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Rising Carbon Dioxide Levels Don’t Increase Earth’s Temperature

  1. Jul 5, 2008 #1
    Six days ago, the Dutch government added a flight fee at Schiphol, the Amsterdam airport, to be used to lower Earth’s atmospheric carbon dioxide (CO2) levels. The Netherlands is one of the four countries that tax carbon put into air in response to advice from the UN-sponsored Intergovernmental Panel on Climate Change (IPCC). I posted a note critical of the carbon dioxide warming model on 10/16/07. It was seen 546 times without any reply. I now offer a specific explanation for why the well-documented rise in atmospheric CO2 content has had no effect on the Earth’s temperature. I wish first to document the observed rise in sufficient detail for its distribution itself to raise doubt about the CO2 thesis. The table below has been developed from monthly values posted by people at the University of Alabama at Huntsville since December 1978. Their values were acquired from a series of polar satellites circling Earth. Values are also available for land and ocean elements of each major listed area and the contiguous 48 US states. They are posted early each month on three sites, http://vortex.nsstc.uah.edu/data/msu/t2lt/uahncdc.lt, .mt, and .ls. Tropospheric warming is concentrated in the northern third of the planet while some southern third areas show cooling. The entire stratosphere has been cooling.
    29.5 year change in degrees Celsius (Kelvin)
    Low Troposphere value SE ratio
    Global mean 0.393 0.033 11.92
    Northern half, 0 to 85 N 0.595 0.040 15.06
    Southern half, 0 to 85 S 0.193 0.035 5.59
    Northern third, 20 to 85 N 0.811 0.046 17.51
    Tropical third, 20N to 20S 0.184 0.052 3.52
    Southern third, 20 to 85 S 0.199 0.037 5.38
    North Pole, 60 to 85 N 1.325 0.120 11.08
    South Pole, 60 to 85 S -0.193 0.131 -1.47

    Mid Troposphere value SE ratio
    Global mean 0.149 0.032 4.72
    Northern half, 0 to 85 N 0.284 0.037 7.66
    Southern half, 0 to 85 S 0.014 0.034 0.41
    Northern third, 20 to 85 N 0.387 0.040 9.67
    Tropical third, 20N to 20S 0.098 0.053 1.86
    Southern third, 20 to 85 S -0.038 0.037 -1.03
    North Pole, 60 to 85 N 0.695 0.108 6.44
    South Pole, 60 to 85 S -0.349 0.116 -3.01

    Low Stratosphere value SE ratio
    Global mean -1.243 0.062 -19.97
    Northern half, 0 to 85 N -1.275 0.076 -16.78
    Southern half, 0 to 85 S -1.210 0.086 -14.15
    Northern third, 20 to 85 N -1.372 0.096 -14.30
    Tropical third, 20N to 20S -1.101 0.124 -8.86
    Southern third, 20 to 85 S -1.261 0.116 -10.89
    North Pole, 60 to 85 N -0.840 0.421 -2.00
    South Pole, 60 to 85 S -1.259 0.354 -3.55

    While many have been discussing green-house gases and their control, a new situation has developed. The price of crude oil, identified by the IPCC as a CO2 generating fossil fuel, has risen fivefold in the last five years. This rise has had a major negative effect on global economics, especially in the last year. The cost of transporting people, food, and maritime, truck, and rail goods has risen rapidly. Higher energy demands are being met more and more by coal, whose combustion generates more nitrogen and sulfur oxides. Rapid urbanization in the “developing” world has made diesel oil used in food production and transport a high demand item. A continued rise in its cost could bring widespread food shortages back to the world. While some environmentalists may see the price rise as beneficial, it is really an omen of future trouble for mankind.

    Kiehl & Trenberth’s 1997 BAMS paper is widely cited as a model showing how rising atmospheric CO2 is driving planetary temperature higher. It supplies acceptable values for the major components of the Earth’s radiation balance and identifies CO2 as blocking 32 W/m2 outward loss compared to water vapor at 75 W/m2. The total after all losses is 235 W/m2. The Earth’s surface generates 390 W/m2 at 15o C., ε=1 (blackbody) and the atmosphere 165 W/m2. The atmospheric radiation figure is derived by subtracting greenhouse and cloud effects from the 390 W/ m2 amount. Infrared spectra obtained from orbiting satellites were used to quantify the effects of water vapor, CO2 and ozone. The satellite observations are labeled TOA (top of the atmosphere) spectra. A striking feature of these spectra is that their nadir in the midst of absorption bands is half or more of the unaffected (Planckian) spectral height. The nadirs of solar Fraunhofer lines are much lower, close to zero.

