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Part II: What Ångström didn’t know

Filed under: — group @ 26 June 2007

By raypierre , with the gratefully acknowledged assistance of Spencer Weart

In Part I the long struggle to get beyond the fallacious saturation argument was recounted in historical terms. In Part II, I will provide a more detailed analysis for the reader interested in the technical nitty-gritty of how the absorption of infrared really depends on CO2 concentration. At the end, I will discuss Herr Koch’s experiment in the light of modern observations.

The discussion here is based on CO2 absorption data found in the HITRAN spectroscopic archive. This is the main infrared database used by atmospheric radiation modellers. This database is a legacy of the military work on infrared described in Part I , and descends from a spectroscopic archive compiled by the Air Force Geophysics Laboratory at Hanscom Field, MA (referred to in some early editions of radiative transfer textbooks as the "AFGL Tape").

Suppose we were to sit at sea level and shine an infrared flashlight with an output of one Watt upward into the sky. If all the light from the beam were then collected by an orbiting astronaut with a sufficiently large lens, what fraction of a Watt would that be? The question of saturation amounts to the following question: How would that fraction change if we increased the amount of CO2 in the atmosphere? Saturation refers to the condition where increasing the amount of CO2 fails to increase the absorption, because the CO2 was already absorbing essentially all there is to absorb at the wavelengths where it absorbs at all. Think of a conveyor belt with red, blue and green M&M candies going past. You have one fussy child sitting at the belt who only eats red M&M’s, and he can eat them fast enough to eat half of the M&M’s going past him. Thus, he reduces the M&M flux by half. If you put another equally fussy kid next to him who can eat at the same rate, she’ll eat all the remaining red M&M’s. Then, if you put a third kid in the line, it won’t result in any further decrease in the M&M flux, because all the M&M’s that they like to eat are already gone. (It will probably result in howls of disappointment, though!) You’d need an eater of green or blue M&M’s to make further reductions in the flux.

Ångström and his followers believed that the situation with CO2 and infrared was like the situation with the red M&M’s. To understand how wrong they were, we need to look at modern measurements of the rate of absorption of infrared light by CO2 . The rate of absorption is a very intricately varying function of the wavelength of the light. At any given wavelength, the amount of light surviving goes down like the exponential of the number of molecules of CO2 encountered by the beam of light. The rate of exponential decay is the absorption factor.

When the product of the absorption factor times the amount of CO2 encountered equals one, then the amount of light is reduced by a factor of 1/e, i.e. 1/2.71282… . For this, or larger, amounts of CO2,the atmosphere is optically thick at the corresponding wavelength. If you double the amount of CO2, you reduce the proportion of surviving light by an additional factor of 1/e, reducing the proportion surviving to about a tenth; if you instead halve the amount of CO2, the proportion surviving is the reciprocal of the square root of e , or about 60% , and the atmosphere is optically thin. Precisely where we draw the line between "thick" and "thin" is somewhat arbitrary, given that the absorption shades smoothly from small values to large values as the product of absorption factor with amount of CO2 increases.

The units of absorption factor depend on the units we use to measure the amount of CO2 in the column of the atmosphere encountered by the beam of light. Let’s measure our units relative to the amount of CO2 in an atmospheric column of base one square meter, present when the concentration of CO2 is 300 parts per million (about the pre-industrial value). In such units, an atmosphere with the present amount of CO2 is optically thick where the absorption coefficient is one or greater, and optically thin where the absorption coefficient is less than one. If we double the amount of CO2 in the atmosphere, then the absorption coefficient only needs to be 1/2 or greater in order to make the atmosphere optically thick.

The absorption factor, so defined, is given in the following figure, based on the thousands of measurements in the HITRAN spectroscopic archive. The "fuzz" on this graph is because the absorption actually takes the form of thousands of closely spaced partially overlapping spikes. If one were to zoom in on a very small portion of the wavelength axis, one would see the fuzz resolve into discrete spikes, like the pickets on a fence. At the coarse resolution of the graph, one only sees a dark band marking out the maximum and minimum values swept out by the spike. These absorption results were computed for typical laboratory conditions, at sea level pressure and a temperature of 20 Celsius. At lower pressures, the peaks of the spikes get higher and the valleys between them get deeper, leading to a broader "fuzzy band" on absorption curves like that shown below.

We see that for the pre-industrial CO2 concentration, it is only the wavelength range between about 13.5 and 17 microns (millionths of a meter) that can be considered to be saturated. Within this range, it is indeed true that adding more CO2 would not significantly increase the amount of absorption. All the red M&M’s are already eaten. But waiting in the wings, outside this wavelength region, there’s more goodies to be had. In fact, noting that the graph is on a logarithmic axis, the atmosphere still wouldn’t be saturated even if we increased the CO2 to ten thousand times the present level. What happens to the absorption if we quadruple the amount of CO2? That story is told in the next graph:

The horizontal blue lines give the threshold CO2 needed to make the atmosphere optically thick at 1x the preindustrial CO2 level and 4x that level. Quadrupling the CO2 makes the portions of the spectrum in the yellow bands optically thick, essentially adding new absorption there and reducing the transmission of infrared through the layer. One can relate this increase in the width of the optically thick region to the "thinning and cooling" argument determining infrared loss to space as follows. Roughly speaking, in the part of the spectrum where the atmosphere is optically thick, the radiation to space occurs at the temperature of the high, cold parts of the atmosphere. That’s practically zero compared to the radiation flux at temperatures comparable to the surface temperature; in the part of the spectrum which is optically thin, the planet radiates at near the surface temperature. Increasing CO2 then increases the width of the spectral region where the atmosphere is optically thick, which replaces more of the high-intensity surface radiation with low-intensity upper-atmosphere radiation, and thus reduces the rate of radiation loss to space.

Now let’s use the absorption properties described above to determine what we’d see in a typical laboratory experiment. Imagine that our experimenter fills a tube with pure CO2 at a pressure of one atmosphere and a temperature of 20C. She then shines a beam of infrared light in one end of the tube. To keep things simple, let’s assume that the beam of light has uniform intensity at all wavelengths shown in the absorption graph. She then measures the amount of light coming out the other end of the tube, and divides it by the amount of light being shone in. The ratio is the transmission. How does the transmission change as we make the tube longer?

