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The IR absorptive characteristics of “greenhouse” gases– Addendum -David Coe

January 22, 2021
tags:

By Paul Homewood

 

 

David Coe, who presented his paper on the IR absorptive characteristics of “greenhouse” gases last week, has now written an Addendum, addressing some of the issues raised:

 

 

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The full addendum, including tables, can be found here:

 

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60 Comments
  1. January 22, 2021 12:21 pm

    The last sentence is the money one: “These results are totally at odds with the IPCC version of climate sensitivity ranging between 1.5 and 5degC and suggest quite clearly that CO2 is not, repeat not, a significant driver of global warming and climate change.”

    Imagine that…..wonder if Michael Mann will sue him also?

  2. Robert Christopher permalink
    January 22, 2021 12:45 pm

    What’s this!!!

    A dialogue???

    More important than any accumulated Scientific knowledge is that dialogue continues, constructively, so that a better understanding of the Science can be accomplished.

    Thank you, to all concerned, in resurrecting this ancient activity.

  3. TL Winslow permalink
    January 22, 2021 12:53 pm

    Why do you keep publishing Coe’s clueless analysis? Photons aren’t all equal. They have energy and thus a limit to the temperature they can raise a molecule to. If he can’t understand that CO2’s radiation absorption/emission wavelength of 15 microns is totally outside Earth’s surface temperature range of -50C to 50C and thus can’t have any effect on climate, making the climate sensitivity zero, he’s stuck at stupid. A hoax is a hoax. Coe should get out of bed with the hoaxers.

    https://www.quora.com/Does-one-body-at-lower-temperature-than-the-surroundings-still-emit-thermal-energy-through-radiation/answer/TL-Winslow

    https://www.quora.com/Where-is-the-earths-evaporator-responsible-for-glaciers-and-cold-conditions-suppose-the-ventilating-atmosphere-was-modelled-for-a-refrigeration-system-comprising-compressor-evaporator-condenser-and-refrigerant/answer/TL-Winslow

    • David Coe permalink
      January 22, 2021 1:17 pm

      Thank you Mr Winslow for your considered opinion.

    • Harry Davidson permalink
      January 22, 2021 3:05 pm

      Just a point. Any post that includes sneers can be safely discarded. As the reader you may not see the weakness of the poster argument, but they see it and they are anxious to disguise it with ad hominem attacks to draw attention away from it.

    • Ed Bo permalink
      January 22, 2021 5:35 pm

      TL – Why do you continue to spout this nonsense? Wien’s Displacement Law does NOT mean what you think it means. Not remotely!

      Electromagnetic radiation of a given wavelength does not ‘have a temperature”. It carries with it NO information about the temperature of the object emitting it. Your body at 37C emits lots of EMR in the 15-um range, and it is no different from the EMR in this range emitted downward from the cool range of the upper atmosphere.

      If that radiation is absorbed, the energy of the absorbing body in increased by the amount of energy in the radiation (simple 1st Law). Most solid and liquid substances absorb over 95% of radiation in the 15-um range. So they end up with higher energy levels than if there was none of this radiation.

      This is basic, basic stuff, but you continue to get it completely wrong!

      • A C Osborn permalink
        January 23, 2021 10:19 am

        Ed, you always quote CO2 Lasers as showing that CO2 radiation at 15 microns makes things very hot, but we both know that you are replacing energy with quantity of excited CO2 photons, you have to put a lot of extra energy in to those photons to get the work out of them.
        What happens if you direct a flow of ordinary CO2 gas photons at an object, what temperature increase occurs?
        Is it even measurable?

        But lets talk about the energy that an upper Tropospheric CO2 Molecule’s photon actually contains.
        Exactly how much is that energy contained in a CO2 photon from a CO2 molecule at -50C to -80C that can be absorbed by a body at 20C should it ever be able to reach the Earth’s surface.

        Last but least please explain why the 300+ Watts/m of backradition cannot do any kind of work. whereas 300 watts of sunlight can.

        I find it very unlikely that any photons can reach the surface from 10Km above the surface through an ever thickening atmosphere.
        Every interaction with another molecule means that half of the resultant photons will be outbound.

      • Ed Bo permalink
        January 23, 2021 11:27 pm

        A C: I keep citing the example of the LWIR laser because it is an ABSOLUTE refutation of the argument put forward by TL and his ilk that these LWIR photons cannot add energy to higher-temperature objects.

        The photons emitted by the laser are EXACTLY the same as those of the same wavelength emitted by normal thermal processes, with EXACTLY the same energy each – there are just more of them. Of course, a lower density of these photons will not add as much energy to the absorbing body as a higher density.

        But it is a VERY basic concept in radiative physics that when an object absorbs a photon, its energy increases by the energy carried by the photon. Conservation of energy works even down to this level. You seem completely unaware of this fundamental tenet of radiation physics.

