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A Saturated Gassy Argument

Filed under: — group @ 26 June 2007 - (Português)

A guest post by Spencer Weart, in collaboration with Raymond T. Pierrehumbert

The simple physics explanations for the greenhouse effect that you find on the internet are often quite wrong. These well-meaning errors can promote confusion about whether humanity is truly causing global warming by adding carbon dioxide to the atmosphere. Some people have been arguing that simple physics shows there is already so much CO2 in the air that its effect on infrared radiation is "saturated"— meaning that adding more gas can make scarcely any difference in how much radiation gets through the atmosphere, since all the radiation is already blocked. And besides, isn’t water vapor already blocking all the infrared rays that CO2 ever would?

The arguments do sound good, so good that in fact they helped to suppress research on the greenhouse effect for half a century. In 1900, shortly after Svante Arrhenius published his pathbreaking argument that our use of fossil fuels will eventually warm the planet, another scientist, Knut Ångström, asked an assistant, Herr J. Koch, to do a simple experiment. He sent infrared radiation through a tube filled with carbon dioxide, containing somewhat less gas in total then would be found in a column of air reaching to the top of the atmosphere. That’s not much, since the concentration in air is only a few hundred parts per million. Herr Koch did his experiments in a 30cm long tube, though 250cm would have been closer to the right length to use to represent the amount of CO2 in the atmosphere. Herr Koch reported that when he cut the amount of gas in the tube by one-third, the amount of radiation that got through scarcely changed. The American meteorological community was alerted to Ångström’s result in a commentary appearing in the June, 1901 issue of Monthly Weather Review, which used the result to caution "geologists" against adhering to Arrhenius’ wild ideas.

Still more persuasive to scientists of the day was the fact that water vapor, which is far more abundant in the air than carbon dioxide, also intercepts infrared radiation. In the infrared spectrum, the main bands where each gas blocked radiation overlapped one another. How could adding CO2 affect radiation in bands of the spectrum that H2O (not to mention CO2 itself) already made opaque? As these ideas spread, even scientists who had been enthusiastic about Arrhenius’s work decided it was in error. Work on the question stagnated. If there was ever an “establishment” view about the greenhouse effect, it was confidence that the CO2 emitted by humans could not affect anything so grand as the Earth’s climate.

Nobody was interested in thinking about the matter deeply enough to notice the flaw in the argument. The scientists were looking at warming from ground level, so to speak, asking about the radiation that reaches and leaves the surface of the Earth. Like Ångström, they tended to treat the atmosphere overhead as a unit, as if it were a single sheet of glass. (Thus the “greenhouse” analogy.) But this is not how global warming actually works.

What happens to infrared radiation emitted by the Earth’s surface? As it moves up layer by layer through the atmosphere, some is stopped in each layer. To be specific: a molecule of carbon dioxide, water vapor or some other greenhouse gas absorbs a bit of energy from the radiation. The molecule may radiate the energy back out again in a random direction. Or it may transfer the energy into velocity in collisions with other air molecules, so that the layer of air where it sits gets warmer. The layer of air radiates some of the energy it has absorbed back toward the ground, and some upwards to higher layers. As you go higher, the atmosphere gets thinner and colder. Eventually the energy reaches a layer so thin that radiation can escape into space.

What happens if we add more carbon dioxide? In the layers so high and thin that much of the heat radiation from lower down slips through, adding more greenhouse gas molecules means the layer will absorb more of the rays. So the place from which most of the heat energy finally leaves the Earth will shift to higher layers. Those are colder layers, so they do not radiate heat as well. The planet as a whole is now taking in more energy than it radiates (which is in fact our current situation). As the higher levels radiate some of the excess downwards, all the lower levels down to the surface warm up. The imbalance must continue until the high levels get hot enough to radiate as much energy back out as the planet is receiving.

Any saturation at lower levels would not change this, since it is the layers from which radiation does escape that determine the planet’s heat balance. The basic logic was neatly explained by John Tyndall back in 1862: "As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial [infrared] rays, produces a local heightening of the temperature at the Earth’s surface."

