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Determining the Temperature of a Planet
--3rd Approximation
The absorbing properties of the earth's atmosphere allow us to develop
a third approximation to the radiating temperature for the earth. The
atmosphere behaves like a one-way blanket that lets in solar energy and
absorbs outgoing infrared energy emitted by the earth. It should be
noted that all the energy emitted by the earth does ultimately escape
to outer space, but the spherical shell of atmosphere interrupts this
flow of energy by radiating some of it back toward the earth, thereby
raising its temperature and causing it to emit even more (as required
by the Stefan-Boltzmann equation). The ultimate balance that is
achieved has a higher surface temperature but the same amount escaping
from the top of the atmosphere to outer space.
If we assume the atmosphere absorbs 90% of energy upwelling from the earth but none coming in from the sun, we get a third approximation to the surface temperature as given in Figure 7. This model of the earth energy budget gives the same effective temperature for radiation to space (256 K or 1.6°F) from the "outer edge" of the atmosphere, but the surface temperature in this model is 283 K, (59°F), the correct present value. This simple model demonstrates the important role of the atmosphere in determining the surface temperature of the planet. And the exact type of gases that compose the atmosphere is the critical factor in determining its overall absorptivity. The important factor, as we will see later, is that the resulting surface temperature allows H2O to exist in all three phases in abundant quantities, thereby simultaneously allowing some H2O to exist as water vapor to trap infrared radiation in the atmosphere and some to exist in condensed form to create global oceans .
To summarize the two main points so far in this unit, (1) the
gravitational field and escape velocity for a planet will determine the
amount of atmosphere it is able to retain, and (2) the laws of
radiation and absorbing properties of the atmosphere determine both the
effective radiating temperature and the surface temperature of the
planet.