        You ask: “What happens if you direct a flow of ordinary CO2 gas photons at an object, what temperature increase occurs?
        Is it even measurable?”

        Yes, it’s easily measurable in the laboratory, and has been done so thousands of times. There are any number of IR sensors that detect this radiation thermally, including FLIR (Forward Looking Infrared) imaging cameras, pyrgeometers, and sophisticated spectro-radiometers (which can isolate particular wavelengths, including the 14-16um from CO2). The more LWIR they receive, the hotter the sensor (which typically increases the electrical resistance of the sensor), even if the sensor is colder than the “reference” sensor.

        You ask: “Exactly how much is that energy contained in a CO2 photon from a CO2 molecule at -50C to -80C that can be absorbed by a body at 20C should it ever be able to reach the Earth’s surface.”

        The energy “e” contained in a photon is given by the very simple equation:

        e = hc/λ

        where h is Planck’s constant, c is the speed of light, and λ is the wavelength. This is true regardless of the mechanism producing the photon. Downthread a little, commenter itdoesntaddup calculates e with this equation for a 15um photon as 1.32×10^-20J. A body (of whatever temperature) that absorbs this photon increases its energy by this exact amount.

        You ask: “why the 300+ Watts/m of backradition cannot do any kind of work. whereas 300 watts of sunlight can?”

        We are not talking about “work” here. Thermodynamic work as a very particular definition, and nothing in the examples we are discussing involves thermodynamic work. You need to familiarize yourself with the most basic definitions in thermodynamics.

        You say: “I find it very unlikely that any photons can reach the surface from 10Km above the surface through an ever thickening atmosphere. Every interaction with another molecule means that half of the resultant photons will be outbound.”

        You misunderstand the overall process. You must consider the upward longwave radiation as well. Roy Spencer has a good conceptual diagram of the overall process. See the fourth figure in his blog post.

        http://www.drroyspencer.com/2010/07/yes-virginia-cooler-objects-can-make-warmer-objects-even-warmer-still/

        People have been patiently explaining these basic concepts to you for years, but you won’t (or can’t) learn.

    • Mad Mike permalink
      January 22, 2021 5:54 pm

      Regardless of the arguments, your comments do not belong here. Calling anyone stupid is for the playground. Either resolve to amend your dialogue or please leave the site.

    • It doesn't add up... permalink
      January 22, 2021 8:20 pm

      The energy of a 15 micron photon (which corresponds to a bending vibration of the CO2 molecule like opening and closing scissors, or a punchball on a stand after being struck – it can punch back!) is hc/λ where h is 6.6×10^-34Js, c is 3×10^8m/s and λ is 15×10^-6m, which works out as 1.32×10^-20 J. The translational kinetic energy of a gas molecule from kinetic theory is of the order of 3kT/2, where k is the Boltzman constant, 1.380649×10−23 J⋅K^−1 and T varies between about 220 and 320K depending on weather and height in the atmosphere: the distribution of energies follows the Maxwell-Bolztman distribution. The energies involved in kinetic motion that gives rise to temperature are therefore about 4.5-6.6×10^-21 J per molecule. The photon is more energetic by a factor of 2-3: it depends how the energy gets distributed across vibrational modes and kinetic motion. Collisions with other molecules can help transfer energy from vibrations to kinetic motions, just as a boxer can knock an opponent across the floor. They may also increase vibrational energy at the expense of kinetic energy (think of a head on collision), and in turn lead to photon emission from a vibrational mode.

      Your limit, given enough of a flux of 15 micron photons, is thus about 640K. Of course, the actual flux of 15 micron photons is far too small to achieve that. And the molecules will lose energy to radiation. At the other end of the spectrum, since the C=O bond has an energy of 799kJ/mol, or about 1.3×10^-18 J, energetic photons of shorter wavelength than about 150nm can break up CO2 molecules.

    • Ray Sanders permalink
      January 22, 2021 8:40 pm

      Gosh a response from “The World’s Greatest Genius”.
      http://tlwinslow.weebly.com/
      Dunning Kruger at its finest.

  4. Broadlands permalink
    January 22, 2021 1:47 pm

    Coe: “We can also note that climate sensitivity remains below 0.65degC under all conditions up to 1000ppm CO2 and for H2O above 0.5% concentration.”

    The geological and geochemical record has recorded conditions above 1000 ppm CO2 with life thriving at the time. A lower pH in the oceans but no damage to the carbonate plankton…

    Nature 461, 1110-1113 (22 October 2009) Atmospheric carbon dioxide through the Eocene–Oligocene climate transition
    Paul N. Pearson, Gavin L. Foster, Bridget S. Wade:

    “Geological and geochemical evidence indicates that the Antarctic ice sheet formed during the Eocene–Oligocene transition 33.5–34.0 million years ago. Modelling studies suggest that such ice-sheet formation might have been triggered when atmospheric carbon dioxide levels fell below a critical threshold of ~750 p.p.m.v. During maximum ice-sheet growth, pCO2 was between 450 and 1,500 p.p.m.v., with a central estimate of 760 p.p.m.v.”

