| ABC of greenhouse effect | |
Lubos Motl, Harvard University
extract from original text found at: http://motls.blogspot.com/2007/06/realclimate-saturated-confusion.html
ABC of greenhouse effect
The greenhouse effect is the absorption of thermal, infrared electromagnetic
radiation emitted from the surface of Earth by the gases in the troposphere -
between the surface and a dozen of kilometers above it. These photons would
otherwise escape to outer space and leave the Earth cooler than it is because of
their existence. The effect is a part of a more complicated energy budget, click
the picture.
The absorption only occurs if these relatively low-energy transitions are found
in the spectrum of a given molecule: recall that the wavelength of ordinary
atomic spectra is typically much shorter and the photons carry much higher
energies, corresponding to higher temperatures. The requirement that low-energy
transitions must be allowed within the molecule is why the mono-atomic inert
gases such as argon or even di-atomic molecules such as nitrogen are not
greenhouse gases. Most of the absorbed infrared rays are instantly transformed
to kinetic energy of the atmosphere and this energy is not re-emitted.
Choosing the greenhouse candidates
It turns out that the relevant greenhouse gases are water (H2O), carbon dioxide (CO2), methane (CH4), and a few others. We will also include oxygen (O2) and ozone (O3).
The graph below shows the absorption spectra of selected molecules for
wavelengths between 100 nanometers and 100 micrometers.
Click to add methane (CH4) and nitrous oxide (N2O).
The y-axis shows the relative absorption by the actual layer of the gas
that is found in the atmosphere. If you're skillful enough, you could calculate
all these graphs from quantum mechanics, at least approximately.
You can see that water is by far the most important greenhouse gas. We will
discuss carbon dioxide later but you may also see that we have included oxygen
and ozone, for pedagogical reasons. They don't have too many spectral lines but
there is a lot of oxygen in the air, a thousand times the concentration of
carbon dioxide! So you might think that the precise concentration of oxygen or
ozone will be very important for the magnitude of the greenhouse effect,
possibly more important than the concentration of carbon dioxide.
The reason why it's not true is that there is actually so much oxygen in the air
that the radiation at the right frequencies is completely absorbed - 100% -
while the radiation at wrong frequencies is of course not absorbed at all - 0%.
At least ideally - when you neglect the Doppler width of the lines and other
effects - it should be so. That's why the greenhouse effect of he oxygen doesn't
depend on the concentration of oxygen in any significant way.
You can see that changes of the concentration matter for the absorption of a
frequency "f" if the absorption rate at this frequency is
comparable to 50%. If it is too close to 0% or too close to 100%, changes of the
concentration don't have too strong an effect. Also, you can see that if two
compounds share spectral lines, they "fight" for the same photons and
the net effect is smaller than the sum of the greenhouse effects in two
fictitious atmospheres where only one of the compounds exists. It's roughly
because the absorption can't ever surpass 100%.
Calculating absorption
With this wisdom, you can reconsider which concentrations of gases will be the most important ones for changes of the strength of the greenhouse effect that can be induced by changes of the environment. This step - focus on the gases and frequencies where the absorption rate significantly differs from 0% as well as 100% - will effectively eliminate oxygen and ozone. You end up with the standard gases - water, carbon dioxide, methane, and a few others.
Moreover, you can use the approximation that the concentration of water in the atmosphere rapidly converges to values dictated by other quantities. This is the sequence of steps that will single out the "usual suspects". You can see that we have made a lot of assumptions, especially about the mechanisms that control the water cycle. Many sane scientists think that whatever we do, the effects of water will decide about most of the weather and most of the climate.
Carbon dioxide: painting your room sixteen times
Fine. So let us focus on the carbon dioxide. You might think that as you
increase its concentration (=effective thickness of the layer) to "C",
it will only allow an exponentially small amount of the radiation at the right
frequencies, "exp(-AC)" where A is a constant, to get out of the
atmosphere. That would mean that the impact of a new molecule would be
exponentially decreasing with the concentration "C", too, making the
whole effect insignificant.
That's almost what happens but not quite. The reason why the decrease of the
strength of the greenhouse effect with the concentration "C" is not
exponential but rather a power law is that you can't strictly divide frequencies
to "right ones" and "wrong ones". As the concentration
"C" increases, the most important frequencies that determine the
strength of the greenhouse effect - those where the absorption rate is close to
50% - keep on changing. The result of this game is summarized by the Arrhenius
greenhouse equation that says that
In words, the greenhouse effect becomes weaker at higher values of "C": recall that the derivative of "ln(C)" with respect to "C" equals "1/C", a function that decreases as "C" increases, but it decreases less quickly than "exp(-AC)". What does it mean numerically?
The conventional quantity that usually measures the strength of the greenhouse effect is the climate sensitivity defined as the temperature increase from a doubling of CO2 from 0.028% of the volume of the atmosphere in the pre-industrial era to 0.056% of the volume expected before 2100. Currently we stand near 0.038% of the volume and the bare theoretical greenhouse effect, including the quantum-mechanical absorption rates for the relevant frequencies and the known concentration, predicts a 0.6 Celsius degrees increase of temperature between 0.028% and 0.038%, roughly in agreement with the net warming in the 20th century.
This bare effect can be modified by feedback effects - it can either be amplified or reduced (secondary influence on temperature-driven cloud formation etc.) - but it is still rather legitimate to imagine that the original CO2 greenhouse effect is the driving force behind a more complex process (see Larry's warnings in the fast comments). The basic facts about the dependence on the concentration are not modified. The bare effect is probably rescaled by a universal factor. That's why we should know how the bare effect depends on the concentration.
In terms of numbers, we have already completed 40% of the task to double the
CO2 concentration from 0.028% to 0.056% in the atmosphere. However, these 40% of
the task have already realized about 2/3 of the warming effect attributable to
the CO2 doubling. So regardless of the sign and magnitude of the feedback
effects, you can see that physics predicts that the greenhouse warming between
2007 and 2100 is predicted to be one half (1/3 over 2/3) of the warming that we
have seen between the beginning of industrialization and this year. For example,
if the greenhouse warming has been 0.6 Celsius degrees, we will see 0.3 Celsius
degrees of extra warming before the carbon dioxide concentration doubles around
2100.
It's just like when you want your bedroom to be white. You paint it once, twice,
thrice. But when you're painting it for the sixteenth time, you may start to
realize that the improvement after the sixteenth round is no longer that
impressive.
Above, we have argued that the extra expected warming in the next century should
be around 0.3 Celsius degrees but special nonlinear feedback effects may modify
this number significantly. But you shouldn't forget that our present theories
behind these feedbacks haven't been successfully validated. The models have been
largely constructed by interpolation of known data, and whenever you interpolate
data, the extrapolation tends to explode out of control even though reality
clearly doesn't (recall the discussion about polynomial interpolation and
extrapolation of functions).
Once again, physics doesn't predict any exponential escalation of the warming
from the greenhouse effect or something like that. Quite on the contrary,
physics predicts a rather significant slowdown of the rate of warming. The only
thing that Spencer Weart and Ray Pierrehumbert can do against this law of
physics is to emit fog - which is precisely what they are doing.
Summary for policymakers
Now, the 20th century warming, even if it were real, hasn't caused any problems
for the society at all, so it is reasonable to expect that an additional one
half of this warming won't cause problems either which is why we should abandon
any attempts to "fight" climate change, whatever is its origin and
numerical magnitude, at least until the year 2100.