Geoscience Reference
In-Depth Information
(5)
where
M
n
is the accumulated March-September ice melt in
meters.
To close these equations,
M
n
must be specified as a func-
tion of known quantities. The total melt consists of the sum
of the surface melt,
M
(
s
)
, due primarily to radiative heating
of the ice surface, and the basal melt,
M
(
b
)
, due to heat trans-
ferred from ocean to ice, where lateral melting is neglected
as it is a small term. While both
M
(
s
)
and
M
(
b
)
increase in a
warming climate, the increase in total melt in CCSM3 arises
primarily from
M
(
b
)
. Therefore, as a further gross approxima-
tion we take
M
(
s
)
to be constant, assigning a representative
value of
M
(
s
0
= 0.4 m. This is considered adequate, given that
the values simulated by CCSM3, low-pass filtered by a slid-
ing 21-year window, differ by less than 0.1 m a
-1
from this
value over the simulated period 1900-2099 (not shown).
because increased OHT into the Arctic Ocean should tend
to warm Arctic waters and because HbT observed that OHT
pulses appear to act as a trigger for sea ice abrupt transitions,
we take the basal melt term
M
(
b
)
to depend on
H
n
. In order
to maintain as simple a set of physical assumptions as is fea-
sible, it is assumed that there is a perfect transfer of heat
input from OHT to melting of sea ice where ice is present,
which implies
M
(
b
)
=
M
(
b
)
+
wH
(
¯
/
A
max
), where
¯
is the an-
nual mean ice extent. Drawing from available information,
we specify the latter as the average of winter ice extent,
assumed equal to
A
max
, and summer ice extent
A
n
, so that
¯
n
= (
A
max
+
A
n
)/2. On physical grounds
M
(
b
)
cannot increase
indefinitely with increasing OHT because total mean melt is
limited by the winter mean ice thickness
T
, i.e.,
M
(
s
)
+
M
(
b
)
£
T
for any particular year. However, applying this constraint
to (7) would prevent
A
from decreasing below (1 -
T
*
)
A
max
,
or approximately 1.45 ´ 10
6
km
2
for the chosen parameters.
Therefore, to enable zero summer ice extent to be attained
we instead limit
M
by
M
(
s
)
+
M
(
b
)
£
T
/
T
*
. The melt param-
eterization thus becomes
Q
n
=
b
(
A
max
−
A
n
)
.
The plausibility of such a relation is supported by Figure 5,
which plots values of annual and areal mean
Q
SW
against an-
nual values of
A
max
-
A
for the CCSM3 run whose summer-
time sea ice retreat is shown in Figure 1a. These two time
series are closely correlated (
r
2
= 0.98). The linear regres-
sion (solid curve in Figure 5) has an offset
Q
0
≈
5
.
5 W m
−
2
at
A
max
−
A
=
0, which is taken to represent ocean short-
wave absorption in leads and through ice and is considered
part of the baseline forcing
F
in (1). by approximation to the
regression slope 1.86 ´ 10
-12
W m
-4
, the shortwave absorp-
tion parameter for CCSM3 is assigned the value
b
= 2 ´ 10
-12
W m
-4
.
3.2.4. Simple equations describing sea ice evolution.
Sub-
stituting (5) describing open water ocean shortwave absorp-
tion into (1) leads to winter ice thickness evolution being
described by
T
n
+
1
=
max
[
F
−
wH
n
−
wb
(
A
max
−
A
n
)
,
0
]
.
(6)
The September ice extent
A
n
for the previous calendar year is
taken to be governed by the open water formation efficiency
relation (2):
A
n
=
A
max
[
1
−
(
T
∗
/
T
n
)
M
n
]
,
(7)
M
n
= min[
M
(
s
)
+
M
(
b
0
+
wH
n
(1 +
A
n
/
A
max
)/ 2
,
T
n
/
T
*
],
0
(8)
with
M
0
(
s
)
= 0.4 m as discussed above and
M
0
(
b
)
= 0.2 m, which
provides a reasonable fit to the initial, approximately linear
increase of
M
with
H
. The modeled variation of
M
n
with
H
n
in the CCSM3 simulation considered previously, low-pass
filtered by a sliding 21-year window, is indicated in Figure
6 by the symbols, whereas the solid curve represents (8) as
computed for similarly low-passed CCSM3
T
n
,
A
n
, and
M
n
.
We note that the albedo feedback, which as discussed by
HbT may contribute to ice melt, is not included in the melt
parameterization (8), and justify this on the somewhat ad
hoc grounds that this heat input is by nature concentrated in
ice-free regions, and in any case its inclusion would worsen
Figure 5.
Symbols denote annual and areal mean shortwave radia-
tion
Q
SW
absorbed in the Arctic Ocean region shown in Figure 2, as
a function of September open water area
A
max
-
A
, for the CCSM3
simulation whose Arctic ice evolution is shown in Figure 1. The
solid line is a linear regression on these values.
Search WWH ::
Custom Search