No, pressure alone does not define surface temperatures!

Eli’s already covered this but I thought I would present a slightly different argument. The topic is a recent paper by Ned Nikolov and Karl Zeller called new insights on the physical nature of the atmospheric greenhouse effect deduced from an empirical planetary temperature model, an earlier version of which was retracted because they had published under pseudonyms (reversing the letters in their names).

The basic argument is that surface pressure sets surface temperatures. The idea being that for a planet like the Earth, we can get the pressure from the weight of the atmosphere and the surface area of the Earth, and that this then sets the surface temperature. This is patently nonsense, and a fairly simple way to see this is via the ideal gas law. The ideal gas law is that the pressure, P, is given by

PV = NkT,

where V is the volume being considered, N is the number of molecules in that volume, k is Boltzmann’s constant, and T is the temperature of the gas. If the gas has mass m and the mean mass per molecule is \mu m_u (m_u being some reference mass, and \mu a constant) then N = m/(\mu m_u) and we can write

P V = \dfrac{m}{\mu m_u} k T \Rightarrow P = \dfrac{m}{\mu m_u V} k T \Rightarrow P = \dfrac{\rho}{\mu m_u} k T,

where \rho is now the mass density.

As should be obvious from the above, the pressure alone cannot tell you what the temperature should be; it depends also on the density. For a given pressure, we could have a hot surface with a low density, or a cool surface with a higher density.

Update (09/08): As per Tom’s comment, their model does include a dependence on solar insolation and albedo and then indicates that the enhanced temperature depends on surface pressure. So, their model is not simply pressure, but it is still the case that surface pressure alone does not determine how the surface temperature is enhanced.

So, what actually sets the temperature?

Let’s imagine we have the Earth, but without an atmosphere (or with an atmosphere that is completely transparent). In such a scenario, the surface must radiate back into space – on average – as much energy as it recieves from the Sun. If it didn’t, it would either heat up, or cool down, until it did so.

If we assume this imaginary Earth has the same albedo as today’s Earth, and orbits today’s Sun, then it would reflect 30% of the incoming sunlight, and would absorb – on average – 240 W m-2. It would also, therefore, radiate 240 Wm-2 and would have an effective surface temperature of 255K. The exact distribution of temperatures on the surface, however, would depend on its rotation and the heat capacity of the surface (as discussed in this paper by Arthur Smith) but, in the absence of an atmospheric greenhouse effect, the surface has to have the same effective temperature as a blackbody that radiates – on average – 240 Wm-2.

Okay, so what about the actual Earth. Well, the surface of the Earth radiates almost 400 Wm-2. This is considerably more than the energy that we receive from the Sun. In the absence of an atmospheric greenhouse effect, the surface would be cooling rapidly, but it obviously does not.

How does this work? Well, there are many ways to explain this, but let’s go back to our imaginary Earth that does not have an atmospheric greenhouse effect. Now add an atmosphere with radiatively active gases. The surface would no longer be able to radiate directly to space. The atmosphere would act to block some of the outgoing longwavelength radiation coming from the surface. The atmosphere would then emit some of this energy back into space and some back down to the surface. However, initially, the amount escaping to space would be less than the amount being received from the Sun. The surface would then warm and emit more energy back into the atmosphere. The atmosphere would also warm, and emit more energy into space, and transfer more down to the surface. This would continue until the system (surface and atmosphere) had warmed until the amount of energy being radiated into space matched the amount of energy being received from the Sun.

A key point is that the amount of energy – on average – being radiated into space has to match the amount of energy being received from the Sun. In the absence of an atmospheric greenhouse effect, this comes directly from the surface. In the presence of an atmospheric greenhouse effect, this comes mostly from within the atmosphere and requires that the surface be warmer than it would be in the absence of the atmospheric greenhouse effect.

So, we can be very confident that Nikolov and Zeller’s argument that planetary surface temperature is set by pressure alone is wrong. Not only does pressure alone not define temperature, in the absence of a planetary greenhouse effect the surface should radiate as much energy as it receives from the Sun, which is clearly not the case for the Earth. The only way to explain why the surface radiates more energy than it gets from the Sun is because of the atmospheric greenhouse effect (to be clear, the surface radiates more than it gets from the Sun, but the planet radiates – into space – the same, on average, as it gets from the Sun). Also, if we add additional greenhouse gases to the atmosphere – as we are currently doing – then we’ll cause the surface to warm even more, as is currently happening.

Links:

Attribution – a post that tries to explain the energy balance.

This entry was posted in Climate change, Greenhouse effect, Research, Science and tagged , , , , . Bookmark the permalink.

134 Responses to No, pressure alone does not define surface temperatures!

  1. dikranmarsupial says:

    Caveat lector: I am not a physcist (as I suspect I am about to demonstrate).

    As I understand it, gas pressure is caused by the force exerted by gas molecules bouncing of the surface that experiences the pressure. The higher the kinetic energy of the molecules, the greater the pressure. This kinetic energy has to come from somewhere, in this case, largely energy radiated/convected from the surface, so isn’t the causal link more in the other direction?

    I wonder if any of this is a misunderstanding of the Kelvin-Helmholz mechansim by which potential energy of the atmosphere is converted into thermal energy (which happens on Jupiter, but not here), but that requires the atmosphere to be contracting and you only use up the potential energy once.

    I think I’ll stop there and go back to statistics ;o)

  2. Dikran,
    Indeed, gas pressure does come from the kinetic energy of the molecules, but it depends on their energy (temperature) and the number of molecules (density). You can’t get temperature (or density) from pressure alone.

    I don’t know if it is related to a misunderstanding of the Kelvin-Helmholz mechanism (which we have had a discussion about here before) but you’re correct, that if an atmosphere contracts it converts potential into thermal energy, but can only do that once, so you can’t sustain a constant atmospheric temperature using Kelvin-Helmholz.

  3. Geoff,
    Thanks, I had seen that, but had forgotten.

  4. dikranmarsupial says:

    Yes, I wasn’t suggesting that you could work out temperature from pressure alone, more that it is the surface temperature that keeps the atmosphere up, so while the two things are related, you can’t say that pressure sets/controls/governs surface temperatures (which I suspect is the thing that interests climate skeptics). In other words, pressure is the dependent variable and surface temperature is the independent variable (the mass of the atmosphere being held constant)?

  5. Dikran,
    At the base of the atmosphere, pressure is determined by the mass of the atmosphere (mass of atmosphere x g)/(surface area of Earth). Temperature is then set by energy balance, which determines the scale height (or vertical pressure profile).

  6. dikranmarsupial says:

    Ah, I see, of course, so it is “effective volume” that is the dependent variable (“surface temperature that keeps the atmosphere up)? I did say I wasn’t a physicist! ;o)

  7. Ed Davies says:

    I think the simplest explanation is to skip all the complexity of radiation between layers in the lower atmosphere and just point out that with extra CO₂ its density at altitude will be higher therefore the effective height at which radiation to space happens will be greater. The adiabatic lapse rates (dry or saturated as appropriate) then have more height to work over so the surface finishes up warmer.

    I understand that this way of looking at it was first published by Nils Ekholm in the QJRMS in 1901 but I don’t have library access to get a copy of the original article in full; I’ve only seen excerpts.

    After all, if some odd bit of chemistry meant that the extra greenhouse effect only happened in the upper atmosphere (e.g., if CO₂ needed to be exposed to UV radiation to make it act as a greenhouse gas or something) then we’d still get much the same warming.

    The effect of extra greenhouse gasses in the lower atmosphere is only to change the proportion of energy transfer done by radiation and that done by conduction/evaporation/convection. The temperature profile (and the emissivities) sets the amount of energy transferred by radiation; convection and co then deal with the rest [¹]. While I expect that’s interesting I think it would have, at most, a second order effect on the surface temperature.

    [¹] When the atmosphere is sufficiently transparent that radiation alone is enough to transfer the energy required then convection stops happening. We call that the stratosphere.

  8. Ed,

    I think the simplest explanation is to skip all the complexity of radiation between layers in the lower atmosphere and just point out that with extra CO₂ its density at altitude will be higher therefore the effective height at which radiation to space happens will be greater. The adiabatic lapse rates (dry or saturated as appropriate) then have more height to work over so the surface finishes up warmer.

    Indeed, and I do like this explanation. I’ve used it before. Was really just trying something different in this post.

  9. There’s also this post that addresses the it’s saturated argument.

  10. What’s interesting to me is how hard it is to argue with people advancing arguments like this. What I’ve realized is that most arguments between scientists are at the margin — scientists agree on almost everything and only disagree on this turbulent interface between what we know and don’t know. If you run into someone who doesn’t agree with you on anything, it becomes essentially impossible to resolve disagreements because there’s no shared basis of knowledge to use.

  11. Andrew,

    What’s interesting to me is how hard it is to argue with people advancing arguments like this.

    Indeed. I keep thinking “okay, here’s something obviously wroong – all I need to do is point it out” and then being surprised by how hard it is. I think you’re right that situations like this are when there isn’t even a shared knowledge about the basics, and so there is virtually no chance of agreement.

  12. Phil says:

    In your thought experiment, could you not modify the composition of the atmosphere of your hypothetical Earth so that the surface pressure (i.e. total mass of the atmosphere) remains unchanged, but the concentration of GHG changes ?

    This would change the amount of back radiation received by the surface. Unless Nikolov and Zeller have problems with the Planck-Einstein relation, its difficult to see how they could not understand this would result in differing surface temperatures for the same surface pressure ?

