onsdag 1 september 2010

Updated Computational Blackbody Radiation

                  Planck in despair: A theoretical interpretation had to be found at any price, 
                                                   no matter  how high that might be...

I have updated the (draft of) Computational Blackbody Radiation which can be inspected here.

I present a mathematical analysis of blackbody radiation, of central importance in climate science, based on deterministic wave mechanics subject to finite precision computation, as an alternative to Planck's classical analysis based on statistics of energy quanta or photons. 

The deterministic finite precision wave model offers the following advantages as compared to Planck's statistical particle model:
  • it is closer to physics: radiation/light is an electromagnetic wave phenomenon and not any stream of particles,
  • it is possible to analyze and thereby understand, while
  • Planck's statistical model was born in an "act of despair" and as such has caused a lot of confusion: blackbody radiation is still hundred years later considered to be "black magic"
  • it shows that the concept of "backradiation" as the driver of the "greenhouse effect" supposedly causing global warming, is fictitious non-physical and confusing,
  • it includes a 2nd law showing that heat energy can be transferred by radiation from a warm body to a cooler body, but not from cold body to a warmer.
This work will be part of my contribution to the Slaying the Sky Dragon of the Greenhouse Effect project.

Comments are welcome.

23 kommentarer:

  1. I skimmed through the article and found it interesting, however, the relevance to the current greenhouse debate remains obscure. Apparently you re-derive the SB-law without statistics and quanta but since climate science always refer to the SB-law I don't see where your analysis points to the mistakes in the climate models.

    You note that the net heat transfer is always from hot to cold, most climatologists would, however, agree with that and claim that the greenhouse gases merely "slow down the cooling of the earth". A possible explanation could be the following:

    Regard the incoming sunlight as an energy source, like electricity transformed to heat by a radiator in a building. Suppose we increase the thickness of the walls in the building. If the heat production of the radiator remains constant the temperature in the building then increases, doesn't it?

    That is the action of the backradiation. It slows down the cooling, but the net heat flow is always from hot to cold.

    What do you respond to this? Where lies the flaw?

  2. A short question from a complete layman:

    If "backradiation" does not exist, wouldn't the implication be that you would have to calculate the "greenhouse effect" in another way, just like you calculate the insulation for a house?

    Just how much "thicker" then would the "wall" (the atmosphere) become from a doubling of CO2?

    Not much, I guess?

  3. The cooling is not slowed down, because still heat in = heat out, but it requires a higher temperature difference the better the insulation is. I want to get "backradiation" (or "backconduction") out of the discussion, because it is confusing and hides elementary facts of heat transfer. Backradiation builds on an idea of two-way stream of particles, which is unnecessary and by Ockham's principle unphysical and only creates confusion. And confusion is not productive in science, only in politics.

  4. Claes,

    My point is that if you divide the atmosphere into different layers, regard them as blackbodies exchanging radiation, in the way you describe in your text, no particles, just radiation waves, then very little (if anything) has changed on the physical level, possibly on a conceptual level. The calculations could be carried out the same way and reproduce the greenhouse effect.


    My own objections so far would be the following. In the case of increased isolation the temperature increases everywhere in the system, nowhere does the temperature decrease. Do you agree? Therefore:

    The greenhouse effect is not an effect equivalent to that of increased isolation and the reason why it isn't could be a difficult (or easy) question to answer and I think you could make a big contribution to that.

    One of the main themes in the G&T paper is to distinguish energy and heat. If energy is to be transformed into heat there has to be dissipation (?) and the dissipation is currently missing. The only thing we have is radiative energy, or radiation pressure as I like to call it. It has direction, it is not random. Surely you distinguish between pressure and heat when you do Navier-Stokes calculation.

    Moreover, I'm surprised that nobody has noted it before.

    For an ideal gas we have

    P = nRT/V

    For a blackbody we have

    P = 1/3aT^4

    Climatologists like to mix these concepts whenever convenient. A parcel of air is an ideal gas and a blackbody at the same time. They can share an intensive variable like temperature but the other thermodynamic variables differ in a quite important way. Note that the pressure of the ideal gas depends on the amount of particles. I think the density (which decreases with height) is one of the overlooked variables in the quuest.


    "Just how much "thicker" then would the "wall" (the atmosphere) become from a doubling of CO2?

    Not much, I guess?"

    I agree

  5. What is then "the greenhouse effect"? Radiation alone cannot say anything meaningful about climate because it results from thermodynamics + radiation. Is "the greenhouse effect" simply Fourier's law for heat transfer?

    I think it is enough to view radiation as a heat source in thermodynamics
    and thus work with thermodynamic temperature.

  6. Obviosly the greenhouse effect is not equivalent to Fouriers law of heat transfer for the reasons I described.

    However, IF you divide the atmosphere into several layers and treat each layer as a blackbody radiating with intensity proportional to T^4 (or to some power of T, not essential), each layer absorbing a certain amount of the incident radiation AND assume that the absorbed radiation is immediately turned into heat AND treat the incident solar radiation as an energy source transformed into heat at the surface of the earth THEN you have reproduced (at least some version of) the greenhouse effect.

