söndag 2 januari 2011

Correct Interpretation of Stefan-Boltzmann's Radiation Law

What is the physical meaning of my formula? I am not sure I know myself. And you?

Stefan-Boltzman's Radiation Law (SB) is commonly written
  • Q = sigma T_h^4 - sigma T_c^4 ~ sigma 4 T_h^3(T_h - T_c),
where Q is radiative flow of heat energy from a hot body of temperture T_h to a cold body of lower temperature T_c, and sigma is a certain constant. We here express SB also in differentiated form.

There are two ways to interprete SB as written:
  • (1) One-way flow of net heat energy Q ~ sigma 4 T_h^3(T_h - T_c) (differentiated form)
  • (2) Two-way circulatory flow of heat energy with a certain net flow (non-differentiated).
Does it make a difference? The formula is the formula and so how can its interpretation be important?

Yes, it is important because CO2 climate alarmism results from a "greenhouse effect" based on (2) with "backradiation" from a cold atmosphere at T_c heating a warm Earth surface at T_h in a circulatory exchange of heat energy between atmosphere and Earth of magnitude ~ 360 W/m2 (with a net flow of 120 W/m2 with T_h - T_c ~ 30 C).

The alarm results from subjecting the 360 W/m2 to a small change, say a 1% change
~ 4 W/m2, which translates into a ~ 1 C change of T_h.

The result is a climate sensitivity of 1 C from a 1% change of the circulating flow. This
"no-feedback" climate sensitivity of 1 C is then augumented to 3 C by feedbacks: Alarm!

Now, 1% is a small perturbation of the circulating flow which thus results in considerable warming of 1 (or 3) C. Alarm from interpreting SB according to (2)!

However, if we instead interprete SB according to (1), then the 4 W/m2 corresponds to a 3% change of the net flow of 120 W/m2, and a 3% perturbation is a no longer a small perturbation.

A 1% perturbation of 120 W/m2 would give a climate sensitivity of 0.3 C = No Alarm!

We see that the interpretation of SB makes the difference between Alarm and No Alarm.
How can we judge which interpretation is the correct one from a physical point of view?

By looking at the derivation of the SB formula. Where do we find it? Well, SB is an integrated version (summing over frequencies) of Planck's radiation law (P) and Planck's derivation of P is based on statistics of quanta, which is difficult to dechiffer and interprete physically because statistics is not physics. Statistics concerns ensembles of physical events and physics does not play with ensembles of events, only with events. In the same way as there is no person identical to Meanvalue-Smith, who you can ask about reactions and opinions. Meanvalue-Smith is a non-physical person with no physical relation to anything and with nothing to say.

A derivation of P and thus SB without statistics, based on deterministic physical wave mechanics, is given in the chapter Computational Blackbody Radiation in our new book Slaying the Sky Dragon: Death of the Greenhouse Gas Theory. This (new) derivation shows that the interpretation (1) is physically correct. There is no circulatory flow of heat energy, because such a flow is unstable.

Get the book and decide yourself between Alarm and No Alarm. You will find that it is necessary to understand the mathematical derivation of a mathematical formula, to properly understand the meaning of the formula. Read and then tell your friends and collegues about your findings.

Compare with the discussion on Science of Doom Understanding Atmospheric Radiation
and the Greenhouse Effect claiming the heat energy radiated from the Earth surface is measured experimentally to be ~ 360 W/m2 (or 390), while acknowledging that the flow of heat energy is calculated from SB: Q = sigma T^4 with a background temperature of 0 K by measuring the surface temperature T.

The instrument reading of 360 W/m2, is thus incorrectly interpreted as a reading of a real physical flow of heat energy of 360 W/m2, by letting the instrument calculate the flow of energy from measuring the temperature, using a physically incorrect interpretation of SB.

This shows that readings of experimental instruments must be interpreted with care, and that the mathematical theory/theorem behind an instrument design must be understood to allow a correct interpretation of instrument readings. Proper understanding of the proof of the theorem is then necessary to secure a correct interpretation of the meaning of the statement of the theorem.

IR detectors or sensors used in IR cameras are sensitive to the frequency of the incoming radiation, from which the emission temperature is calculated (using Wien's displacement law) and from the emission temperature the emitted radiation is calculated (by SB).
Thus frequency is measured and radiated energy is calculated by certain formulas.