  5. David Coe permalink
    January 22, 2021 1:58 pm

    I would suggest that ice sheet growth has absolutely nothing to do with CO2 levels. Higher CO2 levels will simply support more biological activity.

    • Broadlands permalink
      January 22, 2021 3:01 pm

      David… Perhaps you missed the point? Those higher levels of CO2 in the distant past did not raise the global mean temperature as would be predicted by current models. CO2 is not a significant driver of global warming and climate change?

      More biological activity is limited by the oxygen that it creates. The CO2 is recycled by aerobic respiration unless the carbon is buried.

      • David Coe permalink
        January 22, 2021 3:15 pm

        Yes. Sorry, now I see your point.

  6. jack broughton permalink
    January 22, 2021 3:25 pm

    This, and the previous contribution by David Coe are of fundamental importance to anyone looking at atmospheric science, which is regularly stated to be “settled”. The biggest scientific weak-point in the IPCC Technical Assessments was always the estimate of radiant forcing. They made all sorts of assumptions about the gases and dusts in the atmosphere then decided which values to use with no firm scientific basis – the Delphi method was used.

    I have one request to ask of David and that relates to commenting on the radiative interactions between CO2 and H2O molecules. In boilers and furnaces we calculate the emissivity of this mixture in flames and hot gases using fairly old-fashioned approaches (digitised graphs actually). The emissivity of a mixture of these two gases does not follow the simple combined transmittivity rule: e12 = (1-T1 x T2) = (e1+e2)-e1xe2 the reduction is much larger than e1xe2. This effect reduces the climate sensitivity depending on the partial pressures of the two gases. This interaction problem is also an issue in CO2, IRGA analysers and the Keeling method requires all the H2O to be removed before analysis, which has always made me suspect the CO2 history derived from ice samples.

    • DMA permalink
      January 22, 2021 10:15 pm

      “The biggest scientific weak-point in the IPCC Technical Assessments was always the estimate of radiant forcing.”
      That may be the biggest but the assumption that human emissions control atmospheric content and thus are the cause of all the rise from 280 PPM to 400 PPM is at the base of the whole house of cards. It won’t hold up anything that relies on it. See Climate Miracle by Dr. Ed Berry.

  7. January 22, 2021 3:36 pm

    The analysis by David Coe is a welcome addition, in that it takes the IPCC radiation paradigm at face value and shows that on that assumption, claims of a climate emergency are unfounded. As he says, he did not in this essay question numerous assumptions required to do the study.

    That being said, others do challenged the radiative absorption math as it relates to planetary surface temperatures. It is a separate issue, further undermining the “settled science” of CAGW. An introduction is provided by Dr. Peter Ward, my synopsis being:

    https://rclutz.wordpress.com/2020/01/11/light-bulbs-disprove-global-warming/

    “Detailed laboratory studies of absorption of radiation show that carbon dioxide absorbs less than 16 percent of all the frequencies making up the heat radiated by Earth. Just like LEDs, this limited number of frequencies absorbed by carbon dioxide does not constitute heat. This limited number of frequencies cannot cause an absorbing body of matter to get much hotter because it contains only a very small part of the heat required to do so.

    Current radiation theory and current climate models assume that all radiation is created equal—that all radiation is the same no matter the temperature of the radiating body. Current theory simply assumes that what changes is the amount of such generic radiation measured in watts per square meter.

    Extensive observations of radiation emitted by matter at different temperatures, however, show us clearly that the physical properties of radiation, the frequencies and amplitudes of oscillation making up radiation, increase in value rapidly with increasing temperature of the radiating body.

    Climate scientists argue that the thermal energy absorbed by greenhouse gases is re-radiated, causing warming of air, slowing cooling of Earth and even directly warming Earth.

    There simply is not enough heat involved in any of these proposed processes to have any significant effect on global warming. Greenhouse-warming theory “just ain’t so.”

    • January 22, 2021 3:38 pm

      • David Coe permalink
        January 22, 2021 4:17 pm

        Ron

        I have simply calculated the radiation energy emitted by the earth as a consequence of its temperature using the well known Planck equation and using spectral data from Hitran calculated the amount of that energy that is absorbed by the atmosphere. Some of this absorbed radiation will be retained by the atmosphere/earth system. It is a simple matter then to calculate the impact on the earth temperature for varying fractions of this retained energy from 0 to 1, thus covering all possible conditions relating to global warming.