    The high nadirs suggest that the atmosphere itself is radiating infrared Stefan-Boltzmann photons in all directions. This conclusion is supported by the 1969 Pick and Houghton stratospheric rocket experiment that showed nocturnal radiation toward the Earth in a 5-7 micron band at 25 km. More recent infrared spectra also indicate that the atmosphere itself radiates photons in all directions based on local temperature. My calculations indicate that ε≈1 at 25 km above the Earth. It must fall below this value at some altitude, but there is little information on this matter. TOA means that ε<<1 at orbiting satellite altitude, but no evidence supports this. In contrast, astronomical studies of molecular clouds reveal that very low density structures in the galaxy radiate in the infrared and microwave range sufficiently to assign them very low absolute temperatures. They have lower densities than the Earth’s thermosphere and radiate at ε sufficient to be measured.

    In the meantime, ε≈1 thermal photon radiation in the higher than -10o C. upper stratosphere is scattered by CO2 molecules in the same way that atmospheric oxygen scatters Fraunhofer A and B radiation from the Sun, in proportion to local concentration. Stratospheric CO2 density is higher at lower altitude, so that scattering of radiation toward the Earth raises outgoing radiation, to at least half the total, negating its “absorption” near the Earth’s surface. This mechanism explains the high nadirs in the TOA spectra and demonstrates why the great rise in air’s carbon dioxide seen in the last 50 years hasn’t affected the planet’s atmospheric temperature. Other reasons for the essentially regional temperature rise shown in the table should be sought.
  2. jcsd
  3. Jul 12, 2008 #2
    It appears that you have a few subjects too many, which confuses the matter. Taxes and an overexcited fuel market are really different subjects. The quintenses is how sensitive atmospheric temperatures are to doubling CO2. Better concentrate on that.


    I'm not so sure about that. Don't they explain the ~33 degrees difference between black body temperature and actual ground surface temp as solely caused by back radiation? However in the nul hypothesis (no greenhouse effect) there would still be a one way heat transport by conduction. During daylight warm (light) air in contact with the surface would rise and heat the atmosphere but at night time the opposite would not happen since the cooling (heavier) air at the surface remains there isolating the daylight warmed air aloft. Not to be confused with the latent energy from evaporation and condensation. So for the higher air to cool, the atmosphere needs radiative properties, hence greenhouse effect. Do they account for that?

    Could you elaborate a bit more on that? Perhaps a drawing?
  4. Jul 18, 2008 #3
    "Stratospheric CO2 density is higher at lower altitude, so that scattering of radiation toward the Earth raises outgoing radiation, to at least half the total, negating its “absorption” near the Earth’s surface. This mechanism explains the high nadirs in the TOA spectra and demonstrates why the great rise in air’s carbon dioxide seen in the last 50 years hasn’t affected the planet’s atmospheric temperature.

    Could you elaborate a bit more on that? Perhaps a drawing?"

