Robert Brown: What we don’t know about energy flow

Posted: January 2, 2012 by Rog Tallbloke in atmosphere, climate, Energy

I saw this comment on WUWT and was so impressed by it that I’m making a separate post of it here. Dr Brown (who is a physicist at Duke University) quotes another commenter and then gives us all an erudite lesson. If Nikolov and Zeller feel they need to take any of the complaints on WUWT about the way  they handle heat distribution from day to night side Earth seriously, they probably need to study this post carefully. this is also highly relevant to the reasons why Hans Jelbring used a simplified model for his paper, please see the new PREFACE added to his post for further elucidation.

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I can’t speak for your program, but I will stand by mine for correctly computing the ‘mean effective radiative temperature’ of a massless gray body as a perfect radiator. Remember, there is no real temperature in such of an example for there is no mass. It takes mass to even define temperature. (but most climate scientist have no problem with it and therefore they are all wrong, sorry)

I’d like to chime in and support this statement, without necessarily endorsing the results of the computation (since I’d have to look at code and results directly to do that:-). Let’s just think about scaling for a moment. There are several equations involved here:

P = (4\pi R^2)\epsilon\sigma T^4

is the total power radiated from a sphere of radius R at uniform temperature T. \sigma is the Stefan-Boltzmann constant and can be ignored for the moment in a scaling discussion. \epsilon describes the emissivity of the body and is a constant of order unity (unity for a black body, less for a “grey” body, more generally still a function of wavelength and not a constant at all). Again, for scaling we will ignore \epsilon.

Now let’s assume that the temperature is not uniform. To make life simple, we will model a non-uniform temperature as a sphere with a uniform “hot side” at temperature T + dT and a “cold side” at uniform temperature T – dT. Half of the sphere will be hot, half cold. The spatial mean temperature, note well, is still T. Then:

P’ = (4\pi R^2)\epsilon\sigma ( 0.5*(T + dT)^4 + 0.5(T – dT)^4)

is the power radiated away now. We only care how this scales, so we: a) Do a binomial expansion of P’ to second order (the first order terms in dT cancel); and b) form the ratio P’/P to get:

P’/P = 1 + 6 (dT/T)^2

This lets us make one observation and perform an estimate. The observation is that P’ is strictly larger than P — a non-uniform distribution of temperature on the sphere radiates energy away strictly faster than it is radiated away by a uniform sphere of the same radius with the same mean temperature. This is perfectly understandable — the fourth power of the hot side goes up much faster than the fourth power of the cold side goes down, never even mind that the cold side temperature is bounded from below at T_c = 0.

The estimate: dT/T \approx 0.03 for the Earth. This isn’t too important — it is an order of magnitude estimate, with T \approx 300K and dT \approx 10K. (0.03^2 = 0.0009 \approx 0.001 so that 6(0.03)^2 \approx 0.006. Of course, if you use latitude instead of day/night side stratification for dT, it is much larger. Really, one should use both and integrate the real temperature distribution (snapshot) — or work even harder — but we’re just trying to get a feel for how things vary here, not produce a credible quantitative computation.

For the Earth to be in equilibrium, S/4 must equal P’ — as much heat as is incident must be radiated away. I’m not concerned with the model, only with the magnitude of the scaling ratio — 1375 * 0.006 = 8.25 W/m^2, divided by four suggests that the fact that the temperature of the earth is not uniform increases the rate at which heat is lost (overall) by roughly 2 W/m^2. This is not a negligible amount in this game. It is even less negligible when one considers the difference not between mean daytime and mean nighttime temperatures but between equatorial and polar latitudes! There dT is more like 0.2, and the effect is far more pronounced!

The point is that as temperatures increase, the rate at which the Earth loses heat goes strictly up, all things being equal. Hot bodies lose heat (to radiation) much faster than cold bodies due to Stefan-Boltzmann’s T^4 straight up; then anything that increases the inhomogeneity of the temperature distribution around the (increased) mean tends to increase it further still. Note well that the former scales like:

P’/P = 1 + 4 dT/T + …

straight up! (This assumes T’ = T + dT, with dT << T the warming.) At the high end of the IPCC doom scale, a temperature increase of 5.6C is 5.6/280 \approx 0.02. That increases the rate of Stefan-Boltzmann radiative power loss by a factor of 0.08 or nearly 10%. I would argue that this is absurd — there is basically no way in hell doubling CO_2 (to a concentration that is still < 0.1%) is going to alter the radiative energy balance of the Earth by 10%.

The beauty of considering P’/P in all of these discussions is that it loses all of the annoying (and often unknown!) factors such as \epsilon. All that they require is that \epsilon itself not vary in first order, faster than the relevant term in the scaling relation. They also give one a number of “sanity checks”. The sanity checks suggest that one simply cannot assume that the Earth is a ball at some uniform temperature without making important errors, They also suggest that changes of more than 1-2C around some geological-time mean temperature are nearly absurdly unlikely, given the fundamental T^4 in the Stefan-Boltzmann equation. Basically, given T = 288, every 1K increase in T corresponds to a 1.4% increase in total radiated power. If one wants a “smoking gun” to explain global temperature variation, it needs to be smoking at a level where net power is modulated at the same scale as the temperature in degrees Kelvin.

Are there candidates for this sort of a gun? Sure. Albedo, for one. 1% changes in (absolute) albedo can modulate temperature by roughly 1K. An even better one is modulation of temperature distribution. If we learn anything from the decadal oscillations, it is that altering the way temperature is distributed on the surface of the planet has a profound and sometimes immediate effect on the net heating or cooling. This is especially true at the top of the troposphere. Alteration of greenhouse gas concentrations — especially water — have the right order of magnitude. Oceanic trapping and release and redistribution of heat is important — Europe isn’t cold not just because of CO_2 but because the Gulf Stream transports equatorial heat to warm it up! Interrupt the “global conveyor belt” and watch Europe freeze (and then North Asia freeze, and then North America freeze, and then…).

But best of all is a complex, nonlinear mix of all of the above! Albedo, global circulation (convection), Oceanic transport of heat, atmospheric water content, all change the way temperature is distributed (and hence lost to radiation) and all contribute, I’m quite certain, in nontrivial ways to the average global temperature. When heat is concentrated in the tropics, T_h is higher (and T_c is lower) compared to T and the world cools faster. When heat is distributed (convected) to the poles, T_h is closer to T_c and the world cools overall more slowly, closer to a baseline blackbody. When daytime temperatures are much higher than nighttime tempratures, the world cools relatively quickly; when they are more the same it is closer to baseline black/grey body. When dayside albedo is high less power is absorbed in the first place, and net cooling occurs; when nightside albedo is high there is less night cooling, less temperature differential, and so on.