  13. Phil,

    could you not modify the composition of the atmosphere of your hypothetical Earth so that the surface pressure (i.e. total mass of the atmosphere) remains unchanged, but the concentration of GHG changes ?

    That is essentially what I was assuming. The surface pressure depends only on the mass of the atmosphere. The greenhouse effect – as you suggest – depends on the composition.

    Unless Nikolov and Zeller have problems with the Planck-Einstein relation, its difficult to see how they could not understand this would result in differing surface temperatures for the same surface pressure ?

    What I should have mentioned in the post is that there was a very lengthy Twitter exchange with Ned Nikolov involving Scott Denning, and myself, and others. Things that you would imagine would convince him that he was wrong, very obviously did not.

  14. Mal Adapted says:

    Andrew Dessler:

    If you run into someone who doesn’t agree with you on anything, it becomes essentially impossible to resolve disagreements because there’s no shared basis of knowledge to use.

    The most frustrating to me are the ones who think they know what science is, despite not being able to take the first step toward understanding AGW. Where do they get that idea? Who filled their heads with nonsense? It’s as if they attended a madrasa for AGW-deniers instead of high school.

  15. Eli Rabett says:

    About all you can do is try and inform third parties. Mary Beard and Mike Stuchberry have done a great job with different tactics on the issue of who the Romans in Britain were. One thing for sure, you need your own style

  16. Tom Curtis says:

    ATTP, from Nikolov and Zeller’s “functional model” 12, T(s) is proportional to T(na) x P(s)/P(r). In turn, T(na) is a function of a specified albedo and insolation. That is, it is not given by pressure alone, so quoting the Ideal Gas Law does not constitute a rebuttal.

    A more direct rebuttal is to note that functional models 1, 5, 7, and 12 all have R^2 greater than 0.98, and adjusted r^2 greater than 0.9. All but the last of these are purportedly attempts to model a greenhouse effect. Given that all of those models rely on an assumption that the volumetric concentration of CO2 equals the volumetric concentration of CH4 equals the volumetric concentration of H2O, and that the volumetric concentration of all other greenhouse gases equals zero (equation 7), it is clear that Nikolov and Zeller cannot argue that the deficiency in models 1, 5, and 7 is due to deficiencies in the theory rather than the unphysical assumptions in his model.

    What is worse, the theory of the greenhouse effect, properly understood, predicts that the greater the mass (and hence pressure) of all gases, the stronger the greenhouse effect provided that some GHG are present. As I understand it, if the Earth had an atmosphere of 100% CO2, but no more CO2 in the atmosphere than currently exists, it would have a much weaker greenhouse effect than an Earth whose only GHG was CO2, but the composition of whose atmosophere was otherwise unchanged. That the partial pressure of CO2 would fall more rapidly in the former case than in the latter. Therefore the mean altitude of radiation to space by the CO2 would be closer to the ground, and because of the relationship between mean altitude of radiation to space and tropospheric lapse rate to ground temperature, consequently the ground temperature would be lower. Arguably, therefore, the theory of the GHE predicts all of the successful models in Nikolov and Zeller’s paper. That is hardly justification for rejecting that theory in favour of the one model with no explicit GH component.

  17. Tom,

    ATTP, from Nikolov and Zeller’s “functional model” 12, T(s) is proportional to T(na) x P(s)/P(r). In turn, T(na) is a function of a specified albedo and insolation. That is, it is not given by pressure alone, so quoting the Ideal Gas Law does not constitute a rebuttal.

    Indeed, but I think the same basic problem exists. The enhanced surface temperature cannot be determined by the surface pressure alone. Okay, I guess I wasn’t quite clear that I meant the enhancement in surface temperature cannot be determined by pressure alone – I realise that he does have an insolation and albedo dependence.

  18. dikranmarsupial says:

    “What’s interesting to me is how hard it is to argue with people advancing arguments like this.”

    Indeed, this has been my experience with the “rise in atmospheric CO2 is not man made” arguments. They are obviously wrong, but no amount of engaging on the science will convince them, but hopefully it will mean that the other readers won’t be misled by them.

  19. Andrew Dodds says:

    I think that the very first statement in the paper:


    A recent study has revealed that the Earth’s natural atmospheric greenhouse effect is around 90 K or about 2.7 times stronger than assumed for the past 40 years.

    This is something of a warning sign, IMO.

  20. Andrew,
    Indeed. That is based (as I understand it) on a calculation of the average temperature of the surface of the Earth in the absence of an atmosphere, and in the absence of an ocean (i.e., the night side very quickly becomes very cold). The calculation may even be correct, but it simply illustrates a massive confusion about what we mean when we say the greenhouse effect increases the surface temperature by 33K – this is based on effective radiative temperatures (i.e., what would be the temperature of a blackbody that emits the same energy per square metre per second as the surface) not on the actual average of the temperature on the surface.

  21. David B. Benson says:

    A correction: the interior of Terra contains uranium which continues to decay and give off a sensible amount of heat. This needs to be added to the surface IR flux.

  22. David,
    Technically true. In practice, though, this is small and has probably been constant over the timescale of interest.

  23. David B. Benson says:

    Yes, according to Wikipedia only 0.027% of the surface heat budget is from internal heating.

  24. I must say that for a lay audience, it is difficult to beat this 1873 explanation of (what we now call) the Greenhouse Effect, by Tyndall:

    “As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial rays, produces a local heightening of the temperature at the earth’s surface. This, of course, does not imply indefinite accumulation, any more than the river dam does, the quantity lost by terrestrial radiation being, finally, equal to the quantity received from the sun.”
    John Tyndall, “Contributions to Molecular Physics on the Domain of Radiant Heat”, Chapter II, Section 23, Published 1873
    Available on The Internet Archive here
    https://archive.org/details/contributionsto00tyndgoog

    So, adding CO2 to the atmosphere would be equivalent to having a dam, holding back water (energy). If more CO2 is added, then it is equivalent to raising the height of dam, with more energy held back, and thereby, a higher temperature.

  25. Noting that Tyndall understood the importance of the ‘top of atmosphere’, as did Arrhenius. Pierrehumber & Archer (The Warming Papers) discuss how this understanding got lost somehow, even as late as Plass (1955), before it was finally reinstated in mid 1960s. But of course, some folk like to fight old battles from the 1860s, not just the 1960s!

  26. Richard,

    Noting that Tyndall understood the importance of the ‘top of atmosphere’, as did Arrhenius. Pierrehumber & Archer (The Warming Papers) discuss how this understanding got lost somehow, even as late as Plass (1955), before it was finally reinstated in mid 1960s.

    Indeed. This post has focussed a bit on the surface energy budget, but it’s worth highlighting Ray P’s comment, where he says

    The surface energy budget is mostly a sideshow. For the most part, the surface budget (which consists of radiation plus turbulent latent heat and sensible heat transfers) just acts to drag the surface temperature along with the low-level air temperature. Even so far as the downwelling IR goes, the main reason for the increase of downwelling IR is the increase of lower tropospheric temperature (mandated by combination of convection and top-of-atmosphere budget), not the direct effect of increased low-level opacity due to CO2. As the planet warms you do get a significant boost in lower level opacity from increasing boundary layer water vapor, but given that in most places the surface temperature is already close to the low level air temperature, this is not a major player, especially not over the oceans.

  27. Magma says:

    @ David B., average geothermal heat flow is estimated at ~80 mW/m² but it is not all that accurately known due to the technical difficulties of carrying out representative heat flow measurements across the highly varied surface geology/geography of the Earth, and the less complex but also less accessible sea floor.

    For comparison, solar variability corresponds to about 0.1% of the 340 W/m² top of atmosphere insolation, and mostly averages out over the main 11-year solar cycle. Tidal energy dissipation is ~8 mW/m² (mostly in the oceans, but some lost as solid-Earth inelastic deformation and heating. And nobody ever seems to mention the 8 or 9 mW/m² top of atmosphere irradiance from the Moon (inlunation?) consisting of reflected sunlight and blackbody radiation — sad!

  28. raypierre says:

    Many thanks to Ed Davies for the Ekholm reference. I haven’t been able to get hold of the 1899 Swedish original, but did download the QJRMS translation (which also evidently extends the original version). I’m reading through it now — it has a whole lot more in it than just the radiating level formulation of the greenhouse effect. For a long time I’ve been looking for the first published statement of this formulation, which is the most correct simplified way of looking at the phenomenon. If I had known about this paper earlier, David and I might have included at least an excerpt in The Warming Papers.

    I’m no longer inclined to write blog posts, having broken the addiction a few years back, but a discussion of the Ekholm paper would make a terrific historical post. I don’t know if it’s under copyright, so I can’t just post the article publicly, but I think it would be within fair use for me to email to one or two folks who might be interested in writing a piece on it.

  29. Willard says:

    > I don’t know if it’s under copyright

    Ekholm died in 1926, so it’s fair ball.

  30. dikranmarsupial says:

    @raypierre The Ekholm paper was discussed a bit by Steve Easterbrook here. I was surprised to see how old the “modern” mechanism of the greenhouse effect was! Prof. Easterbrook seems to have a book in preparation (which sounds very interesting – “computing the climate”), so he might be interested.

  31. Steven Mosher says:

    More history of science.
    And more rayp.

  32. Phil says:

    ATTP:

    That is essentially what I was assuming. The surface pressure depends only on the mass of the atmosphere. The greenhouse effect – as you suggest – depends on the composition.

    Sorry, I think in part my comment was me working out your OP for myself. So what I was suggesting was not a change to the physics of your explanation, but merely a different way of presenting it that made it easier to see how N&Z’s model was flawed (to me, at least).

