torsdag 13 januari 2011

Isaac Asimov and his Science Fiction of the Greenhouse Effect


In 1977 the famous physicist (biochemist) and science fiction writer Isaac Asimov explains in very calm voice and convincing words in the CBS Radio program Quirks and Quarks, the "greenhouse effect", that the atmosphere acts like a sheet of glass, which "traps radiation" from the Earth surface and keeps it warm.

Asimov convinces the listeners that an increase of CO2 from burning fossil fuels, may cause a rise of the sea level of 200 feet and even trigger a scary "run away greenhouse effect like that on Venus". This is an early example of CO2 climate alarmism at its best.

We now know that the atmosphere does not act like a sheet of glass (preventing convection thus keeping the inside of a usual greenhouse warm), and that the "greenhouse effect" is science fiction without reality, as explained in the new book Slaying the Sky Dragon: Death to the Greenhouse Gas Theory.

But it is instructive to listen to Asimov's arguments, because these arguments represent a widely spread folklore of science (fiction) confusing the minds of people, politicians and in particular physicists, responsible for not debunking the science fiction and disinformation of the "greenhouse effect", of Asimov. This blind spot may show to be one of the most remarkable aspects of modern physics.

Compare with greenhouse doomsday propaganda from 1959 and a little more aged Asimov with even bigger whiskers from 1989, telling us that
  • the most interesting scientific event in 1988 was that everyone started to speak about the "greenhouse effect" just because it was a hot summer, when I had been speaking about it for 20 years.
We understand that physicists have invented the "greenhouse effect". It is now their responsibility to show that the invention is as much science fiction as cold fusion. But physicists say nothing expecting that this will not disturb the flow of money to Big Physics, forgetting that this money will be redirected to stop a "greenhouse effect" they have invented, away from strings of dark matter and dark energy.

But maybe physicists are happy with this telling themselves that also the "greenhouse effect" is physics and so it will be well spent money.

26 kommentarer:

  1. It is quite appaling to see how the minds of ordinary people and scientists have become so twisted. Especially the inability/avoidance to communicate what the ACTUAL greenhouse hypothesis is about, and which has been given a mathematical formulation (although it is very difficult to find for some reason).

    But now when the political spectacle is over it is time to turn the spotlight also on the scientific blind-followers in the form of luke-warmers and other educated idiots which there are plenty of.

    SvaraRadera
  2. I look forward to the article where you demonstrate the flaw in a real paper on the subject, for example, V. Ramanathan and J.A. Coakley’s 1978 paper, Climate Modeling through Radiative-Convective Models - published in Reviews of Geophysics and Space Physics.

    And also where you demonstrate the actual connection between your claims:
    1) "Back radiation", or atmospheric radiation, being a fiction
    2) Planck was wrong about quantization of energy

    You have them both in one of your papers but there is no actual connection between the two. Even if 2) was true (very unlikely) - back radiation is not actually falsified by it.

    Or do you have more revelations? - like radiatively-active gases:
    a) don't radiate at all
    b) have some directional component that no one else has spotted
    c) radiation is also a complete fiction

    You owe it to your readers I think.
    Unless you are having a laugh?

    SvaraRadera
  3. The trouble from physics point of view with two-way streams of photons, which Planck did not invent (he thought of quantization as a math statistics trick without physical reality), is that it is physically unstable (the photons
    would bounce into each other as a simple image) and nature cannot afford to play with unstable flows, only bubble economies and then only for short
    time. As I have said, radiation with "convective adjustment" is just another trick to get some numbers less incorrect, but is not physics.

    SvaraRadera
  4. Well, let's suppose that Planck was wrong.

    Do gases like water vapor radiate in all directions?

    Do gases like water vapor radiate at all?

    SvaraRadera
  5. Is this a quiz? Say what you want to say. We know that all bodies radiate to an
    exterior of 0 K. Is that what you are unsure about?

    SvaraRadera
  6. Claes, it is a quiz.

    I'm not unsure about it at all. I am unsure about what you think about it. Hence the quiz.

    In your paper “Computational Blackbody Radiation” dated September 16, 2010, which is one part "pure physics" and one part "climate science", you make the amazing and totally unsupported claim:

    “A main lesson of this note is that “backradiation” is unphysical because it is unstable and serves no role, and thus should be removed from climate science..””

