Originally posted on 6/27, moved to the top for the discussion to continueThe Gentlemen at RealClimate.ORG have decided that my article about
Who is the expert? Well, it is a noted historian of science whose name is
Weart writes in such a way that the text is well-readable and looks insightful to superficial readers. If you read it carefully, however, you can see that Weart has no idea what he is talking about at the technical level. First of all, the text is completely non-quantitative. All assertions are binary and dogmatic, Yes/No, and no quantitative laws or functional dependences are ever given, not even sketched. His text makes it impossible to decide whether one effect or another effect is important or not, or whether it has already been included or not.
You may also see that methods such as differential equations or dimensional analysis - and order-of-magnitude estimates - go well beyond Weart's abilities when he repeatedly says that having "many layers" of gases makes the whole situation extremely difficult. It is not that difficult and a good physicist knows how to solve the differential equations that arise in this context.
Weart's "wise" comments about the layers have no relevance for the question whether the basic dependence on the concentration exists or not but he's not able to see this fact because you can't really see it without some understanding of the method of rough estimates and without understanding basic features of differential equations. A technically skilled physicist knows that the effect of the CO2 layer - imagining nothing else for a while - doesn't depend on its density distribution as a function of altitude but only the overall, integrated "thickness" which is why Weart's ideas about the altitudes are irrelevant.
But when you don't know how to calculate things, you are tempted, much like Mr Weart, to think that every detail that you don't understand - the layer structure of the atmosphere, in this case - will surely confirm your beliefs and move the predictions in the right direction.
In a crowded "Blaník" cinema, Václav Klaus introduced Durkin's "The Great Global Warming Swindle" into Czech movie theatersSpencer Weart's main goal is to deny or somewhat diminish the importance of the following two observations:
- the greenhouse effect gets weaker as the absorption of the appropriate spectral lines gets saturated
- the overall greenhouse effect from several gases is smaller than a simple sum if their spectra overlap
Needless to say, informed readers know that whatever Spencer Weart writes can't change the fact that the two statements above are correct and important for a detailed treatment of this physics problem. Let us sketch the basics of the greenhouse effect and look at some of the basic consequences of the underlying mathematics.
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. Those absorbed infrared rays that are relevant for the greenhouse effect are quickly transformed to kinetic energy of the atmosphere and this energy is either re-emitted in the downward direction or it is not re-emitted at all.
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 figure above also includes Rayleigh scattering that influences UV rays - that's why the sky is blue - and the location of Earth's thermal and solar radiation.
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 collisional broadening and 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%.
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
- the temperature increase from the concentration "C" of a greenhouse gas equals "B.ln(C/C0)" where "B" is a constant and "C0" is the original concentration.
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.
And that's the memo.
Update: Ray Pierrehumbert has added Part II. It contains more physics but it is still largely non-quantitative. A relatively non-controversial description of these effects including facts about saturation is summarized by breathtaking statements that the saturation argument is "fallacious". It's like believers who are looking at the very same orbiting planets but who see, unlikely you, an old man - God - with long white hair. I just can't understand how someone can be so entirely irrational about things that are as ordinary as the weather undoubtedly is. There are things in between Earth and the Heaven and the troposphere is apparently one of them. :-)
Other well-known climate articles on The Reference Frame
- 1998 no longer the warmest U.S. year, 1934 wins
- Monckton & fears about warming
- Dr Oreskes & illusion of consensus on global warming
- Temperature determined CO2 ppm numbers, not the other way around
- IQ2 US duel: deniers beat alarmists
- Correlation of the sunspots and cosmic rays - and temps
- 2006: a not too strong year for little chickens
- 2006: coolest year after 2001