    In my case one has two situations where the surface pressure is equal but the energy flux at the surface is different. You could also conceive of many other situations (by altering the balance of IR active and inactive gases) where the surface pressure is the same but the energy flux is different. The N&Z model suggests that these should all have the same temperature, despite the differing energy flux – which seems highly implausible.

  33. Ed Davies says:

    @raypierre I’d be grateful for a copy of the Ekholm paper if you email some out.

    https://edavies.me.uk/contact.html

    I think that Steve Easterbrook page that dikranmarsupial referenced was one of the places I saw an excerpt. There was another elsewhere but I really can’t remember where.

  34. Ed Davies says:

    If we’re going to be pedantic about 8 mW/m² of tidal dissipation then I’ll also point out that it’s the weight of the atmosphere which sets the surface pressure, not the mass, as gravity reduces with height.

    For the early versions of the software for these gliding flight date recorders http://ewavionics.com/ I did not take this into account in the software which did the conversion of pressure readings to height with the consequence that the calibration curves had a small but noticeable bias.

    If the atmosphere warms it will expand upwards so, even if its mass remains constant, its weight will decrease slightly so the surface pressure will also decrease, though not by much.

  35. Ed,

    it’s the weight of the atmosphere which sets the surface pressure, not the mass, as gravity reduces with height.

    Indeed 🙂

  36. Eli Rabett says:

    Tyndall was a pretty fair hand at Twitter too:

    The atmosphere admits of the entrance of the solar heat, but checks its exit; and the result is a tendency to accumulate heat at the surface of the planet.

  37. Marco says:

    Ed, maybe you were referring to Doc Snow’s article here?
    https://hubpages.com/education/Global-warming-science-press-and-storms
    If not, at the very least it is a very interesting piece of history that the Doc relates in that article 🙂

  38. Pingback: Cross blogging - Ocasapiens - Blog - Repubblica.it

  39. angech says:

    “The basic argument is that surface pressure sets surface temperatures. The idea being that for a planet like the Earth, we can get the pressure from the weight of the atmosphere and the surface area of the Earth, and that this then sets the surface temperature. This is patently nonsense, and a fairly simple way to see this is via the ideal gas law.”

    Something I am not clear on is the temperature at the bottom of the sea. Not a gas, sure.
    But having the interesting property that it’s solid form is lighter than the liquid so must rise to the warmer surface. Surely what keeps the water liquid at the massive pressures is that the pressures do affect the temperature preventing the water from freezing and rising?

    Relevance?

  40. angech,
    The temperature at the bottom of the ocean is a few oC. Water remains liquid to very high pressures at that temperature.

  41. angech says:

    “So, we can be very confident that Nikolov and Zeller’s argument that planetary surface temperature is set by pressure alone is wrong.”

    Good to see we are both on the same page re the model of radiation into space even if we disagree as to the effects that GHG leads to.

    I would essay that there may be some indirect truth in the statement in that there is a correlation between temperature and pressure as evinced by your ( their) formula hence knowing the pressure could lead to knowing the temp and vice versa. Does this mean one can state that the pressure sets the temp or that the temp sets the pressure or that both are correct?
    I would argue that once you introduce a GHG you have changed not only your mass density but your mass density response to pressure and temperature changes.
    In other words a gas containing a GHG fraction behaves differently to a gas that does not even if of equal initial density the the density changes of the different gas atmospheres would respond differently.
    I would not take it that they are totally wrong, only a flip side of your argument that has some merit if you look at the whole picture. The pressure at a surface is dependent on the actual atmosphere composition that exists.
    Eli savages them for using water as a basic reference. Fair enough. One does have to have some substance to use as a reference point to get their idea across.
    If we all could go that next step to what is the actual reference atmosphere composition then the two ideas are actually scientifically logical and not disproving each other.

  42. angech,
    See, Tom’s comment. There is a dependence on pressure, even in the standard greenhouse effect. The greenhouse effect is stronger if the pressure in the atmosphere is higher.

  43. angech says:

    “, The temperature at the bottom of the ocean is a few oC. Water remains liquid to very high pressures at that temperature.”

    Realised but the deeper it goes the less the heat from the sun can get to it by currents or convection so it should keep getting colder. That it doesn’t is due to the effect of pressure which as it increases must raise the temperature .
    There are no large bodies of earth size or greater that can have an ice core. I would imagine a world sized mass of water could be frozen on the outside but would be hot at its centre due to he pressure from its mass.

  44. angech,
    I’m not an expert at this, but I think water has this property that the density actually decreases if you go from 4oC to 0oC. As you get deeper, the water cools. However, any water that cools below 4oC starts to get less dense, and then rises. Hence, the bottom of the ocean can’t cool much below this and so doesn’t freeze.

  45. angech says:

    dikranmarsupial says:
    “August 8, 2017 at 7:23 pm
    Yes, I wasn’t suggesting that you could work out temperature from pressure alone, more that it is the surface temperature that keeps the atmosphere up, so while the two things are related, you can’t say that pressure sets/controls/governs surface temperatures (which I suspect is the thing that interests climate skeptics).”

    Some climate skeptics.
    Quite correct.
    There are people who do not want the GHG effect to be true by any way and means and this seems to be one of those lines.
    The point is still the composition of earth’s atmosphere along with its size and weight is such that changing the atmospheric composition will introduce a temperature change precisely by the pressure method specified hence it does not obviate the CO2 argument at all.

    My take, which you disagree strongly with, is that the CO2 introduction results in a large number of poorly quantified feedbacks and distributions that might mean ECS is a lot lower than we think. Another story.
    As said most skeptics know that CO2 raises temperature, some still want to buy an easy fix that does not exist.

  46. angech says:

    ATTP thanks it is very vexed that temperature of deep water. Maybe one of the oceanographers here can help. Certainly ice has a lower density (8/9ths) that of water whether at 4, 0, -2.8 (salty) degrees C. I doubt that the water at the bottom of the Mariambad trench is as warm as 4 C. I think it can be colder if the density is higher due to greater depth even if the pressure is stopping it getting colder and freezing.
    In other words what you say is true at the surface, must help the ice form at the surface, but at depths the temperature and density issues must have a different way of sorting out.
    Could even be like a lava lamp at the bottom !

  47. Scptical Wombat says:

    Eli aptly describes this paper as a word salad. When reading papers like this I tend to read them quickly and look for statements that are clearly wrong and show either a wish to be misleading or a profound ignorance of the field. For me the following extract fits this criterion beautifully.

    If gases of high LW absorptivity/emissivity such as CO2, methane and water vapor were indeed capable of trapping radiant heat, they could be used as insulators. However, practical experience has taught us that thermal radiation losses can only be reduced by using materials of very low IR absorptivity/emissivity and correspondingly high thermal reflectivity such as aluminum foil. These materials are known among engineers at NASA and in the construction industry as radiant barriers [129]. It is also known that high-emissivity materials promote radiative cooling. Yet, all climate models proposed since 1800s were built on the premise that the atmosphere warms Earth by limiting radiant heat losses of the surface through to the action of IR absorbing gases aloft.

  48. angech,
    Water is essentially incompressible (the density is not strongly influenced by pressure). What determines the density (as I understand it) is the temperature and salinity.

  49. dikranmarsupial says:

    Interesting question about pressure dependence of the freezing point of water, so I did a bit of googling, which led (via the physics StackExchange) to this phase diagram


    source

    which AFAICS seems to suggest that, freezing temperature is essentially independent of pressure until about a few hundred bar, which I think would cover most of the oceans, but not trenches etc.

    ATTPs suggestion about the density of water near freezing point sounds familiar/reasonable – doesn’t that imply it would be possible to have a “convection current” where the cold water is rising and the warmer water is falling!?

    “I would imagine a world sized mass of water could be frozen on the outside but would be hot at its centre due to he pressure from its mass.”

    now imagine it transported outside the solar system (so the amount of radiation falling on it is negligible). It will radiate heat away according to the Stefan-Botlzmann law and grow colder and colder. AFAICS, if mass/pressure alone kept the center warm we would have an inexhaustible source of energy (and have broken the first law of thermodynamics) as that heat would be continuously transferred to the outer layers of the planet and radiated away.

    caveat: already demonstrated I am not a physicist on this thread!

  50. doesn’t that imply it would be possible to have a “convection current” where the cold water is rising and the warmer water is falling!?

    I probably does, but maybe the timescale is long enough that it’s not all that relevant (I don’t know, though).

  51. raypierre says:

    Regarding the temperature of the deep ocean:

    There is no reason the deep ocean would keep getting colder and colder. Liquid water is so opaque in the infrared, it really has no way of losing heat. Vertical heat transport is fairly small, but insofar as it’s there, the vertical heat transport is downward. And (small though the effect is), heat is coming OUT of the hot interior of the earth into the ocean, not going the other way.

    Since the densest water sinks, the temperature of the deep ocean is set by the temperature of the water at the surface that becomes dense enough to sink. This is not a columnwise 1D process (unlike the tropical atmosphere, which really does behave in a sort of 1D way). The temperature of the deep ocean pretty much follows the polar temperatures, with some allowance for salinity effects.

    As others have noted, the equation of state for water does not come close to the liquid/solid transition even at the large pressures of the bottom of the ocean. On a very water-rich exoplanet, however, with a much deeper ocean, you can actually form Ice VI, which unlike Ice 1, stays at the bottom of the ocean. Very interesting oceanography. But Earth is nowhere near that regime.

