Geoscience Reference
In-Depth Information
visual observations of trained personnel. Secondary in
fl
uence on the radiation level is due
to water vapour, other greenhouse gases, and aerosols.
In the polar zone, sunlight is absent in mid-winter, while in the polar summer the daily
maximums of solar radiation become up to 500
800 W m
−
2
. Albedo of open water, ice
and snow are of the order of 0.1, 0.5 and 0.9, respectively, and therefore the quality of the
surface makes a major contribution to the net solar radiation absorbed by a lake: the net
daily maximum is 50
-
500 W m
−
2
. The net terrestrial radiation
-
Q
nL
¼
e
0
rðe
a
T
a
T
0
Þ
¼
e
0
r
T
Ra
T
0
ð
2
:
15
Þ
50 W m
−
2
. It is in practice always negative and varies during the annual
cycle mostly from
is of the order of
−
80 W m
−
2
. The wavelength band of solar radiation is in
−
20 to
−
practice 0.3
3
ʼ
m, while the terrestrial radiation band is 5
15
ʼ
m. This is why they are
-
-
also called short-wave and long-wave radiation, respectively.
Example 2.6.
A simple planetary climate model (no atmosphere) is based on the balance
between the net solar radiation and the emitted terrestrial radiation from the surface. The
balance and the solution are:
s
ð
1
a
Þ
Q
sc
4
e
0
r
e
0
r
T
0
¼
1
4
ð
1
aÞ
Q
sc
or T
0
¼ 4
where the factor
comes from averaging the solar radiation over the planet. The planetary
albedo of the Earth is 0.3, and taking
¼
ʵ
0
= 0.97, we have T
0
=
16
°
C. For other planets,
-
the albedo can be different and the
'
solar constant
'
is inversely proportional to the square
of the distance between the planet and the Sun.
We can extend this model by adding atmosphere, with emissivity
ʵ
a
, and letting the
solar radiation be absorbed at the surface (b
0
) and in the atmosphere (b
1
), b
0
+ b
1
=1
.
Then we have a pair of equations for the temperatures at the surface and in the atmo-
sphere, and the surface temperature becomes:
-
ʱ
s
b
0
þ
2
e
0
b
1
1
2
e
0
e
a
ð
b
0
þ
b
1
Þ
ð
1
a
Þ
Q
sc
T
0
¼ 4
4
e
0
r
where the factor
comes from the atmosphere losing heat by radiation to its both sides.
On the right-hand side, the
½
first factor constitutes the atmospheric correction, and the
second factor is the no-atmosphere solution. Taking
ʵ
a
= 0.8, b
0
= 0.65 and b
1
= 0.05,
corresponding to planetary albedo of 0.3, we have T
0
= 12.6
°
C, which is not far from the
°
present global average (about 15
C). It is clear that the result is sensitive to the atmo-
spheric emissivity and albedo.
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