    Andre has suggested a figure to help make my point about past omission of upper atmospheric contributions to Stefan-Boltzmann radiation balance. This forum does not allow full size figures. I ask that you visualize carbon dioxide molecules as random redirectors of 13 to 18 micron wavelength photons. Near the Earth’s surface their photon capture is followed by scattering in a spherical pattern, with a just below 50% probability of redirecting a photon toward the Earth’s surface. Consider now an ellipsoidal shell lying between 40 and 50 kilometers altitude above the equator and having an average temperature of -10oC. The outer surface of this shell will radiate into space in the same way as the Earth’s surface. The overall intensity is decreased by 30.4% by the lower temperature and may also be affected by lower emissivity (ε). But at 50 km air’s density is 1/1,000 that at the Earth’s surface. Scattering by carbon dioxide is reduced and a larger fraction of 13-18 micron outward radiation fills some of the spectral deficiency generated below. Replacement of 13-18 micron radiation is furthered by carbon dioxide scattering radiation from the inside of the shell that is directed toward the Earth’s surface. It is also possible that the inner shell surface has a higher emissivity than the outer shell surface. This radiation is moving into areas of greater and greater carbon dioxide concentration. Its scattering into space further fills in the 13-18 micron band. Raising atmospheric carbon dioxide will have slight effects on initially outward radiation but acts at least as vigorously to send downwardly directed radiation into space. The existence of a layer of substantial atmospheric radiation neutralizes carbon dioxide’s rising concentration’s effect near the surface that MODTRAN estimates. The model predicts little or no change in the depth over time of the 13-18 micrometer carbon dioxide TOA spectral notch. If this is true, the greenhouse gas model is incorrect and should be abandoned. As we analyze more infrared spectral data within the atmosphere we need to assign emissivity values to various altitudes and add atmospheric Stefan-Boltzmann radiation to MODTRAN.
  5. Apr 23, 2009 #4
    This thread is discussing effect of CO2 on temperature by analyzing the radiation FROM the earth. Wouldn't the same considerations be worth pursuing in regards to the effect of CO2 on the solar heat incident on the earth (and atmosphere)? It seems to me that because the optical properties of a gas are isotropic, and because the solar radiation is greater in intensity than the earth's (and atmospheric), the loss of incoming heat would be greater than the trapping of heat by "greenhouse" effect. Therefore greater CO2 , if it has any effect at all, leads to cooling, not warming.
    I am a relative amateur in these things, so be kind. Thanks
  6. Apr 23, 2009 #5


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    The price of crude oil and any fees that various governments charge really has nothing to do with the atmospheric physics. Anyhow, since so much of the Netherlands is already below sea level and the oceans are gradually rising from CO2 induced global warming, then it should be little surprise that they are concerned.

    The University of Alabama at Huntsville data link shows cooling only in the South Polar region. All other regions show a warming trend. However, nobody expects the warming to be uniform across the entire planet. So, it might be better to try and argue against rising sea levels than bringing up inconsistencies in satellite temperature measurements.
  7. Apr 23, 2009 #6


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    CO2 is transparent to incoming solar radiation. However, in the infrared, it is opaque.

    Humans can not see in the infrared, so we are not able to directly see the heat absorbing properties of CO2.
  8. Apr 23, 2009 #7


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    A lot of this is actually describing the greenhouse effect. For example:
    I have been told that mentors have some guidelines on diagrams based on the explicit requirement of peer reviewed sources for controversial claims. Making your own diagrams is going to be suspect; but a diagram from a legitimate peer-reviewed source is probably okay. A diagram from some credible information source (like a tutorial at a university website) which shows something basic and not in any dispute should be okay, since it is not controversial. I'm not a mentor myself, and this remark has no authority.

    You're describing Earth's emission spectrum. The details of this spectrum are not in any dispute, and a diagram will help see what you mean. Here's an emission spectrum from the Uni of Colorado, as part of student notes.
    I've given some very similar diagrams calculated for this emission spectrum in a closely related thread: [post=2165483]msg #3 of Estimating the impact of CO2 on global mean temperature[/post], taken from a Uni of Chicago site.

    You can clearly see the window of absorption for CO2, which is from about 13 to 18 microns in the diagram. The bottom of that window shows radiation that corresponds to cooler temperatures, around 220K or so, and this is because in that saturated window, most of the emission to space is coming from up high in the atmosphere, where it is cold. On either side of the 13-18 micron band, the atmosphere is mostly transparent, and radiation is coming straight from the surface. This shows up as around 288K or so: especially in the so-called "infrared window" from about 8-12 microns.

    Right; except that you don't mean reduced by 30.4%. You mean reduced by 69.6%, to be 30.4% of what you'd get from the surface. The ratio can be calculated as (220/288)4; the ratio of temperatures, raised to the fourth power.

    You're not treating emissivity of a gas correctly here. The emissivity ε of a surface does't carry across into transmission medium, like a gas. For a gas, or any transparent medium, the emissivity and absorptivity depends on the path length through the gas. It's no longer a dimensionless ratio, but has units of inverse length. Alternatively, you can speak in terms of "optical depth".

    Much of your discussion on emissivity is a bit muddled as a result.

    There's less downwards thermal radiation than there is upwards thermal radiation. At the surface, the excess is about 60 to 70 W/m2 upwards, with the rest taken up by convection and latent heat. Above the troposphere, the upwards thermal flux is about 240 W/m2.

