Geoscience Reference
In-Depth Information
overlain by a semi-ininite plane atmosphere. Then, Eq. 4.9 is used to calculate
the solar energy absorbed by the slab atmosphere system as 236 W/m
2
.
Several cases of slab atmosphere calculations are presented below to illus-
trate various aspects of the greenhouse effect.
GREENHOUSE CASE I: NO ATMOSPHERE
The simplest case is one with no atmosphere. In this case, the incoming solar
radiation is absorbed at the surface, as illustrated in
Figure 4.8.
Assume that the surface behaves as a perfect blackbody, absorbing and
reemitting all this shortwave radiation. The surface is represented as being in-
sulated on its lower side to account for the fact that radiation does not pen-
etrate far into the earth's surface, and the longwave radiation is emitted back
to the atmosphere (rather than down into the earth). Assuming radiative equi-
librium, so that radiative heating and radiative cooling are balanced and the
surface temperature,
T
S
, does not change gives
S
=
σ
T
4
T
=
254
K
.
(4.11)
&
ABS
S
S
This is the same calculation as in Eq. 4.10. In the “no atmosphere” case, the
surface temperature is
T
E
.
GREENHOUSE CASE II
Add a slab atmosphere over the slab surface, shown in
Figure 4.9
. Even though
the slab atmosphere touches the surface, it is drawn suspended over the surface
so the fluxes between the atmosphere and the surface can be clearly depicted.
Assume the following:
• The surface and atmosphere are both perfect black bodies in radiative
equilibrium.
• The atmosphere is transparent to solar radiation.
• The atmosphere, like the surface, is opaque to longwave radiation and
absorbs all longwave (terrestrial) radiation incident on it.
The slab atmosphere, unlike the surface, emits radiation both upward to space
and downward back to the surface.
F
UP
= σ
T
S
4
S
ABS
= 236 W/m
2
Figure 4.8 Greenhouse slab
model, Case I.
T
S
= surface temperature
