Wednesday, January 6, 2010

Absorption, Not Reflection

Carbon dioxide absorbs infra-red light. Infra-red photons are just right for exciting the atomic bonds within the carbon dioxide molecule. After absorbing an infra-red photon, the carbon dioxide molecule vibrates. The molecule is now hotter. That's what heat is: vibration of atoms.

Carbon dioxide does not reflect infra-red light. Nor does it scatter infra-red light. It absorbs infra-red light and warms up.

Our atmosphere contains carbon dioxide, roughly 0.04% by volume. This carbon dioxide absorbs infra-red radiation from the earth and the sun. Some calculations suggest that the column of air above each square meter of the earth absorbs of order 2 W of infra-red radiation from the earth. If we assume that the atmosphere is, on average, losing heat as fast as it is gaining heat, then we must ask ourselves how this 2 W is leaving the atmosphere.

The 2 W might leave by convection, in which warmer air rises. But there is nowhere for the air to go once it gets to the top of the atmosphere, so convection cannot remove the heat from the atmosphere.

The 2 W might leave by conduction, in which molecules collide with their neighbors. But air is a thermal insulator, and a 1-km column of air with a 10°C temperature difference from one end to the other will conduct only 0.0002 W of heat for every square meter of its cross-sectional area.

By elimination, the 2 W must leave the atmosphere by radiation, in which a vibrating atom emits a photon and so loses heat. This photon may be absorbed by the atmosphere before it travels more than a few hundred meters. It may be absorbed by the earth. Or it may escape the atmosphere and propagate into outer space, in which case its absorption will be greatly delayed.

So, heat leaves the atmosphere almost entirely by radiation.

PS. I am going somewhere with this argument, but I'm hoping to build up some suspense along the way.


  1. I was hoping for the next installment today...guess I'll just have to wait

    Following your line of reasoning, in you summary at the bottom, shouldn't carbon dioxide warm up as it receives radiation from both the earth and sun?

    Also, just to question one of your assumptions, wouldn't AGW advocates argue that the atmosphere is not losing heat as fast as it is gaining it...that in fact it is actually warming up.

  2. Next installment this afternoon. I'm running an experiment right now, with data for the post.

    Most of the sun's radiation is outside the band absorbed by CO2, while a significant portion of the earth's radiation in in this same band, so over-all, the CO2 absorbs more radiation from the earth than from the sun.

    As to what the AGW advocates would argue, I'll leave that until the end of my current sequence of posts.

  3. ""Carbon dioxide absorbs infra-red light. Infra-red photons are just right for exciting the atomic bonds within the carbon dioxide molecule. After absorbing an infra-red photon, the carbon dioxide molecule vibrates. The molecule is now hotter. That's what heat is: vibration of atoms.

    Carbon dioxide does not reflect infra-red light. Nor does it scatter infra-red light. It absorbs infra-red light and warms up.""

    No problem with the above as long as the discussion refers to the 15 micron band. My problem is with the CO2 molecule with sufficient kinetic energy to be able to absorb a higher band or lower band photon. The molecule does not 'know' it absorbed an out of band photon. My layman guess is that the molecule will vibrate as though it absorbed its defined band photon. And again if the CO2 molecule emits a photon, because of the kinetic speed of the molecule, the spectral detector may record an out of band photon. Hence we have so called 'line broadening' but is this really the true energy capacity of CO2 gas in the atmosphere? My layman suspicion is that CO2 performance is being overated.
    Also it does seem that MODTRAN shows lower response from CO2 as the humidity value increases. Again this makes intuitive sense given the far higher density and IR performance of H2O in the lower atmosphere. CO2 should be an excellent coolant above the tropopause and if it mixes up into the thermosphere it should radiate big time.
    Sorry. On reading the above I know I am rambling. My frustration is I don't have the math to express this doubt I have about the climate changing ability of CO2 with respect to all the other variables in the atmosphere of our one and only home planet.

    All the best. Richard111.

  4. What are the higher and lower bands? What is an "out of band" photon?

    We present the absorption spectrum of CO2 in the first 1 km of the atmosphere here. The absorption band is 14-16 um.

    Thus CO2 in the first 1 km of the atmosphere will radiate like a black body for wavelengths 14-16 um, and hardly at all in other places. The absorption and the emission of radiation are related by the principle of radiative symmetry. Are you familiar with this symmetry? If not, then it's important to start with that.