    This is what I am trying to understand.

    What is "unphysical" about "backradiation" ?
    What is "unstable" about "backradiation" ?

    Gases radiate in all directions. It appears you agree.

    Therefore, some of the radiation from the gases is in the direction of space. And some of the radiation of the gases is in the direction of the ground. (And, just to be clear, it is in all directions, so some is at off at "right angles").

    So, what do you mean by your amazing claim that "back radiation" is "unphysical"?

    a) gases don't radiate ?
    b) gases radiate but only in a direction which means the irradiation never meets the ground ?
    c) radiation from gases that finally meets the ground has some amazing property unlike other radiation ?
    d) please state ?

    Or, if you prefer not to clarify, make some vague unrelated answer. I will understand.

    Gerlich & Tscheuschner have done likewise. They apparently believe in "backradiation" and that it "meets the ground" but don't feel it incumbent upon them to explain what happens afterwards.

    Which is really the essence of the whole question of "back radiation".. what happens when it arrives at the ground?

    Luckily, many many people unschooled in the subject of radiation haven't grasped this point. So if you want to make use of that lack of knowledge I recommend not answering clearly.

    SvaraRadera
  7. I say that a two-way stream of photons carrying heat energy back and forth between the Earth surface and the atmosphere, as displayed in the Kiehl-Trenberth energy budget diagram, is unphysical because it is unstable, in the same sense as backconduction or backdiffusion is unstable. Do you understand? Do you believe in backdiffusion?
    There is no backradiation and the heat energy is only radiated from warm to cold. Do you understand? The math details are in the article, and the essence is mathematical. Do you understand the math in the article?

    SvaraRadera
  8. I don't think I do understand your maths.

    You say:

    "The price of throwing out classical wave mechanics is very high, and it is thus natural to ask if this is really necessary? Is there a form of classical mechanics without the ultraviolet catastrophy? Can a cut-off of high frequencies be performed without an Alexander cut-off?

    We believe this is possible, and it is certainly highly desirable, because statistical mechanics is difficult to both understand and apply. We shall thus present a resolution where Planck’s statistical mechanics is replaced by deterministic mechanics viewing physics as a form of analog computation with finite precision with a certain dissipative diffusive effect, which we model by digital computational mechanics coming along with a certain numerical dissipation.
    "

    I believed that what you were trying to do was find an alternative theoretical explanation for the observed "Planck" waveform. That is, explain the observed waveform without the theory of quantization.

    Is this correct?

    The observed spectral intensity vs wavelength (or frequency) is still exactly the same regardless of the pure theory behind their production.

    Correct?

    So this is the connection I don't understand in your theory.

    When the sun irradiates the earth at a peak wavelength of 0.5um (with a near "blackbody" emission curve of 5780K), the earth radiates out at a peak wavelength of 10um.

    Is this "unphysical" ? Or real ?

    When the earth irradiates the atmosphere at a peak wavelength of 10um (with a near "blackbody" emission curve for whichever temperature it is emitting from - 288K as a typical), the atmosphere radiates out.

    But in the case of the atmosphere it is with a very different waveform with lots of "quantized" lines and overall the average wavelength is lower. And the quantized lines experience broadening, primarily with pressure.

    So here is my confusion.

    Are you saying that the measured total radiation of the atmosphere with a pyrgeometer is not real?

    That the spectrum observed with an FT-IR is not real?

    Is the atmospheric radiation "unphysical"?
    Is the earth's radiation "unphysical"?

    The underlying theory of how a body radiates is of mild interest (on a slow day) but not of primary interest to me.

    Are you saying that the measured absolute values and measured spectral values don't exist?

    This is the part I am hoping to glean from you.

    The spectra at the top of atmosphere has clear absorption bands in the waveform, corresponding to 15um, 10um and so on.

    The spectra in the downward radiation from the atmosphere at the surface has very clear peaks at 15um, 10um and so on.

    Are these two sets of corresponding measurements, Fiction? Unphysical?

    Why is the measurement of top of atmosphere radiation around 240 W/m^2, corresponding to an effective emitting temperature much lower than the earth's surface?

    I also note - still in the dark about your real beliefs - that the atmospheric observations (at TOA and at the surface) match the results from the theory of radiative transfer, which only needs to know the absorption and emission spectra of the various gases, but not the theory which results in these absorption and emission lines.