The point is that this is a complex problem, not a simple one. When anyone claims that it is simple, they are probably trying to sell you something. It isn’t a simple physics problem, and it is nearly certain that we don’t yet know how all of the physics is laid out. The really annoying thing about the entire climate debate is the presumption by everyone that the science is settled. It is not. It is not even close to being settled. We will still be learning important things about the climate a decade from now. Until all of the physics is known, and there are no more watt/m^2 scale surprises, we won’t be able to build an accurate model, and until we can build an accurate model on a geological time scale, we won’t be able to answer the one simple question that must be answered before we can even estimate AGW:

What is the temperature that it would be outside right now, if CO_2 were still at its pre-industrial level?

I don’t think we can begin to answer this question based on what we know right now. We can’t explain why the MWP happened (without CO_2 modulation). We can’t explain why the LIA happened (without CO_2 modulation). We can’t explain all of the other significant climate changes all the way back to the Holocene Optimum (much warmer than today) or the Younger Dryas (much colder than today) even in just the Holocene. We can’t explain why there are ice ages 90,000 years out of every 100,000, why it was much warmer 15 million years ago, why geological time hot and cold periods come along and last for millions to hundreds of millions of years. We don’t know when the Holocene will end, or why it will end when it ends, or how long it will take to go from warm to cold conditions. We are pretty sure the Sun has a lot to do with all of this but we don’t know how, or whether or not it involves more than just the Sun. We cannot predict solar state decades in advance, let alone centuries, and don’t do that well predicting it on a timescale of merely years in advance. We cannot predict when or how strong the decadal oscillations will occur. We don’t know when continental drift will alter e.g. oceanic or atmospheric circulation patterns “enough” for new modes to emerge (modes which could lead to abrupt and violent changes in climate all over the world).

Finally, we don’t know how to build a faithful global climate model, in part because we need answers to many of these questions before we can do so! Until we can, we’re just building nonlinear function fitters that do OK at interpolation, and are lousy at extrapolation.

rgb

Comments
  1. Phillip Bratby says:

    Excellent comment by Dr Brown. Well spotted Roger.

    Why can’t these guys get together and produce a really good and comprehensive paper?

  2. Harriet Harridan says:

    Dr Brown does seem to be “the man”.

  3. colliemum says:

    Great catalogue of questions we don’t know the answers to. These are indeed the questions climate science needs to address. It is a great shame that so much time and money has been wasted by fixating on CO2 to the exclusion of the rest. It is even more shameful that in that process what should have been a scientific endeavour has become the political agenda of certain NGOs.

    My wish for 2012 is that, as Phil Bratby suggests above, these Drs get together and write that paper!

    Btw – didn’t quite a few of us say that once the proper physicists get going, climate science as The Team sells it, would be in for a very rude awakening?
    Thanks, everybody!

  4. tallbloke says:

    There’s more: Dr Brown said this in the comment where he gave me the go ahead to repoost his comment here:
    Robert Brown says:
    January 2, 2012 at 10:05 am

    Sure, no problem. Hopefully I did the algebra all correctly — it’s a pain to do algebra at a keyboard when you can’t run latex on the result to look at it. But then, it is pretty simple algebra. I think that this is one of NZ’s most interesting points — I’m not convinced that “pressure” per se is responsible for heat trapping as there is a bit of question begging in there that confuses cause and effect (as noted in a post a few days ago) but I’m very firmly convinced that neglecting effects on the order of dT/T or (dT/T)^2 in BOTH spatial AND temporal averaging is a capital mistake. I also do think that there is very probably a pressure effect, but I’m guessing that it has more to do with convection rates than with ideal gas laws. In any event, the correct rules should involve temperature dependent bulk moduli, not PV = NkT per se, or if you prefer, Navier-Stokes solutions of chaotic complexity.

    What I think that they got right is that there is a strong and largely ignored coupling between contact cooling of the surface via convection (including evaporation and conduction) and radiative cooling and trapping. Convection moves heat up through the bulk of the greenhouse gas column to where it can be efficiently radiated; I suspect that it is favorably driven as long as the surface is differentially warmed and cooled (as it is) to create those colorful, often wet, convection rolls called “the weather”. The weather and the wind are evidence that bulk transport of energy is rather important in the Earth’s dynamic energy balance. Not to mention the fact that northern Europe isn’t one big ice-pack. You’d think that people would learn from the fact that Scandinavia isn’t big ball of ice (but Greenland pretty much is, at about the same latitude). Good old Gulf Stream. Then there is the hypothesis that the Younger Dryas was caused by the interruption of the Gulf Stream when a huge freshwater ice dam broke during the original warming phase of the Holocene.

    =====================================

    Then there’s a brilliant exposition on convection and how it will always balance radiation with a negative feedback which anyone can follow. Hit the link to read the rest.

  5. Caroline Webb says:

    Agreed, Phillip. Work needs to be put into the journals. Trouble is finding an editor who does not fear being pilloried and forced to quit his job by certain powerful scientists.

  6. tallbloke says:

    Caroline: welcome. The brave editor is Sonja Boemer-Christiansen and she is the editor of ‘Energy and Environment’. A much pilloried journal which desrves our support and uplift for the sterling work it has done to keep the flame burning all these years in the face of vicious opposition.

  7. Phillip Bratby says:

    And Wayne also has lots of sense to contribute. Anyone know who he is?

  8. George says:

    This seems to have addressed a couple of problems I have had with these models. First is why they assume the dominant heat transport from the surface is radiative when we know that not to be the case. Anyone who has witnessed a “dust devil” in the desert (or on Mars) can see convection in action.

  9. George says:

    Oh, and the second thing was they assume the heat is evenly distributed. Glad to see someone injecting some real world conditions into things.

  10. Stephen Wilde says:

    Nice to see more and more people coming into line about the power and flexibility of the water cycle as a negative system response in the face of radiative forcing.

    And the need to treat the radiative portion of the greenhouse effect entirely differently to the gravitationally induced portion.

    Now we just need wider acceptance of the point that shifting of the permanent climate zones always accompanies changes in the rate of energy flow through the troposphere.