    Fourier noted that the temperature goes down with depth in the ocean, opposite to the behavior in the atmosphere. He had some attempt at explaining that, but was pretty much off the mark, as he was for the atmosphere as well (though his atmospheric idea would be sort of on the right track for an atmosphere with a radiative-equilibrium rather than convective troposphere). Right about lotsa stuff, tho’

  52. dikranmarsupial says:

    Yes, I suspect the salinity changes (due to formation/melting of sea ice) would be more important in the Arctic, but it would make a cool lab experiment.

  53. raypierre says:

    Forgot to mention that in order to close the ocean circulation, you need to have a mixing process that allows cold water at the bottom to reach the surface. This generally takes some input of mechanical energy in order to mix against a stable density gradient. Without such stirring, the whole ocean fills up with the densest surface water made on the planet, and the circulation then becomes stagnant except for a thin frictional layer at the top. Cf “Sandström’s Theorem”

  54. Ray,
    Thanks, I thought someone who knew more would comment to clarify 🙂

  55. JCH says:

    This dance between upwelling and downwelling is interesting. I keep watching the behavior of OHC and SST: going into the 14-16 El Niño, during it, and after it. I don’t see how it can be squared with low climate sensitivity.

    It’s great to see raypierre commenting here. That should reinvigorate aTTP.

  56. Maybe I’m mistaken but what are the implications of this paper testing literally a dozen different statistical models with 15 variables with only 6 data points? This in itself seems rather dubious.

  57. angech says:

    “Water is essentially incompressible (the density is not strongly influenced by pressure).”

    What I also believed as well until reading about the expansion of solids as they come from the pressure of the depths.
    Different to a liquid at the surface (depths) but if one goes 40 kilometres down say a metal cannonball might conceivably be half the volume for the same mass.
    Water and iron are incompressible on the surface but the greater he depth the more compressible they become.
    Happy to be proved wrong.

    Dikran the larger the mass the more it generates its own heat from the pressure. A mass of water the size of the sun is near impossible but in the temporary time it existed would generate immense heat very quickly presumably leading to its dispersal.
    Meteorite size in absolute space cold
    Moon size. Some energy heat always at the core
    Earth size more so
    Jupiter size type more so but would contract in size
    Super Jupiter say 100 times a quasi sun.
    Sun size always a sun
    I would be interested to hear if astrophysicists have identified large cold bodies Jupiter size or above in space.
    Accumulating enough mass always leads to heat formation.

  58. Ragnaar says:

    Lucia and Curry had threads related to this. Ned Nikolov and Karl Zeller on this subject, sky dragons.

  59. Marco says:

    Ragnaar, did Curry really have a thread about this? I haven’t been at her place for a very long time, so I only remember the time she rapidly withdrew from any discussions with the sky dragons, because somehow they were not to be reasoned with. Which was quite hilarious at the time, considering her demand that climate scientists engage with skeptics.

  60. Ed Davies says:

    Marco: “Ed, maybe you were referring to Doc Snow’s article here?
    https://hubpages.com/education/Global-warming-science-press-and-storms”

    Yes, that was one of them. There’s also some interesting coverage of those attempted polar balloon flights in Richard Holmes’s book _Falling Upwards – How we took to the air_ though obviously with somewhat less about GHGs.

    I think I found the Doc Snow article as a result of searching while reading Spencer Weart’s _The Discovery of Global Warming_ pages, specifically this bit:

    https://history.aip.org/climate/simple.htm#S1C2

    Amusingly, that has a sidebox link just above to an article by raypierre. If only web links were bi-directional.

  61. Ragnaar says:

    https://judithcurry.com/2011/01/31/slaying-a-greenhouse-dragon/
    “I only remember the time she rapidly withdrew from any discussions with the sky dragons, because somehow they were not to be reasoned with.”
    I’ve found skydragons on youtube, and found myself appealing to authority. Finding discussions by Spencer addressing the subject too. And I saw the irony in that. Let’s see if I can offend everyone. WUWT should cut the skydragons loose. Then there’s the ocean skin layer sky dragons. I don’t see that you have to endorse everyone that’s on your side.

  62. MarkR says:

    @ dikranmarsupial, ATTP,

    You established this: pressure comes from air mass + planetary gravity and temperature is set by the energy balance, including the greenhouse effect, so it must be the atmospheric volume that increases or shrinks in response to T (V = nRT/P).

    Now think of Venus. It’s so hot that its surface radiates ~16.5 kW/m2, but it only gets ~0.1 kW/m2 in sunlight. Nikolov and Zeller should be able to explain how that ~16.5 kW/m2 is replaced. There was chat at Tallbloke’s where they and their fans refused to answer, except one person who suggested the greenhouse effect of dust based on a decades-old Hansen paper, which we now know is not the major factor. Nikolov refused to answer.

    You could release the gravitational potential by collapsing the atmosphere of course: Venus’ atmosphere has enough gravitational potential for a few months of those temperatures. That’s obviously not happening. With N&Z if they engaged and talk about the physics it could be useful. For example, if they stated that they reject conservation of energy or the Stefan-Boltzmann law, we could see specifically why their opinion is different from the results of physics. If they accept the laws of physics, then that raises other questions and real scientists would typically be interested in answering questions that come from their ideas.

  63. Pingback: The Virial Theorem | …and Then There's Physics

  64. Pingback: 2017: A year in review | …and Then There's Physics

  65. tallbloke says:

    ATTP: Indeed, gas pressure does come from the kinetic energy of the molecules

    And that kinetic energy comes ultimately from the Sun.

    But the way the gas is pressurised is by gravity acting on atmospheric mass to accelerate it towards the centre of gravity. So the surface air gets compressed to 14psi due to the weight of all the atmosphere above it. If the Sun were suddenly to drop its output, the atmosphere would become denser (and cooler) and the tropopause would be lower, but it would still be at 14psi at the surface, because it’s mass is still the same.

    From this you can see that its not the kinetic energy that sets the pressure, but gravity acting on the mass of the atmosphere. The kinetic energy makes no difference to the pressure, because the atmosphere isn’t constrained to a constant volume.

  66. tall,
    Yes, I know that the pressure at the base of the atmosphere is set by the weight of the atmospheric column. However, this and solar insolation alone do not set the temperature at the base of the atmosphere. This is set by a combination of solar insolation, albedo and the greenhouse effect due to radiatively active gases in the atmosphere.

  67. K says:

    So, the empirical evidence (N&Z 2017) says pressure & solar insolation alone determine surface temperature and you say it doesn’t? Where is your empirical evidence for this argument? The implication is that pressure and solar insolation also determine the the albedo and that gas chemistry has no role. It’s counter intuitive from the short term perspective (enjoying passing clouds on a sunny day) but it’s implied by the NASA data. Look at the albedos of Venus, Earth and Mars. Hmmm those clouds surrounding Venus are doing quite the job stabilizing Venus’ atmosphere from being boiled away. Why doesn’t Mars have more clouds and why does Earth have just exactly the right amount? Genius design if you ask me 🙂

  68. K,
    A fit to some data points, without any physics, provides little in the way of explanation for something. The key problem with the N&Z 2017 interpretation is that if there is no planetary greenhouse effect then the surface should be losing more energy than it is gaining and it should cool. The reason it doesn’t is because of the planetary greenhouse effect which essentially slows the flow of energy from the surface and causes the surface to be warmer than it would otherwise be.

  69. dikranmarsupial says:

    The model fit in the N&Z paper is fundamentally flawed. The model has two exponential components. The first (green) fits all planet from the moon to Titan, but it can’t explain Venus, so they add a second component to bodge the model so it fits Venus as well. This means the model can’t predict the temperature of Venus, just memorise it.

    https://mobile.twitter.com/Gavin_Cawley/status/1057591168631009281

  70. Willard says:

    > Genius design if you ask me.

    You can remove the sock, K.

  71. Tom Martin says:

    Zeller and Nikolov claim to be able to determine the long-term average temperature of Venus, Earth, Mars, Titan (a moon of Saturn), and Triton (a moon of Neptune) by using just two informational values: their distance from the Sun and their atmospheric pressure.

    This article claims instead
    “The basic argument is that surface pressure sets surface temperatures. The idea being that for a planet like the Earth, we can get the pressure from the weight of the atmosphere and the surface area of the Earth, and that this then sets the surface temperature. ”

    Zeller-Nikolov mention Pressure and Distance from Sun
    The article claims it is Pressure and surface area..
    not the same thing

    I think E=MC could easily be disproved
    but not E=MC^2

  72. Tom,

    Zeller-Nikolov mention Pressure and Distance from Sun

    Yes, I know, I’ve said that in the post. Their argument is essentially that pressure enhances the temperature relative to what it would be in the absence of an atmosphere. This is clearly wrong, since if there is no planetary greenhouse effect, then the surface temperature will not be enhanced, since – if it were – it would be losing more energy than it was gaining and it would cool back down.

  73. Tom Martin says:

    Thanks for your reply.
    I’m trying to get clear on something .
    Is there work being done to maintain the temperature gradient we see as adiabatic lapse rate ?
    In case I asked that awkwardly maybe this example will do –
    Death Valley at high noon is generally warmer than top of Mt Everest at high noon even though Mt Everest is closer to the equator so it should get a tad more direct sun, is more work being done to keep death Valley hot then the top of Everest or is it the added atmospheric pressure in Death Valley has a major hand in that?

  74. Tom,

    Is there work being done to maintain the temperature gradient we see as adiabatic lapse rate ?