      • A C Osborn permalink
        January 23, 2021 9:52 am

        David, your statement “Some of this absorbed radiation will be retained by the atmosphere/earth system.”

        Is not correct because a very important word is missing, the word is “temporarily”.
        The time of retention is measured from nanoseconds to seconds, which is why on a clear night all the heat gained during the day is radiated away.
        In fact it can radiate away more heat than received the previous day.
        Only Cloud cover allows any actual retention overnight.
        But cloud cover drastically reduces the radiation received during the day and that energy is far more “energetic” than LWIR.

  8. Vernon E permalink
    January 22, 2021 3:58 pm

    Way above my head. What’s the answer?

  9. David Coe permalink
    January 22, 2021 4:08 pm

    For a given wavelength of radiation the combined transmission through a combination of gases is given by the product of their respective transmissivities at that particular wavelength.
    T = t1xt2xtn
    This follows from the Lambert Beer law. When you try to expand this over a broad spectrum the relationship breaks down. You have to calculate the product at each small wavelength increment and integrate the result over the total waveband. This is what has been done to compute the absorptivities of H2O and CO2 for this paper. Calculations have been done over the wavenumber range of 100 to 3333cm-1(3 to 100micron wavelength) at intervals of 0.1cm-1, some 30,000+ points. Will Happer’s recent paper did 0.01cm-1 increments and 300,000 points. I don’t believe however there is any significant benefit in doing such high resolution work. In any case my excell spreadsheet would have exploded!
    Doing this with flames and hot gases is indeed a problem. The point is that the CO2 and H2O molecules do not interact. They simply compete to absorb the same radiation where their absorption spectra overlap. Once that radiation has all been absorbed, more gas does not have any further impact.

    When using IR spectroscopy to measure the concentration of gases, H2O is a real pain because its complex spectrum overlaps to some extent with the spectra of other gases causing cross sensitivity between H2O and the target gas. The safe solution is to remove the water vapour.

    • Broadlands permalink
      January 22, 2021 4:47 pm

      “The point is that the CO2 and H2O molecules do not interact.”

      They do when visible solar energy is applied. The net result is CH20 plus O2. Photosynthesis. They cannot create organic carbon if the O2 is not allowed to reach and convert to O3 in the stratosphere. That UV protection is what makes this planet habitable and others problematic.

    • jack broughton permalink
      January 22, 2021 9:11 pm

      Many thanks for the detailed reply, David. Your method is far more accurate than the simplified one that I use and I can see that the interaction between CO2 and H2O is properly covered in that. I may try to use Hitran in future as it seems reasonable friendly.

      The fact remains that the simplified methods used by IPCC assume an overall absorption coefficient for CO2 independent of water being present at differing partial pressures through the atmosphere, which substantially overestimates the effect of CO2.

      Apart from the spectral analysis there is another possible explanation for the problems of CO2 / H2O interaction and that is the formation of carbonic acid in the gaseous phase. It is well established in the liquid phase, but is apparently very difficult to detect in the gaseous state, having only been found recently, and is not a permanent gas. I have wondered if this may be the cause of the strange gaps in the spectra.

    • A C Osborn permalink
      January 23, 2021 1:44 pm

      The Climate scientists like to Average everything, take moisture in the Atmosphere.
      They average how much is present, but you can’t use that average to model the affects of clouds.
      Clouds are almost 100% water.

      • tom0mason permalink
        January 23, 2021 9:14 pm

        Exactly A C Osborn,
        and as it is said that climate is the long term average of the weather. However the basic climate model of solar effect does an averaging that removes the equator to poles temperature differential that sets-up the moisture (and precipitation) features in the atmosphere as well as the pressure gradients and cellular atmospheric features that occur all across the Earth.
        Instead of looking at reality (the sun controls our weather and climate) the numbnut climate maniacs average all the sunlight across a flat circle. A flat circle that apparently represents the whole Earth’s area. Then they argue that this represents average solar effect across the whole area of the globe — that it may do. However this nonsense method of averaging single handedly wipes out the weather promoting equator to poles temperature differential, and all the ensuing climate change effects. To restore the weather and climate they then invent the supposition of CO2 back-radiation, a fiction said by these fools, to give us back climate change. It is utter piffle.

      • Ed Bo permalink
        January 23, 2021 11:41 pm

        Tom: You say: “the numbnut climate maniacs average all the sunlight across a flat circle.“

        They absolutely DO NOT! You mistake a very simplified conceptual diagram for the calculations actually done.

        When you read that a given climate splits the globe into 1-degree by 1-degree cells with a 15-minute update period, then for each cell for each period, they start by calculating the solar flux density given the angle of the sun for that cell for that period. Of course, for half of the cells in any given period, the solar flux density is zero. (It’s called “night”.)

