Geoscience Reference
In-Depth Information
For the surface,
S
+=
σ
T
4
σ
T
4
.
(4.20)
ABS
1
S
For atmosphere layer 1,
σ
TT T
4
+=
σ
4
2.
σ
4
(4.21)
S
2
1
For atmosphere layer 2,
σ
T
4
=
2.
σ
T
4
2
(4.22)
1
Simultaneous solution of Eqs. 4.20-4.22 results in
T
S
334 K (very warm!),
T
1
302 K (same as the surface temperature in the single-slab Case II), and
T
2
254 K. The longwave emission from the top of the atmosphere is at the
radiative equilibrium temperature (
T
2
T
E
), the emission temperature needed
to balance the energy absorbed by the system.
The simple slab atmosphere calculations illustrate the redistribution of heat
that occurs in the climate system due to the greenhouse effect while maintain-
ing the state of radiative equilibrium between the earth and the sun. In the
actual atmosphere, increases in greenhouse gases lead to tropospheric and sur-
face warming, but the stratosphere cools when greenhouse gas levels increase.
The effects are different in the troposphere and stratosphere because the radia-
tive sources and sinks of heat are different. In the troposphere, the atmosphere
is warmed primarily by greenhouse gas absorption of longwave radiation and
cooled by the emission of longwave radiation by those same greenhouse gases.
In contrast, the major source of heating in the stratosphere is the absorption
of shortwave (ultraviolet) radiation by ozone. (As discussed in
chapter 2,
this
is the reason for the local temperature maximum at the stratopause seen in
Fig.2.8
.) This heat is transferred to the other molecules in the stratosphere,
including greenhouse gas molecules, in collisions. A heated greenhouse gas
molecule will then radiate longwave radiation and cool the stratosphere. Thus,
when there are more greenhouse gas molecules in the stratosphere, there is
more cooling. An added effect of increased greenhouse gases in the troposphere
is that they reduce the upward longwave flux from the troposphere into the
stratosphere (see
chapter 10
).
4.6 THE EQUATION OF TRANSFER
The
equation of transfer
is used to calculate changes in the intensity of radia-
tion as it travels through the atmosphere. Because transit distances through the
atmosphere are much smaller than the earth-sun distance and the earth's ra-
dius, the 1/
r
2
dependence of radiation emitted from the spherical sun and from
the earth's surface is negligible and the radiation can be accurately treated as if
the beams of radiation were parallel.
The spectral radiance (defined in section 4.1) can increase or decrease as
a beam of radiation passes through the atmosphere. The radiance at a given
wavelength decreases when molecules and particles in the atmosphere absorb