  11. tallbloke supporter says:

    Having read Dr Brown’s comments on convection and Joel Shore’s responses, these past discussions came to mind:

    http://rankexploits.com/musings/2009/how-model-e-deals-with-heat-from-viscous-dissipation/

    and

    http://climateaudit.org/2006/05/15/gerry-browning-numerical-climate-models/

    I’m not sure what the current state of play is – below is one comment from GB on the Blackboard which seems particularly relevant here. There are many informed comments. Apologies if it is a tangent.
    +++++++++++++

    “Gerlad Browning (Comment #8753)
    January 15th, 2009 at 12:51 am

    Dan Hughes (#8639),

    As we have discussed on CA, the climate models purport to solve the viscous, forced NS equations under the large scale assumption of hydrostatic equilibrium. But that is not the case because
    the natural cascade of enstrophy to smaller scales of motion is altered
    1) in the case of inappropriate water vapor parameterizations by convective adjustment, i.e. the convective adjustment redistributes the overturning in a vertical column caused by the inaccurate parameterizationsin in order to force hydrostatic balance. This is an ad hoc attempt to maintain hydrostatic balance and there is no mathematical or numerical theory that supports such a gimmick. In other words the model is no longer accurately approximating the full viscous NS equations.
    2) and because the dissipation in the model is orders of magnitude larger than in the real atmosphere, the cascade in the model is very different
    from the correct cascade. The models achieve a long term balance between the input and dissipation of energy by using forcing terms that are larger than they are in reality. This is why the forcings must be tuned each time the mesh size is decreased. If they were physically accurate,
    that would not be necessary.

    The IVP for the hydrostatic system is ill posed and no numerical method
    will converge to the correct continuum solution. The unbounded exponential growth of numerical solutions was demonstraterd
    by numerical convergence runs on CA and a mathematical reference discussing the issue cited (available on request).

    Jerry”
    ++++++++++++

  12. tallbloke says:

    I think one of the issues Joel has is he sees the world as conforming to the way climate models are constructed, because he believes the programmers of them are really describing the way the climate system operates with their ad hoc parameterisations and kludged heuristic mechanisms.

    This leads to some statements of religious faith which have no empirical evidence to back them up. Like the assumption that the water vapour feedback is positive.

    There are some criticisms of Dr Brown’s comment on Tamino’s blog. I won’t link it from here but I put the link on WUWT in the same thread as the top link.

  13. Roger Andrews says:

    “the fact that the temperature of the earth is not uniform increases the rate at which heat is lost (overall) by roughly 2 W/m^2. This is not a negligible amount in this game. It is even less negligible when one considers the difference not between mean daytime and mean nighttime temperatures but between equatorial and polar latitudes! There dT is more like 0.2, and the effect is far more pronounced!”

    The temperature differential between equatorial and polar latitudes has decreased by about 1C since 1900. Might this account for some of the 20th century warming?

  14. Tenuc says:

    Thanks for posting this Tallbloke – fits exactly with my world view. Until we understand and can quantify how spatio-temporal chaos effects living conditions on our planet all bets are off regarding predicting future states.

    This confirms my view that the current brand of climate science is not even asking the right questions, so no wonder the predictions it makes are so far from reality. It is simply pseudo-science which is designed to scare the masses to follow an agenda they otherwise would not take.

    Dr. Brown has produced one of the best one page summary of the current state of climate ‘science’ that I have ever read… 8-)

  15. tallbloke says:

    There are a few details to mop up. Tamino’s lot have a couple of potentially legitimate complaints.
    I’ll see if Robert addresses them on WUWT or at Tammy’s. If not, I’ll email him later.

    But yes, it looks pretty good on the whole. 8-)

  16. adolfogiurfa says:

    Heraclitus: “Everything flows” Πάντα ῥεῖ (panta rhea) , but proud and self conceit made scientists blind and they do not recognize up to now the primeval laws of music so they don´t know why it flows….
    Magister Ludii can play with colored glass beads to exemplify the simplicity of Nature.

  17. wayne says:

    Phillip Bratby says:
    January 2, 2012 at 8:12 pm

    And Wayne also has lots of sense to contribute. Anyone know who he is?
    —-
    I’m here (spasmodically that is☺), I’m Wayne Jackson from Oklahoma. As tallbloke knows, I jump between here and wuwt and…. Hard to call two fine sites home.

    The trouble is I have so much to say I can’t seem to get in a form that will add smoothly to these very, very important subjects. Dr Brown has laid these out in such a fine manner, he’s gifted, and, those are pretty much the same thoughts I carry in my mind!

    Maybe I could just answer if someone has a pointed question for now and I’ll comment more later when relevant.

    TALLBLOKE: Do you realize the labels on the edit controls used to logon are 1) also white so invisible or 2) not there at all? I’m going to post this assuming the email address goes on top.

    [reply] Wayne, think of the talkshop as home from home, you are welcome anytime. Which browser are you using?

  18. Phillip Bratby says:

    Thanks Wayne.

    Your contributions at WUWT were so clearly written and understandable that it seemed obvious to me that you ought to be collaborating with Robert Brown and others. Too many of the contributors to the debate (eg NZ) seem incapable of writing technical articles in understandable, logical and plain English.

  19. wayne says:

    Phillip asked if I might have some “sensible” input on this subject. Well, possibly but Dr. Brown has pretty well covered it so well.

    If anything my immediate input would be I don’t see why so many people, even warmists, are having such a problem with this concept. Anyone knowledgeable in physics should agree with this below (unless I make a mistake, then let me know)

    I keep saying, and posting around, maybe they don’t realize that pressure in any planetary atmosphere, averaged over the entire globe, is a constant set only by it’s mass, the area, and the gravitational acceleration. But that is in N&Z’s text.

    Maybe they don’t realize that the molar composition in a column vertically, averaged over all of the height is also a constant. And, hopefully they know the gas constant is itself a constant.

    So when you take PV = nRT or PV = NkT and rearrange terms to get density instead of volume as T = PM/(Rρ) and combining the constants to get, let’s use zeta, you end up with T = ζ ρ T = ζ/ρ with ζ being the PM/R constant. It’s all in N&Z’s text but you have to read part between the lines.
    [see foot for correction reference]

    I don’t know about anyone else but if T is in direct proportion to density and density is higher near the surface than high up then it must always be hotter at the surface naturally. So really it is the density, not the pressure we are talking about and no one is speaking of either density or pressure “creating” energy, this is just the way energy itself in a column will organize itself if not already at an equilibrium.

