Solar radiation absorbed by the Earth =
In equilibrium, the total terrestrial flux radiated to space must balance the solar radiation absorbed by the Earth. If in total the spinning Earth radiates in all directions like a blackbody of uniform temperature Te (known as the effective planetary temperature, or emission temperature of the Earth) the Stefan-Boltzmann law gives:
Emitted radiation per unit area = aT (2-2)
where a = 5.67 x 10-8W m-2 K-4 Stefan-Boltzmann constant. So is the
Emitted terrestrial radiation = 4na2ffT|4. (2-3)
Note that Eq. 2-3 is a definition of emission temperature Te. It is the temperature one would infer by looking back at Earth if a blackbody curve was fitted to the measured spectrum of outgoing radiation.
Equating Eq. 2-1 with Eq. 2-3 gives
Note that the radius of the Earth has cancelled out: Te depends only on the planetary albedo and the distance of the Earth from the Sun. Putting in numbers, we find that the Earth has an emission temperature of 255 K. Table 2.1 lists the various parameters for some of the planets and compares approximate measured values, Tm, with Te computed from Eq. 2-4. The agreement is very good, except for Jupiter where it is thought that about one half of the energy input comes from the gravitational collapse of the planet (see Problem 3 at end of this chapter).
However, as can be seen from Table 2.1, the emission temperature of Earth is nearly 40 K cooler than the globally averaged observed surface temperature, which is Ts = 288 K. As we shall discuss in Section 2.3, Ts = Te because: (1) radiation is absorbed within the atmosphere, principally by its water vapor blanket, and (2) fluid motions—air currents—carry heat both vertically and horizontally.
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