    When you add more CO2, or any other greenhouse gas, there are two differences. One is that the optical depth of the saturated 13-18 micron region decreases. Hence radiation that gets out into space is coming from higher in the atmosphere, and is a bit colder. The impact of this is small, but it's relevant to your conceptual model of concentric bands of atmosphere.

    The more important consequence of additional CO2 is that the width of the saturated band extends a bit. This is called absorption in the "wings" of the absorption region, and it should be covered in any undergraduate course covering radiation transfers in the atmosphere. It's not in any doubt at all; the same effect applies for any gas and can be seen in a laboratory. There's a well developed theory for calculating the impact, founded in turn on the quantum mechanical details of how light interacts with matter.

    MODTRAN is state of the art atmospheric transfer code. It's used without qualm as a basic tool of research. The fundamental point you are missing here is that MODRTAN calculates an expanding WIDTH of the 13-18 micron notch. The plots I gave in the other thread were calculated with MODTRAN. I have overlaid the results for 375ppm CO2 and 750 ppm CO2, and you can see in the wings of the saturated band where the additional absorption is occurring. Here are the MODTRAN calculated emission spectra:

    MODTRAN can be used to calculate the forcing from additional CO2, and will give you results that are consistent with basic physics and with the substantial forcing that occurs. In this case, with a US standard atmosphere and a detector at 20km, the forcing is calculated as 3.423 W/m2; more than enough to give a substantial rise in temperature.

    But that IS what MODTRAN is doing.

    The whole point of MODTRAN is to calculate Planck radiation (not Stephan-Boltzmann; that would be a greybody) all the way up and down the atmosphere, using detailed emissivity results line by line through the spectrum, for each gas involved, and taking into account broadening of spectral lines with temperature and pressure.

    It's a great tool for a basic physical calculation of the impact of carbon dioxide.

    Climate is a highly complex matter, filled with areas of uncertainty and open research. Part of the reason discussion of climate gets so vexed is that for some reason lots of people want to deny the link to anthropogenic carbon dioxide emissions. That, however, is one of the most solidly established aspects of the whole problem! The impact of carbon dioxide is very basic physics, and not in any scientific doubt whatsoever. Where you get all the uncertainty and open research questions is in details of response to this impact, and all the complex interactions with all kinds of other less well understood effects.

    Cheers -- Sylas
    Last edited: Apr 23, 2009
  9. Apr 23, 2009 #8
    It seems to me, leaving aside such unscientific appelations as "denier", that the entire global warming as a consequence of increased CO2 proposal, and its sister Catastrophic Climate Change as a result of increased atmospheric CO2 proposal, would be seen immediately unfounded if the last paragraph of DEMcMillan's initial post were written more clearly and for the common man to understand.

    "In the meantime, ε≈1 thermal photon radiation in the higher than -10o C. upper stratosphere is scattered by CO2 molecules in the same way that atmospheric oxygen scatters Fraunhofer A and B radiation from the Sun, in proportion to local concentration. Stratospheric CO2 density is higher at lower altitude, so that scattering of radiation toward the Earth raises outgoing radiation, to at least half the total, negating its “absorption” near the Earth’s surface. This mechanism explains the high nadirs in the TOA spectra and demonstrates why the great rise in air’s carbon dioxide seen in the last 50 years hasn’t affected the planet’s atmospheric temperature. "

    That was actually what I was looking for in my first post asking what about the effect of scatter of the incoming Solar radiance in the CO2 absorption band.

    Upper atmospheric CO2 molecules scatter some amount (perrhaps small) of the infrared portion of the black body radiation (even though at 5300 K) that otherwise would penetrate the atmosphere deeply. This represents a loss of heat from the sun, which cannot be made up by any other means. This is if anything a cooling relative to the temperature that would have resulted if this CO2 were not in the upper atmosphere, certainly not a heating.

    Also I think that most of the energy in the CO2 abosrption region which comes from blackbody radiation from the earth or from the lower atmosphere is absorbed within a few 10s of meters. So if the CO2 concentration were cut in half by some amazing technique, then it would still be absorbed within twice that distance. So the "greenhouse effect" as it is advertised will not be altered at all in regards to the amount of heat captured.