Even a simple explanation can be hard to grasp in all its implications, and scientists only worked those out piecewise. First they had to understand that it was worth the trouble to think about carbon dioxide at all. Didn’t the fact that water vapor thoroughly blocks infrared radiation mean that any changes in CO2 are meaningless? Again, the scientists of the day got caught in the trap of thinking of the atmosphere as a single slab. Although they knew that the higher you went, the drier the air got, they only considered the total water vapor in the column.

The breakthroughs that finally set the field back on the right track came from research during the 1940s. Military officers lavishly funded research on the high layers of the air where their bombers operated, layers traversed by the infrared radiation they might use to detect enemies. Theoretical analysis of absorption leaped forward, with results confirmed by laboratory studies using techniques orders of magnitude better than Ångström could deploy. The resulting developments stimulated new and clearer thinking about atmospheric radiation.

Among other things, the new studies showed that in the frigid and rarified upper atmosphere where the crucial infrared absorption takes place, the nature of the absorption is different from what scientists had assumed from the old sea-level measurements. Take a single molecule of CO2 or H2O. It will absorb light only in a set of specific wavelengths, which show up as thin dark lines in a spectrum. In a gas at sea-level temperature and pressure, the countless molecules colliding with one another at different velocities each absorb at slightly different wavelengths, so the lines are broadened and overlap to a considerable extent. Even at sea level pressure, the absorption is concentrated into discrete spikes, but the gaps between the spikes are fairly narrow and the "valleys" between the spikes are not terribly deep. (see Part II) None of this was known a century ago. With the primitive infrared instruments available in the early 20th century, scientists saw the absorption smeared out into wide bands. And they had no theory to suggest anything different.

Measurements done for the US Air Force drew scientists’ attention to the details of the absorption, and especially at high altitudes. At low pressure the spikes become much more sharply defined, like a picket fence. There are gaps between the H2O lines where radiation can get through unless blocked by CO2 lines. Moreover, researchers had become acutely aware of how very dry the air gets at upper altitudes — indeed the stratosphere has scarcely any water vapor at all. By contrast, CO2 is well mixed all through the atmosphere, so as you look higher it becomes relatively more significant. The main points could have been understood already in the 1930s if scientists had looked at the greenhouse effect closely (in fact one physicist, E.O. Hulbert, did make a pretty good calculation, but the matter was of so little interest that nobody noticed.)

As we have seen, in the higher layers where radiation starts to slip through easily, adding some greenhouse gas must warm the Earth regardless of how the absorption works. The changes in the H2O and CO2 absorption lines with pressure and temperature only shift the layers where the main action takes place. You do need to take it all into account to make an exact calculation of the warming. In the 1950s, after good infrared data and digital computers became available, the physicist Gilbert Plass took time off from what seemed like more important research to work through lengthy calculations of the radiation balance, layer by layer in the atmosphere and point by point in the spectrum. He announced that adding CO2 really could cause a degree or so of global warming. Plass’s calculations were too primitive to account for many important effects. (Heat energy moves up not only by radiation but by convection, some radiation is blocked not by gas but by clouds, etc.) But for the few scientists who paid attention, it was now clear that the question was worth studying. Decades more would pass before scientists began to give the public a clear explanation of what was really going on in these calculations, drawing attention to the high, cold layers of the atmosphere. Even today, many popularizers try to explain the greenhouse effect as if the atmosphere were a single sheet of glass.

In sum, the way radiation is absorbed only matters if you want to calculate the exact degree of warming — adding carbon dioxide will make the greenhouse effect stronger regardless of saturation in the lower atmosphere. But in fact, the Earth’s atmosphere is not even close to being in a state of saturation. With the primitive techniques of his day, Ångström got a bad result, as explained in the Part II . Actually, it’s not clear that he would have appreciated the significance of his result even if he had gotten the correct answer for the way absorption varies with CO2 amount. From his writing, it’s a pretty good guess that he’d think a change of absorption of a percent or so upon doubling CO2 would be insignificant. In reality, that mere percent increase, when combined properly with the "thinning and cooling" argument, adds 4 Watts per square meter to the planets radiation balance for doubled CO2. That’s only about a percent of the solar energy absorbed by the Earth, but it’s a highly important percent to us! After all, a mere one percent change in the 280 Kelvin surface temperature of the Earth is 2.8 Kelvin (which is also 2.8 Celsius). And that’s without even taking into account the radiative forcing from all those amplifying feedbacks, like those due to water vapor and ice-albedo.