To put the results in perspective, it is useful to keep in mind that at a CO2 concentration of 300ppm, the amount of CO2 in a column of the Earth’s atmosphere having cross section area equal to that of the tube is equal to the amount of CO2 in a tube of pure CO2 of length 2.5 meters, if the tube is at sea level pressure and a temperature of 20C. Thus a two and a half meter tube of pure CO2 in lab conditions is, loosely speaking, like "one atmosphere" of greenhouse effect. The following graph shows how the proportion of light transmitted through the tube goes down as the tube is made longer.

The transmission decays extremely rapidly for short tubes (under a centimeter or so), because when light first encounters CO2, it’s the easy pickings near the peak of the absorption spectrum that are eaten up first. At larger tube lengths, because of shape of the curve of absorption vs. wavelength, the transmission decreases rather slowly with the amount of CO2. And it’s a good thing it does. You can show that if the transmission decayed exponentially, as it would if the absorption factor were independent of wavelength, then doubling CO2 would warm the Earth by about 50 degrees C instead of 2 to 4 degrees (which is plenty bad enough, once you factor in that warming is greater over land vs. ocean and at high Northern latitudes).

There are a few finer points we need to take into account in order to relate this experiment to the absorption by CO2 in the actual atmosphere. The first is the effect of pressure broadening. Because absorption lines become narrower as pressure goes down, and because more of the spectrum is "between" lines rather than "on" line centers, the absorption coefficient on the whole tends to go down linearly with pressure. Therefore, by computing (or measuring) the absorption at sea level pressure, we are overestimating the absorption of the CO2 actually in place in the higher, lower-pressure parts of the atmosphere. It turns out that when this is properly taken into account, you have to reduce the column length at sea level pressure by a factor of 2 to have the equivalent absorption effect of the same amount of CO2 in the real atmosphere. Thus, you’d measure absorption in a 1.25 meter column in the laboratory to get something more representative of the real atmosphere. The second effect comes from the fact that CO2 colliding with itself in a tube of pure CO2 broadens the lines about 30% more than does CO2 colliding with N2 or O2 in air, which results in an additional slight overestimate of the absorption in the laboratory experiment. Neither of these effects would significantly affect the impression of saturation obtained in a laboratory experiment, though. CO2 is not much less saturated for a 1 meter column than it is for a 2.5 meter column.

So what went wrong in the experiment of poor Herr Koch? There are two changes that need to be made in order to bring our calculations in line with Herr Koch’s experimental setup. First, he used a blackbody at 100C (basically, a pot of boiling water) as the source for his infrared radiation, and measured the transmission relative to the full blackbody emission of the source. By suitably weighting the incoming radiation, it is a simple matter to recompute the transmission through a tube in a way compatible to Koch’s definition. The second difference is that Herr Koch didn’t actually perform his experiment by varying the length of the tube. He did the control case at a pressure of 1 atmosphere in a tube of length 30cm. His reduced-CO2 case was not done with a shorter tube, but rather by keeping the same tube and reducing the pressure to 2/3 atmosphere (666mb, or 520 mm of Mercury in his units). Rather than displaying the absorption as a function of pressure, we have used modern results on pressure scaling to rephrase Herr Koch’s measurement in terms of what he would have seen if he had done the experiment with a shortened tube instead. This allows us to plot his experiment on a graph of transmission vs. tube length similar to what was shown above. The result is shown here:

Over the range of CO2 amounts covered in the experiment, one doesn’t actually expect much variation in the absorption — only about a percent. Herr Koch’s measurements are very close to the correct absorption for the 30cm control case, but he told his boss that the radiation that got through at lower pressure increased by no more than 0.4%. Well, he wouldn’t be the only lab assistant who was over-optimistic in reporting his accuracy. Even if the experiment had been done accurately, it’s unclear whether the investigators would have considered the one percent change in transmission "significant," since they already regarded their measured half percent change as "insignificant."

It seems that Ångström was all too eager to conclude that CO2 absorption was saturated based on the "insignificance" of the change, whereas the real problem was that they were looking at changes over a far too small range of CO2 amounts. If Koch and Ångström had examined the changes over the range between a 10cm and 1 meter tube, they probably would have been able to determine the correct law for increase of absorption with amount, despite the primitive instruments available at the time.

It’s worth noting that Ångström’s erroneous conclusion regarding saturation did not arise from his failure to understand how pressure affects absorption lines. That would at least have been forgivable, since the phenomenon of pressure broadening was not to be discovered for many years to come. In reality, though Ångström would have come to the same erroneous conclusion even if the experiment had been done with the same amounts of CO2 at low pressure rather than at near-sea-level pressures. A calculation like that done above shows that, using the same amounts of CO2 in the high vs. low CO2 cases as in the original experiment, the magnitude of the absorption change the investigators were trying to measure is almost exactly the same — about 1 percent — regardless of whether the experiment is carried out at near 1000mb (sea level pressure) or near 100mb (the pressure about 16 km up in the atmosphere).


644 Responses to “Part II: What Ångström didn’t know”

  1. 451

    re #450 SBL stands for ‘Stably stratified planetary boundary layer’. I suspect that John is confusing it with the PBL (planetary boundary layer) which convects, unlike the SBL which, as its name suggests, is stable, and is just another name for the PBL at night. See: http://en.wikipedia.org/wiki/Planetary_boundary_layer.

    BTW, TOA is the top of the atmosphere which is roughly in equilibrium 24 hours a day. It is the BOA (Bottom of the Atmophere) where equilibrium only happens twice a day, when in the morning the surface is warmed by the sun to match air temperature, and in the evening when the surface cools below the air temperature.

  2. 452
    Hank Roberts says:

    John Dodds writes:
    > (it takes under a second for a photon to go from ground
    > to space via multiple CO2 absorbtions

    And it takes a good sprinter under a second to run 20 meters.

    But it may take a drunken man half the day to get that far from the lamppost, to where he falls off the curb and ends his staggering.

    Photons are emitted in any direction at random, and with more CO2 in the atmosphere — that’s a “drunkard’s walk” from their starting point.

    The decreasing density of the atmosphere might be like having the drunk staggering about on a slope, rather than on the flat — he may go a bit farther in the easier direction with each stagger.

