Environmental Engineering Reference
In-Depth Information
R
E
where the factor
π
is the disk area presented by the earth toward the sun and where
S
o
=
annual average solar energy impinging on top of the atmosphere, called the solar constant,
1367 W m
−
2
R
E
=
earth's radius, 6371 km
α
=
the present average albedo of the earth, 0.3
±
0.03
The earth's radiative output to space is
R
E
σ
T
E
R
E
=
4
π
(10.2)
R
E
is the total area of the earth which radiates into space and where
where 4
π
8)Wm
−
2
K
−
4
σ
=
Stefan-Boltzmann constant, 5.67 E(
−
T
E
=
equivalent black-body radiative temperature of earth, K
From 10.1 and 10.2 we can calculate the earth's radiative temperature
T
E
:
S
o
(
1
/
4
−
α)
1
18
◦
C
T
E
=
=
(
−
)
255 K
(10.3)
4
σ
where we used an albedo
255 K is the average radiative temperature
of the earth and her atmosphere as it would appear to a space observer looking toward the earth.
Presently, the earth's average surface temperature is
T
S
=
α
=
0
.
3. The temperature
T
E
=
288 K (15
◦
C). The difference
T
S
−
T
E
=
33 K is a consequence of the greenhouse effect. This effect is present on other planets. Mars has
a very thin atmosphere; therefore the effective radiative temperature and the surface temperature
are very close: 217 and 220 K, respectively. On the other hand, Venus, which has a very dense
CO
2
atmosphere, the effective radiative temperature is 232 K, and the surface temperature is about
700 K.
The earth's average surface temperature has varied over past geological ages, as evidenced
by the glacial and interglacial periods. In part, these temperature variations may have been caused
by changing GHG concentrations in the atmosphere. Other factors for global climate change may
have been related to the variations of the earth's orbit around the sun and the tilt of her axis. First,
the eccentricity of the earth's elliptical orbit varies with a period of about 100,000 years. That
changes the average insolation of the earth. Second, the axis of rotation of the earth vis-a-vis the
ecliptic varies between 21.6
◦
and 24.5
◦
(currently 23.5
◦
) with a period of about 41,000 years.
That changes the amount of insolation of the hemispheres. A third possible factor is a change in
the solar constant.
10.2.3
Modeling Global Warming
Modeling of global warming is based on calculations of radiative transfer between the radiating
body (in this case the earth's surface) and atmospheric molecules, together with other energy
transport processes in the atmosphere. The change caused by extra amounts of GHG is called
radiative forcing
. Modeling requires a detailed knowledge of the spectroscopic characteristics of
GHG and the structure of the atmosphere, as well as very high capacity computers on which to
exercise the radiative transfer models.