    I do not understand why this fact is not broadcast fully. All the other arguments become moot.

    Thank you for this opportunity to learn.
  10. Apr 23, 2009 #9
    What you are missing bellatti is that the absorbed energy is then re-radiated by the atmosphere at a rate corresponding to it's temperature, just like the surface.

    The Earth's black body temperature is ~255K or -18C. The Earth's average surface temperature is ~288K or 15C for a difference of 33C. The atmospheric temperature drops ~6.5C per kilometer due to adiabatic expansion and what is known as the environmental lapse rate. (More here) Thermal equilibrium occurs at ~5 kilometers above the surface. What adding CO2 does is make the lower atmosphere optically thicker, which raise the surface temperature, which in turn raises the level in the atmosphere where the radiative balance takes place.
  11. May 6, 2009 #10
    That's silly. The temperature lapse rate to a nearly minus sixty degrees Fahrenheit does not sound like it can "radiate" anything worth while.

  12. May 6, 2009 #11


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    This is basic physics. ANY thing will radiate, even much cooler than that. The greenhouse effect works because so much of Earth's thermal emission is coming from cooler temperatures in the upper atmosphere. Without absorption in the atmosphere, radiation would all just come straight from the surface, and we'd have the cooler temperatures down at the surface as well.

    Skyhunter gives a good first order summary... greenhouse effects mean that much of Earth's thermal emission comes from high in the atmosphere, rather than the surface.

    It's a bit more complicated than a single "emission level", however, because the atmosphere has an "infrared window" from which you get some surface thermal emission, unless blocked by cloud, in which case you get the thermal emission through this window from the top of the cloud layer.

    But look at the emission spectra given above. This is a pretty basic observation, and you can clearly see the temperatures at the bottom of the large chunk cut out by greenhouse effects. It corresponds to radiation at about 220K -- which is about -64F.

    The window around 8 to 13 microns radiates at about surface temperatures, apart from a small chunk with ozone absorption.

    The longer wavelengths show lots of H2O absorption, and hence the emission to space comes from lower in the atmosphere, where there is most of the water vapour. Here the emissions correspond to temperatures of about 240K up to 260K as you approach the big greenhouse chunk... and that's around -28F to 8F.

    ANY temperature will radiate. Even a lot less than -60F. And the whole POINT here is that the greenhouse absorption of thermal radiation lower in the atmosphere means you get the cooler radiation getting out into space.

    The Earth's total radiation averages out to about 240 W/m^2... which would be the same as a blackbody at a uniform 255K, (-18C, or -1F).

    If there was no thermal absorption in our atmosphere, all that emission would be coming from the surface, and Earth's surface would be a chilly -1F, on average.

    Cheers -- sylas
    Last edited: May 6, 2009
  13. May 6, 2009 #12
    Here is a gross map of spheres that constitutes the total atmosphere.

    In my opinion, as far as climate goes, gross is all we have. The finer details(which can make physics and chemistry fun i suppose) are left to molal heat capacity and the coefficient of viscosity. The latter result came as a surprise in the phase shift of matter.
    The former does not quite measure up in quantum mechanics! So, afaict, the gross nonsense of any enhanced greenhouse theory all comes down to being able to count and that count is called the number of degrees of freedom.

    Thank you Sylas for your generous reply(s). I have enjoyed reading or more truly been swamped with regards to your persistent patient efforts. Our posts have crossed in composition and I think I will always have you in mind when I try to address this worldwide issue of something I like to call 'regional seasonal shifts'. I hope I got the code for the URL right.

    In thread id:307685, I believe you mentioned the tropopause as the coldest. I would direct you to the mesopause. Sorry, I don't have a picture of any finer details...
  14. May 6, 2009 #13


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    Good point. Yes, the mesopause is colder. I stand corrected.

    The mesopause is so thin that it has no effect on the energy budget. Effectively all Earth's thermal radiation comes from lower down. The mesopause is also very hard to study. It's too high for radiosondes, and too low for satellites. It's a very difficult part of the atmosphere to study!

    Cheers -- sylas

    PS. Thank you very much!
    Last edited: May 6, 2009
  15. Aug 26, 2009 #14
    [And the whole POINT here is that the greenhouse absorption of thermal radiation lower in the atmosphere means you get the cooler radiation getting out into space.