    The timer ends when the drunk falls off the curb — when a photon goes out of the atmosphere into space.

    There’s no way for the photons to know which way is up, and to prefer that direction, and to be able to choose it.

  3. 453
    Timothy Chase says:

    Re #451

    You are getting a little too good at explaining this sort of thing, I hope you. I believe I actually understood what you had to say – and it was just too easy…

  4. 454
    AEBanner says:

    Re my #419
    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?

    Re Timothy Chase #434

    “Incidently, Alastair brought up something called radiationless transfer at one point, but that is a very specialized phenomena which I believe has nothing to do with the atmosphere. But climatologists would know as they work with radiation physicists who can model this sort of thing: they have even incorporated the fairly esoteric non-local thermodynamic equilibria. But I wouldn’t worry about that for a little while. Throughout most of the atmosphere it isn’t that relevant, and where it does occur it is a matter of gradual deviation from what are called local thermodynamic equilibria.”

    Re Alistair Mcdonald #440
    “I agree with Timothy and Allan that radiationless transfers are just a red herring, and are probably irrelevant to the greenhouse effect.”

    In my #419, I quoted a paragraph directly from the US Department of Energy which was dealing specifically with the GHG effect and “radiationless transfers” of energy.

    So what am I to believe?

  5. 455
    Hank Roberts says:

    John, that document you’re referring to is dated 1994.
    1994 seems like yesterday to me, but that info is quite old.
    Or I am. Perhaps both.

    Are you asking about their use of the term “quenching” to cover all the interactions that transfer heat between gas molecules without emitting photons?

    I doubt that’s the same thing that the quantum physics people are talking about.

  6. 456

    Re #453 & 454

    TC wrote “I believe I actually understood what you had to say…”
    If you are willing to believe what I have to say then you will find it much easier to understand than if you are determined to disbelieve it.

    I should have written that spontaneous radiationless transitions are a red herring. Collision induced radiationless collisions are at the heart of the greenhouse effect, just as the US Department of Energy implied.

    What seems to be the case is that, just as radioactive atoms have a half life, so do (vibrationally and rotationally) excited molecules. A laser works by electrically exciting a molecule (e.b. CO2) and allowing it to naturally relax quickly to a new longer half life state. Lots of molecules can be in that long life state and when one molecule relaxes it causes a chain reaction. The new relaxed state has a short half-life and soon relaxes to the ground state.

    Because the half life of a vibrationally excited CO2 molecule is very much longer than the time between collisions of molecules at STP, then the absorbed vibrational energy becomes molecular translational (kinetic) energy, viz. a gaseous temperature rise.

    This is new! But at STP there are very few collisions (none) which can induce vibrational excitation, but collisions (and spontaneous radiationless relaxation) can chip away at the vibrational energy, turning it first into rotational energy and then into translational (kinetic) energy.

    HTH,

    Cheers, Alastair.

  7. 457
    Ike Solem says:

    When are you guys going to get over this endless and fairly nonsensical discussion of radiative energy transfer in the atmosphere, and move on to the next step, radiative-convective energy transfer in the atmosphere?

    That’s where you include the motion of air molecules in the atmosphere in your model, instead of pretending that the atmosphere is made up of fixed-position molecules.

    Kerry Emanuel’s lectures (biased towards tropical cyclones, but still very applicable) are available online, and everyone here seems to be stuck on this one:

    http://wind.mit.edu/~emanuel/geosys/node2.html

    The conclusion of that lecture is this:
    “So clearly, in radiative equilibrium, the surface air is not in thermal equilibrium with the surface. This creates the potential for convective heat transport away from the surface. This will be the subject of the next lecture.”

    Compare this to Alastair’s statement: “I agree with Timothy and Allan that radiationless transfers are just a red herring, and are probably irrelevant to the greenhouse effect.”

    Ah – let’s just point out here that convection is indeed an example of ‘radiationless energy transfer’ between point A (surface) and point B (upper atmosphere). It’s interesting to watch someone tie themselves into knots verbally, but I would say it’s time to move on to the next lecture in the series:

    http://wind.mit.edu/~emanuel/geosys/node3.html

    Unless of course, you wish to point out any logical or mathematical errors in the first lecture? It seems to me that the endless claims by Alastair that ‘scientists don’t understand radiative transfer in the atmosphere’ are just a backhanded attack on climate models.

    After all, if we believe Alastair’s claims, then the radiative-convective models can’t be right either, nor can the global atmosphere-ocean coupled models, as they all rely on radiative transfer calculations as well.

    Perhaps the really relevant link for this discussion is the following one:

    DeSmogBlog: Clearing the PR Pollution that Clouds Climate Science

  8. 458
    Rod B says:

    Cutting through all of the above for the moment, and given what has been claimed in various posts, I still do not know where the 300+ watts/square meter of infrared radiative downwelling from the atmosphere/clouds to the surface (where it is absorbed) comes from. Odd question, I know, but the forest got lost in the trees somewhere. Anybody know the answer?

    And to raise another old chestnut, likely related to the above question: I’ve looked at 2-3 college texts, including Ike’s reference in #457, and all use Planck’s blackbody function in calculating the energy flux through the atmosphere and between construct slices of the atmosphere. This says the atmosphere (gas) radiates energy in a near continuous spectrum based on the slice of atmosphere’s temperature ala Planck. But, the consensus in these threads (though not near unanimous) is that gasses do not emit so-called blackbody radiation. What gives?

  9. 459
    Timothy Chase says:

    Re Alastair #456

    The whole is greater than the sum of its parts.

    Please accept the compliment in the way in which it was offered.

  10. 460
    Hank Roberts says:

    Rod, all of the gases in the atmosphere, looked at taken together in a snapshot, can be described as radiating approximately like a theoretical black body.

    “Black body” is not a kind of radiation. It’s an appearance, of all the individual events overlapping.

  11. 461
    Ken Newell says:

    As I said before, Ned Ludd would truly enjoy this discussion.

    From the findings of the Intergovernmental Panel on Climate Change (IPCC) working group
    “Our ability to quantify the human influence on global climate is currently limited because the expected signal is still emerging from the noise of natural variability, and because there are uncertainties in key factors”.

    In other words, we know what we want to find. We haven’t found it yet. However, we know it is somewhere in the margins of error of our measurements.

