Empirical results from DIVINER confirm S-B Law was misapplied to Moon

Posted: March 28, 2012 by tallbloke in Astrophysics, atmosphere, climate, Energy, Gravity, Ocean dynamics

UPDATE: 21.10 GMT
Well, at least I was right about one thing; the empirical data is the most important. I’ve just had an update via email to say the latest empirical estimate of mean temperature for the Moon is 192-197K. This figure pretty much splits the difference between the old 255K and Ned and Karls theoretical figure of 155-157K. Karl says they will be working a regolith heat retention term into their equations.

So this makes it easier to understand the falloff in temperature of around 20K through the lunar night, and the curves at dawn and dusk. It also means the Earth’s ‘greenhouse effect’ is around 91-97K. Which more or less matches a dry adiabatic lapse rate of 9.8K/km in a 10km high troposphere, so at least the numbers are starting to make good sense. I’ll do the necessary corrections to the figures in the article as everyone digests the new information. TB

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

Ned Nikolov has kindly sent me a plot of the diurnal lunar equatorial temperature profile as determined by MSU observations carried out by the DIVINER instrument carried on board the NASA’s Lunar Reconnaissance Orbiter.

Ned has been working closely with Dr. Ashwin Vasavada, a senior scientist at NASA’s Jet Propulsion Lab on a paper regarding the grey-body formula; the theoretical average surface temperature of a celestial body with no atmosphere.

Regarding Lunar equatorial average temperature Ned notes that:

Moon’s average equatorial temperature is some 58K lower than the global mean temperature predicted by by the standard SB equation! Hence, the latter cannot be correct.

In their ‘Reply to Comments on the Unified Theory of Climate Part 1’ paper, Ned and Karl showed that the traditional method for applying the Stefan Boltzmann radiation Law to airless celestial bodies is defective. Their new method for performing the integration of incident solar radiation across the sunlit hemisphere (the day-side of a celestial body) and summing this with a space-cold night side is more accurate, despite no account being taken of heat retention in the subsurface. They will be including this in their revised calculation.

Present estimates suggest Ned and Karl’s figure for their theoretical grey-body temperature of the moon of 155K is within 6K ~39K of the actual. This is a vast improvement over the old method, which is about 95K 60K too warm at around 255K.

The profound implications for greenhouse effect theory and the question of the cause of Earth’s substantially enhanced surface temperature above the grey-body value should be obvious to all. Let the debate recommence, re-invigorated by these new, and most importantly empirical data. These data vindicate N&Z’s theoretical method for applying the S-B law, and refutes the idea that the Earth’s average surface temperature in the absence of radiatively active gases in its atmosphere would be at a ‘grey-body’ level of around 255K, a long held tenet of the radiative greenhouse theorists.

If (and it’s a big if) atmospheric radiation is responsible for 33C of the greenhouse effect as is claimed by radiative greenhouse theorists, then there’s another ~97K 66K of ‘greenhouse effect’ which is being caused by something else. This means that the ‘something else’ is causing 2/3 of the greenhouse effect (at a minimum).

Now, a lot of that is clearly due to the effect of the oceans spreading the heat absorbed nearer the equator to the higher latitudes as well as retaining and releasing it overnight, but, we need to remember that without the surface pressure provided by the bulk ~99% of the atmosphere which is not radiative gases (GHG’s), THERE WOULD BE NO LIQUID OCEAN able to spread heat around.  This is because water boils at a much lower temperature as pressure drops. On the top of Mount Everest for example water boils at around 65C. So without an atmosphere the oceans would either evaporate into space or congeal as ice, which is a poor heat conductor, and a good reflector of sunlight back to space (high albedo).

Therefore, even without getting into complex arguments about lapse rates, radiative-convective coupling in models or gravito-thermal effects in the atmosphere, we can say that in a very real sense, Nikolov and Zeller’s hypothesis that pressure (in concert with the throughput of solar energy) is responsible for the enhancement of Earth’s surface temperature over that of an airless grey-body is at least mostly correct.

Of course, their claim goes further than that, but we can at least set off from the firm basis that non-radiative factors  cause the majority of the ‘greenhouse effect’, or Atmospheric Thermal Enhancement (ATE), as they neutrally rename it.

Comments
  1. Hans says:

    Can anybody confirm that the temperature is measured at (approximately) the same area (spot) on the lunar equator during one synodic month?

  2. Harriet Harridan says:

    This. Is. Huge.