  5. Please bear with me. I am not arguing against anything you say. I am trying to understand. Since I do not have the math I tend to use 'thought experiments'. My ability to explain myself clearly at this level is limited.
    In your Radiative Symmetry page you state: ""The second law of thermodynamics states that heat cannot, of itself, pass from one body to a hotter body.""
    I accept that absolutely. It is the cornerstone of all my thinking. I see all CO2 molecules in the atmosphere as individual entities. If and when a CO2 molecule absorbs a 15 micron photon the molecule will vibrate, in this case the bending mode as you pointed out previously, and could collide with an N2 or O2 molecule and raise the kinetic speed of that molecule. That is how I understand the mechanism of heat transfer between a greenhouse gas and the IR transparent atmosphere is said to occur. BUT! My quibble. Wien's Law tells me peak temperature at 15 micron is -80C (+-). Very little of the atmosphere below the tropopause is at this temperature and that accounts for some 80% of the total atmosphere. So my poor layman mind cannot see how any amount of CO2 can warm the atmosphere if we limit this effect to radiation from the surface of the Earth. I am afraid this must apply to the whole 14 to 16 micron band width as well. When I refered to an out of band photon I meant it was not precisely a 15 micron photon. This ability to absorb a narrow band of radiation is a direct function of the SPEED of the CO2 molecule towards or away from the source of radiation. Now my doubting mind asks just how fast must the CO2 molecule be moving towards or away from the source radiation to absorb a 14 micron photon or a 16 micron photon. Taking the speed of light at 300,000,000 metres per second just how fast is that CO2 molecule moving given the kinetic distribution for the standard temperature of the atmosphere? From my reading I understand that molecular speed in excess of 1,500 metres per second approaches escape velocity. That is a small percentage but I don't know how to covert that to a bandwidth centered on 15 microns.
    Now look at this another way. Each and every CO2 molecule is being battered by other molecules in the atmosphere, the ratio being roughly 1 to 2,500, so the CO2 molecule is most likely to acquire a kinetic energy level proportional to the local air temperature which being mostly above -80C should cause the CO2 molecule to radiate 15 micron photons almost continuosly. Can this rate be calculated? The total number of CO2 molecules in a one square metre column of air can be assumed from a mass of about 6kg (out of 10,300kg of air in the column). The rate times the energy of a photon times the number of radiating molecules might give a fairly precise figure for the energy in the 15 micron band arriving at the surface assuming half goes up and half comes down.
    Again, whatever that figure is, this a band of radiation say, as much as 13 to 17 microns, is arriving at the surface which will be radiating those same frequencies back up with knobs on. Then there is the argument of (Td - Tu)^4 (tee down minus tee up to the power of four) but all radiation graphs I have seen show that the higher temperature source has a higher power level than the lower temperature source when looking at any common band of frequencies below the lower source peak frequency. The average global surface temperature is said to be in the order of 15C. That is above the temperature of most of the atmosphere until we reach the thermosphere.
    Gosh, I am carrying on! A quick summary. To me it appears CO2 is an effective cooling agent in the atmosphere at any altitude and is a useless warming agent for the surface because of its highly restricted radiation characteristics.
    Kevan, if this layman waffle is too distracting please delete it. All the best. Richard111

  6. Thank you for taking the time to explain your entire picture to me. Please do not apologize for what you describe as your "waffle". Let me think about the most economical way to clarify the situation for you. I want to make sure I understand exactly what you have said. Right now I am cooking a turkey.

  7. I follow your reasoning. If the facts were as you state them, your conclusion would be correct. You connect your facts accurately, and your intuition about the results of calculations serves you well.

    But three of your facts are wrong, so you come to the wrong conclusion. Let's look at these three one at a time. Today we will look at the absorption spectrum of CO2.

    If you consult the following document (many megabytes) you will find a listing of the absorption lines of CO2 between 12 μm and 20 μm. There are over three thousand of them, of varying strengths. They are particularly common in the 14-16 μm band. Each line has a non-zero width, for the reasons you give yourself. From 14 μm to 16 μm at 330 ppm concentration, 100 kPa pressure and 300 K temperature, the lines merge together, forming a continuous absorption band.

    Part of your argument relied upon the assumption that there is only one CO2 absorption line, and you quite rightly were confused by this assumption.