    [Response: Cites are always interesting. This quote is from the second assessment report (published in 1995). Try the latest version (2007) if you want something a little more relevant. - gavin]

  12. 462
    Ken Newell says:

    Can you describe the Natural Variability filter you constructed in 200 words or less?

  13. 463
    AEBanner says:

    Please can anyone tell me if a GHG molecule can be raised into an excited vibrational or rotational state by collision with a nitrogen or an oxygen molecule?

    Also, a web ref would be gratefully received.

  14. 464
  15. 465
    Hank Roberts says:

    AEB- from much above, any increase in energy is going to very quickly be spread across all the modes.

    I wonder if a chaotic pendulum is a decent analogy for the way energy put into a molecule spreads?
    http://nsdl.exploratorium.edu/nsdl/showRecord.do;jsessionid=37817A0341FA69ECA490A29AD74E8261?id=3611&qid=SAQ-5&itemsPerPage=10&index=8

    (for a better analogy, build a chaotic pendulum that also has a solar panel and a capacitor and laser ….)

  16. 466

    Re 463

    As I understand it, for a CO2 molecule to be excited into the v2 bending vibrational mode of 667 cm^-1, it would have to receive energy equivalent to the average kinetic energy of a molecule at 369C.

    I believe someone else has already done this calculation but I cannot find it.

    For the v3 asymmetric stretching mode of 4.25 cm^-1 the temperature needed rises to 2950C.

    These are the only two modes at which CO2 can absorb or emit radiation.

    Water vapour can emit rotational energy after colliding with a molecule with a temperature of 27 K (kelvin).

    Here’s a link but probably not what you want

    st-socrates.berkeley.edu/~budker/Physics138/Alyssa%20Atwood%20Atm%20Spec5.ppt

  17. 467
    Rod B says:

    Good question AEB (463); I second it…

  18. 468
    AEBanner says:

    Re #464, 5, 6

    Many thanks, gentlemen.

  19. 469
    Timothy Chase says:

    Alastair McDonald (#466) wrote:

    As I understand it, for a CO2 molecule to be excited into the v2 bending vibrational mode of 667 cm^-1, it would have to receive energy equivalent to the average kinetic energy of a molecule at 369C.

    … and as I understand it, this is why we can’t just look at the average velocity but but have to look at the Maxwell velocity distribution.

  20. 470
    Alastair McDonald says:

    Re #469 Where Timothy Chase Says:

    … this is why we can’t just look at the average velocity but but have to look at the Maxwell velocity distribution.

    Yhat is true, but without looking at the Maxwell Distribution it is obvious that we can apply the Equipartition Theorem (Boltzmann’s Disrtibution) to the 27K rotational energy, but that the 2950C v3 asymmetric vibrational energy will be ‘frozen out’ at room temperatures. Nor can I imagine that many molecules in the Earth’s atmosphere have a translational temperature of 396 C.

    This is discussed at http://farside.ph.utexas.edu/teaching/sm1/lectures/node51.html and at http://farside.ph.utexas.edu/teaching/sm1/lectures/node70.html

  21. 471
    Dermod O'Reilly says:

    Re Temperature. The question of vibrational modes in complex molecules is resolved at two levels, I think Boltzman said “(thermodynamic) processes occur according to the probability of the process taking place” This is not rubbish but the meaning is a bit obscure. Consider the temperature of GHGs with different vibrational modes, isolated molecules that are vibrating will continue to vibrate until it can radiate its energy it has an energy related temperature. In general molecules are not isolated and collide with other molecules in a random way which is generally called “thermal”, this random collision process is considered to be “real” temperature by some. The fact is that thermal collisions result in energy exchange between the resonant vibrations (rotation, bending etc.) of the polar molecules; the process is called thermalization. As far as atmospheric thermodynamics is concerned, thermal processes are dying out in the tropopause because the pressure is too low, the gasses above the tropopause undergo other energy transfer processes, it is perhaps a mistake to call their energy temperature.

    I am very encouraged by what I read here, I did not know that GHGs could not re-absorb their own radiation, but it is probably true at least to some extent. The absorption/emission lines of these GHG molecule are not quantum processes, they are more like the twanging of a guitar string, fading with time. As Rod’s (421) comment on 419(AEBanner) says “re 419. This is a BOMB that I trust is a DUD. The words blow a battleship sized hole into the absorption / re-emission process, don’t they?” Well it isn’t a dud and it isn’t the only hole in the GHG idea.

    Another giant hole is the concept of “downwelling radiation”. It is quite impossible for a cold body to transfer energy by radiation to a hot body. The Earth’s surface is warmer than the atmosphere so the idea of 390W being radiated downwards from the atmosphere is basically nuts. What is even funnier, if you can find one of the radiative balance diagrams, you will see that this downwelling stuff is miraculously absorbed 100% without any reflection by what must be a very black body indeed!

    The whole concept of GHDs “blocking” or “trapping” radiation relies a process that, of itself, would produce a temperature gradient in the atmosphere over and above the adiabatic lapse rate due to gravitation, mathematically this would be a diffusion process. Diffusion processes are very slow, like conduction (a diffusion process), convection is much, much quicker and more spectacular, (hurricanes are just a very enthusiastic convection process). In boring old thermodynamic terms, the probability of a convection process occurring is very much greater than a diffusion process. It interesting to note that the heat transfer in the radiation zone of the Sun is by radiative diffusion and it is very, very slow, above radiation zone is the convection zone, the two processes cannot take place together. What is the IPCC going to do when the rest of the world realises it is onto a loser?

  22. 472
    Timothy Chase says:

    Alastair,

    Individual molecules do not have temperatures. Populations/distributions have temperatures. And it does not matter what you can or cannot imagine if we have the satellite images, have performed the experiments and have a fairly solid understanding of the physics.

    You have the ability to make a positive contribution here. I would rather you did. Your intimation regarding Raypierre’s chart was not. Neither is this.

    Quit placing so much emphasis on your imagination and more on the science – please.

  23. 473
    Timothy Chase says:

    PS (to 471)

    Anyway, if you look up the Maxwell velocity distribution, you will notice that it has a very long tail.

    … and honestly, Alastair, I thought you had done a good job of explaining the equilibria in 451, and there have certainly been times when you have made positive contributions, seen things before others. But too often you try to undercut the science in order to feed your own ego and end up making things easier for those who would deny that anthropogenic global warming is taking place or that there is any science. I really don’t think that is your intention.