In any event, modern measurements show that there is not nearly enough CO2 in the atmosphere to block most of the infrared radiation in the bands of the spectrum where the gas absorbs. That’s even the case for water vapor in places where the air is very dry. (When night falls in a desert, the temperature can quickly drop from warm to freezing. Radiation from the surface escapes directly into space unless there are clouds to block it.)

So, if a skeptical friend hits you with the "saturation argument" against global warming, here’s all you need to say: (a) You’d still get an increase in greenhouse warming even if the atmosphere were saturated, because it’s the absorption in the thin upper atmosphere (which is unsaturated) that counts (b) It’s not even true that the atmosphere is actually saturated with respect to absorption by CO2, (c) Water vapor doesn’t overwhelm the effects of CO2 because there’s little water vapor in the high, cold regions from which infrared escapes, and at the low pressures there water vapor absorption is like a leaky sieve, which would let a lot more radiation through were it not for CO2, and (d) These issues were satisfactorily addressed by physicists 50 years ago, and the necessary physics is included in all climate models.

Then you can heave a sigh, and wonder how much different the world would be today if these arguments were understood in the 1920’s, as they could well have been if anybody had thought it important enough to think through.

For Further Reading

References and a more detailed history can be found here and here.

Some aspects of the "thinning and cooling" argument, and the importance of the radiating level are found in the post A Busy Week for Water Vapor, which also contains a discussion of water vapor radiative effects on the top-of-atmosphere vs. surface radiation budget. A general discussion of the relative roles of water vapor and CO2 is given in Gavin’s post on ths subject.

You can get a good feel for the way CO2 and water vapor affect the spectrum of radiation escaping the Earth by playing around with Dave Archer’s online radiation model here. It would help, of course, to read through the explanation of radiating levels in Archer’s book, Understanding the Forecast. A discussion of radiating levels for real and idealized cases, at a more advance level, can be found in the draft of Pierrehumbert’s ClimateBook; see Chapters 3 and 4.

The Monthly Weather Review article commenting on Ångström’s work is here, and Ångström’s original article is here.

281 Responses to “A Saturated Gassy Argument”

  1. 251
    Walter Starck says:

    Spencer,

    You say, “What happens if we add more carbon dioxide? …the place from which most of the heat energy finally leaves the Earth will shift to higher layers. Those are colder layers, so they do not radiate heat as well.”

    It is my understanding that while temperature decreases with altitudes in the troposphere and lower stratosphere, at the altitudes where IR emission into space occurs temperature increases with altitude, not decreases.

    Could you explain a bit more on this point?

  2. 252

    [[It is my understanding that while temperature decreases with altitudes in the troposphere and lower stratosphere, at the altitudes where IR emission into space occurs temperature increases with altitude, not decreases.]]

    Well, IR comes from all levels, in differing amounts. But if you want to deal with an average emission level, it is well within the troposphere. Divide the planet’s greenhouse increment (33° K.) by the mean tropospheric lapse rate (6.5° K. km-1) and that height works out to be about 5.1 km. The tropopause is 10-15 km high depending on latitude.

  3. 253
    Timothy Chase says:

    Walter Starck (#251) wrote:

    It is my understanding that while temperature decreases with altitudes in the troposphere and lower stratosphere, at the altitudes where IR emission into space occurs temperature increases with altitude, not decreases.

    Good recall on the structure of the lapse rate.

    However, from the essay:

    What happens if we add more carbon dioxide? In the layers so high and thin that much of the heat radiation from lower down slips through, adding more greenhouse gas molecules means the layer will absorb more of the rays. So the place from which most of the heat energy finally leaves the Earth will shift to higher layers. Those are colder layers, so they do not radiate heat as well. The planet as a whole is now taking in more energy than it radiates (which is in fact our current situation). As the higher levels radiate some of the excess downwards, all the lower levels down to the surface warm up. The imbalance must continue until the high levels get hot enough to radiate as much energy back out as the planet is receiving.