    Globally, the system is in energy balance, so – on average – it’s in a quasi-steady-state. If the amount of energy coming in, matches the amount going out, then the total energy doesn’t change. However, there are – of course – variations on all sorts of timescales. So, if the environmental lapse rate doesn’t match the adiabatic lapse rate, then it will eventually tend back towards that, unless there is some mechanism that is acting to keep it at its current state. For example, if it is steeper than the adiatic lapse rate, convection will set in and energy will be transported via convection. If it’s shallower, then other processes will act to bring it back towards the adiabtic rate (to be clear, there are many factors that can influence this, so this is over-simplified).

    Death Valley at high noon is generally warmer than top of Mt Everest at high noon even though Mt Everest is closer to the equator so it should get a tad more direct sun, is more work being done to keep death Valley hot then the top of Everest or is it the added atmospheric pressure in Death Valley has a major hand in that?

    This is largely a consequence of the lapse rate. The temperature profile in the atmosphere will tend towards the adiabatic gradient (the dry adiabatic rate is 10K/km, but given the moisture in the atmosphere, the moist lapse rate is 7K/km). Since Everest has an altitude of 8km, this means that it will tend to have a temperature about 56K lower than the surface. [Edit: I initially said 35K. My only excuse is that it’s New Year’s Day.]

    Essentially, the temperature profile in the atmosphere will tend towards the adiabatic gradient (it will be convectively unstable if steeper, and will not be in energy balance if shallower, so will tend to steepen). Hence, the temperature will typically drop with altitude.

  75. Tom,
    This post (by Science of Doom) is quite a good explanation of the various processes that influence the atmospheric temperature gradient.

  76. colin says:

    Tom,
    your presentation can be used to support Nikolov’s theory:
    T=kP
    obvious positive linear relationship as k is positive.
    your observation that “For a given pressure, we could have a hot surface with a low density, or a cool surface with a higher density.” does not refute the obvious linear relationship.

  77. Colin,
    I’m not quite sure what you’re suggesting. There isn’t a simple linear relationship between temperature and pressure. They’re typically associated through an equation of state that depends on pressure, temperature and density. Hence, for a given pressure, there is not a unique temperature. The problem with Nikolov and Zeller’s suggestion is that if there is no planetary greenhuse effect then – at current temperatures – the surface should be losing more energy than it was gaining and should cool. The reason it doesn’t is because of the planetary greenhouse effect that means that energy cannot be radiated directly from the surface to space.

  78. izen says:

    @-Colin
    “…does not refute the obvious linear relationship.”

    That relationship is linear at the level set by the energy input.

    Consider sea level atmospheric pressure. It can vary with weather changes between 800-1000 hPa.
    But the temperature depends far more on the season. High pressure in summer is usually hot, in winter, cold.

  79. K says:

    There is no NZ ‘suggestion’ nor a NZ ‘theory’ but there are many implications from the NZ “DISCOVERY” that the long term (30+ years) global mean (i.e. the whole planet/moon surface) surface temperature, Ts, is a function of 1) the amount of atmosphere measured as a long term global mean surface pressure, Ps, and 2) the top of the atmosphere, TOA, solar irradiance, S: Ts=f(Ps, S). Note that all surface weather pressure changes, cloud changes, albedo, etc. are averaged out in the 30-year context of the NZ discovery. Also the Ts=f(Ps,S) discovery describes global mean Ts’s vs. Ps’s and S’s hence Ts in this context is not linear with Ps as in the idea gas law because we are describing whole and separated planetary means of active atmospheres and not relationships within a simple gaseous P,V,T sample. The reason it’s a discovery vs. a theory is that it is based on vetted NASA data and the regression equation fitted to the data has an r^2 = 0.9999. In addition it has predictive skills that predict within that same r^2=0.9999. You have to read the paper more than once to fully grasp the data and the significance of the discovery. https://t.co/SgWzeWz5WE
    Here is a simple layman’s explanation of the discovery: https://youtu.be/Hc30PoywKV4

  80. K,
    As Gavin Cawley pointed out, your discovery, involves overfitting a few data points. You exclude Titan and then need an extra function just to fit Venus. Also, if you extend your function to higher pressure, the temperature quickly becomes as hot as the surface of the Sun, and then high enough for nuclear fusion. Planets with such high pressures, and similar levels of insolation to the Earth, almost certainly exist. That their surface temperatures can be this high does not make physical sense.

    overfitted empirical model based on some NASA data (but excluding Titan as it doesn't fit) and fudging the model so that it has a separate component just for modelling Venus. The theory isn't the problem, it's the unwillingness to engage with the criticism. pic.twitter.com/gsBOpCxjaE— Gavin Cawley (@Gavin_Cawley) October 31, 2018

    So, if your discovery is not a suggestion, or a theiry, then what is it? If you don’t explain the significance of it, then what’s the point. The suggestion you seem to be making is that your discovery is some kind of challenge to the standard theory of the planetary greenhouse effect. Well, with a planetary greenhouse effect, the surface would be losing more energy than it was gaining and would be cooling. If you’re suggesting that the enhanced surface temperature can exist without a planetary greenhouse effect then your suggestion violates energy conservation.

  81. dikranmarsupial says:

    K “and the regression equation fitted to the data has an r^2 = 0.9999.”

    If you use an arbitrarily complex model, you can always make the R^2 approach 1. which is why a competent statistician would use something like AIC or BIC instead (which include a penalty for the complexity of the model) or properly evaluate the out-of-sample predictions of the model (hint: why didn’t N&Z look at the out-of-sample prediction for Venus?).

    At the end of the day, the model cannot predict the temperature of Venus, it can only tell you the temperature of Venus after the model has forcibly memorised it.

  82. Willard says:

    0.9999 is nothing, sockpuppy.

    Try to get multidecadal climate under one single millikelvin:

    https://judithcurry.com/2012/12/04/multidecadal-climate-to-within-a-millikelvin/

  83. Dave_Geologist says:

    Why doesn’t the paper mention a significance test K? Not even a simple t-Test?

    It’s trivially easy to get an R2 of 1 by over-fitting. And, trivially, such a result has zero significance, zero meaning and zero predictive value.

  84. K says:

    Folks just don’t (or can’t) take the time to study the paper in detail and consider the completeness of the work that we have put onto communicating the discovery and our guesses at it’s implications. Folks critique our discovery based on their current understanding of climate and green house theory. Our discovery portends a new paradigm and that will take study and contemplation to fully grasp as it is completely alien to all our current understandings and beliefs.

    Dave, to provide ‘meaning’ to our discovery, there’s a whole section on ‘model robustness’ where we use only (heaven forbid) 4 data sets, Moon, Triton, Mars & Venus, to generate a separate regression equation who’s parameters turned out to be very close to the original. Then we ‘predict’ (or verify) Earth & Titian’s long-term mean global surface temperature, Fig 6, to be within 1 C using only pressure and solar as input, then later in paper we predict the Ts of Pluto (a tenuous gas atmosphere) prior to verification by Horizon’s flyby measurement. Predictive capability from tenuous to non-tenuous atmospheres with one regression equation says a lot about the veracity of this discovery, I’d love to have such a regression predictor when I’m in Las Vegas. 🙂 We used all the NASA data available, still folks consistantly argue with us that 4 or 5 data points can’t prove anything, great criticism but consider dropping a stone here on Earth and taking 4 accurate time & distance measurements would allow one to extract Earth’s quasi gravitational constant as a fitting parameter with an r^2 close to 1. I’d use that value in Las Vegas in a heart beat.

    Please consider taking a useful approach and help advance climate science in general, we give you the data, check it out to verify that we’re not cheating on the values (especially the Ts we use for Mars), then do the t-Test you’re asking about and publish your findings, show how it debunks (or supports) our ‘robustness’ test then perhaps you will provide proof that it has ‘zero meaning’ or not. Good Luck in any case. Btw, I’m sure you’ve heard this before, my favorite definition of a ‘geologist’ is ‘a slow meteorologist’! which in-turn makes me a ‘fast’ geologist I guess 🙂

  85. K,
    Since you’re using “we” and “our” maybe we can be clear that you’re Karl Zeller, one of the authors?

    Our discovery portends a new paradigm and that will take study and contemplation to fully grasp as it is completely alien to all our current understandings and beliefs.

    You’ve simply fitted a function with a number of free parameters to a few data points. It doesn’t really qualify as a discovery.

    If you’re suggesting (as you seem to be) that this is some new paradigm that is at odds with the standard greenhouse effect, then it may be that you don’t fully appreciate the significance of what you’re suggesting. You’d be suggesting that something fundamental (like energy conservation, or blackbody radiation) must be wrong. Do you really think your fit to a few data points implies something quite that revolutionary?

  86. K so what happens if you leave out Venus and try and make an out of sample prediction using the other planets and moons as the calibration sample?

  87. Dave_Geologist says:

    K.

    Why. No. Significance. Test?

  88. Dave_Geologist says:

    OK I’ll put it another way K. How can you get an R2 of 0.9999 in a correlation involving data which must have a large observational uncertainty – to wit the surface temperature and pressure of distant worlds. Even if the underlying relationship was perfect, the imperfect measured values should lie off the perfect curve. Particularly with a small number of samples, you need to be right on the line to get an R2 of 0.9999 (you can get a high R2 with points lying well off the line, but only when you have a lot of samples, e.g. thousands).

    The obvious explanation is that the actual R2 is 1.0, and 0.9999 is a rounding error. In which case the system is obviously overdetermined, and your function is meaningless.