    Maybe we should email:
    timothychase at gmail dot com

  24. 474
    Timothy Chase says:

    PS to my PS

    I might not be able to email you back right away – I have to meet someone, and it will take a little time, and I have been up since 4:30 AM.

    In the meantime, take care.

  25. 475
    Alex Nichols says:

    #471 “Another giant hole is the concept of “downwelling radiation”. It is quite impossible for a cold body to transfer energy by radiation to a hot body.”

    It’s not impossible. The 2nd Law of Thermodynamics is purely a statistical net effect, not a microscopic physical principle. In fact, the 2nd Law is also time-symmetric. It says that a decrease in entropy is possible, just extraordinarily unlikely.

    How else could clouds can be detected from by surface observations using ground-based remote infra-red sensing?

    The presence of greenhouse gases simply means that the pathway to space is longer and thus slower than otherwise would be the case. A proportion of the radiant energy will “bounce off” GHG molecules several times before leaving the atmosphere entirely.

    Since we are talking about non-equilibrium thermodynamics, it’s the rate at which incoming heat from a low entropy source (the sun) is lost to space that ultimately determines the temperature of the Earth and other planets.

  26. 476

    RE #472-4

    I have no wish to get into a flame war on-line or off-line so I will decline the possibility of emailing you.

    The temperature of a gas is based on the average kinetic energy of its molecules. If you take the average kinetic energy of one molecule, you can obtain its temperature, which will remain constant between collisions. During that time it msy or may not change its excitation level.

    What what you wrote earlier, I gather that you have only been interested in the greenhouse effect for about a year. In that case it is not surprising that you are unaware that gases can have several temperatures. However, if you read the document to which Allan Ames pointed http://www.dodsbir.net/sitis/view_pdf.asp?id=DothH04.pdf
    you find on page 7/8 (14-15) the sentence “Defining a vibrational temperature has proven to be a useful concept because it not only indicates departure from equilibrium but also the extent of this departure.” The idea of translational, electronic, vibrational, and rotational temperatures was not my idea. It is all part of the science. In fact CO2 (molecules) have two vibrational temperatures!

    HTH,

    Alastair.

  27. 477
    Dermod O'Reilly says:

    Re 475 radiative transfer is not a statistical process, the transfer of energy occurs for each individual molecule as if no other existed, this is the process for isolated molecule which I was at pains to point out, yes? It is the difference between the stratosphere and the troposphere, GHGs are themalized in the troposphere.

    You remark “It’s not impossible. The 2nd Law of Thermodynamics is purely a statistical net effect, not a microscopic physical principle. In fact, the 2nd Law is also time-symmetric. It says that a decrease in entropy is possible, just extraordinarily unlikely.” This is an old chestnut about statistical mechanics, there are a lot of variations “what is the chance of boiling water turning to ice?” however you say “a statistical net effect” the chance of a single event taking place is not zero, it is as you say “just extraordinarily unlikely”. Even if it did occur it would be finished before you noticed, think about it! From the moment you start to need a meaningful result in connection with global temperature and catastrophy, you will not feel the need to take sub-microscopic probabilities into account,

    I am fascinated by your point about detecting clouds in IR “How else could clouds can be detected from by surface observations using ground-based remote infra-red sensing?” because the same point occurred to me; I found this: http://en.wikipedia.org/wiki/Infrared check the paragraph “meteorology”.
    Nice that you were interested in my posting.

  28. 478
    Ray Ladbury says:

    Dermod, you seem to have some imprecision in your statements. First, atoms do not ignore the presence of other atoms around them. Lines are broadened, collisional relaxation occurs, etc. And, yes, radiative transfer is indeed an inherently statistical and quantum process.
    On the other hand, you are technically correct that the greenhouse mechanism is not really a source of energy, but rather a decrease in a sink (radiative transfer). In the models, though, this is, irrelevant, as a diminished sink looks like a sink + a source.

    Personally, I think people are getting way too wrapped around the axle about what is blackbody or greybody or quantized… The fact of the matter is the spectrum of radiation emitted by Earth’s surface starts off looking very much like a blackbody spectrum at about 290 K, but by the time it escapes to space, there are big holes in that blackbody spectrum corresponding to the absorption lines of GHGs. That’s the relevant physics.

  29. 479
    Timothy Chase says:

    Alastair McDonald (#476) wrote:

    However, if you read the document to which Allan Ames pointed http://www.dodsbir.net/sitis/view_pdf.asp?id=DothH04.pdf
    you find on page 7/8 (14-15) the sentence “Defining a vibrational temperature has proven to be a useful concept because it not only indicates departure from equilibrium but also the extent of this departure.” The idea of translational, electronic, vibrational, and rotational temperatures was not my idea. It is all part of the science. In fact CO2 (molecules) have two vibrational temperatures!

    It is a fascinating article, Alastair. We live in a world of great beauty.

  30. 480
    Dermod O'Reilly says:

    Re #478 Ray, with respect, I think you may be confused because you do not have a good grasp of what I was saying, probably my fault. Let me try again. Statistical mechanics is the description of a large ensemble of particles with or without electrical characteristics (polarity etc.), parameters such as entropy, kinetic energy, temperature, pressure etc. etc. are assigned to this ensemble. A major feature of this ensemble is that the particles have to be sufficiently close to each other to collide elasticly , no collisions, no thermal process. In addition polar molecules interact with EM waves (infrared photons)and because they are polar some or all of this energy is converted into mechanical energy that is stored in the various oscillatory modes (vibration etc.). The source of this photon is not to be specified, a molecule a million miles away, a free electron laser etc., sure there is some relationship between the source vector and the effective crossection of the molecule but this is not to be confused with the random collision process.

    On quantization (a quantum is just “a defined amount”) it is better to stick to the atomic level where only certain orbits (energy levels) are permitted, this is not comparable to the vibrations of polar molecules, not much dfferent from mass/spring oscillations.

    I am not an enthusiast for blackbody descriptions in connection with planets, Planck was only concerned with “arrays of radiating antennas” (electrons attached to atoms in a fixed arrangement i.e. a solid. So many things are not blackbodies, conductors, transparent material etc.; liquids and gases come nowhere near this.