    I myself have objections to all of the assumptions mentioned above, where do you depart from the standard greenhouse assumptions?

  7. I think you have derived the greenhouse effect yourself in the section "A Simple Radiation Model":


  8. I do not assume that each layer radiates T^4, only that the heat transfer
    between layer 1 and 2 is prop to T_1^4 -T_2^4 with T_1 > T_2. Is this the greenhouse effect? If so, it is a form of Fourier's law, which at least is physical, and does not involve any backradiation. But Fourier's law does not describe thermodynamics, and so alone does not tell anything meaningful about climate. Can you describe what is supposed to be the greenhouse effect?

  9. If an atom can be heated only by incident radiation at a higher frequency than its own resonant emission frequence at its starting temperature, then the ground (hotter) cannot turn radiation from the atmosphere (cooler) into heat, but will immediately reflect or re-emit it:
    "...radiative heating by low frequencies is inefficient."

    So it is not simply "net heat" which is unidirectional, but the ABSORBABLE radiation: downwelling 'cool' (low-frequency) radiation has little effect on warmer material, bodies, or atoms.

  10. Ok, good. Here is where you could make your greatest contribution I guess. First of all, carefully check your own radiation model against that presented in the link provided by Azar and the Lindzen paper, see if you find any crusial differences that I have missed. Secondly, according to the Kirchhoff law, absorptivity equals emissivity. Instead of assuming full absorption/emission, include an emissivity parameter and check how the temperature gradient varies with that (I guess you can answer that straight away). Increasing this parameter I guess corresponds to increasing radiative forcing. Does the temperature gradient get steeper?

    However, I'm suspicious against the model for the following reason. Suppose you set the emission/absorption parameter equal to zero. Do you get an isothermal atmosphere in that case? Can you defend a model that predicts infinite heat conductivity just because some radiative agents are missing?

  11. A basic model takes the fom -d2u/dx2 + alpha u = 0 for 0<x<1, with alpha a coeff of direct emission to outer space, with solution of the form
    u(x)= exp(-ax), which for a =1 is approx linear exp(-x) = 1 - x and for a large alpha drops off quickly to 0 where it stays constant. Large direct radiation without atmospheric absorption thus leads to an isothermal atmosphere, except for layer at x = 0 (Earth surface). Is this what you are looking for? Elementary conduction-reaction?

  12. If I understand your answer correctly I guess it is something like that I'm looking for, though it would be clearer if the equations you present in your model was solved explicitly for a varying absorption/emission parameter (is that very difficult?). Anyway, I guess it has to be presented in article form an not in a blogpost so let's leave it for now.

    If my suspicion is right, namely that zero absorption/emmision of the atmosphere leads to an isothermal atmosphere then as far as I can see there is a conceptual difficulty arising. You claim that the model is equivalent to a Fourier heat transfer problem, anyhow, by putting an absorption coefficient to zero (a physical assumption) you end up with a result that corresponds to infinite heat conductivity (an unphysical result). A possible resolution of this problem is to treat the incoming solar radiation as heat, just as we speak of the outgoing terrestrial radiation as "heat-radiation". In that case, the 2nd law would definitely favour an isothermal atmosphere under all circumstances. But maybe these considerations border to the more philosophical realm. In any case, I think that much of the disagreements around the greenhouse and its relation to the 2nd law stems from this very distinction.

    I suggest you take a look at


    It seems that your model resembles the one presented there, so I believe that you have in effect derived the greenhouse effect, which is good, because then you know exactly what you are dealing with.

    Another problem that I guess will turn up later is the boundary conditions. Where lies the top of the atmosphere? What is its temperature? One of the points I bring up is that the Fourier law of heat transfer never predicts cooling anywhere in the system as a result of SOLELY increasing isolation. But maybe I have got that wrong. The cooling of the stratosphere nevertheless remains a mystery.

  13. The ref studies models of thermal equilibrium as radiative equilibrium with
    "convective adjustments". Very simple with crude thermodynamics and thus with little predictive value. I believe much more realistic thermodynamics must be included, since thermodynamics is so important. On the other hand, crude radiative models may be enough.

  14. You are right in your description that it is a radiative model that is virtually "forced" to comply with the (averaged!) temperature gradient observed in the atmosphere. Anyhow, the entire construction is very strange in my view. First of all they start off with two isothermal atmospheres which are left to approach "thermodynamic equilibrium", which happens to have a rather pronounced temperature gradient. Where else in thermodynamics does this occur, you start off with an isothermal system that installs a temperature gradient on its own. That happens when I cook pasta on my stove, then we can talk about a conduction temperature gradient with "convective adjustment", but that is forced by the heat energy provided by the plate. Therefore my analysis comes to the following conclusion,

    In climatology the heat radiation acts as a heat pump (in violation of the 2nd law), whose efficiency is reduced by convection. In other words, unlike ordinary thermodynamics where the heat radiation between bodies always tends to reduce any temperature differences, the exact opposite happens in climatology.