    The process is taking place in the upper troposphere. The effective radiating layer is at approximately 6 km, which is considerably below the tropopause, and therefore the atmosphere is still getting cooler the farther you climb. The process whereby the upper troposphere heats up until it is able to radiate away thermal radiation as quickly as the thermal radiation is entering the system results in a lag – which is a large part of the reason that, even if we were to stop emitting carbon dioxide today, it would still take some time before the temperature leveled out at its new equilibrium value.

    Anyway, no worries, mate: I made a closely related mistake only a couple weeks ago, I believe.

  4. 254
    Timothy Chase says:

    PS to #252

    Incidently, when the new equilibrium is achieved, the effective radiating layer will be at a higher level, and per Tamino, given the nearly constant lapse rate (i.e., linear drop in temperature with altitude) in the troposphere, implies that the surface must be warmer if the effective radiating layer is to be at the same temperature as before – where the effective temperature is the temperature at which the earth must radiate thermal radiation (as seen at a distance) in order to be in balance with the rate at which thermal radiation is entering the system.

  5. 255
    AEBanner says:

    Re: A Saturated Gassy Argument

    Initially, I was not convinced by this article, which maintained that absorption of photons at high altitudes by increased carbon dioxide could cause a rise in the surface temperature of the Earth. However, on reflection, I thought it would be interesting to attempt to calculate the magnitude of the effect, if any.

    I used a C program which incorporated the Planck distribution and the Stefan-Boltzmann Law. Infrared absorption cross sections for carbon dioxide were obtained from Hitran, and the graph showing Absorption Factor against wavelength, given in Part 2, “What Angstrom didn’t know”.

    Hitherto, I had assumed that there was total absorption of the energy radiated from the surface in the CO2 regions of the spectrum by the CO2 itself and the water vapour, and so no increase in CO2 concentration could produce further heating. However, energy balance considerations with the C program showed that this would cause too much surface heating because of the GH effect of the water vapour. In order to get the surface temperature down to 288.0 K, only about 86% of the emitted energy could be absorbed by the water. So about 14% of the energy would be transmitted to higher altitudes.

    Now the only energy which can be absorbed at high altitudes is the energy of the “wings”, or side bands, of the CO2 region, namely the wavelengths 10, 11 and 12 microns, and 17, 18 and 19 microns. The absorption cross sections for these wavelengths is very small, even at sea level, and the air density is also decreasing with altitude, so further reducing the probability of absorption. Therefore, the overall effect of this postulated high altitude absorption has only a very minimal effect on surface temperature. The results of the calculations are given below, for a doubling of CO2.

    Altitude_____Surface Temp.
    (Km)________Rise deg C

    10___________0.09
    20___________0.02
    30___________0.01

  6. 256
    Jim Eager says:

    Re 255 AEBanner: “Now the only energy which can be absorbed at high altitudes is the energy of the “wings”, or side bands, of the CO2 region”

    But as altitude increases water vapor decreases while CO2 remains well mixed, thus CO2 becomes the dominant absorber in the entire active band, not just in the wings.

  7. 257
    Timothy Chase says:

    AEBanner (#255) wrote:

    In order to get the surface temperature down to 288.0 K, only about 86% of the emitted energy could be absorbed by the water. So about 14% of the energy would be transmitted to higher altitudes.

    Can the same photon get absorbed only once?

  8. 258

    [[I used a C program which incorporated the Planck distribution and the Stefan-Boltzmann Law. Infrared absorption cross sections for carbon dioxide were obtained from Hitran, and the graph showing Absorption Factor against wavelength, given in Part 2, “What Angstrom didn’t know”.

