Friday, June 29, 2007

Dynamics of greenhouse effect

Saturated confusion of RealClimate.ORG
Originally posted on 6/27, moved to the top for the discussion to continue
The Gentlemen at RealClimate.ORG have decided that my article about
climate sensitivity
and similar articles by others are too dangerous because they show that every new molecule of CO2 causes smaller greenhouse effect than the previous molecule: the absorption rate gradually approaches saturation. Such a conclusion could diminish the holy power of the enhanced greenhouse effect and undermine the global efforts of scientists of good faith - and their friends, politicians of good faith, lawyers of good faith, singers of good faith, and publishers of good faith - to globally regulate the greenhouse effect.
Update: Why is the warming proportional to the logarithm of the amount of CO2?
They must be applauded for giving others the opportunity to study and discuss this question more carefully because the more people know, the more they will see why the hysteria is unjustifiable. So what do these eleven climate scientists think about the dependence of the strength of the greenhouse effect on the concentration? Well, they live in the state of scientific consensus which means, in this case, that none of them has any idea what the answer could be. So they invited an expert to clarify the situation.

Who is the expert? Well, it is a noted historian of science whose name is
Spencer Weart, a guest blogger at RealClimate.ORG.
Ray Pierrehumbert has helped Weart to reduce excessive hyphenation. Weart is the author of a painful book that celebrates a greedy group of researchers who were dreaming about grants and who finally got them after they constructed the man-made global warming theory.

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 theaters
Spencer 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%.

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

  • 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


  1. Spencer Weart here. For the record, I wrote my book on "The Discovery of Global Warming" without differential equations etc. so that ordinary people could read it. I hold a PhD in physics & astrophysics, and the graduate course I took in radiative transfer (which is what this is all about) was one of the most difficult ones I had to pass. It ain't simple.

    The interesting thing about the post here is that it entirely fails to address, or even mention, the main arguments in the essay. Pierrehumbert and I tried to explain things clearly, and I hope that readers will take a look and perhaps understand why the world is getting warmer. The warming, by the way, is exactly as predicted a quarter-century ago by several scientists, notably Jim Hansen, who did not gain but LOST government funding as a result of his public warnings.

  2. Dear Dr Weart, you probably live in a different Universe.

    Hansen's 1988 predictions were wrong by 200-300%, depending how you count it. The reality followed his mildest scenario even though the CO2 concentrations rose according to his "catastrophic" business-as-usual scenario.

    His was about the worst prediction one can get in science, after a Planckian prediction of the cosmological constant.

    You also live in a different word concerning Hansen's funding. For example, in 2001, a few months after he provided John Kerry with support, he happened to win 250,000 USD Heinz award. The relation between Kerry and Heinz is a pure coincidence, isn't it?

    To improve his account, he has also received $1 million Dan David Prize. For his actual science, I would fail him in a physics course that would expect the students to exhibit calm, rational thinking.

    If someone asked me what all of this money transfer is, I would answer that it is a big scale organized crime.

  3. We understand that your book was written for 13 year olds and shouldn't be taken seriously by anyone.

    I'll take a good look at the realclimate post.

    I'll be back if there's anything of interest, but my expectations are very low.

  4. (I've read your book and realclimate posts before. Let's just say that it won't take much to impress me fantastically. If you don't hear back from me here this week, consider suicide.)

  5. This comment has been removed by the author.

  6. "Hansen's 1988 predictions were wrong by 200-300%..."

    This quote proves you have a political ax to grind and are not interested in the science.

    Hansen gave a range of possible outcomes depending on future emissions and other climate parameters. There is a 200-300% difference between present warming and worst case. If you look at the three actual graphs he produced you'd see that the actual temperature increase is within the bounds of the three sensitivity studies he showed.

    But that wouldn't matter if all you wanted to do is sell the idea that there is this great conspiracy...

  7. Here is the big question - how do we, or do we know were the CO2 saturation point is?

  8. There is not point, you approach saturation, but never reach it.

  9. Ken, I haven't look at the Hansen chart in a long time, but here is where you're off track. Lets say I make a prediction, based on a virtual world GCM, that states that when CO2 levels rise by, say 5% of the current level, then the temp will rise by 1 degrees. In the real world the the CO2 did rise by that 5% from the time I made that prediction, but the temp only increased by .2 degrees. That would, in normal scientific community, be classified as being a highly inaccurate prediction.

  10. Aaron, you're right. Poor choice of words on my part. Rephrased - how do we know where we presently are on the saturation scale?

    Gotta go work now.

