Tim Folkerts: Simple argument supporting a radiative greenhouse effect

Posted: December 6, 2012 by tallbloke in atmosphere, Energy, general circulation, methodology

My thanks to Tim Folkerts, who braves the generally sceptical stance on the talkshop to fight his corner for the climate mainstream paradigm of the radiative greenhouse effect. Tim has written a pared down synopsis of the fundamental points he believes makes the existence of the radiative effect certain. I suggest we try to restrict ourselves to dealing with the specifics of the article, mentioning in passing those aspects we might feel overly restrict the debate by their omission.

Simplified Greenhouse Effect
by Tim Folkerts – Dec 2012

This is about the simplest, most intuitive, most irrefutable argument I can come up with for why gases like CO2 and H20 in the atmosphere (“greenhouse gases”) must warm the surface.

There are only three fundamental requirements for this argument:

  1. 1.    The ground is a good emitter of thermal IR (ie it is reasonably close to a black body).
  2. 2.    The atmosphere contains gases that can absorb and emit IR radiation (“greenhouse gases” = GHGs).
  3. 3.    The “top of the atmosphere” (TOA) (as related to IR emissions) is cooler than the surface.

Note that all three of these are confirmed by experiment for the Earth: the emissivity of the surface (especially the oceans) is close to 1; GHGs like CO2 and H2O definitely absorb and emit IR in particular wavelength bands; the radiative “top of atmosphere” is near the top of the troposphere, where temperatures are ~ 220 K (or -55 C or -65 F)

Note also that pretty much any other details are not critical.  It doesn’t matter why there is a lapse rate; there is no need to calculate averages over the surface of the earth; feedback is irrelevant; exactly where and how the sun shines does not impact the fundamental argument.

For the sake of discussion, let’s look at a specific patch of the surface where the temperature happens to be 290K.  Lets further assume that patch has an emissivity of 1.00 (ie it is a perfect black body).  The spectrum for the thermal IR emitted from such a patch can be calculated, and is shown by the green curve in the graph below.

If there are no GHGs in the atmosphere, then this green 290 K curve in the graph below would also be the spectrum of the thermal IR leaving the earth.  It is relatively easy to determine that the total radiation in this particular case would be 401 W/m^2 — either by integrating the area under the curve on the graph, or by using the Stefan-Boltzmann Law.

If we add some GHGs that absorbs IR in a band near 15 μm but transmits other wavelengths (sort of like CO2), and if this gas is at the top of the atmosphere where the temperature is 225 K, then that gas will emit a spectrum like the blue line on the graph.   My hypothetical gas happens to emit 14 W/m^2 at 225.  (This value can be found by integrating under the blue curve but again, the exact value is not critical).

So what will the spectrum of the thermal IR leaving the earth look like when the GHG is present?  It might be tempting to ADD the two curves, getting a total of 401 W/m^2 + 14 W/m^2 = 415 W/m^2. This would result in a net cooling effect from the extra GHGs, but this it NOT correct.  The photons near 15 μm that were emitted by the surface don’t leave the earth, but rather get absorbed on the way up through the greenhouse gas.  Instead, the radiation from the gases higher in the atmosphere REPLACES the radiation from the surface.  The net radiation will be the dashed line.  The area under this curve will be less than the radiation from the surface — 377 W/m^2 vs 401 W/m^2, for a net change of – 24 W/m^2 in our particular case.


The implications should be obvious, but let me spell it out.

For a given surface temperature, less radiation leaves a world with cool greenhouse gases than a world with no greenhouse gases. This applies to each and every patch of surface around earth (at least as long as the three conditions hold).  Less radiation leaving means more energy staying.  More energy staying means the world with GHGs cools more slowly at night and warms more quickly during the day. This inevitably leads to a warmer world if GHGs are present.

We could also play with the numbers to discover that world with the surface at 295 K and this GHG at 225K would radiate 401 W/m^2.   Again the implications are obvious.  A warmer world with GHGs can radiate away the same energy as a cooler world with no GHGs.  For this particular parcel of surface in this hypothetical world, the warming effect was 5 K.  Other parcels at other temperatures in other worlds with other GHGs would have different warming effects, but all parcels in all GHG worlds will have some degree of surface warming due to the presence of GHGs.



