SSDD
Gold Member
- Nov 6, 2012
- 16,672
- 1,968
- 280
- Thread starter
- #21
The Greenhouse Effect
The treatment in the textbook (box on page 43) illustrates the greenhouse
effect by assuming an isothermal atmosphere-- (an atmosphere that is
all at the same temperature) that is perfectly transparent to solar
radiation, but acts like a blackbody in the infrared part of the
electromagnetic spectrum, where the planet emits radiation. It
absorbs all the radiation emitted from the surface of the planet, and
re-emits it: half in the upward direction to space, and half in the
downward direction, back to the surface of the planet. The problem is
solved by means of simultaneous equations: one is the radiation (or
energy) balance for the surface of the planet and one is for the radiation
balance of the atmosphere. Here is one alternative approach, which doesn't require solving simultaneous equations.
A simple approach
We can get the above results directly by recognizing that the top
layer of the atmosphere must emit 239.7 W/m2 of infrared radiation
to space (same amount of solar radiation that enters the atmosphere:
what goes in must go out). The bottom layer of the atmosphere
will emit an equal amount downward to the surface of the planet.
Hence, for thermal equilibrium, the surface of the planet must emit
enough radiation to balance not only the amount it receives from the
sun (239.7 W/m2), but also what it receives in the form of downward
infrared radiation from the atmosphere 239.7 W/m2). Hence, its emission
must match 239.7+239.7 = 479.4 W/m2. Applying the Stefan-Boltzmann
law: constant x T 4 = 479.4 W/m2. We thus calculate T = 303 K.
The figure below illustrates this calculation. Contrast it to the figure
above where we assumed no atmosphere, and you will see where
the greenhouse effect comes in.
![]()
The effective temperature we calculate in this manner is much warmer than the actual temperature of the Earth (288 K), because we made a number of simplifying assumptions.
Limitations of this calculation
1) It's assumed that the atmosphere is isothermal. The layer of the
real atmosphere that's most important in terms of the greenhouse
effect is the troposphere, where temperature decreases with height.
Because of this height dependence, the real atmosphere emits more
radiation in the downward direction than in the upward direction (88
units vs. 70 units in Fig. 3-19).
2) It's assumed that the atmosphere absorbs all the outgoing
radiation at all wavelengths in the infrared part of the
electromagnetic spectrum. In reality, the absorption of radiation by
the atmosphere is highly wavelength dependent. At some wavelengths
there's very little absorption and the radiation emitted by the
earth's surface escapes to space, while at other wavelengths it gets
absorbed, reemitted, absorbed and reemitted many times before it
finally escapes. To carry out this calculation accurately it has to
be done wavelength-by wavelength... to capture the fine scale detail
in the spectrum requires literally thousands of calculations
analogous to the one we did in class.
3) Radiative transfer isn't the only process by which energy escapes
from the earth's surface. Conduction of heat and evaporation of water
transfer about twice as much energy from the earth's surface to the
atmosphere as the net upward flux of infrared radiation from the
radiation does. If the temperature distribution on earth were
determined only by radiative transfer (as in this example) the Earth
would be so hot as to be uninhabitable. In this sense the true
'greenhouse effect' on Earth is much larger than the 33 K difference
between the observed surface temperature (288 K) and the effective
radiating temperature (255 K) ascribed to it in your text.
ATM S 211 - Notes
So the scientists at the University of Washington have a far different view of what is happening than you do, SSDD. Seems that most would go with the scientists at the U of W.
All I am asking is if that graph depicts the basic mechanism of the greenhouse effect...I have never seen such equivocation over such a simple question...either the graphic depicts the basic mechanism and the information is useful...or it doesn't and the university is publishing shit...which is it?