  11. sweart, I haven't read your addtional readings linked after your post, but so far don't see any reason for you to turn your car engine off or open the garage door.

    sonic, not sure. I'm at work now too. Lubos's post is a good start. His graphs should give you a good idea. You could look and see if Weart's links have anything.

    arrhenius shows were pretty damned saturated, but Weart has qualms with arrhenius which he doesn't get into. Perhaps his links do.

    Basically, warming that happens in the upper atmosphere is warming that won't happen in the lower atmosphere. And based on weart description, increased warming in the upper atmosphere should case cooling instead of warming since more heat will be exist in the radiative layers of the atmosphere.

  12. Herr Koch et al not Arrhenius.

    Sorry, I really shouldn't even be writing.

  13. sonicfrog,

    You need to get your facts straight. Hansen offered multiple possible outcomes some which he deemed less probable than others. The 200-300% error canard which continues to kick around the critics world was the least likely (worst case) of the three projections he tested. Here is a little news item snippet that may be a little more helpful.

    In 1998, Michaels criticized NASA scientist James Hansen, a leading
    global warming scientist. He said Hansen had been way off on his key
    1988 prediction of warming over the next 10 years.

    Hansen and other scientists said Michaels misrepresented the facts by
    selectively picking the worst and least probable of three possible
    outcomes Hansen presented to Congress. The temperature rise that
    Hansen said was most likely to happen back then was actually slightly
    lower than what has occurred.
    [end quote]

  14. But assumed a lower concentration of CO2, right?

  15. Ken, I never said the error was 200% to 300%. What I did say was that his prediction was not accurate based on the levels of current GHG's and the amount of warming he predicted for that amount of GHG's in the atmosphere.

    Aaron, that was going to be my point. The CO2 concentration is actually higher at the present moment than what was predicted in Hansen's prediction for this period in time. Here is Hansen's graph. In this article and the comments the question seems to be whether Scenario B or C is the correct value. But, if you consider the underestimation of the rise in CO2 in recent years, plus the exponential growth of the emerging markets of India and China (the latter just surpassed us in CO2 emissions), then the GHG levels of Senario A are closest to the actual current levels. This would mean there should be more warming than we are seeing.

  16. You made it clear.

    I don't know what Ken thought he was trying to pull.

    Thanks for the details.

  17. Posted also at realclimate

    The problem I have is that a Havard string theorist like Lubos

    can write a plausible critique of your work and people will accept it because he is a scientist. Now how do I know who is correct? With my lack of qualifications in any of the disciplines how do I know what is the correct science?

    In reading the two articles I do notice one striking difference. The RC article from Spence and Ray includes copious references to other people's work and includes no implied or otherwise insults to other researchers.

    Lubos on the other hand, as I read it, seems to think that just because he can understand differential equations that he is correct and everyone else is wrong. Lubos in following comments also disparages consensus as being weak however to me other people confirming what you are saying with peer reviewed work is a sign, at least to a layperson such as myself, that you have a greater chance of being correct.

    The radiation budget of the Earth is a very difficult subject and contains many non obvious traps for beginners that I think even a string theorist can fall into. Just because you understand strings does not mean that the subject of radiation is easy.

    Again thank you Spencer and Ray for your contribution to helping the understanding of science challenged people such as myself. I know which one has the greater chance of containing at least what truth we know of with our present knowledge.

  18. Stevegloor, your problem with string theorists is easy to resolve. You need to realize that the science has a certain hierarchy of conceptual complexities, and the scale of complexity is pretty wide. You also need to acknowledge that people also have different capabilities. The hint to your reconciliation is that while a string theorist is clearly capable of approximating measurements of, say, profiles of atmospheric temperature, and solve integral equations of radiative transport, I somehow doubt that a climatologist can make a contribution to the string theory. The other fundamental misconception of yours is in your usage of "understand strings": it is grossly insufficient just to "understand" things; you need a deep grasp of the whole physics to be a contributor to the theory. There is a substantial distance from elementary thermodynamic concept of radiation and absorption of gases to a string theory. I am afraid that a layman cannot even grasp the distance: you definitely need to master (not just understand) at depth the statistical physics, general relativity, all levels of quantum physics, classic and quantum field theory, and a lot of mathematics you have never heard of (like Grassman algebras, differential topology, etc.).