        I’ve seen the source code of a major climate model, and it does exactly this.

        The climate models have MANY problems, but when you make ridiculously false assertions like this, you just discredit skeptics.

      • tom0mason permalink
        January 24, 2021 7:25 am

        So Ed Bo,
        So you agree that the simplified concept upon which all the numbnut idiocy of climate seance relies is wrong. Well thank-you!
        Wrong in concept, wrong in methodology wrong in application, the climate model and the idea that atmospheric CO2 powering the weather and climate is just wrong.
        Rip it up and try again, it is wrong, VERY wrong from the very roots.

        You Ed Bo, not I, do discredit skeptics cause by kowtowing to this gross stupidity where so call science is built on FAULTY foundations.

      • Ed Bo permalink
        January 24, 2021 4:41 pm

        No Tom, I am not so obtuse as to believe that the mere existence of a simplified diagram of a scientific topic automatically becomes the foundation for that topic.

        It is very common to see the explanation for the workings of an incandescent light bulb as follows (using North American values):

        The bulb has a 240-ohm resistance and is supplied with 120 volts. So the power dissipated is:

        P = V^2 / R = 120 * 120 / 240 = 60 watts

        But that calculation uses constant input! In reality, the input is varying between +170 and -170 volts 60 times per second. So:

        V(t) = 120 * sqrt(2) * sin (2*Pi*60t)

        and P(t) = V(t) * V(t) / R

        which gets you closer. But R is a function of temperature, so also varies with time.

        But do I think the common use of the simplified constant-power explanation is the “foundation” for light bulb science, invalidating all further analysis? Of course not! That would be absurd! And so is your argument.

        There exist simplified explanations for virtually every complicated technical subject. By your logic, all the further analysis for all of these topics would be invalidated.

  10. January 22, 2021 6:26 pm

    What about ‘climate sensitivity’ to the sun? Discarded by alarmists as it casts doubt on their unproven theories.

    • Phoenix44 permalink
      January 23, 2021 9:51 am

      I think the point about climate is that it is essentially hugely insensitive to anything because it is such a large, complex, non-linear system full of ways to avoid sensitivity. We think its “sensitive” based on our definition of sensitive but the Earth doesn’t care about us and laughs at what we think “sensitivity” is.

      Humans will have come and gone in the time in takes the Earth to blink. It won’t even have been aware we were here.

  11. Cheshire Red permalink
    January 22, 2021 7:00 pm

    The very fact that conclusions like this are being reported confirms the science isn’t settled!

    • jack broughton permalink
      January 22, 2021 9:17 pm

      The science is “settled” in the same way that religions have “settled” their beliefs: terrorise and brainwash into submission.

  12. It doesn't add up... permalink
    January 22, 2021 8:28 pm

    Clive Best has a couple of highly relevant posts related to this topic. The first from 2010:

    http://clivebest.com/blog/?p=1169

    where he discusses the effects of doubling CO2 levels, and the second from 2013:

    Abstract

    This post describes a new approach to calculating the CO2 greenhouse effect. Instead of calculating radiative transfer from the surface up through the atmosphere to space, exactly the opposite is done. IR photons originating from space are tracked downwards to Earth in order to derive for each wavelength the height at which more than half of them get absorbed within a 100 meter path length. This identifies the height where the atmosphere becomes opaque at a given wavelength. This also coincides with the “effective emission height” for photons to escape from the atmosphere to space. A program has been written using a standard atmospheric model to perform a line by line calculation for CO2 with data from the HITRAN spectroscopy database. The result for CO2 is surprising as it shows that OLR from the central peak of the 15 micron band originates from high in the stratosphere. It is mostly the lines at the edges of the band that lie in the troposphere. The calculation can then show how changes in CO2 concentrations affect the emission height and thereby reduce net outgoing radiation(OLR). The net reduction in OLR is found to be in agreement with far more complex radiative transfer models. This demonstrates how the greenhouse effect on Earth is determined by greenhouse gases in the upper atmosphere and not at the surface.

    http://clivebest.com/blog/?p=4597

  13. David Coe permalink
    January 23, 2021 9:21 am

    This and some other posts shows how the arguments can get bogged down in complexities. I don’t disagree with what you say. I actually don’t know. The point is that no-one has a proper grasp of atmospheric thermodynamics. It is after all a chaotic system. The bid issues are, firstly, what will be the temperature response to increasing CO2 values. Governments throughout the western world are after all embarking on the biggest experiment ever, based on nothing more than a cult theory. The second big issue is that whatever theories are put forward it is important to be able to show how current earth temperatures can be explained.
    Unless they can do that with actual numbers, not hand waving, they are actually useless.

    • Phoenix44 permalink
      January 23, 2021 9:53 am

      Exactly. My scepticism begins and ends with a belief that we have so little understanding of climate that making any kind of decision based on existing knowledge is foolhardy.