A few notes …

1) The specific numbers above are presented simply to have concrete numbers to refer to.  As long as the three conditions are met, the general conclusion will hold — ie that a world with GHGs can have a higher surface temperature and still radiate away the same energy as a cooler world with no GHGs.

2) The form of the curve (the bite removed from the black body curve) is confirmed by satellite measurements and by more sophisticated calculations.   (NOTE: These are plotted vs wavenumber rather than wavelength, so the shape is a little different).

3) This says nothing about what might happen with MORE GHGs.  If more GHGs make the “bite” deeper or wider, then the warming effect would increase, but such details are for a different discussion.

4) Water absorbs over wider bands, but tends to do this at lower altitudes (where it is not as cold).  This makes for wider but less deep “bites” in the spectrum.  Even if water and CO2 absorb in the same band, the CO2 will still matter because it will tend to be at a higher elevation and a lower temperature, creating a deeper “bite”.

5) Details about evaporation, convection, distribution of sunlight, lapse rate, etc are certainly interesting, and could affect the magnitude of the effect.  But none of these can change that fact that GHGs do indeed radiate to space from high in the atmosphere where it is cold.

6) The spreadsheet that calculated all this is available.  There are no “instructions”, but there are a few comments that should make the spreadsheet’s set-up reasonably intuitive.
The shapes and values ARE accurately calculated (for the idealized emissivities)  You can try playing with the temperatures or emissivities if you are so inclined.

7) “Surface” means the physical surface of the Earth — the land and water.  One could also talk about the “effective radiating surface”.  The “effective radiating surface”, would be somewhere between the physical surface and the TOA and on earth would have a temperature around 255K.  But this level is determined by the GHGs in the atmosphere (with no GHGs the effective radiating surface would BE the physical surface), so even this approach relies on the presence of GHGs to warm the surface. 

8.) Nothing here violates any laws of thermodynamics.

I can’t really understand how anyone with even a decent understanding of science could think that GHGs have no effect (or worse yet, that GHGs cool the surface!).  The ability of GHGs to warm the Earth is confirmed by multiple lines of reasoning. Furthermore, there is the simple fact that the surface is much too warm to be due to sunlight alone, with no warming from the GHGs.

  1. Mod: For the record, LWIR above should read SWIR.

    [Reply] The page is too long for my lappy to load, and I don’t know when you made the comment above. In order to get you and Tim to write the new articles you have promised, I will close comments on this thread soon.

  2. […] of the AGW theory and frequent blogger. He bravely agreed with TB to write an article entitled:  Tim Folkerts: Simple argument supporting a radiative greenhouse effect. The other thread was initiated on 14 Dec 2012 by TB himself entitled: Emissivity puzzle: energy […]

  3. There is a love of theoretical minutia, coupled with a disragard for observation, in many of these comments. The discussion of gravity is a case in point. The density and pressure of the atmosphere are largely determined by gravity. However, the temperature dependence of the atmosphere is dominated by the absorption of solar radiation. The temperature drops in the troposphere, rises in the stratosphere, drops again in the mesosphere and rises again in the thermosphere. This W cannot be understood except in terms of solar wind and ozone’s UV absorption. So handwaving about radiation and the kinetic energy of gasses, enthalpy etc. without calculations to show that you are ‘in the ballpark’ with observation are akin to metaphysics. Please focus on the empirical and observation.

    The discussion of Prevost’s Theory, which predates any modern understanding of radiation or the atomic theory of matter, is woefully inappropriate for a discussion of the interaction of radation and matter in an atmosphere, espeically when there is a absorption spectra involved. In what sense does IR radiation behave like a ‘rare fluid’ in the presense of a molecule with an aabsoption line in the midle of the frequencies in question? So rather than looking to thermodynamic arguements of dubious applicability, why not pay more attention to observations of the atmosphere? The point of a simple theory, as Tim presented, it to give a reasonable explanation of observation. It is to capture the essence, not to demonstrate a knowledge of every aspect of a physical system.