34 kommentarer:

  1. Claes, I have not wasted my time replying to Science of Doom (SoD). He may have a way with words but he either has no understanding of heat transfer which is an engineering subject(from his writings it appears he has no engineering knowledge or skills) or like some AGW alarmist he twists the truth.
    There is no instrument which directly measures radiation energy. The instruments which have been described as measuring radiation actually measure either a small voltage or current at a measuring point junction in comparison to a base reference connection point eg a thermocouple with a junction of two selected dissimilar metals (eg iron/constantin) or a resistance thermometer (ususally platinium). Properly calibrated they will give an indication of temperature at the measuring point but errors can be significant. This temperature is then used to calculate the radiation using the the Stefan-Boltzman equation. Cheap instruments assume black body emissivity of 1. More expenive ones allow an adjustment of emissivity but any adjustment is a guess. It is necessary to separately measure the reference temperature. Cheap instruments either have an assumed offset or allow a zero (ambient) adjustment. Finally, there is no exact knowledge of where the assumed radiation comes from ie if it has been emitted of reflected at a point of interest or if there is interference from another heat source (eg the hands of a person holding the intsrument. Also, it should be recognised the Stefan-Boltzman equation only is applicable exactly,when adjusted for emissivity of the sorce and receiver, in a vacuum. When there is a fluid between, other heat transfer mechanisms occur in preference or at the same time
    It appears to be normal for scientists to have little understanding of the working of instruments and the errors in measurement and evaluation.
    Happy and healthy New Year to all

  2. I think that you are making a mistake in thinking that the cold atmosphere is heating the hot ground.

    The ground is heated by the sun. And what the back radiation process does is slowing down the process of loosing heat to space.


  3. Just to check if I understand what you are saying:
    Suppose we have two copper plates, one hot and one cold, with their broad sides facing each other. You say that
    1. the traditional interpretation is that both plates emit heat, which gives rise to a net heat flow.
    2. the correct interpretation is that only the hot plate emits heat, giving rise to the same net heat flow.
    Or have i misunderstood something?

  4. Interesting information. For a long time now I have been thinking what a thermometer really measures. It might come as a surprise to many people, but the question GE-theory seeks to answer is:

    Why isn't the atmosphere (on average) isothermal?

    It should be, according to the zeroth (second) law of thermodynamics. But as we go upwards in the atmosphere thermometers indicate something different. The solution they come up with is greenhouse gases. In other words:

    The zeroth (second) law of thermodynamics is valid, but only so long as there are no greenhouse gases around.


    But wait a minute! Who demonstrated that thermometers measure temperature? Noone did, because it is a definition! Another definition.

    It is a little bit like turning a definition into a physical fact, or what do you say Claes ;)

  5. To Felics: I say that there is a two-way wave mechanics connection between the two plates with a one-way transfer of heat energy from hot to cold. There is no circulation of heat energy with a net transfer from hot to cold. Circulating flow of energy (by itself) is unstable and thus non-physical.

  6. Temperature is a measure of heat energy which is a from of "internal energy". The total energy is the sum of internal, kinetic and potential energy and the 1st Law states conservation of the total energy.

  7. /D

    Can you explain why a mechanism involving a net heat transfer from hot to cold obstructs cooling.

  8. I don't speak about "obstructing cooling".

  9. No, but the signature D did.

  10. I agree with Cementafriend that the one known as "ScienceofDoom" is not worth talking to; I have established to my professional satisfaction that he is an educated idiot. So are Eli Rabbett (sp.?), Chris Colose, the IPCC scientists, and so many more who infest the internet, pretending to be authoritative climate scientists. As a physical scientist, I have used the term "incompetent" to describe those who promulgate or subscribe to the climate "consensus", in particular to the notion of a greenhouse effect due to massive backradiation. But the simplest, most direct evidence does not dent their belief, so it goes beyond incompetence. They are fundamentally deluded, and not functioning as scientists at all, with respect to that theory. One cannot get through to them by reasoning, or pointing to the facts that disprove their belief. And to "/D", I would say, simply, "both plates emit heat, but the radiation from the colder plate cannot be absorbed by the hotter plate, while radiation from the hotter plate can be absorbed by the colder one". The "colder" radiation does not have enough energy to excite the hotter molecules in the second plate to their next higher energy level.

  11. Claes,

    when you write,
    "I say that there is a two-way wave mechanics connection between the two plates with a one-way transfer of heat energy from hot to cold. There is no circulation of heat energy with a net transfer from hot to cold. Circulating flow of energy (by itself) is unstable and thus non-physical."

    Can you elaborate what you mean with two-way wave mechanics connection, and Circulating flow of energy (by itself) is unstable and thus non-physical.

  12. Harry Dale Huffman,
    your last remark, isn't it directed to Felics?

    What /D seem to say is that thermal energy gets trapped a longer time between the hot body, surface of earth and cold body space outside the atmosphere, than if it where emitted directly from earths surface to space without any scattering events. Nothing about radiating plates.

