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Greenhouse Gas Effect and Carbon Dioxide

  1. Jun 12, 2006 #1
    Greenhouse Gas Effect and Carbon Dioxide

    I have been having some difficulty with this, so perhaps someone could please sort out any mistakes, and let me know.

    Consider a vertical column of the Earth’s atmosphere based on a square of area 1 m^2.

    This air column has a mass of 1.01×10^4 Kg.m^-2.

    The mass of the neutron (& proton) is approximately 1.67×10^-27 Kg.
    So the mass of the nitrogen molecule is 4.68×10^-26 Kg.

    Therefore, the number of N2 molecules in the column is approximately 2.15×10^29.

    Now, carbon dioxide is currently present at the level of about 380 ppm by volume, and so the number of CO2 molecules in our 1 m^2 column is about 8×10^25.

    The absorption cross section of a molecule of CO2 for an infrared photon of 14 micrometres wavelength (the optimum) is about 5×10^-22 m^2.

    Therefore, the number of CO2 molecules required to ensure 100% probability of absorption of a photon emitted from anywhere within the 1 m^2 base area is 2×10^21 molecules.

    The energy of a 14 micron infrared photon is 1.34×10^-20 Joules, and so the 2×10^21 molecules providing the absorption cover can absorb 26.8 Joules.

    But, there are 8×10^25 molecules of CO2 in the column, and so the 100% cover can be provided
    8×10^25 / 2×10^21 times over, ie. 4×10^4 times. So the energy which can be dealt with by the CO2 is 26.8×4×10^4 Joules, in the base area of 1 m^2. ie about 10^6 Joules.

    Given a relaxation time of 10 microseconds for the CO2 molecule to decay from its excited state, it follows that the process just described can be repeated 10^5 times within 1 second. And so the possible power which the carbon dioxide could cope with for 100% absorption is 10^11 Watts per square metre.

    However, the limit is set by the Earth’s energy balance to about 235 W.m^-2.

    So the carbon dioxide is grossly oversubscribed by a factor of 4×10^8.

    This means that although the original GHG effect works very well, the idea of anthropogenic “enhanced” greenhouse effect is totally non-viable as far as carbon dioxide is concerned, because there has long been far, far more carbon dioxide in the atmosphere than required, and so another 30% ( or several orders ) extra will have absolutely no effect.

    Aubrey E Banner, Sale, Cheshire, UK
     
  2. jcsd
  3. Jun 12, 2006 #2
    Where can you get more information on the numbers you give for the saturation limit of 235 Watts per meter squared?

    I've long since had concerns over the popular hype of CO2 as the greenhouse gas to be concerned about. For one, CO2 is a real poor absorber and reemitter of radiation because it doesn't have a whole lot in the way of vibrational modes, as compared to CH4 or even H20. That and since it's already in existance in our atmosphere, increasing CO2 levels would seem to me to have a minor effect when compared to introducing a new molecule with different absorbtion bands to cover more of the infrared spectrum.

    An analogy I use with folks I know is that the Greenhouse effect is like a window in your house that lets in sun. Each molecular species is like covering that parts of that window with a strip of tape. The greater abundance of the molecule, the darker the tape. With this analogy, good Greenhouse Gasses (such as methane and water) are molecules that allow you to put many strips of tape up (a large number of energy states in that region) while poor GHG's (like carbon dioxide) only let you put a few strips of tape up. I don't care if you use electrical tape to cover the CO2 bands, you won't be blocking the radiation from coming in (or going out in the case of the Earth).

    But I'm curious where you developed your theory on the limiting energy of CO2 absorption in the Earth's atmosphere. I'll admit that I haven't done a lot of research in atmospheric sciences.

    Not that I'm denying that there might be an anthropogenic contribution to the Greenhouse effect, it's just I can't see how CO2 is the culprit.
     
