sea ice toward a new
equilibrium state after the system crosses from one basin
of attraction into another, and that the ice-albedo feedback
and increasing summer open water are likely to be impor-
tant factors.
3.3.3. Two-dimensional nonlinear model.
We investigate
the above ideas by making a small modification to the equa-
tions (2). We add a quadratic term to the equation for thin
ice:
d
x
/
d
t
=
a
(
t
)(
1
−
x
−
y
) +
b
(
t
)
x
+
c
(
t
)
y
+
a
(
t
)(
1
−
x
−
y
)
2
d
y
/
d
t
=
d
(
t
)(
1
−
x
−
y
) +
e
(
t
)
x
+
f
(
t
)
y
,
(4)
where α(
t
) is negative in summer and zero otherwise. The
quadratic term simulates enhanced melting of thin ice in
summer as the fraction of open water increases. Equation (3)
is therefore modified by adding a corresponding quadratic
term:
D
x
k
=
a
(
1
−
x
k
−
y
k
) +
bx
k
+
cy
k
+
a
(
1
−
x
k
−
y
k
)
2
+
error
,
(5)
k
where we specify a negative value of α for the June-July and
July-August equations, and α = 0 otherwise. We then solve
for
a
,
b
, and
c
as before using the PIOMAS model output
and a standard least squares procedure. We need only do
this for the june-july and july-August thin ice equations;
all the other coefficients remain the same. Having found the
new coefficients, we then integrate the equations (4), with
specified initial conditions for thin ice and thick ice in Sep-
tember. (If a negative value of
x
or
y
is obtained for a given
month, it is reset to zero before continuing the integration.)
The results are shown in figure 8,
using ad hoc values of
α = -3 for June-July and α = -6 for July-August. There are
now two equilibrium cycles, one with perennial ice and
one with seasonal ice, depending on the initial conditions.
If we start the integration in September within the gray tri-
angle (bottom left), the trajectory evolves to the seasonal
ice cycle. If we start outside the gray triangle, the trajectory
evolves to the perennial ice cycle. Comparison of the peren-
nial ice cycle with that of figure 5 obtained from the linear
equations (2) shows that the thin ice and thick ice fractions
match within 0.02 in every month: the perennial ice cycle is
nearly unchanged. The quadratic nonlinearity has allowed
the emergence of a seasonal ice cycle, which can only be
sustained if the summer open water is sufficiently large. The
seasonal ice cycle resembles the annual cycle for the year
2044 in CCSM3 (figure 7). Comparing the size of terms in
equations (2) and (4), we find that when the open water frac-
tion 1-
x
-
y
becomes greater than about 0.2, the nonlinear-
ity becomes important, with increasing dominance as 1-
x
-
y
increases.
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