  3. tallbloke says:

    Hans: I don’t know if Ned can answer that for you. If not, there is a page of publications with links to documents here:
    http://diviner.ucla.edu/publications.shtml

    Maybe you can glean something from thhis one?
    http://diviner.ucla.edu/docs/6028.pdf

  4. tchannon says:

    The shape matches simple radiative process modelling, as of course it will given the moon is a simple body. When I did this I made little attempt to achieve correct values, but it ought to be possible to find them. There is nothing new in this or the shape, only the values.
    Useful for a planet with atmosphere? No, far too may unknowns.

  5. kim2ooo says:

    Whoa Pony………….

    This is interesting.

  6. tallbloke says:

    Tim: You are right about the complexity of Earth compared to the Moon, but I think that’s not the important point here.

    The point is that if (and it’s a big if) atmospheric radiation is responsible for 33C of the greenhouse effect as is claimed by radiative greenhouse theorists, then there’s another ~97K of ‘greenhouse effect’ which is being caused by something else. This means that the something else is 3/4 of the greenhouse effect (at a minimum).

    Now, a lot of that is clearly due to the effect of the oceans spreading the heat absorbed nearer the equator to the higher latitudes as well as retaining and releasing it overnight, but, we need to remember that without the surface pressure provided by the bulk ~99% of the atmosphere which is not radiative gases (GHG’s), THERE WOULD BE NO OCEAN. It would evaporate and boil off into space.

    Therefore, even without getting into complex arguments about lapse rates and gravito-thermal effects in the atmosphere, we can say that in a very real sense, Nikolov and Zeller’s hypothesis that pressure is responsible for the enhancement of Earth’s surface temperature over that of an airless grey-body is at least 3/4 correct. 🙂

    Of course, their claim goes further than that, but we can set off from the firm basis that non-radiative factors are the cause of the large majority of the ‘greenhouse effect’, or Atmospheric Thermal Enhancement (ATE), as they neutrally rename it.

  7. Joe's Lalonde says:

    TB,

    That is another area scientist conveniently forget is pressure.
    Compressing gases into a cylinder would take different pressure to turn the different gases into liquids. Pounds per square inch is volume but what is the actual pressure point that would change the many different gases to liquid?
    We don’t play with super heated gases that vibrate…but they can compress much denser due to the vibrating. This would give a reading of a solid mass compared to liquid mass.

  8. adolfogiurfa says:

    @TB: “Now we get back down to some serious stuff.”. Everything you publish is serious. You do not need to justify your deep intuitions before any inquisitorial jury. You see what other don´t that´s all!

  9. tallbloke says:

    I wonder if Steve Mosher will be along to tell us we have to believe greenhouse theory in order to accept MSU measurements of airless celestial bodies again… 🙂

  10. adolfogiurfa says:

    greenhouses heat up and stay warm by confining heated air rather than by trapping IR
    http://www.giurfa.com/gh_experiments.pdf
    Has anyone experienced the temperature fall during an eclipse?

  11. Brian H says:

    Well, tb, you’re 50% correct this time. It’s like throwing dice!!

    “active gases in it’s atmosphere ” – wrong
    “(and it’s a big if)” – right.

    😉
    ;p
    LOL

    [Reply] Heh. Not bad eh? 🙂

  12. Brian H says:

    Since the N&Z method works better, it’s righter. While GHG theory keeps showing itself to be wronger and wronger.

  13. tallbloke says:

    Their SB integral method is pretty much spot on for what it claims to do, which is calculate for a grey-body of negligible heat capacity.

    They could add in a term for the heat retention in the regolith of the Moon’s surface. What I find interesting is that it makes so little difference. Of course, it must be remembered that Lunar night is 28 times the length of Earth’s night, and the regolith is a poor conductor of heat between latitudes and day/night side.

  14. Hans says:

    To me it quite obvious that temperature data from a planetary body without an atmosphere and one with an atmosphere have to be treated differently. The approximate method NASA uses is at adantage for bodies with atmospheres, the denser they are the bettter.

    The reason is that an atmosphere will always distribute energy to all parts of its surface. The atmosphere on earth does a decent work meaning that the Outgoing Longwave Radiation vary from about 120 W/m^2 (South Pole) to 350 W/m^2 (desserts during day time). This correspond to the black body temperatures of 214 K and 280 K respectively. Using the NASA rather rude approximation of average IR emission as 1367/4×0.7 gives 255 K (-18C). It is a rather good estimate of the AVERAGE emission temperature from earth as seen from space.

    This situation is far better on Venus since the emission temperature only vary by about 5 K on the night and day side. The NASA IR average emission should be
    2614/4×0.1 and the corresponding temperature is 260 K (-13C) (NASA has changed its value in the fact sheet for some reason or it is a typo). The actual regional OLR between day and night only varies about +/- 10% which is far less than the earth values.