  13. I think if people learn the difference between:

    absorption - dissipation

    on the one hand, and

    radiation pressure - heat transfer

    on the other hand, things will start to move.

  14. To Anonym: I explain two-way wave and one-way heat transfer in Slaying the Sky Dragon book.

  15. I'm not interested in buying a whole book to see the argument.

    I have a lot of peer review magazines to my disposal. Is the theory published somewhere?

  16. If you send me an email I will send a copy. It will be published in peer reviewed journal in different form.

  17. Thank you for the article Claes.

    Am I right in my interpretation that your argument for the alternative wave-model rests on an assumption that light couldn't be of a quantized nature?

  18. What is "quantized nature"? Stream of photon particles? I believe light is
    an electromagnetic wave phenomenon described by Maxwell's equations?
    What equations are streams of photons described by? Physics without (differential) equations is empty physics.

  19. The nature of light is a very interesting question. I recently started to study quantum optics and QED and it's really fascinating.

    The implications of the photoelectric effect is of course interesting, but not really illuminating for this particular question I guess, since there are, as I understand it, classical/semiclassical treatments that "explains" the phenomenon. And the same goes for black-body radiation (which you seem to give one version of).

    Streams of photons can be modeled with operators acting on a vacuum state and in the case of a minimized uncertainty it is possible to describe near classical coherent states. Maxwell's Equations (ME) can not be the final say, since they (ME) can not describe non-linear phenomena like photon - photon scattering. As I understand it, QED do provide versions of Maxwell's Equations but with an additional possibility of non-linear interaction.

    I also come thinking of an interesting experiment published as,

    Grangier et al. 'Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Ligth on Single-Photon Interferences.', Europhys. Lett, 1 (1986), 173-179,

    where the claim is that single-photon states are created.

    Interferometers and beam-splitters are of course interesting since they provide quite bizarre effects that can not be treated in a classical way.

    Well, as I said, I only recently started studying these topics and I can not claim any full grasp of the subject. It is really an overwhelming topic and it would be interesting to hear the opinion from somebody with working knowledge in the field.

  20. I agree, but it seems that physicists after Planck have lost interest in macroscopic phenomena like blackbody radiation and thus have little to say.
    To believe that the truth lies in photon-photin interaction seems very narrow-minded to me. Both the Earth and atmosphere are severely macroscopic and must be studied as such, I believe.

  21. I don't think climate science ever refers to QED so I don't really understand this discussion about photons or no photons. Maxwell will do well for our purposes.

    On the related subject, do you Claes have any experience on simulating magneto-hydrodynamics?

  22. We are planning to expand our hydrodynamics codes to MHD.

  23. Anders,
    the remarks mentioning quantum optics and QED is a reflection on the article I got sent to me from Claes, and is not directly connected with climate science.

    If I interpret it right, in the first paragraph it is argued that the greenhouse effect is based on the notion of streams of particles and that by replacing this with computational wave mechanics there is no process that can work as a greenhouse effect.

    From my philosophical ground, a kind of empirical skepticism, the thing that bugs me with this is the fact that we really seems to observe something quantized (single photon states), that is in some sense particles, albeit not of corpuscular nature. As I understand it, the theory of the nature of light is not in a definite form today (and maybe never will), and many incomplete models (like a wave package models) are circulating in the physical community. Maybe that is one of the interesting aspects of the subject.

  24. The way I think about it is the following:

    Let's make it a simple threebody problem:

    Two massive particles A and B at rest in our reference frame and un upward going photon. The photon can be viewed as a packet of momentum and energy. Suppose the two particles A and B absorbs the photon and hence the center of mass is accelerated upwards.

    Now suppose the particles reemit the photon downwards. By the momentum conservation law the center of mass has to be accelerated further upwards, but by emmiting the photon they have to relase the energy gained in the first reaction.


  25. Anders,
    Shouldn't your statement read, Clearly the Momentum can not be conserved...?

    But if "the" (identity should be pretty lost after absorption) reemitted photon changes frequency, doesn't that open some possibilities...?

  26. Well, momentum can technically be conserved if the particles take the recoil, but in that case they must either create energy from nothing or reemit at a lower frequency as you say.

    But what it tells us is that the idea that many people walk around with, namely that a single CO2 molecule can absorb and reemit photons at the same frequency in any direction they please is clearly false. Moreover, it puts far distance electromegnetic interactions and direct molecular collisions on the same footing as concerns thermodynamics.

    The real problem must thus be solved using the full machinery (MHD), and if it is done i suspect the greenhouse effect will disappear, if a nonexisting effect can do that.