    To my mind, TIm has provided a concise explanation of how the green house effect does manage to warm the Earth. That the greenhouse effect of carbon dioxoide does warm the Earth has been non-controversial since the time of Arrhenius. Without a greenhouse effect, we would still be living on a snowball Earth. Why is the Earth currently warmer than 255 K? The Earth has seen several episodes of snowball earth, as evidenced by drop stones on the equator. But greenhouse warming resulted in the habitable world that made the Cambrian explosion, and our modern world, possible.

  4. tallbloke says:

    Robert asks: “Why is the Earth currently warmer than 255 K”

    Actually, the question is: Why is the Earth warmer than ~206K – The average surface temperature of the Moon, which is at the same distance from the Sun. That’s an issue I started investigating here:https://tallbloke.wordpress.com/2012/12/10/why-earths-surface-is-so-much-warmer-than-the-moons-part-1/

  5. Max stated:

    “I have an experiment I performed which had a rather pronounced cooling effect from adding a bag filled with CO2 to one of my test boxes, various forms of this experiment had what I took to be anomalous results where the CO2 addition appeared to give a half a degree or even a degree of cooling, but it’s difficult to read on the thermometers, and I could never get anything significant enough to be certain.”

    As far as I know, dry ice is the only practical way to get a ‘bag full of CO2’ (Carbon dioxide at room temperature, is of course a gas,and bags of gas are not very common. An inflated diver’s vest would count, so perhaps you did actually have a bag of CO2 gas. Please explain your bag of CO2 and include the relative volumes of the test box and CO2 bag. Also discuss your experience with calorimetry.) Adding anything at −78.5 °C to a test box at room temperature is likely to cool the test box, this would explain your observations but has nothing to do with the greenhouse effect. As a self-described climate skeptic, I’m sure you understand the importance of healthy skepticism of claimed experiments that contradict published results.

    I suggest that you watch following experiment from Mythbusters, which was conveniently recorded on Youtube: http://www.youtube.com/watch?v=pPRd5GT0v0I (or search youtube for “Mythbusters greenhouse”, it will be your first link). Apparently, they have a bigger budget for thermometers than you do since were able to measure the temperature increase.

    It should be easy to convince me of your claims – I am a skeptic, not a contrarian. Write up your experiment with enough detail that it can be reproduced. We can then discuss the results and determine the correctness and relevance of your claims. If there are questions about the experimental results, we can simply repeat the measurements to confirm your results.

  6. Steven Wilde states,
    “The total amount of KE stays much the same because any attempts by GHGs to change it are cancelled out by an adjustment of the relative proportions of KE and PE.”

    The potential energy of a molecule near the surface of the Earth is given by mgh, e.g. it’s height. The KE is determined by it’s translational and vibrational degrees of freedom. When a molecule absorbs radiation, it can gain vibrational energy. This can be transferred to other molecules by collisions. This will tend to increase the kinetic energy of all the molecules in the gas. This will also cause the atmosphere to rise slightly. (statistically speaking, the molecules go up slightly)

    So the radiant energy, along with the kinetic energy and potential energy of the molecule all follow the Boltzmann distribution. See http://courses.physics.illinois.edu/phys213/lectures/lecture12.pdf for lecture notes on this; I’m sure there are many more discussions of this on the internet or in general texts of undergraduate physics. There simply is no ‘canceling out’ – if you dump energy into a system, it will be distributed between all available degrees of freedom in accord with the Boltzmann distribution.

  7. David Socrates states,
    “This obviously creates a zero KE-to-photon-to-KE energy balance. So the total KE in the bulk of the atmosphere (and hence its temperature) is statistically unaffected by these photon creation/anihilation events going on in its midst.”

    There are two subtile, but fundamental, mistakes in these two sentences.

    1. If the energy of the photons is higher than the average kinetic energy of the gas, the effect of atom/photon interactions is to increase the temperature of the gas. If the gas has a higher temperature (average energy per degree of freedom), the gas will loose energy to the photons. So we will head toward a thermal equilibrium as long as there is a mechanism to achieve thermal equilibrium. (if the gas is transparent to the photons, there need not be a thermal equilibrium between them.) So the temperature of the gas is affected by KE-photon-KE interactions.

