Geoscience Reference
In-Depth Information
sunlit months to continue to decline after September ice ex-
tent
A
n
has saturated at zero. To examine the importance of
this effect, we first express annual mean ocean shortwave
absorption due to open water in terms of monthly open water
fractions W
n,m
for year
n
as
ness
T
n
and annual melt
M
n
via (7) and (16), but without
truncating at the physical maximum value unity for W
n
. For
consistency we replace expression (8) for
M
n
, which was
based on a two-season approximation of annual mean ice
cover, with
ocn
)
1
M
n
=
M
(
s
)
0
+
M
(
b
)
0
12
m
W
n
,
m
F
SW
,
m
,
Q
n
= (
1
−
+
wH
n
(
1
−
W
n
,
m
)
,
(18)
D
(15)
where a
ocn
is ocean albedo as in section 3, and
F
SW,m
, the
monthly incident shortwave fluxes, are assigned values in
Table 3 obtained from mean CCSM3 fluxes in the Arctic
region for 1950 - 1999. The summation is over all sunlit
months, including minor February and October contribu-
tions not listed in Table 3.
To close this expression, we first examine the extent to
which W
n,m
can be deduced from September open water frac-
tion,
where`W
n,m
is the annual mean open water fraction. (The
two-season approximation adopted in section 3 corresponds
to `W
n,m
= (1 -
A
n
/
A
max
)/2.) From (7) and (16), we thus have
W
n
= (
T
∗
/
T
n
)
M
n
,
(19)
with
M
n
given by (18). The monthly open water fractions,
truncated to physical values, are then given by
W
n
,
m
=
min
[
a
m
W
n
,
1
]
.
(20)
W
n
≡
(
A
max
−
A
n
)
/
A
max
,
(16)
when W
n
< 1. Table 3 shows the correlations between W
n
and March-August open water fractions in CCSM3 for
years 1900-2049 prior to
A
n
saturating near zero. The cor-
relations range from approximately 0.83 to 0.99, indicating
that monthly open water fractions W
n,m
are to a reasonable
approximation proportional to W
n
. The constants of propor-
tionality are taken to be the coefficients of regression
a
m
be-
tween CCSM3 September open water fraction and that in
other months, indicated in Table 3 (the constant terms in the
regressions are negligible). Obtaining monthly open water
fractions from W
n,m
=
a
m
W
n
, annual mean ocean shortwave
absorption continues to be given by (5), but with
Equations (18) - (20) form an implicit relation which must
be solved for the W
n,m
to obtain
Q
n
through (15).
Under ice-free September conditions
~
n
³ 1, the above
relations become complicated enough to impede analytical
progress. To illustrate differences between the approach de-
scribed here and that of section 3 numerically, we consider
H
n
increasing according to (3) over 1900-2100 and decreas-
ing in the same manner over the subsequent two centuries
(Figure 17a). For simplicity, the stochastic component of
H
n
is ignored. According to the section 3 formulation (solid
curves in Figures 17b and 17c),
A
n
and
T
n
decrease until
A
n
collapses to zero shortly before 2040. After
H
n
decreases
back through its critical value,
A
n
recovers (with some hys-
teresis) around 2170. The section 4 formulation (dashed
curves in Figure 17) yields comparable behavior prior to
2040 (the decline occurs a little more rapidly because (18)
implies slightly more melt than (8)). At this stage a signifi-
cant difference is that
T
n
also collapses, implying perennial,
as opposed to seasonal, loss of ice. In addition, the hysteresis
is more extreme, so much so that ice cover fails to reappear
even when
H
n
has returned to 1900 values. This phenom-
b
=
(
1
−
ocn
)
A
max
1
12
m
a
m
F
SW
,
m
.
D
(17)
Assigning a
ocn
= 0.1 gives
b
= 2.06 ´ 10
-12
W m
-4
, similar to
the value determined in section 3.
To obtain
Q
n
when September is ice free (
A
n
= 0, W
n
=
1),
we continue to assert a proportionality W
n,m
=
a
m
~
n
, where
~
n
is determined in the same manner as W
n
from March thick-
Table 3.
quantities Relating to Parameterization of Monthly Ocean Shortwave Absorption
March
April
May
June
July
August
September
Mean ↓ SW
F
SW,m
(W m
-2
)
33.2
130.8
219.2
231.5
174.7
99.8
37.9
Correlation coeficients
b
0.874
0.866
0.826
0.828
0.940
0.990
1
Regression coefficients a
b
0.012
0.012
0.021
0.078
0.287
0.814
1
a
CCSM3 mean monthly incident surface shortwave fluxes for 1950-1999.
b
Correlation and regression coefficients relating CCSM3 monthly open water areas to September open water area
A
max
-
A
n
for years 1900-2049.
Search WWH ::
Custom Search