    But what are the temperatures? That causes me to ask, what about the speed of the molecules within such a static column of the atmosphere. (notice, I made it static to remove local effect here for simplicity as convection, evaporation, absorption) To me the molecules must all have the same speed all of the way up the column or they would be out of equilibrium and would eventually correct this imbalance. And everyone should be saying to themselves… it only depends on the total energy within a column, but, we really all knew that!

    And that seems to be the answer. The temperatures at BOTH the bottom and the top of the atmosphere, are strictly set by one parameter, the speed of the molecules. Makes sense to me. And, the density at any given layer is equal to the temperature adjusted by that constant.

    Lapse rate is the next big bug-a-boo, but, does everyone agree (and am I right) with each of those points before jumping there?

    CAVEAT: so far this is all about an averaged, static, homogenous world so don’t pick on local variances yet, there aren’t any.

    (Phillip, just read your commenting while posting this, thanks so much, make my last two years very worthwhile)

    [Edim @ January 3, 2012 at 3:25 pm and wayne @ January 3, 2012 at 6:34 pm -- Tim]

  20. wayne says:

    Oh, tallbloke, it’s IE 8, video 32 bit, first thing I checked, I was writing a game months ago and thought… oh, have I always been in 8 or 16 bit? Well, no. And I can see very faintly some bold ~36pt above this edit, Begins with ‘Leave’ ends in ‘y’ but can’t make out the rest. So the type is there. Never have hit this problem on any other site and I visit many, but somewhat limited to maybe twenty or so. It used to be there, I do know that, and I believe since they impounded your laptops, what was that.. end of November. I was on your site many times then.

    [Reply] I.E.8 is useful; for downloading Firefox. ;)

  21. wayne says:

    OK, OK. I’ll give up the IE ghost, Downloaded Firefox and you are right, the type is back. Whoa, shadowed! But what of the old geezers still on IE? Huh? You might still consider letting those holdovers a change to comment here should you?

    Man, already like this! Spell checker right in the edit control, fantastic!! Does it do math too? If not they need my physics script language I wrote a year ago. Latin symbols, 78000 units automatically converted on the fly when needed. Well, even without math i will still like this. Thanks for pushing me over hump Tallbloke.

  22. Eli Rabett says:

    The statement that “The point is that as temperatures increase, the rate at which the Earth loses heat goes strictly up, all things being equal.” is where the good Doctor Brown goes GIGO. It is correct that the rate at which the Earth’s SURFACE loses heat goes strictly up, but the surface is NOT where most of the thermal IR is emitted to space.

    That is rather high up in the atmosphere, which can be seen by comparing the emission to space with the Planck distribution of thermal emission from the surface (here for example, but there are plenty of accurate measurements and models). The point at which the emission curve matches a blackbody curve tells you what the temperature of the effective altitude at which emission is occurring to space. Raising the greenhouse gas concentration raises the level at which the emission to space occurs to a colder level, and thus one where emission is slower. To make up for that the surface has to warm in order to push more energy through the open window directly into space

    Arthur Smith handled the surface temperature distribution issue in some detail. To cut a long story there short, assumption of a uniform surface temperature UNDERESTIMATES the effect of greenhouse gases on surface temperature. To return to the first paragraph, DECREASING the temperature at which the Earth’s atmosphere radiates to space by increasing greenhouse gases, requires that the surface temperature INCREASE in order to restore radiative balance.

  23. tallbloke says:

    The point at which the emission curve matches a blackbody curve tells you what the temperature of the effective altitude at which emission is occurring to space.

    I’ve read this sentence several times now, and it looks borked to me. Try this:

    The point at which the emission curve matches a blackbody curve tells you the temperature of the effective altitude at which emission to space is occurring.

    Is that what you mean Eli?

    By the way, if radiation was the whole story, I’d agree with you.

  24. Edim says:

    Wayne, isn’t it T = ζ/ρ with ζ being PM/R? At the surface, assuming PM/R is constant, temperature and density are inversely proportional. Higher the temperature, lower the density (expansion).

  25. wayne says:

    Edim caught an error in my post above.

    Was erroneously given as T = ζρ

    Definitely should have been T = ζ/ρ

    Thanks Edim. Maybe with my new browser I can spend less time trying to catch missed spellings and pay attention to what I am really doing.

    [original error marked and corrected, if I am wrong say and I'll restore --Tim]

  26. [...] by way Watts, excerpted by Tallbloke, via a comment at Open Mind, comes another example, one Robert Brown, PhD, at Duke who offers up a [...]

  27. wayne says:

    I have one more big correction. My example above (January 3, 2012 at 10:54 am) is wrong… false. After some detailed thought I realized that the molecules within an atmospheric column in gravity will never be the same at different altitudes, just as pressure and density. Any molecule moving downward will always accelerate and that is why, at the molecular level, the gases lower in a gravity well will always be warmer as Nikolov and Zeller claimed. The opposite if moving upward. Bingo!

    I don’t know why I always have to know science down to such a core level, down to the guts, but I always do. To me being wrong while searching for truths is ok, not understanding exactly why is not, every time. Thanks for bearing with my persistence.

  28. [...] Tattersall (aka Tallbloke) writes on his blog of a WUWT comment. Unfortunately WUWT gets so many comments a day that I can’t read them all [...]

  29. Bill Clinton says:

    What is the temperature that it would be outside right now, if CO_2 were still at its pre-industrial level?

    Well, I can’t say what temperature it would be, but I am pretty confident it would be cooler, which by the way, would not be a good thing. I am personally grateful things have warmed up some.

  30. J Martin says:

    Wayne, I was about to question you on this statement you made; “To me the molecules must all have the same speed all of the way up the column or they would be out of equilibrium and would eventually correct this imbalance. And everyone should be saying to themselves…”

    When you then re-posted and said, “I realized that the molecules within an atmospheric column in gravity will never be the same at different altitudes, just as pressure and density. Any molecule moving downward will always accelerate and that is why, at the molecular level, the gases lower in a gravity well will always be warmer as Nikolov and Zeller claimed.”

    I am greatly relieved, as I had struggled for days to deal with some of the criticisms of the concept that Ira and Roy had raised, until finally something N&Z said in a post brought it home to me and I understood the concept and realised where I had gone wrong in my understanding. Which in my case was the idea that if you increased the pressure, then the temperature would also rise, but that the temperature would then fall to that of the surroundings.