    Hitherto, I had assumed that there was total absorption of the energy radiated from the surface in the CO2 regions of the spectrum by the CO2 itself and the water vapour, and so no increase in CO2 concentration could produce further heating. However, energy balance considerations with the C program showed that this would cause too much surface heating because of the GH effect of the water vapour. In order to get the surface temperature down to 288.0 K, only about 86% of the emitted energy could be absorbed by the water. So about 14% of the energy would be transmitted to higher altitudes.]]

    The atmosphere isn’t wholly radiative. At the surface and near it, convective effects are very important. If you match the radiative effects alone to a surface temperature of 288° K., you’ll get the wrong answer.

    What you appear to be trying to do is write a column model of Earth’s atmosphere. The simplest kind of such model that is reasonably realistic is called a radiative-convective model, and they can be quite complicated. If you’re interested I can send you a (very rough) first draft of a book on writing such models that I’m working on. All the code is in Fortran, but that shouldn’t be too hard to convert to C. The math is almost all the same, except that Fortran has an exponentiation operator and C doesn’t (a big drawback of C, in my view).

  9. 259

    Re #257 Yes, a photon can only be absorbed once, but some visible photons, especially blue ones, can be scattered several times.

  10. 260
    mg says:

    I have read the Myhre paper that establishes the Radiative Forcing equation for GHG’s. It is a simple equation that is still widely accepted today.

    I also have just enough spectroscopy knowledge to be dangerously ignorant. It is this ignorance that leads me to ask questions.

    1. Do the Einstein Coefficients (Absorption, Spontaneous Emission, and Stimulated Emissions) need to be taken into account when determining the radiative forcing of CO2? They weren’t in Myhre (as far as I can tell, anyway).

    2. Does Beers law need to be taken into account? As photons travel through a medium they can be absorbed or induce stimulated emission, which will reduce the intensity of the radiation as distance from radiation source increases.

    Would these two factors have any appreciable factor on the radiative forcing of the GHG’s? Why or why not?

    Like I said, I have just enough knowledge to be stupid.

  11. 261
    Hank Roberts says:

    > a photon can only be absorbed once

    The photons aren’t somehow stored and then released again.
    Nor do they disappear.
    The energy changes form. The molecule can emit another photon, if the energy isn’t transferred in some other way.

  12. 262
    AEBanner says:

    Re #256, Jim Eager wrote: “But as altitude increases water vapour decreases while CO2 remains well mixed, thus CO2 becomes the dominant absorber in the entire active band, not just in the wings.”

    As I understand it, the GH effect works by absorption of infrared photons mainly by CO2 and water vapour, and then by re-emission of new photons of corresponding energies, with 50% going down to the surface and producing extra heating, and 50% going upwards and escaping to space. In the process, many more intermediate absorptions and emissions may occur, but the overall, final result is 50% to Earth and 50% to space.

    In my program for #255, I dealt with the effects of CO2 at wavelengths from 13 through 16 microns, with large cross sections, at the equivalent of low altitudes, and so this left only the wings to be dealt with at high altitudes. The absorption cross sections of CO2 are small, or very small, for the wavelengths in the wings and so the corresponding photons could “slip through”, in the words of the initiating essay, to high altitudes.

    The main point to remember, I think, is that once any particular wavelength has been dealt with, that is with 50% of the photons going down and 50% going upwards, you do not repeat the process for that wavelength.

  13. 263
    Hank Roberts says:

    > As the higher levels radiate some of the excess downwards,
    > all the lower levels down to the surface warm up. The imbalance
    > must continue until the high levels get hot enough to radiate as
    > much energy back out as the planet is receiving.
    — from the original post

  14. 264
    Jim Eager says:

    Re 262 AEBanner: “The main point to remember, I think, is that once any particular wavelength has been dealt with, that is with 50% of the photons going down and 50% going upwards, you do not repeat the process for that wavelength.”

    Why not, since the 50% that go down can be absorbed and then re-emitted (as new photons), with 50% of them going back up?

  15. 265
    Hank Roberts says:

    The temperature of the gas limits the wavelength and energy of the photons emitted.

