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So the atmosphere is, for e < 1, cooler than Te (since the emission is then only partly from the atmosphere). Note, however, that Ta < Ts; the atmosphere is always cooler than the ground.

2.3.3. A more opaque greenhouse

Previously we considered a leaky greenhouse. To take the other extreme, suppose that the atmosphere is so opaque that even a shallow layer will absorb all the IR radiation passing through it. Now the assumption implicit in Fig. 2.7—that space and the surface both "see" the same atmospheric layer—is wrong. We can elaborate our model to include a second totally absorbing layer in the atmosphere, as illustrated in Fig. 2.9. Of course, to do the calculation correctly (rather than just to illustrate the principles), we would divide the atmosphere into an infinite number of thin layers, allow for the presence of clouds, treat each wavelength in Fig. 2.6 separately, allow for atmospheric absorption

3Kirchhoff's law states that the emittance of a body, which is the ratio of the actual emitted flux to the flux that would be emitted by a blackbody at the same temperature, equals its absorptance.

FIGURE 2.8. A leaky greenhouse. In contrast to Fig. 2.7, the atmosphere now absorbs only a fraction, e, of the terrestrial radiation upwelling from the ground.
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