    I finally realised that we are talking about a situation where there are no surroundings to disturb the temperature, an experimental column would be perfectly insulated and placed on a surface where gravity existed. No equalisation or external disturbance should take place. A control column should be located in space, both would be identical in size, shape amount of gas and temperature and pressure etc, etc. Put one in orbit around the moon and one on the surface of the moon and measure the temperatures at different heights of the column and the one in space would have the same temperature and pressure and density throughout, and the column on the surface of the moon would have a higher temperature near the base and a lower temperature at the top.

    It makes sense.

    Probably wouldn’t cost anything like the $100 billion dollars thus far wasted on trying and failing to prove that co2 is a danger to mankind or any part of the environment.

  31. tallbloke says:

    Steven Mosher says:
    January 6, 2012 at 11:46 am
    Finally, pushing heat “past” the GHG blanket at the surface, doesnt really get the job done.
    why? because its the C02 in the stratosphere ( which is dry) that really matters.

    Good to see the warmateers in full retreat to points beyond the tropopause. ;)

    Hey! You! Get off of my cloud!

    Lol.

  32. Dodgy Geezer says:

    A comment on a blog is nothing. This needs to be published in a peer-reviewed journal as a letter, or comment otherwise it can be ignored.

    And good luck getting anything into a journal which casts doubt on the multi-trillion industry that is global warming….

  33. [...] Tattersall (aka Tallbloke) writes on his blog of a WUWT comment. Unfortunately WUWT gets so many comments a day that I can’t read them all [...]

  34. tallbloke says:

    Heyup Dodgy Geezer.
    I think the day of the learned journal is just about done. We are advancing the science in the open at no cost far more quickly these days. If the big boys want to writhe in ignorance while we do their job for them, so be it.

  35. Dodgy Geezer says:

    @tallbloke

    ” I think the day of the learned journal is just about done. We are advancing the science in the open at no cost far more quickly these days…”

    Sorry – I should have made myself more clear. I wasn’t talking about the science. I was talking about the politics. That’s why I was suggesting that the item should be offered up to a major political magazine. Perhaps ‘Nature’….

  36. Jeff Id says:

    Good stuff.

  37. Dave Springer says:

    “That increases the rate of Stefan-Boltzmann radiative power loss by a factor of 0.08 or nearly 10%. I would argue that this is absurd — there is basically no way in hell doubling CO_2 (to a concentration that is still < 0.1%) is going to alter the radiative energy balance of the Earth by 10%."

    Absurd? Really? I can take a few grams of black soot and distribute it evenly over the top of a white automobile with a mass of millions of grams and it will change the radiative energy balance of that car tremendously. Sometimes a little can do a lot. One needs to think twice about calling something absurd. At sub-atomically small and cosmically large scales absurdity abounds. A Duke physicist ought to know that.

    In any case the measured average temperature of the lunar surface at mid-latitude locations is 250C and the albedo is the same as the earth's albedo would be without an atmosphere (or oceans or life). Whatever hypothetical collection of calculations is offered to produce a hypothetical temperature of the earth its first test is to be in agreement with actual observed temperature of the moon.

  38. Dave Springer says:

    Oops – the moon’s average temperature I cited above should be 250K not 250C. It’s -23C.

  39. Dave Springer says:

    Eli Rabett says:
    January 3, 2012 at 2:21 pm

    The statement that “The point is that as temperatures increase, the rate at which the Earth loses heat goes strictly up, all things being equal.” is where the good Doctor Brown goes GIGO. It is correct that the rate at which the Earth’s SURFACE loses heat goes strictly up, but the surface is NOT where most of the thermal IR is emitted to space.

    That is rather high up in the atmosphere, which can be seen by comparing the emission to space with the Planck distribution of thermal emission from the surface (here for example, but there are plenty of accurate measurements and models). The point at which the emission curve matches a blackbody curve tells you what the temperature of the effective altitude at which emission is occurring to space. Raising the greenhouse gas concentration raises the level at which the emission to space occurs to a colder level, and thus one where emission is slower. To make up for that the surface has to warm in order to push more energy through the open window directly into space

    Arthur Smith handled the surface temperature distribution issue in some detail. To cut a long story there short, assumption of a uniform surface temperature UNDERESTIMATES the effect of greenhouse gases on surface temperature. To return to the first paragraph, DECREASING the temperature at which the Earth’s atmosphere radiates to space by increasing greenhouse gases, requires that the surface temperature INCREASE in order to restore radiative balance.

    Close, Eli. Something has to warm up but it isn’t necessarily the surface. For instance evaporation, convection, and condenstation could increase and then the warmer surface would be the tops of clouds not the top of the ocean or top of the crust.

    In fact I believe that is exactly what IS happening which is why observations don’t make much sense until you come to accept that downwelling IR does not slow down the rate at which the ocean cools. At least not by much. The ocean cools primarily by evaporation not radiation. Downwelling IR is absorbed in the first several micrometers of the ocean’s surface and does little more than raise the evaporation rate. Because the energy is carried off as latent heat it does nothing to warm either the ocean or the air at the interface. It warms the atmosphere at the cloud layer.

  40. Dave Springer says:

    tallbloke says:

    January 7, 2012 at 5:58 pm

    “Dave: Please review Ned Nikolov’s comment here:
    http://tallbloke.wordpress.com/2011/12/28/unified-theory-of-climate-nikolov-and-zeller/#comment-13201

    This is actually where Brown’s criticism strikes paydirt. The rotation speed effects the mean temperature not just the distribution.

    I’ll bet you dollars against donuts that Nikolov’s poster which didn’t get much attention at the scientific conference, translated by popular non-scientific demand into a blog article, doesn’t get published in a peer reviewed journal of any import without major corrections. Gravity simply doesn’t work the way the authors believe it does. If they were correct we’d have the underlying principle for a perpetual motion machine. This will be soundly rejected by any peers with a better grounding in atmospheric physics.

  41. Dave Springer says:

    @Tallbloke

    In addition Nikolov makes a grave mistatement of fact that 250K never appears as the mean surface temperature anywhere on the moon.

    In fact it appears quite consistently at one meter deep in the regolith where two different Apollo missions to mid-latitude locations buried temperature probes from the surface to a depth of 3 meters to measure regolith thermal conductivity. These experiments sent data back to the earth for a period of 4 years. At any depth exceeding 1 meter the temperature was constant at -23C (250K) for the entire 4 year period. Does it really take a rocket scientist to know that when you dig down far enough into perenially dry soil to reach a constant year-round temperature it is in fact the mean temperature of the surface?