    • Broadlands permalink
      January 23, 2021 1:10 pm

      Climatologist Dr. Reid Bryson in 1980 about his own models…

      “There are many areas of uncertainty remaining in the Bryson-Dittberner model. These include means to improve the parameterization of the effects of external factors such as solar variation, anthropogenic factors and volcanic influences, inclusion of more feedback mechanisms such as between albedo and temperature, latent heat and cloudiness, and cross-equatorial heat transport, etc. It is our hope that further consideration of these problems will lead to improvements in realistic, physically-based climate models. We cannot have much confidence in modeled future climates unless the model realistically simulates the past.”

  14. Old Grumpy permalink
    January 23, 2021 10:13 am

    Some of the incoming radiation is converted to chemical energy by photosynthesis.
    How is this accounted for?

  15. It doesn't add up... permalink
    January 23, 2021 3:01 pm

    I followed through on the comment I made on the previous article to look at the geometry of emissions and absorptions.

    Consider a point P on a spherical shell of atmosphere, a height H above the surface or H+R from the Earth centre, O. By symmetry, we can consider a disc through the poles. Draw a tangent plane to the spherical shell passing from A through P. Draw a tangent to the Earth passing through P and meeting the Earth surface at S: this defines the horizon visible from P (ignoring refraction effects etc.) PS is sqrt((R+H)^2+R^2) by Pythagoras. The angle APS equals the angle POS and is acos(R/(R+H)).

    Draw a chord of the shell through P intermediate between AP and PS and its bisector OB meeting the chord at B, and consider this as a ray along which a photon is emitted. Consider a point Q on the chord between B and P, and define x as the distance BQ. The first aim is to ascertain the local atmospheric density at the point Q, which we assume is determined by h, its height above the surface (more sophisticated treatment would vary this by latitude, and you can go even more sophisticated – see for example OCO satellite maps of atmospheric CO2 concentration that are very non-uniform). OQ=R+h. Call the angle APB that the chord makes with the tangent AP =θ, which is also the angle POB. Then we have that OB=(R+H)cos(θ). By Pythagoras we have

    h(x,θ)=sqrt( x^2+(R+H)^2(cos(θ))^2) – R

    By symmetry, the other half of the chord projected has similar conditions. If we assume an exponential atmosphere, with density ρ(h) = P0 exp(-λh) where λ is the rate of decline (equal to ln(2)/(height at which density halves) and P0 is density at the surface, we can deduce the local density of the atmosphere at distance x along the semi-chord BP. x varies between 0 at B and (R+H)sin(θ) at P, so we need to integrate the density along the chord BP between those values and multiply by 2 (except for the horizon chord)

    2 x Integral from 0 to (R+H) sin(θ) of ρ(h(x,θ)) dx

    to find the relative density of the path along the chord, and thence the chance of absorption inside the shell (recognising that rays that intercept the earth’s surface will be absorbed also, while rays that go above the tangent plane are spaceward). Whilst the integral doesn’t admit of a simple analytical solution, it is easy to estimate numerically in a spreadsheet, and explore the effects at different heights H of the shell, and different ray angles. It soon becomes evident that only the lower atmosphere offers much absorption, and that only rays close to the horizon ray are heavily attenuated at heights above 25km.

    • David Coe permalink
      January 23, 2021 4:53 pm

      Why all the complexity and confusion. This is always the problem when discussing climate change. Keep it simple. The only question to ask, since we know exactly how H2O and CO2 absorb IR, is how much of the absorbed radiation is retained by the earth/atmosphere. It is this alone which governs temperature, apart from, that is, any variance in the sun’s irradiance. That question is in fact also answered because that retention is responsible for the current global temperature. This gives us a calibration point which suggests that the retention is approximately 50%. From that we can calculate that climate sensitivity is in the range 0.2 to 0.5degC. CO2 is not the cause of climate change, if indeed there is such a thing.

      • It doesn't add up... permalink
        January 24, 2021 1:06 am

        Why complicate things? Because they are a little more complicated than the simplest models allow. I have now concluded that in terms of the overall radiation balance, I was going off at a tangent (!) because it’s reasonable to look at the effective emission surfaces as being Lambertian – that is to say you can ignore the detail of what happens at lower heights.

        But be encouraged: your original paper engaged me in a way that had me starting to think about your result, and had me stirring up the deep recesses of my memory on spectroscopy and quantum chemistry. So I started to search for more work in similar vein. I came across a PhD on the calculation of the locations and intensities of CO2 absorption lines based on a complex Hamiltonian approximation and integrations of Schrödinger equations that was actually used to enhance the HITRAN data at the level of different isotopic species, so not just 16O=12C=16O, but exotics with different isotopes of C and O. I also found Clive Best’s work, and I’ve read the Wijngaarden/Happer paper too, which is slightly more sophisticated in considering how concentrations of GHGs vary with altitude (although CO2 appears to be well mixed at all levels, water clearly is not, and nor are other gases they consider).

