Geoscience Reference
In-Depth Information
For the surface temperature between
-
30 and 0
°
C, this radiation ranges between
-
200
300 W m
−
2
. The terrestrial radiation from the atmosphere is much more complicated.
It comes from different altitudes, each altitude having its own temperature and emissivity,
and usually such detailed information is not available. For standard weather data, a grey
body analogical model is used with air temperature (at 2-m level) as the reference tem-
perature and effective emissivity depending on the humidity and cloudiness N:
and
-
Þr
T
a
Q
La
¼
e
a
e
;
N
ð
ð
4
:
7b
Þ
where e is the water vapour pressure (at 2-m height). The effective emissivity of atmo-
sphere depends primarily on the water vapour pressure and cloudiness and its formula-
tions vary widely. The air humidity also represents the altitude of 2 m. A common
empirical approach has been to give the emissivity as the product of clear sky emissivity
and cloud cover in
fl
uence as
ʵ
a
=
ʵ
ʱ
1
(e)
ʵ
ʱ
2
(N). Brunt (1932) introduced a widely used
form for the clear sky emissivity:
p
e
e
a1
¼
A
þ
B
ð
:
Þ
4
8a
where A and B are the Brunt formula parameters, with typical values of A = 0.68 and
B = 0.036 mbar
-
½
. The parameter A represents the dry atmosphere emissivity, while the
square root term re
ects the vertical distribution of water vapour. For the cloudiness factor
there are several approaches. A common form is:
fl
e
a2
ð
N
Þ
¼1
þ
CN
2
ð
4
:
8b
Þ
with a normal value of C = 0.18. As in the case of solar radiation, the in
uence of
cloudiness is the most uncertain factor in the estimation of the atmospheric thermal
radiation. The minimum atmospheric emissivity is A = 0.68, and at 0
fl
°
C the maximum is
(6.11 mbar
½
)
(A+B
·
·
(1 + C)
≈
0.91; for the air temperature range from
30 to 0
°
C the
-
280 W m
−
2
. If the air temperature and surface
temperature are equal, the terrestrial radiation loss is 20
atmospheric thermal radiation is within 140
-
90 W m
−
2
depending on the
-
humidity and cloudiness.
Example 4.1.
radiation increases. Then we have a balance at
¼
1
a
ð
Þ
cos
ðÞ
Tr
Q
sc
e
0
r
T
a
1
e
a1
1
þ
CN
2
ð
1
c
N
N
Þ
≤
≤
This equation has a solution for N, such that 0
N
1, when the ratio on the right-hand
side is about 0.35
0.45. Such case is feasible, and an equilibrium cloudiness exists but this
equilibrium is not stable. A disturbance would not return, and if the disturbance is large
enough no equilibrium can be reached.
-
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