    2. As the gas heats, the distribution of the height of the molecules, which obey the Boltzmann distribution, e.g. exp(-mgh/kT), will also increase. It is not only the KE that increases with temperature, the PE also reaches thermal equilibrium. So all of the arguments that equate temperature with only kinetic energy are simply incorrect.

    Have a look on YouTube under ‘Yalecourses’; they have the lectures for the class “The Atmosphere, the Ocean and Environmental Change” (GG 140). Episode 04 is “Vertical Structure of the atmosphere; residence time.” The density of the atmosphere decreases with exp(-gh/RT). (h=height, g=acceleration of gravity, R is gas constant and T is temperature). Why is this exponential and why does this vary with g, h and 1/T? It can all be derived in a few lines from the Boltzmann distribution and the ideal gas law. This can also be found in all the standard texts. This is not controversial or fringe, this is well established by theory and confirmed by measurement.

    The Feynman Lectures have a wonderful discussion of thermal equilibrium using a ratchet and pawl (in Vol 1, as I recall.) Or just read about the ‘Brownian ratchet’ on Wikipedia. This is fun stuff, so read it if you want to refine your arguments about statistical physics.


    As you may have guessed from our names and similar ages, Tim is my more patient brother. I also have a daughter with a recent degree in Earth Sciences who is currently experiencing and combatting some of the consequences of global warming near the Sahel. I thank everyone on this forum who has avoided pseudonyms; our children and grandchildren will be able to go back and Google our words. If they have to deal with the increasing consequences of climate change, they can understand why nothing was done sooner. Or maybe mainstream science is wrong; then our children and grandchildren can look back and laugh at me for being such a Henny Penny. You know how I am betting.

  8. tallbloke says:

    Hi Robert and welcome. My name is Roger Tattersall, I’m a Mech Engineer with a degree in the history and philosophy of science. Just a quick point about the ‘mythbusters’ experiment. While none of us here are in any doubt that a doubling of co2 in a test like this will produce around a K of warming of the control volume, we doubt whether this fact has much relevance in the open where convection and latent heat control the temperature of the bulk atmosphere. Without getting into discussion of the Maxwell distribution, it’s worth pointing out that the PE contained in water vapour is a much more efficient energy store than gravity is. This is because as Peter Berenyi pointed out, the the latent heat required to evaporate a molecule of water is equivalent to the amount of energy used in raising that molecule 264km from the surface aganst gravity. Given that the troposphere is only about 18km high at the equator…. well, I won’t insult your intelligence by labouring the point.

    Mythbusters has nothing whatsoever to say about water vapour and their experiment is therefore utterly worthless in relation to an understanding of the real atmosphere. It’s effectiveness as propaganda is a different question, which we don’t need to clutter this thread with.

  9. oldbrew says:

    Robert Folkerts says:

    Some good points there, until the last paragraph. The theories of Arrhenius were debunked 100 years ago by a simple experiment.


    [see para. 3.3]

  10. Oldbrew,

    Arrhenius had the microscopic mechanism wrong; given that the infrared spectrum of CO2 was published on Jun 17, 1932, I think that is understandable.

    But it is certainly the case that infrared (of certain frequencies) will excite CO2 which is then very likely to reemit the photon in a random direction. However, it is also possible that the molecule in question will suffer a collision and the energy will be converted to the motion of the other atoms of the gas.

    The first mechanism results in a very long random walk of IR photons that will form a ‘gas’ in their own right. This gas exchanges energy with the gas of molecules. Within the range of frequencies where a molecule (or water droplet, or aerosol…) can absorb and reemit, the radiation and molecules in the gat will come to a thermal equilibrium. The details of the mechanism are not important to thermodynamic arguments. Arrhenius was certainly a master of chemical thermodynamics; as anyone who has studies rate equations in chemistry should recall. Disproving Arrhenius’ mechanism does not necessarily disprove his thermodynamic arguments.

    So let us return to our microscopic picture of solar radiation. You have a photon of visible light that is absorbed on a rock, heats the rock. The hot rock is now a blackbody in its own right. If it emits a photon is of a a frequency that is not absorbed, the photon will freely escape into space. If the photon is of a frequency that is absorbed, its energy will reside longer in the atmosphere until it is either emitted into space or converted into molecular motion (or increasing the distance between water molecules, or any of the other things that energy can do in the atmosphere.