    The mean temperature of the moon is 250K. That isn’t hypothetical. It’s measured. Nikolov et al must not be aware it is a measured number not a calculated number. Oops. Open mouth, insert foot.

  42. tallbloke says:

    Dave, mid latitude readings are not going to give a mean temperature for the entire surface. That is one of Ned’s points. This is because of the obliquity of a hemi-sperical surface north or south of, say, around 50 degrees.

    Oops. Open mouth, insert foot.

    Indeed.

  43. tchannon says:

    Dave,

    South pole

    North pole is similar except has a large crater, with it seems a dome object at the pole, various theories to do with frozen stuff.

    These never face the sun.

    Now compute the whole surface temperature.

  44. wayne says:

    J Martin, there you go and sorry for little two day mental bobble on that subject. I believe you are the first I have run into in these threads to really get it and explain why, not just blind acceptance.

    Do you by chance remember what Dr. Nikolov said that keyed you? I’m trying to gather up some ‘tools’ like that for I’m already having resistance from many to even consider it. And you know, I can see that, that concept on the surface almost seems to break basic thermodynamic and radiative principles but it doesn’t. They forget to account for the potential energy and most thermodynamic equations have no height, gravitational, or potential energy terms.

    We learn two parcels of gases at two different temperatures will always equalize by energy spontaneously flowing from hotter to colder by radiation or conduction. But not in this gravitational case. Two parcels at two different altitudes will always have the same TOTAL energy, Ek+Ep, but the temperatures will be different, temperature is defined by kinetic and does not ever account for the gravitational potential energy. I guess you call that situation parcels in thermal stasis instead of thermal equilibrium.

    I have a book named ‘Gravitation’ totally explaining general relativity and I am beginning to wondering now if radiation also flows only when TOTAL energy is out of balance, not just temperature difference when gravity is involved, just like conduction I was describing in the paragraph above. Hmm. If I find something, it’s some 1300 pages, lots there to dig through, I comment back to this thread. may be N&Z will answer that in there expanded explanations.

    It’s going to take some work to get others to open their minds a bit to realize this IS the correct physics, Nikolov and Zeller are correct in this respect.

  45. tallbloke says:

    Wayne, good stuff. The bit I’m still trying to get my head around is the molecular level. The problem is that we still don’t know what gravity is. Now, it may well be that relativity will save the day, but at the moment I’m having problems understanding how the curvature of spacetime affects the temperature of a molecule or air packet.

    I totally get the idea that the total energy less the gravitational potential leaves the amount of energy available to be measurable heat from a Newtonian mechanics standpoint. And I can see why the groups of molecules at higher altitude have less kinetic energy by the time they got there and are maintained in that location by interactions with molecules from below. It’s the rate of the conduction of energy which bothers me a bit. The real interation of particles.

    Having said that, I noted with some amusement the other day that the lecture notes on a modern meteorology course someone linkked the other day used exactly the same unproven concepts of molecules in a gas attracting a t one distance apart, and repelling at a closer distance. The terminology was straight out of Maxwells 1857 conjectures following his reading of Clausius.

    Are we still relying on thought experiments for this stuff?

  46. J Martin says:

    Wayne,

    It was this;

    ρT = const. = P M / R

    This means that the product of temperature (T) and air density (ρ) is an invariant quantity (with respect to energy input) that depends on pressure (P). Therefore, increasing P in an isobaric process will cause an increase in both temperature and air density for the same energy input. What is unknown from this equation is how T will exactly change with P, i.e. in a linear or non-linear fashion, which is why we searched for and derived Eq. 7. But the concept that an equilibrium change in P must lead to an equilibrium change in T should have poised no difficulty to a physicists mind.

    found in the following comment;

    http://tallbloke.wordpress.com/2011/12/28/unified-theory-of-climate-nikolov-and-zeller/#comment-12892

    Though as science is never settled, I am finding discussions about enthalpy to be an added complication to my understanding. At this stage I would just like Russia and the US to get together and put a tall well insulated column of gas on the moon and in orbit with the necessary means of measurement and hopefully bring some clarification to this subject.

  47. Tenuc says:

    tallbloke says:
    January 7, 2012 at 8:46 pm
    “…The bit I’m still trying to get my head around is the molecular level…

    I’ve been pondering this for some time, but still don’t have all the answers. My thoughts to-date are that as the air is at its densest near the ground outgoing photons have more chance of hitting a molecule and increasing its KE (=temperature). As molecules are close together, an impacted molecule is likely to quickly have collision(s) with neighbouring molecule(s) and the energy from the photon impact is quickly shared.

    Those molecules higher up are further apart and have fewer photon collisions, so less KE. They also share the extra photon impact KE less with other molecules as they are further apart.

    So going up into the atmosphere you get a high density of high energy molecules with a fairly even energy distribution near the ground, which are constrained from rising because of the apparent downwards acceleration of gravity. At higher levels you get a lower density of lower energy molecules with a more uneven energy distribution.

    I’ve still to try and work out the effect of side winds, the Coriolis effect and how the photons being ejected by the molecules themselves interact.

    Any thoughts will be gratefully received…

  48. wayne says:

    Tallbloke says:

    “The problem is that we still don’t know what gravity is.”

    Really? Could have fooled me.

    “The bit I’m still trying to get my head around is the molecular level. ”

    Me too. That’s everything I have written here (and elsewhere). I think I have it almost down to the core but I’m not sure you saw to the bottom of what I was saying. Maybe so. It was not on heat transfer or conduction though moving molecules performs that too. It was about *temperature*, the thermodynamic definition, it’s very meaning in the context of a gravity as in our atmosphere. It’s a new thought, to me anyway, and I am investigating it, digging into it, and most likely am not putting into the best words. I have read some 100,000+ comments on wuwt and no one to date has laid it all out for everyone to know, or maybe I just missed it.

    OK, answer this question to see if we agree, if so, you did understand what I was saying:
    I see it right now, after my digging in the last two days, that the warmth near the surface, due to pressure, in a calm static atmosphere, will NOT naturally conduct to the colder air higher in the atmosphere (and it all has to due with gravity as I was speaking to J Martin).
    Do you see it that way? Has that light bulb gone off in your mind? It did in J Martin’s. I don’t know what Ned said but then he also understood.

    And tallbloke, let me know if I’m going too deep here, I can stay light if necessary, just talk of others’ papers and stay in the box. I’m new here and haven’t quite attained the flow here yet.