    I do think you are quite right about the importance of convection. All the modellers using absorption/radiation (A/R) seem not to realise that this is a diffusion process which is VERY SLOW, it cannot account for the difference of surface temp. and top of atmosphere radiation temp. Convection arises from gravity which also happens to account for the adiabatic lapse rate which in turn, if you look with open eyes, explains the difference between surface temp and top of atmosphere radiation temp. Convection moves the energy from where it arrives to where it leaves, why should anyone want to look for anything else?

  31. 481
    Rod B says:

    re 472,3,4, et al. Just my two cents worth. The single molecule having temperature discussion has been dormant here for a while, though never resolved; I suspect the positions of the statisticians and the “simple body” folks are intractable. I still think a single molecule zipping around can crash into something and cause a jump (albeit a teeny tiny one) in a thermometer. But, who knows?

    I’m also still bothered by the multiple temperatures of a molecule, though starting to comprehend it. Is a “useful definition of vibrational temperature”, which sounds like an abstract construct, “real” temperature? As I’ve asked before, will the measured temperature of a mole of gas with translation and vibration/rotation energy be greater than a mole with just translation (theoretically)?

  32. 482
    Alex Nichols says:

    #477 I wasn’t using the point about the statistical nature of the 2nd Law as an explanation for infra-red photons reaching the ground from the atmosphere, merely suggesting that there’s nothing inherent in the law that rules it out.
    However, a few things I’ve seen recently claim it’s a “physical impossibility”.

    As far as I can see, all you can really say about temperature and emissivity is that colder bodies emit less photons at longer wavelengths and hotter bodies emit more at shorter wavelengths, according to a 4th power Law.

    Nothing’s colder than the CMB radiation, including the instruments used to detect it, yet they seem to be able to detect the presence of the photons it emits. (O.K, in this case, in the radio wavelength)

    Perhaps someone could explain the ground-based cloud measurements in the infra-red too.

    e.g:-

    “Ground-Based Infrared Remote Sensing of Cloud Properties over the Antarctic”

    ASHWIN MAHESH,* VON P. WALDEN,1 AND STEPHEN G. WARREN
    Geophysics Program and Department of Atmospheric Sciences, University of Washington, Seattle, Washington (22 August 2000)”

    Obviously the contrast with a cold sky is important, but they needed to adjust their radiometers to avoid the
    667-700 cm2 wavelengths of the atmosphere which would otherwise have swamped their readings, so these are detectable from the surface too, although perhaps just from close to the instrument.

    The ARM observatory also does a lot of work in this area.

  33. 483
    Rod B says:

    Fascinating post (471) Dermod. As a scientific skeptic, it is appealing, but…. if the downwelling IR radiation is severely constrained, where does the 320-350 watts/m>sup>2 shown on various radiation budget diagrams come from? Or, if the actual downwelling is a mere fraction of those numbers, this is not just a debate over relative degrees — but most of the fundemental GHG theory just got canned. This seems a bridge way too far.

    On the other hand, this is the area of my biggest question. Intuitively it’s hard to comprehend how the IR surface absorbed downwelling is almost as much as the surface emitted IR and almost twice the absorbed solar radiation. The explanations, while maybe proven correct, are extremely complex and call upon whole bunches of the most esoteric physics, and to a simple Iowa farm boy sound a little bit like the HPFM process..

    A minor point: I have no difficulty seeing the earth as a near blackbody in the IR spectrum. The Earth absorbs about 85% of solar radiation reaching it, and most of the stuff that reflect solar rays absorb IR radiation.

  34. 484
    Hank Roberts says:

    > single molecule zipping around can crash into something

    Then, we are no longer dealing with a single molecule, and we have a measurable temperature.

  35. 485
    Dermod O'Reilly says:

    Re 483 You have problems with radiation budgets? One of my problem is: which one to believe? I tend to use the same one as the IPCC : http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Pub_Ch01.pdf (page 4 of 36 Fig.1) that anyone should suggest that the surface could radiate 390W/m2 into an atmosphere is at most 50C cooler beggars belief. Battered by this absurd suggestion I am driven to silence when I see that this cold atmosphere radiates 324W/m2 into a surface that is warmer. There is nothing in this IPCC citation that would indicate where “CO2 caused” global warming is coming from.

    Other models propose that radiation is absorbed and re-emitted, they also rely on downward radiation and they are no more believable.

    [Response: Now downward radiation doesn't exist? What pray have people been measuring then? - gavin]

  36. 486

    Re #484

    True!

    But don’t forget the saying accredited to Richard Feynman:
    Anyone who claims to understand quantum mechanics is either lying or crazy.

  37. 487
    Timothy Chase says:

    Rod B (#481) wrote:

    I’m also still bothered by the multiple temperatures of a molecule, though starting to comprehend it. Is a “useful definition of vibrational temperature”, which sounds like an abstract construct, “real” temperature? As I’ve asked before, will the measured temperature of a mole of gas with translation and vibration/rotation energy be greater than a mole with just translation (theoretically)?

    Well, I tend to think that my hand is an abstraction.

    I speak of it as a separate object which nevertheless belongs to me and which I use to perform various tasks – such as typing – so that it has functions which I find useful. But it isn’t really separate, is it? It is a part of a whole which is potentially separable but not actually separate, and if it were separate, it wouldn’t really be my hand any more, would it? At least not in any normal functional sense, although I suppose I might still have uses for it. But there are also properties and attributes which aren’t actually separable “except in thought only.”

    We can speak of the length of an object, but the length isn’t something which exists apart from the object which is long, and when we choose to call one “thing” length, another width and another height, it really all is a matter of perspective now, isn’t it? All of these aspects are real in the sense that they exist, but they exist as different aspects of the same entity. Concepts such as “temperature” permit you to look at things from a certain perspective, regarding them in a certain way, where you are able to bring some of those aspects from the background into the foreground as an object of consideration through a process of articulation.

    So I guess the long and the short of it is that I regard all of those temperatures as abstractions in one sense or another, but the kinetic undoubtedly has a wider range of applicability and is what we will know first – given the nature of the human beast. As for the measured temperature of your mole, how do you propose to measure it, theoretically or otherwise?

    This might have some bearing on the answer that you receive.

