Radiative Processes in the Climate System - Climate Dynamics - page 80

S ABS = 236 W/m 2 F UP = σ T 4

F UP = (1 - f )σ T 4

T A = atmospheric temperature

F UP = f σ T 4

F DOWN = σ T 4

S ABS = 236 W/m 2

F UP = σ T S 4

Figure 4.10 Greenhouse slab
model, Case III.

T S = surface temperature

As indicated in Figure 4.10, the heat balances for the atmosphere and the sur-
face, respectively, yield the following two equations:

fT σ

4

= 2 σ T

4

(4.15)

S A

S += σ T

4

σ T

4

. (4.16)

ABS A S

Then,

J

2

N

4
S

σ = T S . (4.17)

K O

ABS

2 − f

L P

Note that this case reduces to Case I if f  0 and to Case II if f  1. When more
longwave radiation is absorbed by the atmosphere, that is, when the green-
house effect is more powerful, f is larger and the surface temperature is higher.

GREENHOUSE CASE IV

Assume that rather than being transparent to solar radiation, the atmosphere
absorbs 10% of the solar radiation and 100% of the longwave radiation. In
that case, which is drawn in Figure 4.11 , the heat balance equations for the
atmosphere and the surface are,

F UP = σ T 4

S ABS = 236 W/m 2

T A = atmospheric temperature

0.1 S ABS

F DOWN = σ T 4

0.9 S ABS

F UP = σ T 4

Figure 4.11 Greenhouse slab
model, Case IV.

T S = surface temperature