  49. tallbloke says:

    Wayne: I ‘got it’ as soon as I read it as regards the naturalness of the gradient in an equilibrium atmosphere subject to gravity. What I’m having problems with is the nitty gritty of how that relates to the various schemes we use to conceptualize the microscopic and the cosmic scales. i.e. molecular level forces and relativistic space-time curvature.

    I ask again, are we still relying on Maxwell and Einstein’s thought experiments, or are there usable equations of motion which will solve the issues?

    Maybe I should just take Hans’ advice and stick to packets of molecules around a billion at a time.

    Tenuc, I haven’t got as far as photons, I’m having enough trouble with molecules which attract each other at one distance and repel at closer distances. Maybe it’s a bit like Miles Mathis’ concept of the fundamental repulsion of the EM field in contrast to the gravity ‘field’.

  50. J Martin says:

    Wayne, I missed this part out from my Ned Nikolov quote, perhaps the most important part.

    ” Yet, what I’m finding (even among eminent scientists) is this unphysical belief that a change in pressure would only cause a transient response in T, which will eventually return to its per-disturbed value … How could have this most fundamental premise of classical thermodynamic been forgotten?! ”

    In other words, it stays at it’s new value and doesn’t return to it’s old value. So two tall columns in orbit above the moon (or Earth) at equal pressure temperature etc. One stays in orbit and one is brought down from orbit and placed upright on the surface, the one in space won’t change, but the one on the surface now has gravity affecting it. What now takes place in the column and what can be measured, do we see a temperature inversion ? Is that even possible ? is it an even temperature distribution, but with a difference in enthalpy (whatever that is, internal energy ?).

    Perhaps in practise the experiment is impossible,it would take too tall a cylinder.

  51. tallbloke says:

    J Martin: Did you review the experimental results from Graeff on the Loschmidt thread?

    He claims to have successfully measured the gradient in a 0.85m tall column.

    http://tallbloke.files.wordpress.com/2012/01/graeff1.pdf

    In Sheehan’s description of Graeffs experiments some columns were inverted to discount instrumental bias and they re-establihed the gradient within 36 hours or so.

  52. wayne says:

    J Martin, thanks for getting that, looks very familiar. ☺ That equation queued me to try a chart Venus, Earth and Mars and how about that… they do relate! Woke me up.

  53. p.g.sharrow says:

    @Tallbloke , I read the linked papers for the gravity test effects on temperature in a fluid. Nicely done experiment, simple and robust. Gets rid of any convection or outside radiation in or out.
    The only thing that concerned me was the need for brass fines to act as an energy stabilizing sink at one end. The claim that the device could be reversed with the same results calmed my concern.

    Reminds me of a series of gravity batteries that I created. Always negative on the bottom and positive on the top. No discernible useful current flow but definite potential. pg

  54. wayne says:

    J Martin : “What now takes place in the column and what can be measured, do we see a temperature inversion ?”

    That’s a good explanation from Ned and your question is very valid. Seems BenAW said it best in a later thread (exactly the way I tend to see it):
    “This would cause the whole column to be “sorted” in the long run, with the warmest air at the bottom. When stable, the total energy (sum of thermal end potential energy) at each level should be equal.”

    This is without any energy entering or exiting the column, right?

    I’ve been thinking how to better describe what happens in order of dependency: 1) The potential energy gradient is just “there”, imbedded in space itself, it is the gravitational field in a sense. You can’t create it or destroy it. If it does not exist there is no sorting and the temperatures stay homogeneous throughout. 2) The pressure and density gradient would occur *almost* instantaneous, that is logical and some what slowed by how fast the mass could move the distances needed (amount of acceleration, how long the column is). 3) The molecules … …. need some help here, why would the molecules sort, highest velocity at the surface? My gut says it would, but the mechanism doesn’t pop right out. See, I’m digesting this in real time so I’ll just go ahead and post this now and get back if and when I can intelligently answer it. If anyone can, have at it.

    You picked a good one J. Wow, this is like a physics twister that Feynman always came up with.

  55. wayne says:

    Tallbloke, just noticed the papers. Man you pulled those fast. So it does occur. And as always I will later want to know why, tell me why!

    I do wonder question why they came up with 7 K/km instead of 9.8 K/km in air’s case. Was it inaccuracy, I really doubt it. I thought that difference of 2.8 K/km was due to the extra energy in the troposphere from condensation but maybe I have the wrong sense on that too. Wow, that’s fantastic! Good work everyone. Real science questions being answered right here at Tallbloke’s TalkShop! Now to get some sleep. ☺

  56. tallbloke says:

    “The molecules … …. need some help here, why would the molecules sort, highest velocity at the surface? My gut says it would, but the mechanism doesn’t pop right out.”

    Wayne: Excellent! We are back on the same page. This question of yours goes straight back to the question Loschmidt was trying to answer. He thinks it must be a conduction effect. If so, it seems to be a function of the extra acceleration due to gravity adding velocity (and therefore collisional energy) to downward moving particles and the converse for upward moving particles.

    Graeff excluded radiative effects by filling the column with ground glass to absorb radiation.

    Sheehan has some complaints about Graeff’s interpretation of results which seem to hinge around not allowing for other effects he thinks must be present. Maybe Sheehan should do some experiments himself. :)

  57. Tenuc says:

    wayne says:
    January 8, 2012 at 2:23 am
    “…3) The molecules … …. need some help here, why would the molecules sort, highest velocity at the surface?…”

    Gravity gradient is highest at ground level. Greater number photon/molecule collisions at ground level, increases KE.

    Molecules at ground level have already realised there PE. The higher gravity at ground level reduces the possibility of upward mixing. It takes a central hit(s) by inbound or outbound photons to move molecules up and down the column. I’ve still to work out how wind, Coriolis effect and air molecules own photon emissions create mixing. However, as it is a dynamic process, I think this will be were spatio-temporal chaos kicks in, so I don’t expect a simple answer. Also wonder what happens at night, when only a low density of photons from above, but still high density from below???

    Help needed please!

  58. tallbloke says:

    Tenuc: AFAIK there are many more collisions (more correctly close encounters and consequent repulsion events if Maxwell’s imaginings are correct (cf Mathis)) between molecules and other molecules than between photons and molecules. Why the photon fixation? We don’t need them to explain conduction of energy in matter.