        In trying to consider why you conclude that CO2 doubling would only result in 0.65K increase, whereas Wijngaarden/Happer estimate 1.4K (and 2.2K including water) at the surface, I suspect the answer is because you are assuming an isotropic atmosphere, rather than one where the conditions vary with altitude (and latitude). The quid pro quo is that the higher atmosphere becomes cooler. Your answers are probably very similar if you average out the energy of the variable atmosphere. Wijngaarden/Happer effectively acknowledge that their model is far from complete – it really only applies to cloudless conditions. And of course clouds are where climate modelling goes completely astray.

  16. Vernon E permalink
    January 23, 2021 3:18 pm

    This is all too complicated and inconclusive. Shouldn’t the approach be to achieve a consensus of understanding of past climate conditions first. After all, isn’t the scientific method to observe, explain and predict?

  17. John D Warren permalink
    January 23, 2021 4:03 pm

    Please excuse my ignorance: what are the physical characteristics of CO2 that makes this molecule such a dastardly device for increasing global heat?

    • Peter permalink
      January 23, 2021 4:48 pm

      It has a dipole moment. Think of the H2O molecule with the central negatively charged oxygen and two positively charged hydrogens sticking out at angles. As the molecule vibrates, for example in a bending motion, then the charges move with respect to each other. If you imagine the charges as fields or flux then they will interact with each other. It is this charge interaction that enables the molecule to absorb IR at a charcteristic wavelength.

      The CO2 molecule does much the same especially in bending mode when the charges move out of line with respect to each other. However, it is a linear molecule with the charges usually in line, so symetrical oscillations like a spring cancel out any dipole. Molecules have a number of possible vibrational modes.

    • David Coe permalink
      January 23, 2021 5:01 pm

      That’s the point. CO2 is not a dastardly device. Please see the paper “Miracle Molecule” from a week ago. CO2 is a very strong absorber of IR energy at certain wavelengths. Once all the energy at those wavelengths has been absorbed, adding more CO2 has very little further impact. CO2 on its own is incapable of warming the earth by more than 10deg over the zero atmosphere temperature of 255K or -18degC.

  18. tom0mason permalink
    January 24, 2021 8:57 am

    This song spells out that heat flows from hot to cold and not as the climate mystics have it from cold to hot.

    • tom0mason permalink
      January 24, 2021 10:19 am

      NASA spells it out
      https://www.grc.nasa.gov/WWW/K-12/airplane/thermo2.html

    • David Coe permalink
      January 24, 2021 11:59 am

      Don’t want to burst your bubble but the only significant variation of CO2 with latitude is caused by biospheric absorption. Plants sucking in CO2 for photosynthesis. This is particularly significant in the northern hemisphere, where of course the majority of land mass is located. This causes the annual cyclic variation in CO2 levels seen in the Mona Loa record. It has absolutely nothing to do with temperature.

      • tom0mason permalink
        January 24, 2021 2:50 pm

        David Coe,
        I have no bubbles to burst! My point is that unlike the UN-IPCC blessed models (where CO2 is “well mixed” ), NASA shows this too, like so many of their (the IPCC’s) untruths, is not what reality shows. And like so much in the climate it is a variable, dynamic parameter.
        You may (oe not) be interested in this take on CO2 distribution and its thermal interactions https://setpublisher.com/wp-content/uploads/2021/01/JBASV16A13-Lightfoot.pdf . As far as I can tell it is self published idea.

        If you look at the global temperature rise over the last 150 years or so then it is very apparent that it is well within normal NATURAL range of change. As the planet warms up it NATURALLY vents CO2 from the soils, rocks, and oceans. There is nothing alarming about this — the planet has been here many times before and had atmospheric CO2 levels much higher than currently seen. The planet did NOT overheat then, it will not overheat now.

        Personally I hope CO2 levels rise at their current rate (or faster) until we are at 0.08% (800ppmv) or even 0.1% (1000ppmv) so that people will finally see that CO2 levels have a negligible affect on the climate; it just gives life an easier time converting CO2 and water to more complex chemicals while using the available energy from the sun. Unlike the gas CO2, this abundance of life will greatly affect the weather and so the climate.

        IMHO on climate matters there is NO authority, most of what is written is pure conjecture and hardly worth a spit. If anyone believes they understand the climate, then let tell me precisely (within a 5 years) when will be, in the next 100 years, the wettest, driest, hottest, and coolest decades. Future generations can then have a laugh at this loser.