    Cheers -- sylas[/QUOTE]

    I find the above statement badly irrelevant because of the actual values for absorption. The 15 micron band (13-18) seems to me to have its primary absorption (the first absorption event for the photon) within 2 meters to the 99.99% probablility. I have found this via an interesting model and thought experiment. Specifically the height at which 63 % of the photons are absorbed is given by the formula

    H = k * T / ( C*X) where T is the kelvin Atmospheric temp, C is the concentration of CO2, X is the crossection of absorption for CO2 at 15 microns.
    k is a constant = (1.36*10^-22 cc/deg K).

    This turns out to be 21.7 cm at 303 deg K. By compounding 9 times, 99.99% absorption is reached.
    Doubling the CO2 concentration clearly just lowers the "saturation" level to 1 meter. I have not added a correction factor for pressure, but it goes in the denominator. This same result would apply elsewhere in the atmosphere for secondary photons of atmospheric black body origin.

    If the result was 10 km vs 5 km when the CO2 is doubled, I could see some possibility for the upper atmosphere machinations to be useful, but not if the values are 2 m and 1 m.
    Last edited: Aug 26, 2009
  16. Aug 26, 2009 #15


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    This misses the point. Look again at [post=2171458]msg #7[/post], and in particular the two compared spectra for emission to space for 375ppm CO2 and 750ppm CO2.

    The primary difference is not a change in optical depth at the main saturated bands, but an increase in the width of main saturated region.

    You are looking at the effect of additional CO2 only for radiation right in the middle of the main absorption band; and indeed these frequencies are not relevant to the forcing. Neither, of course, is radiation in the "windows" where CO2 has very weak interactions with radiation. But in the boundary region, where radiation is intermediate between strong and weak absorption, there is a considerable difference in optical depth, and this is where you get the additional greenhouse impact.

    This is called increased absorption in the "wings" of the main saturated band. You should find this covered in any basic text on atmospheric physics that deals with how radiation is absorbed in the atmosphere.

    For example, there is a convenient on-line text Principles of Planetary Climate by R. Pierrehumbert at the Uni of Chicago, that covers the relevant physics in considerable detail and in a general context that can apply for any planet and any atmosphere.

    Here's an extract, including figure 4.12, on page 186. I'll put the extract in blue.

    Figure 4.12: Lower panel: The absorption coefficient for CO2 at 1 bar and 300K, in the wavenumber range of interest for Earthlike and Marslike planets. The horizontal lines show the wavenumber range within which the optical thickness exceeds unity for CO2 paths of 1/10 , 1 and 1000 kg/m2. Upper panel: The corresponding OLR for the three path values, computed for the same temperature profiles as in Figure 4.5. The OLR has been averaged over bands of width 10 cm−1.​

    Figure 4.12 explains why the OLR reduction is approximately logarithmic in greenhouse gas concentration for CO2 and similar greenhouse gases. The key thing to note is that the absorption coefficient in the principal band centered on 675cm−1 decays exponentially with distance from the center. Hence, as the CO2 path is increased by a factor of 10, from 1/10 to 1 kg/m2, the width of the ditch within which the radiating temperature is reduced to cold stratospheric values increases only like the logarithm of the ratio of paths. This is true for paths as small as .01 kg/m2 and as large as 100kg/m2. However, when the path gets as large as 1000kg/m2, the weak absorption bands on the shoulder, near 950 and 1050 cm−1 start to become important, and enhance the optical thickness beyond what one would expect on the basis of the central absorption peak. 1000 kg/m2 corresponds to a partial pressure of CO2 of about 100mb for Earth’s gravity, or equivalently a molar mixing ratio of about 10 % for Earth’s current surface pressure. This is far in excess of any CO2 concentration on Earth likely to have been attained in the past 300 million years [...]. Many greenhouse gases also have a central absorption peak with exponential skirts, and these will also exhibit a nearly logarithmic dependence of OLR on the concentration of the corresponding greenhouse gas.

    I repeat, this is fundamental physics for how matter and radiation interacts. It's basic common ground to the debate from which you can proceed to consider all the many genuinely open questions about climate, and it is shared alike by critics and supporters of the notion of AGW who come to the issue with some background in the details of atmospheric radiation physics.