    I hope you can take the time to spell out your theory in relation to my questions.

    I believe that they would be asked by anyone who understood the theory of radiative transfer. Or who was familiar with observations of surface and top of atmosphere radiation.

    SvaraRadera
  9. If you don't understand the math, what do you want me to do? Explain without math, in just words? That is not physics, only hand-waving. Is that
    what you want?

    Yes, I derive a Planck law from a wave mechanical model without statistics of quanta, and the model shows one-propagation of heat energy from warm to cold under two-way wave propagation. The model has no backradiation. Do you understand that?

    I have discussed measuring DLR in a recent previous post, and shown that the instrument measures essentially temperature through a spectrum, but the connection to outgoing radiation is ad hoc invented according to a Planck law with exterior at 0 K, which is not applicable,
    because the exterior = atmosphere is not at 0 K. Understand?

    SvaraRadera
  10. Claes, you say "but the connection to outgoing radiation is ad hoc invented according to a Planck law with exterior at 0 K, which is not applicable, because the exterior = atmosphere is not at 0 K."

    In order for this to be relevant you must show how large the deviation from the case with a 0K exterior is. If the modification due to the exterior temperature is small then, as an engineer, I do not see how it is relevant.

    Do you have a theoretical derivation of the size of the deviation is? Or a simulation for a simple system which indicates that the deviation is large?

    I am an engineer, I want quantitative arguments, not arguments based on appealing to authority or fame.

    /David

    SvaraRadera
  11. Well, you know that the Planck law with an exterior temp of T_ext takes the from Q = sigma T^4 - sigma T_ext^4, and so the exterior temp is
    crucial. E.g. if T_ext = T then Q =0 . The difference can be monumental.

    SvaraRadera
  12. Claes, I'm trying to understand if it is worth taking the time to try and understand your maths. My maths and classical physics are very rusty.

    Sometimes there is no alternative to understanding the maths - I agree, as I explain myself. But mostly, with a few exceptions, the principles can be understood without a complete maths treatment. Usually the maths is needed for proof.

    Now providing more than the shortest of answers usually seems like too much trouble for you.

    You don't have to answer questions if you don't want to, but it seems like you would want to popularize your theory.

    The first place to look is what does experimental data show? And does this experimental data falsify your theory. There is a lot of data and it needs explaining.

    Even after the many questions I have asked, I still cannot really fathom what you think of the experimental data. All invalid? All supports your theory? I still don't know.

    It's not for lack of asking.

    The fact that most of your articles are not showing the flaws in "real atmospheric physics" but instead "Isaac Asimov" type characters seems to indicate that either you don't know anything of atmospheric physics of the last few decades, or are just not interested in the last few decades of atmospheric physics.

    Yet you appear to be interested in climate science.

    So perhaps you want to take more than a few sentences to explain what implications you believe your theory has for the measurements. And more importantly, to explain the measurements in the light of what you claim your theory says.

    Or perhaps not.

    Here is what I would propose if you are serious about explaining your theory and how it relates to the climate system:

    - Explain what you believe the various radiometers measure at top of atmosphere
    - Explain what you believe the various FT-IR devices measure at top of atmosphere
    - Explain why the spectrum at top of atmosphere has the shape it does
    - Then the same for the surface downward radiation

    - I'm sure the rest makes sense from there, e.g. if radiometers measure nothing of real value, what are FT-IRs doing? If they measure nothing do we know anything of radiation? Is there a device which can measure something useful. And so on.

    SvaraRadera
  13. For the discussion I think one can view radiative heat transfer
    as a form of conductive heat transfer following a Fourier law with
    heat flow prop to temperature drop or negative gradient. Nobody
    believes that there is a two way conductive flow of heat. Nobody
    believes there is backconduction.

    To measure heat flow one essentially measures change of temp,
    and by analogy radiative transfer through temp. But one has to be
    careful in the translation from temp to radiative flow. To say that
    Upwelling LR is 390 W just because that fits with Plancks law with
    T = 15 C and exterior temp 0 K, is incorrect since the atmospshere
    Temp is not 0 K.

    SvaraRadera
  14. What do you believe about the spectrum that is measured at the top of atmosphere?
    For example, the first graph under "Richard M. Goody" in Theory and Experiment – Atmospheric Radiation

    Is this measurement valid?
    If so, what is the explanation for this spectrum?