  4. Jun 12, 2006 #3

    Gokul43201

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    Banner, your calculation is wrong in parts (eg: it doesn't take 1/A molecules to get a 100% probability of absorption, it in fact takes an infinite number of molecules) and is physically meaningless in others (ie: the quantities that you calulate are not physically relevant to the problem). For example, what does the energy of N photons actually represent?. It's not like these photons are permanently absorbed by the molecules - that's what a finite relaxation time tells you. Instead the CO2 molecule (just like all other molecules) is a Rayleigh (and Raman) scatterer with a larger scattering cross-section at IR wavelengths than N2 and O2. A photon emitted from the earth undergoes several scattering events - sort of like the random walk problem. The correct calculation is then a very complex energy balance relation.

    Fianlly, your conclusion that the present CO2 levels are way (by a factor of several million) over than necessary to saturate CO2 absorption is at odds with the rest of the scientific community. Even those that conclude that AGW is overestimated by the IPCC (see Cess and Myhre below) only believe that present CO2 levels are pretty close to saturation levels.

    Cess, R.D., and 29 others, 1993. Uncertainties in Carbon Dioxide Radiative Forcing in Atmospheric General Circulation Models. Science 262, 1252-1255

    Courtney, R.S. 11 Jan 1999. Private Communication (Email)

    Houghton, J.T., G.J. Jenkins, and J.J. Ephraums, (Ed) 1990 Climate Change :The IPCC Scientific Assessment Cambridge University Press

    Houghton, J.T., L.G. Meira Filho, J. Bruce, H. Lee, B.A. Callander, E. Haites, N. Harris and K. Maskell, 1994, Climate Change 1994. Cambridge University Press.

    Keihl, J.T. and R.E. Dickinson, 1987 Study of the Radiative Effects of Enhanced Atmospheric CO2 and CH4 on Early Earth Surface Temperatures. J. Geophys. Res.92 2991-2998

    Myhre, G., E.J. Highwood, K. Shine and F. Stordal, 1998. New estimates of radiative forcing due to well mixed greenhouse gases. Geophys Res Letters 25 (14) 2715-2718

    Wigley, T.M.L., 1987, Relative Contributions of Different Trace Gases to the Greenhouse Effect. Climate Monitor 16 14-29.
     
  5. Jun 13, 2006 #4
    As the relationship between back radiation and concentration of greenhouse gas is logarthmic, technically there is no saturation point as a rise of CO2 from 10% to 20% in the atmosphere still should have the same effect as a rise from 0,00028 to 0,00056 parts per volume, which is what we are talking about.

    There is little discussion here and with a pure primary physical model MODTRAN you can do several runs with doubling CH4 or CO2 and see that the output has a near constant difference with the half values.

    I did that here:

    http://home.wanadoo.nl/bijkerk/modtranrun.GIF

    to show that CH4 is not nearly as strong as CO2, when looking at comparable concentrations

    and on a logarithmic scale:

    http://home.wanadoo.nl/bijkerk/modtranrun2.gif

    Y-axis scale is the relative difference with no greenhouse gas in the atmosphere. So no absolute saturation but when values seem rather impossible to get like >0,001 practically you could speak of a saturation point but with a different definition.

    So if this little physical exercise is just as solid as the boiling point of water for instance, futile too discus, what then is the Casus Belli?

    The question is what doubling CO2 does to the global temperature. Using plain physics on a black body with albedo effect (several older threads here) the Stefan Boltzmann law will bring you to about 0,7 degrees per doubling CO2 as instantaneous effect, however if we add that temperature to the basic temperature the new temperature is around 0,9 degrees and so on, the limit of that effect would be about 1,2 degrees but it takes centuries for this effect to balance and we are still talking about Earth as a black body.

    So from the simple basic physics there is not much to get excited about, it's what happens if you turn black body earth into a planet with an atmosphere, water oceans land and a history. There is simply not enough modelling power to understand the thermodynamics of that system and here separates the scientific opinion. The majority, presently in charge for governing the climate, believes that this system puts a positive feedback to that doubling (actually gain, feedback is something different). This has been based previously on a certain hockeystick, and it's now mainly based on highly simplified assumptions about palaeo-climatic observations in the ice cores et al. A minority of these 'warmers' (Hansen Overpeck cs) believe that the observed strong isotope excursions of the ice age and the Palaeocene Eocene Thermal Maximum 55 million years ago, can be projected on present climate and whenever a tipping point is reached, the positive feedback goes out of control and the temperature skyrockets. Obviously this tipping point is near.