  16. 266
    Timothy Chase says:

    AEBanner (#262) wrote:

    As I understand it, the GH effect works by absorption of infrared photons mainly by CO2 and water vapour, and then by re-emission of new photons of corresponding energies, with 50% going down to the surface and producing extra heating, and 50% going upwards and escaping to space. In the process, many more intermediate absorptions and emissions may occur, but the overall, final result is 50% to Earth and 50% to space.

    The main point to remember, I think, is that once any particular wavelength has been dealt with, that is with 50% of the photons going down and 50% going upwards, you do not repeat the process for that wavelength.

    Let’s see. You are leaving convection out of the process altogether and wondering why you are getting too much surface heating (#255) so you are reducing absorption by water vapor down to 86% (ibid.) when in reality its about 100%, you are assuming that any longwave at the relevant wavelengths which gets absorbed by water vapor and emitted towards space doesn’t get re-absorbed along the way and then wondering why doubling carbon dioxide has little or not effect upon the greenhouse effect…. I would assume that in your model, when radiation gets emitted towards the ground and then absorbed at ground level it gets re-emitted towards space…?

    The greenhouse effect is a feedback process.

    We don’t just assume that once some radiation has been absorbed then re-emitted its out of play. If one did that, no wonder, in one’s model, the upper layers couldn’t possibly be effective. And just as radiation which is absorbed by the atmosphere and re-emitted to the ground will get re-emitted as thermal radiation which may once again be absorbed by the atmosphere and re-emitted towards the ground, but with a smaller and smaller proportion every time, radiation may be absorbed and re-emitted in both directions at each layer of atmosphere.

    This is part of the feedback process. Even with Gavin’s simple model from a little while ago which consisted of a single layer of paper-thin atmosphere, I had to go through something in the neighborhood of sixty generations before the values finally settled down – and thats part of the process through which one identifies how the system settles down to an equilibrium and what that equilibrium is with the thermal radiation entering the system being balanced by the thermal radiation which was leaving the system.

    And once you start dividing the atmosphere up into layers, you will have feedback between the different layers. If you throw it away as being just too messy, then you aren’t really modeling the greenhouse effect. But you will also want to track their temperatures, thermal expansion, etc..

  17. 267
    Timothy Chase says:

    PS to 266

    I guess the following might help in getting across my point – otherwise it might seem that I am simply trying to make things overly complicated.

    To treat things as if the thermal radiation as if upon its first absorption and re-emission, it either goes immediately to the ground or to space on the reasoning that this is where it must eventually go is only one step removed from modeling the greenhouse effect with thermal radiation being emitted by the ground and going immediately into space on the reasoning that it must eventually reach space, no matter how complicated things may be before it gets there. But of course, the latter approach would mean that thermal radiation didn’t interact at all with the atmosphere, in which case there wouldn’t even be so much as the simplest pretense at modeling the greenhouse effect.

    To model the greenhouse effect, one has to have the feedback between the ground and the atmosphere. But if one wants to model the greenhouse effect in such a way that one is modeling the role of water vapor and the role of carbon dioxide, then one needs at a minimum two layers of atmosphere, the first consisting of water vapor, the second higher layer consisting of carbon dioxide, and then feedback between the ground and the water vapor layer, and feedback between the carbon dioxide layer and the water vapor layer. But this will give you too strong a greenhouse effect if you don’t include convection. And even then, one isn’t getting any of the dynamic evolution of the system if one doesn’t include the warming and thermal expansion of the layers.

    Anyway, I haven’t gotten that far as of yet. However, one thing to keep in mind before you go too far rolling your own: Nasa makes available its models for free – with all of the source code. I believe that is standard operating proceedure in climatology. You get the model and you can examine or even modify the formula to see what the consequences are. The only thing is that these models are fairly large. They had been weighing in at 100,000 lines, but the more recent versions are in the neighborhood of a million.

  18. 268
    AEBanner says:

    Re #264 Jim Eager

    The absorption and emission process can occur many times, but the overall effect is still 50% up and 50% down. I think that a program should deal with this once only.