    Have I understood you correctly so far?

  8. Spot on. I obtained an old copy of Perry's from my local library and took a copy of this emission chart.
    Wien's Law and the doppler effect and the atomic structure of the carbon dioxide molecule have been the focus of my thinking.
    I make the assumption that a 15 micron photon will always be emitted when an electron orbit relaxes to a lower shell. I also make the assumption that this must be the lowest viable emission level from CO2 as there seem to be no longer-wavelength emissions. The chart shows a bandwidth of roughly 13 to 17 microns at the 0.5 emissivity level. At a temperature of 1,500K this seems quite reasonable to me. It also clearly shows the 4.3 and 2.7 micron bands with 2.7 microns showing some limitation, doesn't quite reach emissivity of 1. There also seems to be a tiny band at 2.1 microns. I am not aware of all the other bands you mention. The chart shows, at the zero level a bandwidth of 9 to 20 microns which may contain the bands you mention. But how effective will they be at 288K and lower?
    I attempted some time ago a simple layer check with each layer being a fixed temperature lower but the CO2 level decreasing with altitude and concluded CO2 is most effective at transporting energy UPWARDS in the atmosphere. My next point of confusion is just how much energy can the CO2 absorb in the 15 micron band when it is already warmed way above the peak blackbody emission temperature of 193K for the 15 micron band? I see the atmosphere as a transparent black body EXCEPT in the 14 to 16 micron band (ignoring for now all the other stuff.) Thus a block of air will be emitting in that band at say 14C, half up and half down, but the surface is emitting at 15C ALL UP. Looking at the first link below I can see for any specific temperature the level of any emission band at 15 microns will always be higher than the identical band with a lower peak temperature. So it does indeed look like the atmosphere is absorbing some specific amount of radiation from the surface but to my simple calcs very, very little. And moving up layers I see each layer feeds a fraction more up than it recieves down so after the intial 'charge' it appears to me no further change takes place up the air column. The air itself acts as an insulator for the surface. It will restrict surface cooling via radiation because the heat capacity of the air will feed back via conduction. (ouch, this got me thinking about surface radiation and temperature inversion :-( ,another time)
    I hope you can follow this. Some links below that I look at in the hopes of absorbing any killer fact that will prove the innocence of CO2 with regard to AGW.


  9. You are confusing "absorption line" with "absorption band". Because of this confusion, your subsequent reasoning is incorrect and you will not be able to make sense of the experimental facts.

    An "absorption line" corresponds to a transition between two states of a gas molecule. An absorption line centered at wavelength λ indicates the absorption of photons close to energy hc/λ, where h is Plank's constant and c is the speed of light. Call the two states of the molecule A and B. We have E(B) - (A) = hc/λ where E(A) and E(B) are the energies of the two states. A molecule in state A can absorb a photon of wavelength λ and move to state B. Conversely, a molecule in state B can move to state A and emit such a photon.

    Given that gas molecules have hundreds of possible states, there are thousands of pairs of states A and B, and thousands of absorption lines.

    The ideal absorption line has zero width, but the doppler effect and other effects cause the lines to be broadened, so that they have a vaguely gaussian shape with width 0.01 um or something like that.

    Between 14 um and 16 um, CO2 has thousands of absorption lines, and they overlap to form a continuous "absorption band". A CO2 molecule anywhere in the atmosphere can emit or absorb a photon of ANY wavelength between 14 um and 16 um. That's right: ANY wavelength.

    The absorption spectrum pointed to by your link shows three bands centered upon 3 um, 4.5 um and 15 um (roughly). Each of these bands is made up of many overlapping absorption lines.

  10. Ah! Enlightenment! (I think). I've been assuming any particular emission band is centered on a specific frequency and 'broadening' was entirely due to the doppler effect. This did bother me because when I tried to work it out I got some horrendous kinetic speeds, far beyond the escape velocity of the molecule. Your explanation above makes it clear 'broadening' for any frequency is in the order of +-0,01 microns. This explains how multiple closely spaced lines overlap and appear as a much broader band. I now need to look at the document of many megabytes you mention above but can't detect where the link is.
    Kevan, I find this all very helpfull and do appreciate the time you are taking on this. Thank you. Do you mind if I mention this discussion on other blogs?