  89. K says:

    please read the paper to understand how the data was vetted. We spent about a year after we got the 0.9999 trying to find our mistake because we too thought it was too good to be true. You do the work: go in and find any error in our data. We give you the sources, most folks agree about our Mars value because it’s not published separately, but we have a whole Appendix explaining that value – so study it and tell us where we screwed up.

  90. K,
    You’re not really engaging with what is being said. As Dave points out, there must clearly be observational uncertainty in the datapoints. Hence, your extremely strong correlation seems suspiciously high. Dikran has made a similar point.

    Also, as I’ve been trying to point out, simply putting a line through some data points tells you very little. On what basis do you regard this as somehow groundbreaking. If you’re really claiming that it challenges the mainstream view of the greenhouse effect, then it actually suggests that you’re questioning something much more fundamental (like energy conservation, or blackbody radiation). Do you at least recognise this issue?

  91. Dave_Geologist says:

    We spent about a year after we got the 0.9999 trying to find our mistake because we too thought it was too good to be true.

    Function (5) has got four coefficients. Figure 12 has got only five data points. The system is over-determined. The result is meaningless.

  92. dikranmarsupial says:

    K why won’t you answer the question about the out-of-sample prediction for Venus? It has been raised three times already, and you have ignored it each time.

  93. Dave,
    I’m not even convinced it’s really 5 data points. I think the Moon essentially fits by default.

  94. Dave_Geologist says:

    Because it’s a vacuum I presume, ATTP. But I might give them that one, as long as they didn’t force-fit it to go through the Moon, which would be like forcing a linear regression fit to go through [0,0].

    And of course even if the t value was not undefined, they’d have to do a Bonferroni correction to compensate for the p-hacking involved in giving themselves twelve bites at the cherry.

  95. Dave,
    I think there function is essentially Ts/Tna (where Ts is the surface temperature and Tna is the temperature with no atmosphere). Since the Moon has no atmosphere, Ts/Tna = 1 and a very low pressure. The function is essentially pre-determined to go through that point.

  96. Willard says:

  97. Dave_Geologist says:

    I see that ATTP. If they had more data points, you could use the fact that the Moon has to be [1,0] as a test of the functional form (by not forcing it to pass through that point). Does it pass through the Moon with it included in the regression? Without it included in the regression?

    I do also have a suspicion that ratioing the pressure and temperature will lead to violation of energy conservation, which is essentially additive not multiplicative. What if you added ten times as much atmosphere? A hundred times as much? A million times as much? I guess that’s another way of saying you could end up with something hotter than the surface of the Sun, or hot enough to initiate nuclear fusion. So quite apart from the lack of statistical significance, the function advocated is obviously unphysical.

    Ho hum, Martin Gardner beckons. At least that is explicitly designed for amusement. BTW Figure 12 in my earlier comment should have read Figure 2, Model 12.

  98. Dave,

    I guess that’s another way of saying you could end up with something hotter than the surface of the Sun, or hot enough to initiate nuclear fusion. So quite apart from the lack of statistical significance, the function advocated is obviously unphysical.

    Already checked that. A planet with a hydrogen-rich atmosphere with a surface pressure 20 times that of Venus would have – according to Nikolov & Zeller – a temperature high enough for fusion to take place on its surface. I’m pretty sure such planets exist. I’m also pretty sure that their surface temperartures are not sufficient for hydrogen fusion. As you say, it’s unphysical.

  99. Michael D Sweet. says:

    ATTP,
    Upthread they discussed the density of sea water. Sea water is most dense at its freezing point (about -2C) http://www.wwnorton.com/college/geo/oceansci/cc/cc6.html. Fresh water is most dense at 4C but salt water is different. I am not sure why the deepest water in the ocean is 0-3C instead of -2C. People often confuse the 4C temperature for fresh water for the lower temperature of salt water.

    Deep water forms at the poles when salty water is cooled to its freezing point. Often the water left over after sea ice forms is extra saline and very dense so it sinks. If you want details contact the NSIDC which can inform you better than I can.

    Your threads are very informative. I recommend your blog to those who want detailed scientific answers.

  100. Michael,
    Yes, you’re quite right that the density of sea water increases as temperature decreases for all temperatures above freezing (i.e., there isn’t a peak density below which it is still liquid). I think parts of the ocean can be below 0C. My understanding is that the temperature of the deep ocean is basically set by the temperature of the water at the poles, that then sinks (because it is densest) and then follows the ocean circulation.

  101. Nelson says:

    Great thread. I looked for an answer to a question that has been puzzling me but I didn’t see it. So let me ask a very straight forward question.

    I can take the molar form of the ideal gas law and solve for T. I can then get estimates for all of the variables on the RHS of the equation. I plug them in and get something very close to 288K. The difference of 33K from the SB 255k is called the greenhouse effect, but nowhere did I need the composition of the atmosphere to get my result. I think this is what confuses people.

    If you say that the 33K is all the radiative greenhouse effect are you saying that air pressure due to gravity has no effect on temperature? Put another way, is it possible to start with the earth’s data at the surface and start substituting CO2 for oxygen in the ideal gas law equation in such a way that PVM/mR doesn’t change? Obviously, if I can, then T doesn’t change. In the same way, can’t I use the same formula to calculate the impact on T from increasing CO2 from 400ppm to 800 ppm. This is not my area of expertise, but it seems strange to me that the 98% of atmospheric gases that are non-radiative have no role in determining temperature, yet gravity would certainly still create about the same pressure. Thanks

  102. Nelson,
    The atmosphere is roughly an ideal gas, so there is a relationship between temperature, pressure and density. However, you need to know the values for two of these to work out the other. In the case of the Earth’s atmosphere, we know the pressure at the base of the atmosphere (it’s basically the weight of the atmospheric column). The temperature at the base of the atmosphere is essentially set by energy balance (what does the surface temperature need to be for the system to be in energy balance). The ideal gas law (equation of state) then tells us what the density must be.

    This, however, doesn’t play much of a direct role in the greenhouse effect (pressure does influence the width of the spectral lines, so does actually influence energy transfer, but this isn’t really a direct effect). If you really want to understand the impact of CO2, then you need to do quite a complex radiative transfer calculation.

    However, you can do a simple calculation of the following form.

    The incoming absorbed flux is

    E_{in} = \pi R_p^2 (1 - A) \frac{4 \pi R_*^2}{4 \pi a^2} \sigma T_*^4 = 4 \pi R_p^2 (1 - A) S_o,

    where S_o = 1360 W/m^2 is the solar constant. This tells us how much energy we get from the Sun.

    You can then write that the outgoing flux is

    E_{out} = 4 \pi R_p^2 \epsilon \sigma T_p^4,

    where T_p is the surface temperature and \epsilon is how much the surface flux is attenuated by the atmosphere (\epsilon \sim 0.6).

    If we have an estimate for how much adding CO2 reduces the outgoing flux, then we can roughly estimate how much the surface would need to warm to return to energy balance. This is very rough, but in the absence of feedbacks it would be about 1.2K of warming for every doubling of atmospheric CO2. Feedbacks are likely to amplify this to around 3K of warming for a doubling of atmospheric CO2.

  103. Nelson says:

    Thanks. I get what you are saying mathematically. I do find it a bit strange that to get to 3K of warming the feedbacks are greater than the initial forcing of 1.2K. In feedback theory, the gain is greater than the initial forcing. This makes for a very unstable system.

    I guess I am still confused. Here is a short video that uses the ideal gas law to calculate near surface temperature

    We have measures the parameters needed so we can solve for T. I’ve replicated the exercise.

    It seems to me that there should be a reconciliation between your equations and what is shown in the video. By that, I mean the energy from the sun has to drive density. Right? If we didn’t have the sun’s energy continuously hitting the earth, the atmosphere would collapse to the earth’s surface. The energy from the sun drives the height of the troposphere, stratosphere, etc. along with gravity. So my intuition is that there has to be a way to reconcile the two approaches mathematically.

    I don’t think the ideal gas law is wrong and I don’t think the radiative physics is wrong.

    As I asked before (and I have no right to your time to answer) and I am still puzzled about: is it possible in the ideal gas law equation to substitute CO2 for oxygen in a way that the parameters in the video (or the ratio) stay constant and hence temperature stays constant. I think you would argue that it is not possible because as you increase the amount of radiative gas in the atmosphere the temperature has to rise. The implication is that there isn’t a way to do the substitution of CO2 for oxygen.

    Thanks for your time

  104. Nelson,
    Well, the video is wrong. Pressure, by itself, doesn’t heat a gas. What can cause a gas to get hotter is if the pressure increases, or the volume gets smaller. Given that everything radiates, in the absence of a change in pressure, or volume, the gas would cool (if the pressure was fixed, it would also get denser). What maintains the surface temperature on the Earth is the planetary greenhouse effect. The radiative properties of gases in the atmosphere prevent the long-wavelength radiation from the planet’s surface from being radiated directly into space. This causes the surface to be warmer than it otherwise would be.

    If you substitued O2 for CO2, then the atmosphere would become almost transparent to infrared radiation, and the surface temperature would be lower (there would still be some clouds and water vapour, though, but not much in the way of non-condensing greenhouse gases).

  105. Nelson says:

    So I guess the implication of what you are stating is that a planet with an atmosphere on 80% nitrogen and 20% oxygen and no greenhouse gases would have a surface temperature of 255K no matter the surface pressure.