    SvaraRadera
  15. To /David:

    I think everyone is being obtuse. Step back for a bit:

    The "radiational energy budget" of the Earth-atmosphere system is famously given in the Trenberth and Kiehl diagram, going back to 1997 or so, which shows the surface emission to be 390 W/m^2, which is really just that necessary to allow climate scientists to consider the surface as a blackbody radiator (390 W/m^2 corresponds to a blackbody temperature of 288K = 15C, which is the temperature at the Earth's surface).

    What Claes is saying (this is the only sense I can make of it) is that the surface of the Earth is not a blackbody radiator, because between it and the 0K of space is our atmosphere. That is unarguable, but as I just showed above, the climate consensus (and ScienceofDoom's "theory of radiative transfer") depends on considering the Earth's surface a blackbody emitter (that is the only justification for showing its emission as just that of a blackbody at the temperature of the Earth's surface).

    I am a physicist, and I want physical understanding, not arguments based on meaningless numbers. Claes Johnson is saying, by way of his mathematical derivations, merely that heat transfer (including of course the exchange of infrared radiation) can indeed only be from warm to cold, and since the established lapse rate of the atmosphere makes the surface warmer than at any altitude above it, there can be no effective backradiation, in opposition to what both classical thermodynamics and his own mathematical modelling say is the natural heat flow upward. It is obviously "unphysical", as he has often said. He is unique, in my limited experience, in calling it "unstable", but if you read more of his work you will eventually see why he advances that terminology, as essential to understanding not just climate thermodynamics, but a general principle of approaching a wide array of mathematical physics problems (I can only be vague on this point). If he allows this comment by me, then I will consider I am not too far off from understanding him on a basic level; I do not claim to be an studied expert on his views, and let's see how hard he laughs at me (he has a great sense of humor).

    I am fairly certain I haven't given anyone satisfaction by my words above, but if you are a defender of the climate "consensus", as ScienceofDoom is, that is because you are deluded, and will not hear the bitter truth, no matter how it is put to you.

    If you are interested, the simplest, definitive disproof of the "greenhouse effect" comes from comparing the actual measured temperatures at corresponding pressures in the atmospheres of Venus and Earth. I have done so in an article entitled "Venus: No Greenhouse Effect" on my blog, "The Earth and Man: Setting the Stage."

    SvaraRadera
  16. To Sod: It seems to me that measuring OLR from TOA is based on measuring temperatures:

    "Notice the important point that to calculate the OLR (outgoing longwave radiation) measurements at the top of atmosphere we need atmospheric temperature and water vapor concentration"

    The very good fit between measured and computed radiation indicates that the instrument does a from of computation to get radiation from temp.

    I deleted your last comment by mistake: Resend.

    To Harry: I am happy to send that you agree.

    SvaraRadera
  17. To Harry:

    I guess we are on the same side, but for the discussion:

    "the established lapse rate of the atmosphere makes the surface warmer than at any altitude above it"

    Who or what established this lapse rate?

    SvaraRadera
  18. Good Morning, Anders:

    I might better have said, generally accepted and widely disseminated as authoritative. It is "established" in the mathematical definition of the "standard atmosphere", but since you asked, I looked in my copy of it, and it says at the beginning:

    "The 'Standard Atmosphere' is a hypothetical vertical distribution of atmospheric properties which, by international agreement, is roughly representative of year-round mid-latitude conditions. Typical usages include altimeter calibrations and aircraft design and performance calculations. It should be recognized that actual conditions may vary considerably from this standard."

    I have usually mentioned there are obvious deviations, such as localized areas of temperature inversion, when communicating in places where the standard atmosphere may be not well-known. Talking to scientists, I just acknowledge, with a word like "established", the general agreement I have found exhibited elsewhere.

    Physically, the lapse rate follows from the ideal gas law and hydrostatic equilibrium equations, very simply. Everyone should derive it, to understand that it is the heat capacity of the air molecules that "traps heat", not the addition of more infrared absorption (and emission) by increases in carbon dioxide or other supposed "greenhouse gases." In my view, the latter only aids in the heat transfer that is required by the general atmospheric conditions and thermodynamics -- by the lapse rate, that holds from the surface (where the "global temperature" of the climate scientists is defined) through the troposphere. The lapse rate basically establishes the heat-carrying structure of the atmosphere, in that part relevant to weather and climate as we experience them, on the surface.