  11. Splendid. Your summary is correct. So: you see that your calculations of the Doppler effect were correct after all. I hope you will have more faith in your own mathematical abilities in future. You will find the list of CO2 absorption lines here. I forgot to paste the link in last time. And of course I would be honored to have you mention this discussion on other blogs.

    When you have enjoyed your new enlightenment for sufficient time, I will be happy to move on to what I think is the second of three ways in which you have been misinformed about the experimental facts.

  12. Have the file thanks. Just under 6 megabytes. Not too bad. Seems to be pages and pages of tables. Will spend a few hours on it and return with more questions. :-)

  13. I figured those pages and pages of tables were necessary to support my claim that there were thousands of CO2 absorption lines. I'm not sure what other use you will get out of them, but I look forward to being surprised.

    I think you were not clear on how CO2 will radiate heat. So I will offer a clarification.

    Suppose you have a gas that has absorption lines at all wavelengths, and they are overlapping, so that it absorbs and radiates at all wavelengths. This would be a "black body". The absorption spectrum of a black body has value 1 for all wavelengths, indicating that the fraction of radiation is absorbs is 100% for all wavelengths.

    The power a black body radiates is observed to be given by the curves we present in Total Escaping Power. The graph alone is here. The area under each curve gives the power radiated per square meter of a black body's surface. The curves are given by a formula, but they were observed first, fitted to a formula second, and only decades later was the explanation for the formula discovered.

    Now, if you want to know how much CO2 will radiate, you consider that CO2 lacks most of the absorption lines of a black body. It has absorption lines only at 3 um, 4.55 um, and the 14-16 um band. You take the absorption spectrum of your body of CO2, which will have value 1 in its absorption bands and less than 1 elsewhere. Zero in some places. You multiply for each wavelength (well, try in steps of 0.1 um) the black-body emission graph by the CO2 absorption graph, and you obtain the CO2 emission graph.

  14. Thank you Kevan. This is all interesting and usefull stuff for my learning curve. I am working on a more comprehensive post that your BBR graph above will help me explain my thinking. Hopefully in a manner which will help me learn more.
    I have made a post here:
    I am also trying to follow a post on Joel Kauffman's work:

    It will take me a few days to absorb what I can of all this info.

  15. Blast! Foiled again by my lack of knowledge. I was hoping to create a simple line graph using bands 1 - 4, which look to have highest intensity of all the bands, from Table 1 of the NASA data file. Then it looked like I would have to use a log scale but the final straw was when I noticed some values increased as temperatures decreased. Lost me completely that did.
    I was recently reminded of Joel M. Kauffman's essay, Climate Change Re-examined, wherein there is an absorption spectrum, "Fig. 7. Infrared spectrum of air at sea level, 760 torr, 288, relative humidity 76%, 29 June 1999. Absorbance vs. frequency in wavenumbers (cm-1) corresponding to wavelengths of 2.5–25 um". I was intrigued by the different traces at 4.3 um and 15 um which are both CO2 active bands. I make the assumption that this is a 'sunshine' record which explains the 4.3 um trace. There must be some surface insolation loss, to my mind, in excess of the nighttime effect of the 15 um band. I've not encountered any discussion regarding this daytime/nighttime difference.
    You mentioned your BBR graph earlier. I was happy to see that as you have computed blackbody IR in 10 degree steps. This shows clearly the total energy available at each temperature. If you look at the 13 to 17 micron band and block in the difference between two adjacent traces the energy level is small but the higher temperature trace always has that bit more energy.
    Applying this thinking to layers in the atmosphere and assuming a temperature difference of say, -1K per layer, then each lower layer will be emitting IR in the 13 to 17 micron band that tiny but MORE than the layer above. Thus my intuition sees that CO2 in the atmosphere channels IR in the 13 to 17 micron band UP the air column. I see no path for 'backradiation'. Bit like a diode I suppose. :-) I can also accept there must be a tiny amount of heat (kinetic energy), transfered to other air molecules by collision, but it does not seem to be enough to effect the lapse rate. Only the water molecule as it changes state from gas to liquid and back to gas again seems to have the ability to do that.
    All fascinating stuff to this layman but I think I need to read more of your postings. I keep finding more to read. Many thanks for your time and advice.