    Cheers -- sylas
    Last edited: Aug 26, 2009
  17. Aug 27, 2009 #16


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    This is a common, but elementary error. It is based on thinking that the atmosphere is a kind of passive "filter" of outgoing radiation, and that the only way of cooling is direct emission from earth's surface into space, and that the rest is simply "not emitted" or "not transmitted" and hence, remains at the surface. So it looks like there are just a few "windows" where radiation can "escape", and then other, blocked windows, where radiation is "held back". But this is not how it works. When radiation is "helt back" it heats in fact the layer that is "holding back", which, by itself, re-emits a thermal spectrum that is now somewhat more intense and so on. So even in "totally blocked" windows, heat eventually gets out, but it takes more "stages of absorption - thermalisation - re-emission". The "denser" the blocking, the more stages. And the more stages, the higher the delta-T is to get a same amount of radiation out in that window. But it WILL eventually get out. So if you increase the number of "blocking layers", you will increase the necessary delta-T to get a given amount of radiation out.

    A simple illustration of this is the sun: if "blocking layers" would block radiation like a filter, then the sun wouldn't shine, because the heat generated in the sun's core cannot get out directly, at all, at no wavelength. The fact that the sun shines means that eventually, the radiation gets out. However, it has nothing to do with the initial spectrum. The radiation we get from the sun is essentially visible light from a gas layer at about 5000 K. The initial radiation is X-ray radiation from a core at several millions (edited, said billions before) of degrees, of which almost NOTHING gets out directly.

    What you have is a temperature profile in the atmosphere, and each layer emits thermal radiation at that temperature. In the end, you have to have that the earth emits a certain amount of radiation into space, and, according to the frequency, that radiation is emitted at a particular average depth of the atmosphere, different for each frequency. For frequencies where there is a lot of absorption, this average depth is high up in the atmosphere, for frequencies where there is moderate absorption, this average depth is deeper into the atmosphere, and for frequencies where the atmosphere is very transparant, this is the surface. The integral of all these contributions must equal the outgoing radiation flux of the earth, and so the "average temperature" of these emission layers must be constant. That is, the earth must have an "average temperature of outgoing radiation" which is constant, and given by the amount of radiation that the earth is to lose.

    Now, the more "absorber" in the atmosphere, the higher up is this average depth of emission, which means that these higher layers must now be at that "average emission temperature".

    There's a kind of compensation: frequencies which have high absorption (short absorption lengths) must be emitted by the highest-laying layers - which are often the coldest - so they do not contribute, finally, enormously to the outgoing spectrum. Frequencies which have low absorption come from lower layers or the surface, and hence from hotter layers, so they are intenser. As, in the whole IR spectrum, there are all kinds of absorption intensity, the depths and intensities of emission in the final spectrum depend on the frequency, and each line contributes in its own way. Concentrating only on the "black" or the "white" part of the spectrum misses most of the radiation transport dynamics.

    However, don't make the mistake of thinking that you can do the transport problem for each frequency band individually. Indeed, emitted radiation in a certain frequency band is absorbed and re-thermalized, which means, re-distributed over a black-body spectrum, and other means of heat transport (convection, latent heat) also contribute to this.
    This is why you can't see the atmosphere as just a passive filter of outgoing IR radiation from the surface.
    Last edited: Aug 27, 2009
  18. Aug 27, 2009 #17


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    This is true enough... but it's still very instructive to look at the contributions for different frequencies.

    Bellatti spoke specifically of the 15 micron frequency, which is where CO2 absorbs most strongly; and in fact his argument is correct if limited to this central peak of absorption. This frequency contributes very little to the additional forcing as CO2 concentrations increase, and the reason is as he says... this band is saturated already, and the mean emission altitude hardly alters at all. It is already at the top of the atmosphere, for this frequency.

    When CO2 levels increase, almost all the additional energy comes as a result of those frequencies which are neither completely absorbed, nor those which are passed through easily, but rather those for which roughly half the photons get blocked as they pass through the atmosphere. That is, the major additional energy comes because of bands that have "optical depth" neither very small, nor very large, but about unity.