    An opposite view is presented by William C. Gilbert in


    Personally I don't think he has got it quite right either, but I guess he is on the right track. It would be interesting to discuss that too.

  15. Here is a link to a slide show where on the 10th slide and forward they motivate the convective adjustment from the ideal gas law (unembarrassed that they in the previous slides treated the layers as black bodies)


    Then compare with the comment by W.C Gilbert in


  16. Yes, "radiative equilibrium with convective adjustment" is not science, only
    dust to hide ignorance.

  17. Claes said:..."I want to get "backradiation" (or "backconduction") out of the discussion, because it is confusing and hides elementary facts of heat transfer"...
    But Claes, I think that "backradiation" is one of the components that decides the climate. I look at backradiation as a very weak electromagnetic radiation but of course it can increase the movement amplitude (energy)of a hot ion or dipole molecule. The e-m force (N/C or V/m) doesn´t measure the temperature of the electric charged object before it acts on it; it just acts. I can´t see why this should violate some thermodynamic law. The electromagnetic wave doesn´t know that it comes from a cold object and hits a warm one.
    But I am just an MS in electric engineering ;-) so I don´t know much about thermodynamics.

  18. Yes, the incident electromagnetic wave "knows" its emission temperature because that is represented by the spectrum: the higher the emission temp is the higher are the frequencies emitted, all according to Planck's Law. "Backradiation" is as unphysical as "backconduction" or "backdiffusion" which nobody speaks about because it is pure fiction.

  19. Lasse H,

    Good you mentioned force. The total force excerted by the atmosphere on the surface is governed by its weight, no more, no less. Part of this force comes from electromagnetic interactions of course. If the total force exceeds the weight of the atmosphere is starts to escape the earth and if it is less it contracts.

  20. I still haven't managed to get my head around what you're saying, Claes (Perhaps because I'm very simple-minded).

    Why does it matter whether radiation is treated as particles or waves? You have described the Planck/Newton particle/photon theory as a "spitting competition", and I understand what you mean.

    But what happens when I point my 5 volt torch at the sun? Does my torch say, "Sorry, I can't shine any light at the sun, because it's much hotter/more powerful than I am. I give up."? Does none of my torch's light ever reach the sun? I suspect you would say that it doesn't, because to see it that way is to see it as a "spitting competition" between my torch and the sun, and that's not what's happening, because light is made of waves and not particles (of spit).

    But when I look at waves, I often see waves going backwards and forwards. When I drop a lump of sugar into my cup of tea, it sends a series of waves out from the centre of the cup to the edge, and there they get reflected back, with the outgoing waves often crossing the incoming waves. So I see waves travelling in two directions, back and forth. Isn't that a sort of "spitting competition" between waves (the particles in this case are just jiggling up and down)?

    And if we want to think about light waves just like waves in water, then we can think of a "hot" object vibrating in the water with some frequency and amplitude (and emitting waves through the water), and a "cool" object as one which is vibrating at a lower frequency/amplitude. Wouldn't these two vibrating objects in a pool of water send waves towards each other, in opposite directions, just like what I see in my teacup? Isn't that just a "spitting competition" with waves rather than particles?

  21. Yes, waves travel in both directions, but what they carry/deliver = net heat energy, only goes one way: from warm to cold. A blackbody subject to incoming radiation (like the Earth subject to radiation from the Sun) reads the temperature of the incoming radiation from its spectrum (mainly in the visible range emitted at 5778 K from the Sun), compares with its own temperature (15 C), notes that 5778 K is bigger and then decides to absorb and then heat up/radiate infrared until equilibrium. If the incoming radiation has lower temperature, then it is directly emitted without heating effect.

    It is thus necessary to distinguish between waves traveling both ways, and energy absorbed and stored as heat, which only goes one way. If you consider light to be particles, this distinction is impossible, since the energy is tied to the particles, rather than being carried by the particles. OK?

  22. Claes,

    There might be some substance to the claim that low-frequency radiation is re-emitted rather than absorbed by a hot object. But even in a particle spitting competition the net heat transport is from high temperature to low temperature.

    Think about heat conduction. The low temperature reservoir spits momentum to the hot reservoir and vice versa. Neither system checks the temperature of the other system before spitting. However, the temperature change per unit time decreases as we approach thermal equilibrium. Can you explain this slow-down without some "backspitting"?

    Actually I don't think the "back-heating" or (maybe a better term) "thermal inertia" is the main issue here. The delicate question which nobody seems to be willing to deal with is whether the incoming heat from the sun is to be treated as a heat transfer. In that case the earth doesn't need to "cool" since it is (on average) thermally equilibrated to its surrounding. And then the natural question arises why the upper atmosphere supposedly maintains a lower temperature than the surface.

    This is the tricky question that needs an answer. The greenhouse hypothesis addresses this very question, even though its proponents like to portray it as some trivial phenomena that I child would understand, and this of course for political reasons.

    Has anybody (apart from a few marginalized engineers) thought about this question, any reflections? The question was raised already in the nineteenth century you know.