  59. Tenuc says:

    tallbloke says:
    January 8, 2012 at 9:59 am
    …Tenuc: AFAIK there are many more collisions (more correctly close encounters and consequent repulsion events if Maxwell’s imaginings are correct (cf Mathis)) between molecules and other molecules than between photons and molecules. Why the photon fixation? We don’t need them to explain conduction of energy in matter.

    Hi Rog, photons are important because they constantly introduce energy into the system, via collision.

    They also give direction to energy flows – molecular collisions are in random directions while collisions between photons and molecules are always at 90 degrees to the emitting surface and acting in the same direction as gravity.

    This means that a collision with a photon emitted by the earth will tend to move the molecule at some angle upwards, while a photon from above will tend to push it down. In any dynamic situation, the ubiquitous photon has a part to play.

  60. tallbloke says:

    Tenuc: OK, but everone keeps telling me photons are ‘massless’. How do they push molecules around? Aren’t molecule-molecule interactions more common, and more effective?

  61. Tenuc says:

    tallbloke says:
    January 8, 2012 at 11:31 am
    …Tenuc: OK, but everone keeps telling me photons are ‘massless’. How do they push molecules around? Aren’t molecule-molecule interactions more common, and more effective?

    The ‘massless’ photon is just another theory of today’s standard model. Have a read on Miles Mathis for a detailed explanation of the size and mass of the photon – may take a bit of searching there, but worth the effort! (May even be in his previous book?)

    Since the ridiculous Copenhagen interpretation back in the 1920, physics became remote from explaining thing by physical phenomenon, like photon impacts, and instead chose the wrong road that lead to virtual particles, vacuum energy, the Higgs boson and dark matter, in ever more mystical attempt to protect the status quo. That’s why little real progress has been made by physics in understanding the fundamentals like how does gravity work, what is magnetism e.t.c.

    I prefer a simpler more physical type of physics, where all matter is bound by the same rules and energy is transferred by real collisions, the universe of hard knocks, so to speak… :-)

    Concerning molecule-molecule interactions, yes these do transfer KE, but the billions of tiny photons passing through every square millimetre per second add energy to our climate system. Without the photon energy coming from the sun and all other matter in the galaxy our planet would cool in a fairly short time and life as we know it would cease to exist.

  62. tallbloke says:

    Ah, ok. Just so long as everyone is aware we are moving outside the bounds of the present discussion into speculative territory. As you know, I do find Miles Mathis’ theory of a fundamental E/M field interesting… and about as plausible as the mainstream sub-atomic theories. More work required :)

    Now, still including Mathis’ ideas, how about engaging with the issue of MAxwell’s deductive reasoning regarding the interaction of molecules? He says they attract when further apart, and repel when close together. This is similar to Mathis’ idea that planets nearing collision will develop a repulsion due to the EM field which will overcome the gravitational ‘attraction’. (Let’s leave his ideas on expansion out of the discussion for now, as he himself states an equivalence).

  63. Tenuc says:

    tallbloke says:
    January 8, 2012 at 12:19 pm
    “…Ah, ok. Just so long as everyone is aware we are moving outside the bounds of the present discussion into speculative territory. As you know, I do find Miles Mathis’ theory of a fundamental E/M field interesting… and about as plausible as the mainstream sub-atomic theories. More work required :)

    Now, still including Mathis’ ideas, how about engaging with the issue of MAxwell’s deductive reasoning regarding the interaction of molecules? He says they attract when further apart, and repel when close together. This is similar to Mathis’ idea that planets nearing collision will develop a repulsion due to the EM field which will overcome the gravitational ‘attraction’. (Let’s leave his ideas on expansion out of the discussion for now, as he himself states an equivalence).”…

    Most of the ideas being kicked around on this thread are speculative i think, Rog, as little work has been done regarding gas laws since Boyle et al. Physicist would rather spend billions on sexy colliders rather than ‘waste time’ experimenting and checking previous work to make sure nothing had been missed or over simplified. The idea of ‘perfect elasticity in an ideal gas’ is non-physical, and the reasons for the very small differences between experimental results and theory,perhaps, needs to be checked experimentally and fully understood.

    Regarding Maxwell’s conjectures I think that as each molecule in the air will be emitting a charge field, dependant on it’s density and radius, the following will happen…

    In static situations the apparent attraction of gravity will pull the molecules together when at some distance but as they get closer together their repulsive photon charge field will try to puch them apart. In real world dynamic situation, I think it likely that this effect will be swamped by the higher density charge field for sun and Earth.

    This is what I’m trying to get my head around as I posted in a previous thread – any help gratefully received please!

  64. eyesonu says:

    This is a very interesting thread.

    Thank you Robert Brown and Tallbloke.

  65. [...] comentario causó sorpresa, y fue elevado a la categoría de entrada; primero en lo de Tallbloke [-->], y luego en [...]

  66. Michael Hart says:

    tallbloke, Tenuc,
    If I understand your questions correctly, the atomic/molecular repulsions and attractions you refer to are well covered by quantum-mechanical molecular-orbital theory and solutions to the Schrödinger equation. That is, the forces of attraction and repulsion are, ultimately, almost entirely electrostatic, and governed by the electron probability-distribution around, and between, the nucleus/nuclei. Most of this probability (in the gas phase, at least) of finding the electrons falls within a very few atomic radii. [In fact, I would say that the interacting properties of such systems is the single best description of the subject called Chemistry.]

    Tb, a good example of a parameterized attractive-repulsive energy-well such as you ask about, is a Lennard-Jones potential. [Wikipedia has diagrams] As soon as you progress from hydrogen to more complex atoms and molecules the increasing asymmetry of mass and electron charge-distributions causes ever more complex deviations from the perfect gas law. [Those pesky hydrogen bonds make water the insufferably awkward molecule that it is because they are highly "directional", nothing at all like a perfect sphere]. I recall “virial coefficients” being added to the gas law to better describe all real gases, but that’s a bit of chemistry I was not so fond of. One for the Chemical engineers [but a lot of work has been done on it, Tenuc].

    Apologies if you know all this already. Below the ionosphere I’m also not sure that it really makes much difference to your discussions here: With simple, electrically uncharged molecules like N2 and O2, the inter-molecular interactions quite rapidly become vanishingly small and less frequent, with increasing distance between them. [As pressure decreases, gases behave more "ideally"].

  67. [...] new WUWT guest post star Robert Brown (originally promoted here at the talkshop after a stonkingly interesting comment at WUWT), in which Robert seems to be retreating from his earlier hardline anti N&Z position. [...]

  68. guscost says:

    Well, I’m a refugee now. Hi everyone.