    SvaraRadera
  19. Harry,

    I agree with most of what you said, in particular:

    "it is the heat capacity of the air molecules that "traps heat", not the addition of more infrared absorption (and emission) by increases in carbon dioxide or other supposed "greenhouse gases."

    "the latter only aids in the heat transfer that is required by the general atmospheric conditions and thermodynamics"

    Which are very important observations, however there appears to be unsolved mysteries regarding:

    "Physically, the lapse rate follows from the ideal gas law and hydrostatic equilibrium equations, very simply."

    Have a look at

    http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.1508v2.pdf

    It appears as if you can construct a variety of hydrostatically stable lapse rates from the ideal gas law. I have for a long time wanted an in-deapth discussion on this topic, since it strikes at the heart of the problem. It was brought up by Jelbring and Gilbert recently but passed virtually unnoticed since few people seemed to understand its relevance.

    Intuitively it seems obvious to me that gravity should have a warming effect on the lower atmosphere and a cooling effect of the upper atmosphere, the opposite holding in GE-theory, where the gravitationally driven "convective overturning" moderates the otherwise too steep temperature gradient that would obtain as a result of an unrestrained GE-heatpump.

    But the detailed mathematical formulation seems to be missing still on our part. Can we repair this?

    SvaraRadera
  20. I discuss this aspect in my article Climate Thermodynamics in the Sky Dragon book.

    SvaraRadera
  21. Yes, Anders, I have a copy of that 2010 paper, "On The Barometric Formulas and Their Derivation..." by physicists Gerlich and Tscheuschner, and have even referred to it on my blog once before.

    Nothing I have said is new, except perhaps my more detailed deductions from the Venus/Earth data; I am late to the climate science controversy, and I don't want to step on the rights of others who have made or tried to make many, even most, of the points I have raised, but have been zealously and dogmatically dismissed. It is important, in my opinion, not first to solve the detailed mathematical problem of the thermodynamics of the atmosphere. My first goal is to point out that the solution advanced by the IPCC and the "consensus of 97% of all climate scientists" has IN FACT already been disproved.

    I think my position is like that of Gerlich and Tscheuschner. They do indeed note (in the appendix of the article you cited) that "In the speculative discussion around the existence of an atmospheric natural greenhouse effect...or the existence of an atmospheric CO2 greenhouse effect, it is sometimes stated that the greenhouse effect could modify the temperature profile of the Earth's atmosphere." The reference they cite for this "speculative discussion" is just a New York Times blog site, so that speculation appears to be just that, and not a detailed mathematical demonstration of the possibility of such a modification of the lapse rate.

    It is instructive to quote further from G & T's article, because they essentially say what I would say: That the Venus/Earth atmospheric temperature data already disproves the greenhouse effect, definitively and finally. Specifically, they write, immediately after the above quoted text:

    "This conjecture is related to another popular but incorrect idea communicated by some proponents of the global warming hypothesis, namely the hypothesis that the temperatures of the Venus [atmosphere] are due to a greenhouse effect."

    They then go on to dispel this idea: "On the one hand, since the venusian atmosphere is opaque to visible light, the central assumption of the greenhouse hypothesis is not obeyed."

    They then administer the final blow: "On the other hand, if one compares the temperature and pressure profiles of Venus and Earth, one immediately will see that they are both very similar."

    I did not read this paper before I did just that, compared the Venus and Earth atmospheric temperatures at corresponding pressure levels, over the range of the Earth atmosphere from ~ 1 atm. down to 0.2 atm. (essentially covering the entire troposphere of the Earth atmosphere). And my realization was immediate, and my judgment final: There is no greenhouse effect (atmospheric warming due to increases in the concentration of CO2). Period, done, final, no more arguments possible.

    Therefore, even if increasing the CO2 concentration COULD change the lapse rate, that can have no effect on the atmospheric temperatures. Indeed, the observed lapse rate for Venus, with 96.5% CO2, is larger than that for the Earth -- but it has not warmed the "Earth-portion" of the Venusian atmosphere one iota over the Earth's own atmosphere. The only difference in their temperatures is entirely explained by their relative distances from the Sun. This is a monumental finding, in the context of the global warming debate, because it is so simple, and could have been done anytime since 1991, when the Venus data was obtained by the Magellan spacecraft. A student could do it, and the climate scientists should have done it, long ago.