  27. Isn't the greenhouse effect an experimental fact? I recall experiments that are so simple that one can practically do them in ones own kitchen.

    Take the following clips from youtube




    I was under the impression that this is the greenhouse effect. An interpretation of Stefan-Boltzmann must be consistent with what is happening in the bottles/tube of the experiments that is shown on youtube.

  28. If you claim that a simple kitchen experiment can say something meaningful about the complex climate system, you have to be a true master cook.

  29. Anonymous,

    The experiment clearly shows a physical effect, but it is not the greenhouse effect.

    A lamp is used which is driven by electricity, thus entropy increses during the experiment. The CO2 clearly acts as a heat insulation, increasing the temperature in the bottle.

    So far I agree. But the atmospheric greenhouse effect supposedly creates a temperature gradient in an atmosphere that would otherwise be isothermal, hence entropy decreases in violation of the second law.

  30. But your claim seems to be that carbon dioxide can't trap heat.

    How do you explain the experiments of the type that are seen in the youtube clips?

    Is the interpretation of Stefan-Boltzmann's law scale dependent?

  31. First of all one should remember that CO2 also emits radiation.

    What is shown in the film is that you can create a controlled environment where CO2 acts as an increased heat insulation.

    However, the atmospheric greenhouse effect works in a completely different way. It relies on an atmospheric radiating shell some kilometers up in the sky which is maintained at a lower temperature than the surface. This is necessary since, as I pointed out, greenhouse gases also emit radiation.

    Here is the point where most people get completely lost. The EXPLANATION given why this temperature difference EXISTS is, yes: greenhouse gases.

    See for example:


    From this point onwards things get more subtle, and that is probably the reason for much of the controversy. But it is an interesting problem I must admit.

  32. There is a saying "a little knowledge is dangerous". In the situation of the videos it can be said it is easy to confuse people with limited knowledge by providing limited information. None of the Youtube videos has anything to do with the earths atmosphere. For any experiment with the atmosphere one needs to consider at least the following conditions 1) temperature, density and pressure reduce as one moves away from the surface due to gravity effects (the effective height where gravitational force is zero is about 8.4 km and the environmental lapse rate is about 6.5C per 1000m) 2) An imaginery cube on the surface has only one of the 6 sides closed ie it is open on 5 sides for the exchange of heat and mass 3) The lower atmosphere contains only an average of about 380ppm CO2 but has according to proxy records been upto 7000ppm in the past (because humans breath out CO2 it likely the CO2 in a bedroom will be higher upto double and in submarines can get to 8000ppm without danger) 4) 70% of the earths surface is covered by water which can absorb and give off CO2 5) Evaporation of water (mass and heat transfer) is affected by insolation and air movement. 6) water (H2O) in solid, liquid and gaseous forms is a much greater aborber and emitter of energy in the wavelength range 2 to 20 micron than CO2 which is only significant around 15 micron. 7) instruments have error ranges and need to be properly used in the context of their limitations and specification. 8) laws and equations need to be applied and adjusted to take account of limitations and boundary conditions 9) etc etc
    Stephen Wilde makes the intersting comment "it looks like solar/atmospheric chemistry is the real issue and not radiative physics" in http://wattsupwiththat.com/2011/01/08/new-rate-of-stratospheric-photolysis-questions-ozone-hole/#comments "
    No one to date has an understanding of the complex interactions between the sun's energy emissions, the oceans, global surfaces and the atmosphere. AGW proponents by their very stance demonstrate that they have no understanding of technology and science.

    This blog, Claes' input and many of the comments are useful and helpful by improving knowledge.
    Best regards to all

  33. Forgive a laymans thoughts...
    I saw the YouTube experiment...
    Convincing? Well, maybe not, really. The heat/IR could be totally diffused by the CO2, which means that you instead would have a slightly more redish tint over the entire area and in all directions -Ok? Meassure the dT (by the very small color-shift) and add it up for all directions. Voila! Or?

  34. BoE,

    Well there is a tremendous amount of problems to be solved, I don't think anybody has an overview of that yet. You could perhaps first consult the G&T paper, especially section 4.2.

    But I think there are some general comments that could be made.

    First of all, the moment you specify a certain direction of your energy flow, let it be a material flow or the poynting vector of propagating light, you are not considering a heat transfer but rather some kind of organized motion which maybe during time is thermalized by dissipation. Hence, the IPCC radiation diagrams you often see do not represent any heat flow, possibly a force.

    As an example, for a grvitationally bound system like the atmosphere there must be forces acting upwards to maintain hydrostatic balance, but these are not thermalized.