  19. 269
    Ray Ladbury says:

    AEBanner–In science a model needs to be as simple as possible–and no simpler. Your model throws off some very important physics–like convection and conduction, evaporation. These are the main modes of heat transfer in the troposphere. Because of this, the upper troposphere is much warmer than it would be otherwise. It is mainly in the upper troposphere and into the stratosphere that radiation becomes dominant.
    Because the atmosphere is cooler at this altitude, emission in the IR is significantly lower. Moreover, if you add CO2, more of the IR radiated from the lower warmer regions of the atmosphere is absorbed. Some of it is then re-radiated (50% up and 50% down, but some of it goes into heating the atmosphere by collisional relaxation–another process you ignore. Ultimately, it comes down to conservation of energy–if energy isn’t escaping, it is warming the planet until a new equilibrium is reached.

  20. 270
    Hank Roberts says:

    Well, everyone is entitled to their own beliefs.

    This may be valid as historical re-enactment of the stages in the AIP History. Seems you’re around the era when people had not yet understood the reason there’s a lag time of centuries after increasing CO2 before the planet comes back to equilibrium at a higher temperature?

  21. 271
    AEBanner says:

    OK, I’ve thought some more, and I now accept the reasoning of the Saturated Gassy Argument. I wish to thank the several people who have replied to my comments, particularly Timothy Chase, for the help they have extended to me to get my ideas on the right track. My thanks also to Mr Levenson for the offer of a draft copy of his forthcoming book, but I fear it would be far too advanced for my present needs. I retract my #255 and any other negative comments.

    Two questions.
    Can someone please give a figure for the surface temperature rise for a doubling of CO2?

    How does the rate of emission of photons from a gas depend on temperature? Ie. Does it follow Stefan-Boltzmann, as for a solid, black body?

  22. 272
    Hank Roberts says:

    First question:
    > Can someone please give a figure for the surface temperature
    > rise for a doubling of CO2?

    That’s a definition of “climate sensitivity” (as it will be measured at the end point of the process, after centuries, once the whole system is at radiative equilibrium again). You can find the range of estimates by searching.

    Second question:
    http://www.google.com/search?q=How+does+the+rate+of+emission+of+photons+from+a+gas+depend+on+temperature%3F

  23. 273
    Tim McDermott says:

    The short name for “surface temperature change for a doubling of CO2” is climate sensitivity. IIRC, the IPCC gives a range of 1.9 to 4.5 degrees C, with the most likely value being 2.8-3.0.

  24. 274
    Hank Roberts says:

    On arguments for clean coal, this has policy implications:

    http://www.iht.com/articles/2007/07/31/america/nuke.2-106441.php
    “The little-noticed provision in the Senate bill refines and expands the loan guarantee program that Congress passed in the Energy Policy Act of 2005…. the bill essentially allows the Department of Energy to approve as many loan guarantees as it wants for both new nuclear plants and those that use other “clean” technologies.”

    So this research may suggest moving the definition of “clean” for coal plants to mean only those run as closed cycle plants.

  25. 275
    Hank Roberts says:

    Dang, wrong thread. That belonged in the current Ozone thread. Ah well.

  26. 276

    [[Can someone please give a figure for the surface temperature rise for a doubling of CO2?]]

    If all else is equal, doubling CO2 should cause a radiative forcing of about 3.7 watts per square meter. With a climate sensitivity of 0.75° K. per watt per square meter, this would correspond to a 2.8° K. rise in surface temperature. Both figures are a little shaky. For more on climate sensitivity, I have a web page full of estimates through a link off my main climatology page:

    http://members.aol.com/bpl1960/Climatology.html

    [[How does the rate of emission of photons from a gas depend on temperature? Ie. Does it follow Stefan-Boltzmann, as for a solid, black body?]]

    Usually not; it would be far greater at or around the location of emission lines and near-zero between. But you can use the Stefan-Boltzmann law by chopping up the spectrum into bands and assigning a different (appropriate) emissivity factor between 0 and 1 to each band. Thus a mass of carbon dioxide would have an emissivity around 1 near 14.99 microns but near 0 around 1.0 microns.