  106. Nelson,
    Actually, the surface pressure is simply the weight of the atmospheric column. So, if the planet had the same mass and radius as the Earth, and the atmosphere had the same mass as the Earth’s, then the surface pressure would be the same, irrespective of the composition of the atmosphere, or the temperature. However, yes, I am saying that if the atmosphere was predominantly oxygen and nitrogen, and if the albedo was about 0.3, then the average surface temperature would be close to 255 K (I have to admit that I’m not sure what level of atmospheric water vapour could be sustained, but since this precipitates, it probably wouldn’t be very substantial).

  107. Nelson says:

    In terms of the video being wrong, I don’t think the part of calculating T using the molar formula of the ideal gas law is wrong. I have done the calculation. You get a number very close to 288K

    In term of what it says about the greenhouse effect, I have no idea. As I stated above, it seems to me there should be a reconciliation.

    Here is a link to a paper that addresses the issue

    https://www.omicsonline.org/open-access/ideal-gas-law-and-the-greenhouse-effect-2157-7617-1000468.pdf

    His conclusion is that the ECS is quite small.

    I’d be curious where you think it goes wrong. From my viewpoint, the first part of using the molar form of the gas law is just very straight forward and not wrong. The rest I have no idea.

    My last formula math class was a graduate seminar in the Theory of Partial Differential Equations. The focus was on characteristics of systems of PDEs that can actually be solved. My take away was how restrictive the assumptions had to be to get a solution. I bring this up because while we understand radiative physics fairly well, convective forces not so much. In the Troposphere, the interaction of radiative, convective and conductive forces create an extremely complex system that boggles my mind.

  108. Nelson,
    The atmosphere is close to being an ideal gas. If you plug in the pressure and density then of course you get something close to 288K. Would be remarkable if you didn’t. It doesn’t tell you why it’s 288K though.

  109. Nelson says:

    So we agree that the ideal gas law gives approximately the right answer for the surface temperature.

    I don’t understand your statement that the ideal gas law doesn’t tell you why. Of course it does. It is just the basic property of ideal and near ideal gases.

    What you and others fail to address is that if the claim is that the greenhouse effect adds 33K of warmth to the SB 255K temperature to get 288K and the ideal gas law gives you the same 288K, then there should be a way of reconciling the two. This is a big intellectual failure to not have one.

    My guess is that as time passes and CO2 increases and the temperature doesn’t, there will be a re-think of the derivation of the ECS. As I am sure you are aware, when you take the current parameter values used in the ideal gas law for earth’s surface and you assume a doubling of CO2, you get an ECS of basically zero. It is a straight forward calculation to do. My point is that if you want to claim that a doubling will lead to 3 degree increase you should be able to explain why the ideal gas law isn’t giving the right answer. Handwaving does work for me.

  110. Nelson,

    I don’t understand your statement that the ideal gas law doesn’t tell you why. Of course it does. It is just the basic property of ideal and near ideal gases.

    I just mean that there are 3 variables. Pressure, density and temperature. Pressure is essentially the weight of the atmosphere, so we know that, but how do we know – from first principles – the density and temperature? We know what they are because we can go outside and take some measurements, but this doesn’t tell you why they have these values.

    What you and others fail to address is that if the claim is that the greenhouse effect adds 33K of warmth to the SB 255K temperature to get 288K and the ideal gas law gives you the same 288K, then there should be a way of reconciling the two. This is a big intellectual failure to not have one.

    The ideal gas law is essentially a closure relation. For example, if you do hydrodynamics, you can have an equation for mass conservation (density), you can have an equation for momentum conservation (velocity), and an equation for energy conservation (internal energy). However, you need some kind of closure relation that relates this internal energy to pressure (since you need to include pressure in the momentum equation). This closure relation can be the ideal gas law.

    So, a gas always obeys the ideal gas law, but this – by itself – cannot tell you what the pressure, density, and temperature should be. If you want to understand the temperature in the atmosphere, you need to model the flow of energy through the atmosphere (greenhouse effect).

  111. Nelson,
    We already know that the ECS can’t be zero. Not only have we warmed this century (and in line with what we expect from climate sensitivity) if it were zero, we would never have moved out of past ice ages.

  112. Willard says:

    > My guess is that as time passes and CO2 increases and the temperature doesn’t, there will be a re-think of the derivation of the ECS.

    My own guess is that necromancing a thread just to ask questions may have reached diminishing returns, Nelson:

    Doesn’t the ability to model ECS depend on an accurate model of the earth’s climate? Given data from the Greenland ice cores that shows significant variability that we can match to the written record, I am constantly amazed that the modelling community can’t come close to generating a model that produces anything like what the historic record shows for the North Atlantic.

    https://wattsupwiththat.wordpress.com/2016/04/09/do-the-adjustments-to-sea-surface-temperature-data-lower-the-global-warming-rate/#comment-2186189

    Thank you for your concerns.

  113. dikranmarsupial says:

    “As I am sure you are aware, when you take the current parameter values used in the ideal gas law for earth’s surface and you assume a doubling of CO2, you get an ECS of basically zero. ”

    This makes absolutely no sense whatsoever AFAICS. AIUI the ideal gas laws don’t say anything about radative absorbtion or emission, so how can you work out ECS in that framework?

  114. Nelson says:

    Let me put some numbers to what we are talking about

    I think we all agree that the gas constant R is 8.314

    For the earth, the following are the Pressure, Mean Molecular Weight and Density
    P=101.3 kPa
    M= 28.97 gm/mol^-1
    D= 1.225 kg/m^3

    This gives us the value of 288.14K
    So if we double CO2 from the preindustrial level we go from .03% to .06%

    If we believe the IPCC, the changes to the parameters will yield an answer of 291.14K

    in the following formula

    T = P/(R*(D/M))

    So it comes down to what happens to P, M and D

    This is where I get stuck as I am not sure. How much will pressure change if we add .03% to the atmosphere? My first guess is that it increases by .03%, which yields 101.33

    How much will density change? Well…Co2 is somewhat heavy so lets assume it increases by .05%. This yields D=1.2256

    My first guess is that M increases by .03%, which yields 28.979.

    If we plug in these numbers we get 288.12, which basically gives an ECS of 0

    Now, I think its likely the case that my assumptions are wrong. It seems to me that those who claim an ECS of 3, should be able to produce estimates of the gas law parameters that yield 291.14.

    Without thinking about it too much, it seems to me that it shouldn’t be impossible to experimentally estimate the parameter changes.

  115. verytallguy says:

    Nelson, by your analysis, if the sun is turned off, the temperature does not change.

    Ask yourself how this tells you where you have gone wrong.

  116. dikranmarsupial says:

    The mass of the atmosphere, and thus pressure is fixed. Thus the two free variables are temperature and the scale height of the atmosphere (and thus its density). It isn’t too surprising that this equation holds, but that doesn’t mean pressure determines the temperature. It doesn’t it is fixed and the density of the atmosphere depends on its temperature.

    If you work out ECS without considering energy balance it is hardly surprising you don’t get a sensible answer.

    “Without thinking about it too much”

    A bit too much of that already, perhaps? ;o)

  117. Everett F Sargent says:

    If there were no GHG’s then there is a delta of 33C.
    Using the IGL then implies that the surface density (rho) of our atmosphere would be 288/255 of it’s current surface density,
    Check with this (using 0 and -33) …
    https://www.digitaldutch.com/atmoscalc/
    P = rho * R * T / M (P, R and M are constants, so it is a trade off between rho and T)

    You need another relationship than the IGL to account for the GHG’s (what ATTP wrote). :/

  118. Everett F Sargent says:

    https://en.wikipedia.org/wiki/Ideal_gas_law#Molar_form
    Defining the specific gas constant Rspecific as the ratio R/M …
    P = rho * Rspecific * T (P = constant because weight of atmosphere is constant)

  119. Dave_Geologist says:

    What you and others fail to address is that if the claim is that the greenhouse effect adds 33K of warmth to the SB 255K temperature to get 288K and the ideal gas law gives you the same 288K, then there should be a way of reconciling the two. This is a big intellectual failure to not have one.

    Just as well there is a way of reconciling the two. And therefore no intellectual failure. The Earth’s surface temperature absent greenhouse gases would be 255K. The atmosphere is close to an ideal gas, so if there were no GHGs, and you calculated the surface temperature from the surface pressure and density, you’d get 255K. The Earth’s surface temperature with greenhouse gases is 288K. The atmosphere is close to an ideal gas, so if you calculate the surface temperature from the surface pressure and density, you get 288K. It’s true because it’s a truism. One that doesn’t tell you why it works for both 255K and 288K.

    My guess is that as time passes and CO2 increases and the temperature doesn’t, there will be a re-think of the derivation of the ECS.
    My certitude is that there will not. Because I can’t just do arithmetic, I understand the physics. And. as per the site’s name, Then There’s Physics. BTW the temperature hasn’t stopped rising, has it? Even the “pause” was not statistically significant. And it’s half a decade in the rear-view mirror now. Here’s a fun quiz question: of the ten warmest years on record, how many were (a) this decade, (b) last decade, (c) last century, (d) last millennium, (e) last 10,000 years. No handwaving, look it up. And not on WUWT. How about the fifty warmest?

    As I am sure you are aware, when you take the current parameter values used in the ideal gas law for earth’s surface and you assume a doubling of CO2, you get an ECS of basically zero a Gas Constant of 8.314 J/K/mol.

    There, fixed it for you. You can’t get ECS from that equation. Try a bit of dimensional analysis, then explain how it works when the units of ECS are not J/K/mol. It’s as meaningless as using weight divided by length to derive speed.

    Handwaving doesn’t work for me.