    But this vision has no consensus as it is believed that the climate has two balance points, cold and warm, we appear to have tipped over to warm after the ice age and another double tipping over has not been proven in palaeo-climate.

    Opposing the government is the underground resistance, the partisans, headed by Dick Lindzen cs. Many of them are meteorologists who simply do not see it happen. They believe that negative gain or feedback factors will limit the double CO2 temperature to below one degree Celsius (Lindzen: 0,5 due to his iris hypothesis) and they have good reasons for that assumption. Not a lot of them are palaeo-climatologists though so if the indications of the past suggest strange illogical things with climate, better recheck those indications.

    Now in a theoretical ideal world, we would jointly investigate the true nature of the palaeo-climate phenomena as it is clear to many that a lot of that evidence is enigmatic and is not concurring with the present paradigms. That’s what I try to do. But the real world is a bit harsher. This is not really an encouragement to do some objective investigations.
     
  6. Jun 19, 2006 #5
    Greenhouse Gas Effect and Carbon Dioxide

    This is a revised version of my previous post #1.

    When in energy balance, the Earth radiates from the top of the atmosphere at 235 Watts per square meter (1).

    Radiation from the greenhouse gases goes in all directions, and so, effectively, half is radiated out into space, and half is returned to the Earth’s surface and so helps to increase the surface temperature up to a value for which the radiated emission is twice that from the ToA to outer space. ie. the Earth’s surface radiates at 470 W.m^ -2.

    Carbon dioxide has an absorption peak at almost 14 micrometres, but very little at longer wavelengths. The energy of a 14 micron infrared photon is 1.34×10^ -20 Joules. Therefore, the emission from the surface is about 3.5×10^22 photons/second per square metre.

    Given a relaxation time of 10 microseconds for the CO2 molecule to decay from its excited state, then a 1 second time interval can be considered as 10^5 periods of 10 microseconds each.

    Assuming an even distribution of emission across the area of 1m^2, and a uniform time rate of emission, then the number of photons emitted in each 10 microsecond period is 3.5×10^17 photons in 1m^2.

    In order to ensure 100% absorption of these photons, the 1m^2 area must be “covered” by sufficient molecules of CO2. Now, the absorption cross section of a CO2 molecule for a 14 micron photon is about 5×10^ -22 m^2 per molecule, and so the number of molecules required to cover the area is 1.0 / 5×10^ -22, ie. 2×10^21 molecules per square metre.


    Now consider a vertical column of the Earth’s atmosphere based on a square of area 1 m^2.

    This air column has a mass of 1.01×10^4 Kg.m^ -2.

    The mass of the neutron (& proton) is approximately 1.67×10^ -27 Kg.
    So the mass of the nitrogen molecule is 4.68×10^ -26 Kg.

    Therefore, the number of N2 molecules in the column is approximately 2.15×10^29.

    Now, carbon dioxide is currently present at the level of about 380 ppm by volume, and so the number of CO2 molecules in our 1 m^2 column is about 8×10^25.

    Therefore, the 100% cover can be provided 8×10^25 / 2×10^21 times over, ie. 4×10^4 times. .

    So the carbon dioxide is grossly oversubscribed.

    This means that although the natural GHG effect works very well, the idea of anthropogenic “enhanced” greenhouse effect is totally non-viable as far as carbon dioxide is concerned, because there has long been far, far more carbon dioxide in the atmosphere than required, and so another 30% ( or several orders ) extra will have absolutely no effect.



    Reference
    (1) Kiehl and Trenberth, 1997
    http://stephenschneider.stanford.edu/Climate/Climate_Science/EarthsEnergyBalance

    Aubrey E Banner, Sale, Cheshire, UK
     
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