  27. 277
    Timothy Chase says:

    AEBanner,

    My apologies for not having read your earlier posts more carefully. I had assumed all too quickly that someone had come in who was merely interested in attacking the science rather than someone who genuinely seeking to understand. Had I read the posts more carefully, I believe I would have noticed that you had put some real thought into this. I will endeavor not to make that mistake again.

  28. 278
    AEBanner says:

    I found this passage recently in a piece from the Energy Information Administration of the US Department of Energy

    http://www.eia.doe.gov/cneaf/alternate/page/environment/appd_a.html

    “What happens after the GHG molecules absorb infrared radiation? The hot molecules release their energy, usually at lower energy (longer wavelength) radiation than the energy previously absorbed. The molecules cannot absorb energy emitted by other molecules of their own kind. Methane molecules, for example, cannot absorb radiation emitted by other methane molecules. This constraint limits how often GHG molecules can absorb emitted infrared radiation. Frequency of absorption also depends on how long the hot GHG molecules take to emit or otherwise release the excess energy.”

    Surely, this cannot be correct?
    Please can someone advise?

  29. 279
    John Dodds says:

    Re 278. The first 3 DOE sentences are valid. The rest is true but irrelevant since it is not constraining on the total process.
    When the CO2 absorbs the energy & returns it to the air mostly by collisions but a little by re-emission, (once a hot CO2 collides once, then it loses enough energy that it canNOT reemit a photon of the specific wavelength that can be absorbed by another CO2) the surrounding air reabsorbs the energy within microseconds and within centimeters (at ground level) and since the air’s temperature is unchanged (conservation of energy) then the air will reemit IR energy per Wein & Stefan-Boltzmann in the wavelength range that CAN be absorbed or reabsorbed by the CO2, continuously, forever. This is HOW CO2 transports energy to higher elevations & out to space. Since the air & CO2 density is lower at higher elevations. a photon travels further going up than it does going down, hence energy is transported out to space. (in a zig-zag process of many absorbtions, at one microsecond per absorbtion, you can get a million absorbtions in a second!!)

    Another comment on saturation. When CO2 absorbs a (typical IR) photon, the molecule goes to ~900K. THEREFORE, the only way all the CO2 can be saturated is WHEN all the air is at ~900K. Otherwise the CO2 will collide with the air and cool back down to unsaturated conditions. OR looking at it in another way, IF all the CO2 DID stay saturated, then CO2 could not absorb photons, and the IR radiated photons would go directly to space faster, and hence cool down the air. We will not survive too well at ~900K. The saturation concept is a waste of energy! :)

    A side comment- the concept that CO2 “TRAPS” photons is totally absurd. There is NO way in the world, that a ~900K CO2 molecule can exist for more than a few microseconds aurrounded by 288K air molecules. Besides if CO2 traps the energy & doesn’t give it back, then how does the energy warm the air? CO2 “catches and releases” energy. It just slows the transport to space process down, which is why GHGs cause warming.

    My next question is since the air is now warmer, why doesn’t the Stefan-Boltzmann equation, that says that the energy transported out is proportional to T^4, simply transport out MORE energy faster at the warmer temperature, to return the air to the original equilibrium temperature? ie Mother Natures natural compensation process for the greenhouse effect?

  30. 280
    AEBanner says:

    Re #278

    Please note that I had no replies to my #278 for 4 days, and so I posted it again, in the Part 2 thread “What Angstrom didn’t know”, at #419. Good response.

  31. 281

    [[ When CO2 absorbs a (typical IR) photon, the molecule goes to ~900K. THEREFORE, the only way all the CO2 can be saturated is WHEN all the air is at ~900K. Otherwise the CO2 will collide with the air and cool back down to unsaturated conditions.]]

    First of all, assigning a temperature to a single molecule is meaningless, since temperature is based on the root-mean-square velocity of a number of molecules. Second, you seem to be picturing energy disappearing when collisions take it away from CO2 molecules. Energy is conserved. The energy going into collisions is gained by the molecules in the collisions, and will therefore raise their temperature (T = M V2 / (3 R)). Since temperature will equalize for all molecules, the CO2 will also be warmer, and will radiate more. That’s how the greenhouse effect works.