    See page 160 of the "Principles of Planetary Climate" reference, end of section 4.2.2:
    Typical greenhouse gases are optically thin in some spectral regions and optically thick in others. We have seen that the infrared heating rate becomes small in both limits. From this result, we deduce the following general principle: The infrared heating rate of an atmosphere is dominated by the spectral regions where the optical thickness is order unity. If an atmosphere is optically thick throughout the spectrum, the heating is dominated by the least thick regions; if it is optically thin throughout, it is dominated by the least thin regions.

    There is no single emission altitude. Each frequency has a different emission altitude. Optical depth of unity means that the mean emission altitude for that frequency is somewhere in the middle of the atmosphere. Frequencies for which the mean emission altitude is increasing most rapidly will give the greatest contribution to the additional heating as concentrations of the absorbing gas increase.

    Cheers -- sylas
  19. Aug 27, 2009 #18


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    Right. I had understood from his post - maybe erroneously - that it couldn't "get higher up from the surface than a few meters".

    What I wanted to point out is that even if the atmosphere is "totally black 20 times over", there is STILL emission of this radiation ; only it will come from the highest layers. And if you double that, the emission will not alter much, but still a bit because the emission must now come from still somewhat higher up - although I grant that the difference in temperature of these two layers will not be much. However, they also don't represent much in the outgoing radiation balance. Even though the "black" parts represent important chunks of the spectrum, they don't represent a large part in the OLR, so saying that they won't change much, doesn't affect the fact that the parts that DO have strong emissions in the OLR spectrum can change notably.

    Maybe I misunderstood his post, and was this already understood.
  20. Aug 27, 2009 #19


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    I think he is referring to "mean path length" of a photon; and he also speaks also of "secondary photons" emitted from the atmosphere itself. Doubling concentrations does tend to halve the mean path lengths, as he describes.

    In fact, quoting the end of his post:
    This is actually quite correct... and it really IS those parts of the spectrum where the mean path length is of the order 2 to 20 km which are the ones that are most important for each increment of additional heating as concentrations rise.

    What bellatti misses is that this is not the 15 micron band, but a region somewhere between the maximum and the minimum of absorption; and there are always some parts of the spectrum where this is the case, at least for atmospheres with anything from 10 to 10000ppm CO2.

    Here is figure 4.12 from "Principles of Planetary Climate" again:

    15 microns corresponds to a wavenumber of 667 cm-1. Now the bottom half of the figure shows the absorption co-efficient of CO2 for each frequency, and the vertical lines show which absorption co-efficient gives optical depth of unity for a given CO2 concentration in Earth's atmosphere. The 1 kg/m2 line is of the order of Earth's atmosphere. The spectrum looks like a very solid black line because in fact there are very fine absorption lines compressed together on this scale. If you have the book downloaded, look also at figure 4.7 on page 182 to see what the spectrum looks like when you zoom in.

    Cheers -- sylas
  21. Aug 28, 2009 #20


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    Well, that's what I thought too. But when you look at the text output, I don't think that MODTRAN alters any temperature profile. (I'm talking here about the only MODTRAN calculation I have access to, which is the web interface by Archer).

    So I'm not so sure anymore what MODTRAN does, and does not. It seems that MODTRAN takes a user-given temperature and composition profile and calculates the emissions (based upon that temperature profile) and absorptions (as "deletion of radiation"), in other words, a radiation transport calculation in a fixed medium with fixed thermal properties, upward and downward, but doesn't do any energy balance. That's apparently the responsability of the user, to introduce a good T-profile. I thought before that MODTRAN re-calculated the temperature profile based upon a new energy balance, but apparently no.

    You can see this when, all else equal, you add a temperature offset. This is bluntly added to the temperature profile up to 10 km or so, and higher up, things are unchanged.

    So MODTRAN looks like a radiation transport code in a "frozen-in" atmosphere (worse, frozen-in with thermostats for each layer), where thermal emission and emissivity is taken into account and absorption is taken into account, but that's it.

    So, given what you said before, I don't think that the full Planck response (including the "temperature profile adaptation" of which it was explicitly argued that this is not an "added feedback" but inherent in the Planck response) is calculated by MODTRAN, if the user didn't take the responsibility to change the temperature profile. Maybe more evolved versions of MODTRAN can do this, I don't know.

    BTW, do you know what the "water vapor scale" parameter means ?

    EDIT: oops, you said "Planck radiation" and not "Planck response". Makes my point moot, because I argue exactly that.
    Last edited: Aug 28, 2009
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