  16. You are right about heat going up the air column. Of course it must be that way, because heat cannot, of itself, pass from a cooler body to a hotter body. We can confuse the issue by separating the heat flow into two artificial components. One is the heat radiated by the surface and the other is the heat radiated by the atmosphere downwards. As you point out, the heat radiated by the surface in 13-17 um is greater than the heat radiated by the atmosphere downwards in 13-17 um. Nevertheless, we call the component that goes up the "upwelling" radiation and the component that goes down the "downwelling" or "back radiation". The distinction does not make much sense during the day, but at night, things get turned upside down, and the back radiation helps keep the surface warm, as we discuss in Back Radiation. It gets cold in the desert at night. Without back radiation, it would get even colder.

  17. Sorry to trouble you again Kevan, butI came across this interesting lecture file: Absorption/emission by atmospheric gases. Solar, IR and microwave spectra of main atmospheric gases . and note that N2 and O2 are not IR active. (Ar is not mentioned so also inactive I guess). O2 is active in UV and promotes O3 but is any heat energy absorbed? Seems very likely to me.

    IR is absorbed by 'greenhouse gasses' in the troposhere and warms the atmosphere along with heat conducted directly from the surface. The only path out for all this accumulated heat energy is via IR to space. But the main atmospheric components are IR inactive!

    It seems to me CO2 above the 300mb level is the prime agent for radiating IR to space. Low level absorption of IR and any heating effect is incidental. The atmosphere is quite capable of warming via conduction from the surface and there is the UV question.

    It looks to me as if the whole 'greenhouse effect' is being inverted for some strange reason.

  18. Dear Richard111 (for I assume it is you), You are correct that CO2 is the gas that radiates atmospheric heat into space. At the same time, it absorbs heat radiated by the planet surface. You are incorrect when you say "low level absorption of IR and any heating is incidental". If there were no CO2, the planet surface would radiate heat directly into space. The atmosphere would be at a uniform temperature, say T1. It would not be hotter lower down, because there would be no heat moving through it into space. Suppose the temperature of the planet and its atmosphere were T1. Now add CO2 to the atmosphere. The CO2 is at temperature T1. Whatever it absorbs in the 14-16 um band, it radiates just the same amount into space. But it also radiates the same amount back down to the planet surface, which means it starts to cool down. At the same time, the planet surface starts to warm up.

    We broke the Greenhouse Effect into several case studies here. I invite you to take a look at Extreme Greenhouse, Part Three, where you will see how an IR-absorbing Filter Gas affects the equilibrium temperature of the surface.

  19. "black body" Please be aware that the black body model for Earth atmosphere is a very bad model. A black body requires full thermalization, and that is not happening in our atmosphere. You might check that by looking at the emission spectrum, which fits the black body spectrum very badly. This black body is a source of some bad thinking in the AGW religion.

  20. Some random thoughts about the spectrum.... First, indeed the transitions between vibrational levels will give lines in IR. Transitions between rotation levels will give lines in microwave. But a transition from one vibrational level to another might change also the rotation level (that is, the rotation changes, too). When taking into account rotations, one should also take into account that the molecule could deform due of the centrifugal 'force'... Anyway, this gives birth to a splitting of the pure vibrational lines. There are other factors involved, as the temperature (kinetic energy of a molecule - this widens the lines due of Doppler shifts), pressure (collisions among molecules - those also might lead to non radiative transitions), there are many details that have to be taken into account when calculating the spectrum. One looks for example to symmetries, because those give rise to degenerate levels (by the way, CO2 is a linear molecule, H2O is not, you quickly find degenerate modes to CO2). More, to radiate, a charge must move. Not all vibrations/rotations would lead to radiation. For CO2, one would learn that it is not a polar molecule. H2O is, though. Luckily, CO2 is composed of more than two atoms, not identical. Now you know why N2 and O2 do not present IR spectrum as CO2: they are linear, composed from two atoms. This means non polar, and there are not vibrations that would move charge to radiate (unlike CO2, where for example the carbon in the middle can move in a different direction than the two oxygen atoms, making a moving charge to appear). H2O, being polar and non linear, has a richer spectrum than CO2. Second, I see that in the discussion above there is the assumption that a transition due of a photon absorbtion must be thermalized. This is not true. Some will be, some not. A transition back might happen before a collision (that takes out the energy causing a non radiative transition).

  21. Above, "they are linear, composed from two atoms" should read: "they are linear, composed from two identical atoms" - the word 'identical' matters :)