  38. 488
    Rod B says:

    484 & 486: Well that’s taking the quantum mechanics postulate — it ain’t there ’till we measure/look at it — to fun but ridiculous extremes. I’m safe as I do not claim to comprehend quantum mechanics. I think some of the earlier quantum pioneers said roughly the same thing.

  39. 489

    Re #485

    Dermond,

    Basically you are correct. The air at the base of the astmophere is warmed by absorption of blackbody radiation from the surface of the Earth. Gavin’s scheme where the air re-emits the absorbed radiation and is then heated by conduction with the surface only applies to the continuum radiation produced by water vapour vapour and its evaporation which provides a means of conduction through latent heat.

    The down-welling radiation that Gavin’s pals are measuring is mostly from clouds. The bit that they can’t find – sometimes called The Energy Balance Closure Problem or The Blue Skies Anomaly – is from CO2, because it does not radiate back to Earth, only to space where it cannot be absorbed.

  40. 490
    Timothy Chase says:

    Alastair McDonald (#489) wrote:

    The down-welling radiation that Gavin’s pals are measuring is mostly from clouds. The bit that they can’t find – sometimes called The Energy Balance Closure Problem or The Blue Skies Anomaly – is from CO2, because it does not radiate back to Earth, only to space where it cannot be absorbed.

    The blue skies anomaly is a phenomena involving the absorption of solar radiation, not the climate’s thermal emissions.

    Are you saying that CO2 doesn’t reradiate in the earth’s atmosphere?

    That would be hard to square with satellite images at over 2000 wavelengths, limb measurements and those being performed by planes, not to mention those done in the labs – under conditions involving the same physics. I believe the climatologists and radiation physicists have a fairly solid understanding of the reemission by carbon dioxide – right down to the quantum physics which is involved.

    Don’t you agree, captain?

  41. 491
    Rod B says:

    Dermond (485), I think Planck radiation is dependent only on the temperature of the radiating body, not on any other body or stuff. That’s how a hot sun radiates a bunch into a pretty cold “ether”.

    Timothy (487), don’t be silly [;-). The reference said it was “defining a useful” term. That sounds like an abstraction. “Temperature” (ought to) refers to the non-abstract (and let’s not get all bollixed up with Plato, Satre, et al) feeling/measurement we call hot or cold. It ain’t complicated. If someone wants to come up with a useful term for something that is neither “hot” or “cold” they shouldn’t use “temperature” but rather invent a term not so confusing, like “goowan”.

    Does vibration/rotation energy make the mole of gas “hotter” or not? Measure it any way you wish (while accounting for the “hotness” change resulting from the measurement itself.)

    Alastair (489), cloud down welling sounds plausible, but is there enough energy in liquid/solid water in the sky to account for the roughly 320 watts/m2 of down welling? Sounds like a long row to hoe.

  42. 492
    Timothy Chase says:

    Rod B (#491) wrote:

    Timothy (487), don’t be silly [;-). The reference said it was “defining a useful” term. That sounds like an abstraction. “Temperature” (ought to) refers to the non-abstract (and let’s not get all bollixed up with Plato, Satre, et al) feeling/measurement we call hot or cold. It ain’t complicated. If someone wants to come up with a useful term for something that is neither “hot” or “cold” they shouldn’t use “temperature” but rather invent a term not so confusing, like “goowan”.

    Actually I was being quite serious – on a number of different levels.

    With regard to the different temperatures, they are all aspects of the same thing, and therefore unified in their existence by the thing which “possesses” them – much like the dimensions of length, width and height. Not only are they related, but intimately so through various transformations of energy from one form to another in accordance with physical laws. On a number of occasions, Tamino has even pointed out that at a fundamental level in terms of statistical mechanics they may be defined in the same way.

    In fact, I believe the following was the incantation of illumination that he cast:

    Perhaps once one retires, as both you and Alastair have, you begin to feel that the world doesn’t have quite so much use for you anymore. That isn’t true – but lets set that aside for a moment.

    Feeling this way, both of you would appear to enjoy playing all sort of mischief so as to insure that world knows you are still here. But I know. So do the rest of us. You may also feel that with the darkening of the twilight you have little investment in what occurs forty or a hundred years hence. But wouldn’t you like to be remembered – and to leave a benevolent legacy for those who come after you?

    I know I would – and I do.

    According to legend, King Arthur will return when England needs him most.

    We have need of you now. Please find a way to make yourself useful. Seeing the sorts of games you play I know that you have untapped intelligence and skill. Having played the games you have, you would be quite adept at uncovering the games that others play. And having learned what you have of arts as diverse as diverse as ethics and physics and human psychology, you could cast a light so that others may follow.

    We are now living in times of shadow and darkness – and the world has need of your good will.

    You have the time. Please give this – and us – some consideration.

  43. 493
    Timothy Chase says:

    Gavin,

    The Latex library at:

    /usr/www/users/realc/latexrender/class.latexrender.php

    … seems to have a bit of a problem. As this works with other LaTexs, I would assume that the problem has something to do with the changes which have been made, quite possibly in Unix directory structure, having inadvertently broken something.

    [Response: I have no clue why it is no longer working. Directory structure is fine, but no output is being generated in the tmp file, hence the errors. I'll think about this some more when I get a chance. Sorry... - gavin]

  44. 494
    Timothy Chase says:

    gavin (inline to #493)

    Response: I have no clue why it is no longer working. Directory structure is fine, but no output is being generated in the tmp file, hence the errors. I’ll think about this some more when I get a chance. Sorry…

    No worries – and my apologies.

    Honestly, I regard your time as rather valuable and this is quite small in scheme of things. Like others no doubt, I am just grateful that you are willing to spend time on Real Climate, its essays and participate in the discussions.

    Thank you.

  45. 495
    Rod B says:

    Timothy, O.K. not silly, but awfully esoteric. I understand how a thing possesses its length, width, and height; but how does it possess its length, length, and length? The molecule has some quality called temperature that stems from different energy levels of vibration… and another temperature from rotation levels… and another from translation. It’s doubly confusing since the amount or energy in each degree of freedom is 1/2kT ! So, does a molecule actually have different real temperatures among its energy stores? At least until it equalizes the energy stores ala equipartition? And then are the temperatures equal?