    So let me repeat: Belief in the greenhouse effect is not just premature, not just overblown, not even just wrong. It is FUNDAMENTALLY INCOMPETENT, and has been for nearly 20 years. The debate of today is not a scientific one, it is an ideological one, and a political one.

    SvaraRadera
  22. Harry,

    I agree that OBSERVATIONAL evidence has already disproved the greenhouse hypothesis. The most compelling evidence I find in the "atmosphere" of Jupiter (quotation marks since Jupiter is a gas planet).

    Jupiter has a lapse rate although its main constituents are hydrogen and helium, which do not absorb IR-radiation. This I think falsifies the entire hypothesis, since it does in fact predict an isothermal atmosphere in the absense of greenhouse gases (few people are aware of this).

    However, for our own understanding there are some interesting observations to reflect upon:

    In our own atmosphere, on a daily basis the lapse rate (as a function of altitude) varies. In general if it is hotter the lapse rate is flatter, if it is colder it is steeper.

    You state that the lapse rate is steeper on Venus despite the fact that the force of gravity is weaker there, why is it so? Could it possibly be because CO2 molecules are heavier than N2 and O2?

    I have a (possibly silly) hobby hypothesis of my own, which maybe somebody could dismiss for me. Suppose that a reduction in air density causes thermometers to show a lower temperature, after all, vakuum out to be pretty cold, am I wrong?

    If we consider an isothermal atmosphere, the slope of the density curve depends on two variable parameters

    1. Temperature

    2. Weight of the molecules

    3. Gravitational acceleration

    Moreover

    4. Density follows pressure

    Thus, assuming that the readings of thermometers follow density (but not proportional to it), it seems to be in accord with several observational facts. But this of course assumes that thermometers measure "their own temperature" rather than the temperature of the surrounding.

    Expressed in terms of statistical mechanics the density function for an isothermal parcel of air takes the form

    \rho(h) = C*exp(-mgh/kT)

    Hence it could be interesting to compare the ratios

    mg/T

    for different atmosperes, where the absolute temperature T of course has to be postulated.

    SvaraRadera
  23. Anders

    ..."Suppose that a reduction in air density causes thermometers to show a lower temperature, after all, vakuum out to be pretty cold, am I wrong?"......

    I'm pretty sure that a mercury thermometer suspended inside an evacuated flask would read the same temperature as the walls of the flask if allowed to reach thermal equilibrium.

    Your comments on the atmosphere of Jupiter I found very interesting

    SvaraRadera
  24. Anders,

    This would be a good time to say I don't have all the answers, and have never claimed to have them. The answers that I do have, I try to communicate as clearly, simply, and forcefully as I can.

    I can answer your question about the lapse rate of Venus. If you go through the derivation I mentioned previously, you will find the lapse rate is gM/R, where g is the acceleration due to gravity, M the mean molecular weight of the atmosphere, and R the gas constant. So yes, the larger Venusian lapse rate is because CO2 (M=44) is a good deal heavier than O2 and N2 (aver. M=29, closely)

    SvaraRadera
  25. Pardon me, I should have said the lapse rate is proportional to gM/R, and it's more complex than that, too (since it also depends, not just on R, but the number of degrees of freedom that contribute to the mean specific heat, C_p). I will see if I can work out a more complete answer later. Nevertheless, the M factor is in there, as you thought.

    SvaraRadera
  26. Harry and Bryan,

    Thanks for the comments.

    The case of a mercury thermometer in equilibrium with the walls of an evacuated flask i guess would constitute some kind of radiative equilibrium and could quite possibly give the same reading, but maybe it would reflect geometrical aspects such as area versus heat capacity and so on. Anyway, I don't have many answers myself, especially not in the field of experimental thermodynamics.

    Nevertheless, I think some of the dynamical aspects of the lapse rate should guide us towards the correct solution. If it had been a straightforward heat conduction problem I presume increased solar forcing should correspond to a steeper lapse rate, since more heat must be transported, but nature seems to tell another story. As regards the thermodynamic approach of rising expanding / decsending compressing parcels of air we need to pay attention to the fact that also deep mines exhibit a higher temperature than the surface.

    Anyway, nice discussion, let's continue throw ideas.

    SvaraRadera