The Atmosphere and Climate Modeling - Introduction to Carbon Capture and Sequestration - page 49

where is the Stefan-Boltzmann constant. Assuming that the earth is in

equilibrium, all the energy the earth is receiving is ultimately emitted by
radiation (i.e., earthshine):

σ

out 4

Earth

J =σ T

We can now construct an energy balance (see Figure 2.2.1 ), where
we have to take into account that only a very small fraction of the total
energy emitted by the sun hits the surface of the earth. The amount of
energy reaching the top of the earth's atmosphere on a square meter
facing the sun each second during the daytime is about 1,370 J. If we
average this out over the entire planet (day and night), we obtain 25% of
this, or 341 W/m 2 . According to Stefan-Boltzmann's law, this energy cor-
responds to a planet with a temperature of approximately 279K (6ºC).
The actual average temperature is about 14ºC. We will show that our
simple calculation gave a lower temperature because we have ignored
the effect of the atmosphere.
Figure 2.2.2 shows the fate of the energy that hits the upper part of
the atmosphere [2.1]. Not all solar energy reaches the surface of the
earth, as part of this energy gets refl ected by the clouds and aerosols

Figure 2.2.1 The earth in thermal equilibrium
The energy the earth receives from the sun is emitted as blackbody radiation.