## The Greenhouse Effect

The global average mean surface temperature of the Earth is 288 K (Table 2.1). Previously we deduced that the emission temperature of the Earth is 255 K, which is considerably lower. Why? We saw from Fig. 2.6 that the atmosphere is rather opaque to IR radiation, so we cannot think of terrestrial radiation as being radiated into space directly from the surface. Much of the radiation emanating from the surface will be absorbed, primarily by H2O, before passing through the atmosphere. On average, the emission to space will emanate from some level in the atmosphere (typically about 5 km) such that the region above that level is mostly transparent to IR radiation. It is this region of the atmosphere, rather than the surface, that must be at the emission temperature. Thus radiation from the atmosphere will be directed downward as well as upward, and hence the surface will receive not only the net solar radiation, but IR from the atmosphere as well. Because the surface feels more incoming radiation than if the atmosphere were not present (or were completely transparent to IR) it becomes warmer than Te. This has become known as the greenhouse effect.2

### 2.3.1. A simple greenhouse model

Consider Fig. 2.7. Since the atmosphere is thin, let us simplify things by considering a planar geometry, in which the incoming radiation per unit area is equal to the average flux per unit area striking the Earth. This average incoming solar energy per unit area of the Earth's surface is average solar energy flux intercepted incoming radiation

Earth's surface area Sena2 S0 4na2 = "4".

We will represent the atmosphere by a single layer of temperature Ta, and, in this first calculation, assume: (1) that it is completely transparent to shortwave solar radiation, and (2) that it is completely opaque to IR radiation (i.e., it absorbs all the IR radiating

2It is interesting to note that the domestic greenhouse does not work in this manner! A greenhouse made of plastic window panes, rather than conventional glass, is effective even though plastic (unlike glass) does not have significant absorption bands in the IR. The greenhouse works because its windows allow energy in and its walls prevent the warm air from rising or blowing away.

FIGURE 2.7. The simplest greenhouse model, comprising a surface at temperature Ts, and an atmospheric layer at temperature Ta, subject to incoming solar radiation So/4. The terrestrial radiation upwelling from the ground is assumed to be completely absorbed by the atmospheric layer. FIGURE 2.7. The simplest greenhouse model, comprising a surface at temperature Ts, and an atmospheric layer at temperature Ta, subject to incoming solar radiation So/4. The terrestrial radiation upwelling from the ground is assumed to be completely absorbed by the atmospheric layer.

from the ground) so that the layer emitting to space is also ''seen'' by the ground. Now, since the whole Earth-atmosphere system must be in equilibrium (on average), the net flux into the system must vanish. The average net solar flux per unit area is, from Eq. 2-6, and allowing for reflection, 1/4(1 - a^) So, whereas the terrestrial radiation emitted to space per unit area is, using Eq. 2-2:

Equating them, we find: 1

using the definition of Te, Eq. 2-4. We see that the atmosphere is at the emission temperature (naturally, because it is this region that is emitting to space).

At the surface, the average incoming shortwave flux is also 1/4 (1 - ap) S0, but there is also a downwelling flux emitted by the atmosphere, a 4 = T = T

The flux radiating upward from the ground is

where Ts is the surface temperature. Since, in equilibrium, the net flux at the ground must be zero,