    Me neither. So why did you appeal to your intuition a couple of posts earlier, and to guesswork in this one?

  120. henk korbee says:

    Thanks for the information. But please don’t mix science with politics, you will get a mess. Pollution is the problem not climate. To every claim about climate there is an opposite one so it isn’t an issue for the public not to speak about politicians who are searching a base for their agenda.

  121. henk,
    I’m not quite sure where you’re getting the “mix science with politics” from, but I think I’ll stick with deciding myself what I choose to mix with what.

  122. geoffmprice says:

    “To every claim about climate there is an opposite one”

    The existence of opposing claims is unsurprising – tells us about the market demand for ideas, not the validity of ideas.

    The thing that is unique to science is that assigns validity to claims according to how they hold up when tested against observations in reality. A highly recommended approach for learning to differentiate “claims”.

  123. K says:

    What is it about the NASA-data measured long-term mean global surface temperature of our Moon being 197K and given that Moon & Earth are equidistant from the Sun that makes Earth’s no-atmosphere so-called SB effective temperature 255K valid? A simplified SB calculation is not data, it’s a simplified calculation! And no, the albedo of Earth with no atmosphere would not be ~30% but will approach ~12-13% like other spherical no-atmosphere celestial bodies (Moon, Mercury, etc.). Does O2 & N2 somehow provide for the 255-197 = 58K difference? God has provided ‘and then there’s physics’ folks with the Moon as a clue & this paper uses His clue to explain the discrepancy: https://springerplus.springeropen.com/articles/10.1186/2193-1801-3-723. 🙂

  124. K,
    It’s clear that you’re confusing the average of the temperature, and the effective temperature. The Earth has an albedo of 0.3 and so – given the Solar insolation – has an effective radiative temperature of 255K. Of course, if the Earth didn’t have atmosphere, it would have a different albedo, but that doesn’t change that with an albedo of 0.3, its effective radiative temperature is 255K. The Moon has an albedo of 0.12, which gives it an effective radiative temperature of about 270K. This is not the same as the average of its temperature. It tells us what temperature a blackbody would have that radiative the same amount of energy per square metre per second as the Moon would need to do in order to be in energy balance (i.e., for the incoming flux to match the outgoing flux).

  125. Karl Zeller says:

    OK, 255K is the temperature of a perfect black body at Earth’s distant from Sun, an easy calculation to make based on the SB law & it is called the effective emission temperature.
    Building on that with some additional (physical?) reasoning: given that the long term global multiple-year mean surface temperatures as measured, (i.e. real non-calculated values), for Earth & Moon are 288K and 197K respectfully, we can surmise that those are the actual non-blackbody (grey-body) surface temperatures as lived. And that those T values are the result of Earth & Moon both being in radiative equilibrium with the Sun at the mean multi-year distance between them & Sun. Here we’re addressing the resulting actually energy-balance values (288 & 197) of being in radiative equilibrium and not the SB blackbody equivalents (255 & 270) of an energy-balance based on a simple application of the SB theory; actually kind-of the SB theory applied to each sq. unit of Earth’s surface from perpendicular equator to tangent poles then summed up for the day-side adding almost nothing for the night side (yes there is stored heat, cosmic background, etc.). These actual values (288 & 197) result from the integration of the plethora of processes happening within the Earth’s & Moon’s complex material systems.
    Now we have an opportunity to compare Earth’s measured Ts 288K mean with both the effective Te 255K and the Moon’s Ts 197K. Here I am proposing that if Earth lost it’s atmosphere, it would eventually become Moon like and it’s energy equilibrium would make it’s mean global surface temperature also 197K – just a proposal based on reasonable conjecture for me and most likely unreasonable for some others, but a proposal just the same. So for Earth Ts/Te = 288/255 = 1.13 & Ts/Tna = 288/197 = 1.46; i.e. using Moon’s Ts as Earth’s no-atmosphere Tna. Given these T ratios we can quantify the greenhouse effect of Earth’s atmosphere in addition to the well known 33K (=288-255) as providing for 13% more warmth based on Te or for 46% based on Tna. In addition to an exact number with units (33K) we can also use this ratio to quantify the greenhouse effect. For Venus Ts/Te =3.98 and Ts/Tna=3.18; for Moon Ts/Te=197/270=0.73 & Ts/Tna=1, etc. Note that Tna for celestial bodies with atmospheres is provided by a quasi analytical formula derived by integrating the SB law over a sphere https://springerplus.springeropen.com/articles/10.1186/2193-1801-3-723. So which ratio better describes Earth’s greenhouse effect 13% or 46%? If we separately plot each Ts/Te and Ts/Tna vs. a non-dimensional surface pressure we get a much tighter exponential function regression fit with the Ts/Tna ratio. See models 11 & 12 in https://www.omicsonline.org/open-access/new-insights-on-the-physical-nature-of-the-atmospheric-greenhouse-effect-deduced-from-an-empirical-planetary-temperature-model.php?aid=88574.
    I would say this demonstrates Ts/Tna is a ratio worthy of further research. Many folks mostly say that the tight temperature ratio to pressure ratio data fit proves nothing because there are only 5 or 6 data points. But why not look deeper? The physics question to study further is the similarity of temperature to pressure relationships between the planetary atmospheres (Model 12 & Eq 10) and the P-T relationships shown in Fig 7 for Poisson’s law and the SB radiation law: all three have asymptotic relationships at both the tenuous gas & the higher pressure ends with similar transition curves between.
    Any calculated Te value that has no equivalent T measurement(s) to validate against and Te does not appear to provide any new integrative insight across our solar system vs. a calculated Tna that has been validated with measurements that seems to help account for a continuum of an atmospheric P-T relationship providing predictability. This in itself begs for more research and understanding of how climate science understands the basics of planetary atmospheres, Earth being one.

  126. Karl,
    I’m not following your comment at all. Could I suggest that it’s not the scientific community that needs to improve their understanding of planetary atmospheres.

  127. Steven Mosher says:

    ” Many folks mostly say that the tight temperature ratio to pressure ratio data fit proves nothing because there are only 5 or 6 data points. But why not look deeper?”

    Err because

    1. They fudged the mars data
    2. They used the wrong temperature for earth
    3. They fudged the Lunar data

    An most importantly, Planetary Climate models need to explain more than temperature before they become plantary climate models. They need to explain the vertical structure of temperature,
    the spatial structure, winds, everything!. For example, even something as simple as both minimum and maximum temperature. And because they have to connect or build upon
    prior known physics.

    Here is another reason about “why not look deeper?”. When you have physics that explain planetary climates ( past and present) resorting to statitistical curve fitting a single paramater
    is going backwards in understanding. When we have zero clue about the physics we might resort to statistics to get an idea about what variables may be salient. But in the end a bad physical explanation that is built on the entire fabiric of physics, trumps a curve fit .

    Finally, why not deeper? the paper you cited cites source that is pretty much of a hoax with the authors real names spelled backward.

  128. Karl Zeller wrote “Many folks mostly say that the tight temperature ratio to pressure ratio data fit proves nothing because there are only 5 or 6 data points. ”

    The fact that you won’t address the fact that the modelast can’t give a reliable out of sample prediction for Venus suggests you know it proves nothing. You have been challenged to comment on that several times on this thread, but ducked it each time.

  129. dikranmarsupial says:

    I should also point out, that all things being otherwise equal, I would expect the conventional mechanism of the greenhouse effect to be greater on a planet with a more massive atmosphere. More atmosphere (all things being otherwise equal) the higher the effective radiating layer will be (as it is the amount of GHG above that layer that matters), and a more massive atmosphere gives more scope for a large temperature difference between the surface and the effective radiating layer, simply because the atmosphere would have a greater scale height.

    Of course it would be daft to expect a straightforwad relationship as all things are not equal, as the atmospheres of the Earth, Venus, Mars and Titan have different compositions, especially with regard to GHGs. Thus if you get a smooth relationship (especially when you fit a model with four parameters to four datapoints – you get the moon for free as it has no atmosphere) it is probably over-fitting as it ignores well understood physics that suggests otherwise.

  130. Note, also, that if pressure alone could generate heat, atmospheres would be perpetual motion machines of the first kind.

  131. K says:

    [You keep repeating the same talking points. Please desist. -W]

  132. Everett F Sargent says:


    New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model
    https://www.omicsonline.org/open-access/new-insights-on-the-physical-nature-of-the-atmospheric-greenhouse-effect-deduced-from-an-empirical-planetary-temperature-model.php?aid=88574
    Ideal Gas Law and the Greenhouse Effect
    https://www.omicsonline.org/open-access/ideal-gas-law-and-the-greenhouse-effect-2157-7617-1000468-101034.html

    FTC hits predatory scientific publisher with a $50 million fine
    https://arstechnica.com/science/2019/04/ftc-hits-predatory-scientific-publisher-with-a-50-million-fine/

    “The practices of the companies, as documented by the FTC, are pretty egregious. While the OMICS Group claims that its publications are peer reviewed, two different journalists have submitted nonsense papers to its publications and had them accepted without revision. Scientists who have submitted articles indicate that they came back from review in a matter of days; the court recognized that peer review typically takes months. In some cases, the manuscript was simply published without warning after submission.”

  133. Eli Rabett says:

    Since this has come to life, and Eli knows that is perhaps not the right word perhaps a word on the moon. A major problem with Nikolov and Zellner’s first paper is that they did not consider rotation. If you do that for the moon, you get that the average temperature is well below the effective temperature.

    See Figure 2 in https://arxiv.org/pdf/0802.4324.pdf

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.