    How is that not an insulating layer? An insulator does not function to add or remove heat, it simply slows the transfer of heat. A random walk in three dimensions is vastly longer than than a straight path. That makes it an insulator. During this long random walk, the energy of the photon is likely to be exchanged with other degrees of freedom. So we have a microscopic mechanism that does work as Arrhenius predicted from thermodynamic reasoning.

  11. Tallbloke states:

    “While none of us here are in any doubt that a doubling of co2 in a test like this will produce around a K of warming of the control volume…”

    Max stated:

    “I have an experiment I performed which had a rather pronounced cooling effect from adding a bag filled with CO2 to one of my test boxes…”

    So at least one of us here does have doubts about CO2 producing warming and goes so far as to say he has an experiment that showed cooling. I realize that this is a public forum and Tallbloke is not responsible for the content of Max, but he did go on to claim a community norm that clearly is not shared by all members of this community.

    I am standing by Tim’s analysis, not only because he is kin but because his arguments are based upon well established thermal physics AND they are largely consistent with observation. I have challenged the arguments of others based upon the physical principles as understood by physicists and most climate scientists. I will not appeal to community norms to make an argument about a physical system.

  12. Tallbloke states,

    ” it’s worth pointing out that the PE contained in water vapour is a much more efficient energy store than gravity is. This is because as Peter Berenyi pointed out, the the latent heat required to evaporate a molecule of water is equivalent to the amount of energy used in raising that molecule 264km from the surface aganst gravity. ”

    It comes as no surprise that a van der Waal’s (electrostatic) attraction id much stronger than gravity at the molecular level. Since the mean free path of a molecule in the atmosphere is well under 264 km, I’m pretty sure that the water will reach thermal equilibrium with the surrounding molecules well before it travels that far. So even if you postulate a mechanism to transfer this potential energy to kinetic energy, I don’t see how that changes much. As long as we have a mechanism to exchange energy, we should expect the system to approach thermal equilibrium by purely statistical arguments. After all, the density of the atmosphere does obey exp(-mgh/kT).

    It is also clear that because of this van der Waal attraction, the water in the atmosphere does condense and it largely found in the bottom 10 km of the atmosphere, e.g. the troposphere. By contrast, carbon dioxide is much more evenly distributed throughout the atmosphere. So in the stratosphere, CO2 is interacting with the infrared radiation and providing an insulating effect even when there is (relatively) no water to be found. So I will gladly grant you that the PE due to the latent heat of water is much greater than the gravitational energy between the earth and a molecule. Will you agree that this latent heat is the reason that water is largely restricted to the troposphere? By contrast, carbon dioxide remains at about 330 ppm up to an altitude of 80 km.

  13. tallbloke says:

    Hi Robert and thanks for your reply. It’s always interesting when new people come along and make novel arguments about the greenhouse effect. Up until now the theoreticians have been saying that additional co2 will cause the troposphere to warm and the stratosphere to cool. Now you seem to be saying that the ‘insulation’ of additional co2 in the stratosphere will cause it to warm. The data says the stratosphere has been neither warming nor cooling since 1995 when the after-effects of Pinatubo wore off. There does seem to be a deal of confusion over absolute temperature levels however:

    Given the much wider open ‘window’ up there (due to low density), I would expect the co2 above the tropopause to do a pretty efficient job of cooling the planet by radiating to space. Maybe you can point us to some technical information on this?

    You said:
    “I’m pretty sure that the water will reach thermal equilibrium with the surrounding molecules well before it travels that far. So even if you postulate a mechanism to transfer this potential energy to kinetic energy, I don’t see how that changes much.”

    The mechanism is condensation, and I don’t need to postulate it, because what goes up must come down. Water vapour sneaks energy in the form of PE locked up in the latent heat of evaporation up past the co2 in the lower troposphere and condenses out, releasing that heat at an altitude where LW radiates pretty freely to space from the cloud-tops. Thus the hydrological cycle is in dominant control of the troposphere.