    Speaking about radiation exchange in the atmosphere, one can try the layman level explanations of the whole process and do a lot of had waiving as Spencer and Ray are doing. But it is not a simple "radiation budget" as you led to believe. The final value of surface temperature can be only determined from calculations of global hydrodynamic model of atmosphere coupled with self-adjusting boundary and distributed radiative effects. Reasonable solution to atmospheric convection (with active tracers as water vapor and corresponding cloud formation) is not possible. As result, all their talk about which "layer" gets colder and which warmer, and what it supposed to emit, is a sheer groundless speculation and wishful parameterization of complex physics and dynamics.

  19. Lubos, I can't access the fast comments here. This is meant for the thread.

    As for CIP on the oceans, infinite slab etc. The mechanism described by Weart wouldn't cause warming of the oceans other than by conductive contact with the warmer atmosphere.

    Or does additional CO2 in the oceans cause the blanket effect to persist there. Is CO2 in water blocking large amounts of radiation from the depths too ;) !?

  20. Steve

    There is no such thing as "correct science".

    The basic physics presented here by Lubos is verifiable by experiment. It is called a fact.

    I may add this explanation is also shown in a simpler manner on the Numberwatch by John Brignell.

    And oddly this explanation refutes the Carl Sagan's invention of a runaway greenhouse effect on Venus.

  21. Lubos, I've just started looking at this but already it seems to me you are being a bit dense about this.

    The folks at realclimate are not denying what you say. You are simply ignoring their points.

    Simple question for you (hint: requires no string theory) how did Venus get to be as hot at the surface -- i.e., below the atmosphere -- as it is?


  22. Temperature on earth drops with height due lower pressure.

    Dry air 1 deg C/100m (standard atmosphere)
    Humid air 0.5 deg C/100m (Standard atmosphere)

    Standard temp at sea level is 15 deg C.

    Pressure falls with 1 hPa/8 meter up to aprox 5000 meter, 1 hPa/16 meter over 5000 meter.

    Venus(30 bar) atmosphere is 30 times more dens than Earths atmosphere(1 bar)

    So I guess 30 times more pressure is the reason for Venus being so warm?

  23. Actually, the number I am looking up says 92 bar at the surface of Venus.

    You are right that the temperature at the surface is not because Venus is close to the Sun. In fact, the clouds are so thick that a small fraction of the sun's radiation reaches the surface.

    As you say, one can think of Venus as like an Earth with an extra very thick blacket of atmosphere.

    My question for Lubos is, how did it get to be this way?

  24. That's blanket... not a blacket of atmosphere, of course :)

  25. This page by G.Novak intimates radiation from the ground is insignificant.
    Do you (or any fellow posters) know any site that has ground level based empirical measurements? I'm having trouble finding 1.
    If he is right, there's a whole new ballgame.

  26. This comment has been removed by the author.

  27. Plus, Venus is much much more volcanically active that earth. That means you can't compare Venus's current temp situation with Earth.

  28. I found Sweart's layers argument unconvincing.

    I once did some computer modeling to figure out a science fiction planet. I enquired on sci.geo.meterology about the possible cooling effect of CO2, and deduced the following:

    If a layer in the atmosphere is heated by means other than long-wave radiation, then adding CO2 will have a cooling tendency, as the CO2 will overall tend to emit more LW radiation than it absorbs.

    The stratosphere is heated by O3 trapping UV. It is cooled by CO2 emitting LW radiation. It is of the order of 1 degree cooler, partly due to O3 depletion, partly due to extra CO2.

    The upper troposphere is heated by convection from below, as well as LW radiation from below. Extra CO2 both warms and cools. These effects balance. Its temperature has not changed.

    The critique of Kochs experiment is utterly unconvincing. It is unsupported by any observational evidence.

  29. I am having trouble understanding what the vertical axis in the absorption curves means. I know it is "% absorption" but is there an assumption about the amount of gas being used to make the measurement? Is it the amount that is absorbed by a single molecule? There seem to be problems with either of these ideas so maybe it is something else.


  30. Dear frost, it is the percentage of radiation absorbed by the actual amount of the molecules that are present in the atmosphere - all of them, the whole segment of the atmosphere. Best, Lubos

    For a single molecule, you couldn't write the rate as a percentage - you would need to define a cross section. ;-)

  31. Frankly , I don't see how isotropically changing the color of a radiantly heated ball ( or disk ) can change its mean temperature at all . If it can , you would be able to make a perpetual heat engine between them .

    So Sagan is responsible for the notion that Venus can be > 2 times the Stefan-Boltzmann calculated temperature of a black body in its orbit because of heat trapping by its dense CO2 ? Insane . SB says it is radiating > 16 times the energy it receives from the sun . And it's doing that front and back . Besides volcanism , perhaps tidal friction in the lower atmosphere might be the source .