    Looking just at translation T = mv2 / 3k. When all degrees of freedom get energy to their fullest is the temperature of the molecule (shuddup you statistical guys!) now T = mv2 / 7 k, for example (using just the translation kinetic energy)? Or do you now also add the 1/2mv2‘s and (1/2)Iw2‘s of the vibrations and rotations and then divide by 7k to get T. What it T now? Is it still different? Or does the energy get added to vibration and rotation without a change of T?

    Same question I’ve been asking for some time, with different answers depending on the day of the week. You’re (all) giving me an astute analysis of the progression and development of the game replete with an in-depth psychology affecting the players. I just want to know the score. And I do mean “all”; Not picking on Timothy by a long shot. No one on RC nor none of the web-based forums, university lectures, astute papers and lab treatises that I’ve found (so far) simply tell (and describe) the score, just recite stuff that really does sound like incantations. (Maybe it’s me…)

    Tamino might be right, but I like my Dad’s theory of the great benefit of getting old: you no longer have to be nice to people!.

  46. 496
    Hank Roberts says:

    Try asking what coursework or material you’d need to understand to understand their “incantations” — usually there is some science education at some level required and missing, when the answers seem indistinguishable from magic. Since you’ve said you want a Newtonian explanation and don’t want any quantum mechanics you may be asking people who are too young to answer your question in the terms you’re requiring. Seriously, everything I’ve seen looking into the answers, once I start reading the footnotes and following references, does get into quantum math.

  47. 497
    Timothy Chase says:

    Rod b. (#495) wrote:

    Same question I’ve been asking for some time, with different answers depending on the day of the week. You’re (all) giving me an astute analysis of the progression and development of the game replete with an in-depth psychology affecting the players. I just want to know the score. And I do mean “all”; Not picking on Timothy by a long shot.

    Rod, I am serious.

    At the same time, I was also trying to be as polite as possible while calling attention to the obvious. Beyond a certain point, it became obvious that you weren’t directing questions to Alastair because you thought him an expert but because you wished to bait Alastair into arguing against well-established physics. You knew that there were people who have every right to claim a degree of expertise, and while directing some questions to them, you were directing others to him oftentimes in the same post for the purpose of stirring up trouble for your own entertainment.

    To the extent that you did this, you were gaming him and us. But Alastair had his own game, so I suppose he at least should not complain. Each of you had a way of playing on sympathy and goodwill.

    Honestly, I think that both of you could put your intelligence and talent to better use. This isn’t a game. The people here are trying to make a difference. You may or may not like them or identify with them. It shouldn’t matter – given what other people will be facing in the coming decades. And while I may seem naive to you, I am not so naive as to think that you will actually want to help. I am simply pointing out that it is an option.

    Regardless, I strongly suspect that the old games are over.

  48. 498

    Re #490.

    Timothy, you are correct. The Blue Skies anomaly is for solar not terrestrial radiation. I spotted that after I had posted the message.

    I am saying that the radiation to space in the 15 micron band is emitted from the Non LTE region at the top of the atmosphere. In lower regions of the atmosphere there is no radiation in that band because the time between collisions is shorter than the half life of the vibrational excited molecules.

    This has been said before by Jack Barrett “The roles of carbon dioxide and water vapour in warming and cooling the Earth’s troposphere” Spectrochima Acta Vol. 51A, No. 3, pp. 415-417, 1995.

    He argued that this meant increasing CO2 would not cause global warming, and so was not believed.

  49. 499
    Alex Nichols says:

    Re #482 Remote infra-red sensing studies.

    I made a mistake in the units I quoted from the paper, when transferring a snippet from pdf to text.

    It should read ’667-700 cm-1 wavelengths’, not cm2, which would be a very strange wavelength!

    Part 1 of the paper is at:-
    http://www.atmos.washington.edu/~sgwgroup/sgwReferences/maheshWaldenWarren2001I.pdf

    There’s a technical description of an IR radiometer from the manufacturer here, which may help elucidate exactly what they are measuring with modern instruments: -

    http://www.yesinc.com/products/data/tir570/index.html

  50. 500
    Timothy Chase says:

    Alastair McDonald (#498) wrote:

    I am saying that the radiation to space in the 15 micron band is emitted from the Non LTE region at the top of the atmosphere. In lower regions of the atmosphere there is no radiation in that band because the time between collisions is shorter than the half life of the vibrational excited molecules.

    This has been said before by Jack Barrett “The roles of carbon dioxide and water vapour in warming and cooling the Earth’s troposphere” Spectrochima Acta Vol. 51A, No. 3, pp. 415-417, 1995.

    He argued that this meant increasing CO2 would not cause global warming, and so was not believed.

    Yes – he has been on the list of “skeptics” for quite some time.

    Have you considered the fact that if “the time between collisions is shorter than the half life of the vibrational excited molecules” prevented a molecule from gas from reemitting, then water vapor could not reemit at the surface?

    At one level, the argument which you are making regarding collision rates and half-lifes has a certain logic to it.

    If a molecule could reemit only at or after the half life but was interrupted each time, then carbon dioxide and water vapor could not reemit under the very same circumstances that physicists say is required to achieve local thermodynamic equilibria. But the term is “half life.” This means that it is probabilistic – and has no memory of how long the molecule has been in the excited state. It parallels subatomic particle decay. This sort of thing is fairly basic, and should be dealt with in any undergraduate level course which touches on quantum mechanics even at the most introductory level.

    If the gas is a certain temperature, then a certain percentage of molecules will be in the excited state (which will largely be a function of the Maxwell velocity distribution, at least under local thermodynamic equilibria conditions), and it does not matter which molecules are in the excited state or how long they have been so. Over a given duration, a certain percentage of them will reemit as determined by a law of exponential decay. Thus it is not the molecule which reemits, but one molecule which absorbs, and then after so many collisions another which emits, so that it is only the gas, the population, which reemits by both absorbing and emitting the radiation.

    However, even if it made theoretical sense in terms of the physics that somehow a high rate of collision would prevent reemission, there would still be the lab experiments that we have been performing for over a century, the satellite images of reemission at various parts of the spectra and at various altitudes, and the measurements of reemission performed by planes.

    As it is, theories, lab experiments and empirical measurements of reemission the atmosphere are all in agreement. The science is about as solid as it gets.


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