  19. cookers52 permalink
    January 24, 2021 11:45 am

    I have looked for an explanation of this for many years.

    My conclusion, nobody knows.

    • David Coe permalink
      January 24, 2021 4:24 pm

      Tom, I’m afraid Mr lightfoot doesn’t know what he is talking about.e.g.

      The Gas Law of Charles/Gay-Lussac states that at constant pressure the volume of a gas is proportional to the absolute temperature. Thus by applying this law, the CO2 concentration is always higher at the Poles than at the Equator. Thus, when moving from the Poles to the Equator, temperature goes up, CO2 goes down and water vapor goes up.

      Yes the density of the gases varies with temperature. The concentration remains the same, because all the gases are varying in density in the same way.

      However I don’t disagree with your thinking. It is my belief that CO2 concentration is controlled by the oceans which contain 100 times more CO2 than the atmosphere, most of it disolved in the deep ocean. This is Henry’s Law. And if it was not for the prodigious amounts of CO2 being removed by the biosphere for photosynthesis CO2 levels would be much higher than we see today. Fossil fuel CO2 emissions are simply helping the ocean to keep things in control. When we witness CO2 levels falling in the summer months it is because of photosynthesis. How do the atmosphere CO2 levels recover in the winter? It is not because of vegetation decaying as claimed by the IPCC, but because the oceans are continually striving to maintain equilibrium.

      Control of atmospheric CO2 levels is just another thing our climate science geniuses have got totally wrong. I had a series of papers on this subject posted a few years ago at Bishop Hill. Perhaps I should give them another airing if Paul agrees.

      • tom0mason permalink
        January 24, 2021 5:19 pm

        Thanks for the reply David, we seem to be of a similar mind about Mr. Lightfoot’s ideas, and also about atmospheric CO2 levels and the oceans’ ability to be a major regulator of it. Ocean dynamics are just one of many IPCC’s blind spots.
        Another that should show up is how as atmospheric CO2 levels rise the planet will green-up. Some researcher think they have a handle on this, though it appears this is mostly estimation and modeling — https://doi.org/10.1111/gcb.14950 .

  20. Geoff Sherrington permalink
    January 26, 2021 6:29 am

    My main comment relates to the physics of emission of radiation from a molecule of either water vapour or CO2 somewhere in the atmosphere. It is a common assumption that there is a 50/50% split between up and down welling, but the matter goes further.
    If the molecule is near the top of the atmosphere, the upwelling goes off to space and out of the equation. The downwelling does not reach the ground in this assumption and so it lacks a sink. That downwelling radiation can activate another molecule that has a similar fate. Summing it all overall, the upwelling radiation all goes to space, while the downwelling stays around for a bit, being reduced in intensity as fractions in a series of 0.5, 0.25, 0.125 etc … until there is no more because all of the original downwelling has been converted to upwelling and become lost to space. That series sums to unity. Any attempt at heating the atmosphere is short-lived.
    In the other extreme, we assume that the emitting molecule is close to the Earth’s surface. The downwelling radiation is close enough to give up energy and warm the surface (though with big reservations about what happens over water if it is long wavelength IR). The upwelling cannot reach top of atmosphere in this assumption, so it becomes downwelling by the same fractional series, with the result that all of it goes into heating the solid sink adjacent.
    It is only at some intermediate altitude that the fractional series can apply, in cases where some of the radiation heats the ground and some escapes to space and some heats the air. I have no solution to the question of what that intermediate altitude is. It has a dramatic effect on the “parameter n”, the fraction of outgoing radiation energy that is retained by the earth/atmosphere system and has a value between 0 and 1.

    • A C Osborn permalink
      January 26, 2021 9:51 am

      Geoff, don’t forget it is not only Radiation that is involved, that lower radiation warms the lower atmosphere, which immediately rises from convection.
      So that really upsets the equations.

  21. Jack Broughton permalink
    January 27, 2021 4:39 pm

    In simple terms, this posting demonstrates that the CO2 single parameter models are defective with respect to the radiant properties of CO2 /H2O mixtures, clouds and ocean /atmosphere exchange of CO2. How can any scientist seriously believe that climate models are other than first approximations with very little forward projection capability???

  22. MikeHig permalink
    January 27, 2021 6:16 pm

    David Coe, I’d be grateful if you could answer a layman’s question.
    Aside from it’s dominant role in adsorbing radiation, what is the overall impact of water vapour’s unique role in transferring energy from the surface to higher altitudes by evaporation/condensation?
    My simplistic view is that this must result in the surface being cooler and a segment of the atmosphere being warmer than would otherwise be the case if water vapour was just a simple gas. In turn this will lead to more heat being radiated away to space.
    So, as well as its warming effect per your article, does water vapour also have a cooling effect, per the above, and is it significant?
    Thanks in advance.

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