    On Jupiter and saturn it is obvious that atmospheric phenomena has an impact on the IR emission temperarature to space (spot temperatures) as is also true in the solar atmosphere (Sunspots are about 2000 k cooler than the solar surface).

    As shown above it the possibility to distribute the solar energy to all parts of a planet which is the crucial factor deciding the existence of a well defined “greenhouse” effect.

    The lunar temperature data is very interesting but there are two (at least) completely different physical processes governing the the surface temperature on moon. The concept ATE certainly is to prefer from a lingustic point of view but in physics it mixes oranges and apples as defined by N&Z. It makes it harder to understand and identify what physical processes are actually creating the observed temperature difference between average surface temperature and average IR emission temperature on planets that do have an atmosphere. That is where the greenhouse effect can be observed and it is almost independant of greenhouse gases. It has to exist, always.

    The Greenhouse Effect (GE) simply cannot be defined in a proper way on a planet without an atmosphere since it is a product of the atmosphere.

  15. Hans says:

    tallbloke says: March 28, 2012 at 3:33 pm

    “Their SB integral method is pretty much spot on for what it claims to do, which is calculate for a grey-body of negligible heat capacity.”

    The temperature curve in the head shows that the heat capacity almost can be neglected as you say but there are severe problems claiming that the measured temperature curve in the head supports the SB law. My former question was to get sure that the curve isn´t mainly a model construction. If the temperature curve is (approximately) correct as I tend to believe after some reading the SB law has to be questioned.

  16. steveta_uk says:

    Isn’t this just a disagreement about the meaning of “average”?

    The “global mean temperature predicted by by the standard SB equation” is the temperature that the entire surface of a black body would be at if radiating the same energy is the object being studied.

    I cannot beleive anyone ever expected this number of actually represent anything that really exists, so why the surprise when the measurements are different?

  17. David Springer says:

    Barnstorming is aerial acrobatics in farm country. Brainstorming is mental acrobatics in think tank country.

  18. tallbloke says:

    Steve, it’s much worse than that. As Ned said:

    “Moon’s average equatorial temperature is some 58K lower than the global mean temperature predicted by by the standard SB equation! Hence, the latter cannot be correct.”

    That’s putting it very politely.

    Don’t forget the old method of applying the SB law was supposed to account for day/night differences.

    I don’t think there’s much wriggle room here for the radiative greenhouse effect theorists. They screwed up very, very badly.

  19. David Springer says:

    This is a straw man:

    “Moon’s average equatorial temperature is some 58K lower than the global mean temperature predicted by by the standard SB equation! Hence, the latter cannot be correct.”

    The standard SB can be applied to a superconducting sphere with zero mass. Beyond that you have to make some adjustments. The problem Nikolov seems to be struggling to grasp here is that energy loss rate increases as the fourth power of temperature. Thus the high afternoon temperature of the regolith bleeds off energy much faster than it leaks out at night. This lowers the mean temperature far below what a superconducting zero mass sphere would have.

    The earth is far different than the moon in that it doesn’t not have a large enough diurnal temperature range to make a difference like it does on the moon. This is particularly true for the ocean which has effectively zero diurnal temperature variation.

  20. tallbloke says:

    Dave, I don’t think Ned Nikolov is struggling with anything. His method gets very close to the actual measured average.

    As for Earth, I put it in capitals in the headline post but I guess it still bears repeating for those who are struggling:

    WITHOUT AN ATMOSPHERE A GREY BODY EARTH WOULD HAVE NO OCEANS.

    Being at the same distance from the Sun as the Moon, the Earth’s grey body temperature would therefore be the SAME AS THE MOON’S.

  21. Harriet Harridan says:

    Err Tallbloke Help me out, what am I missing?
    N&Z calculate 155k
    Nasa calculate 255k
    Ned says “[the moon is] 58K lower than the global mean temperature (255)” = 197k
    then the figure says 213k

    So which is it? 213k, 197k, 155k, 255k or what? 🙂

  22. tallbloke says:

    Harriet, Ned’s quote is regarding the average temperature of the Moon’s equator, not the average temperature of the entire lunar surface, which is about 6K warmer than the 155K Ned and Karl derived from their theoretical work.

  23. David Springer says:

    Hans says:
    March 28, 2012 at 3:47 pm

    “To me it quite obvious that temperature data from a planetary body without an atmosphere and one with an atmosphere have to be treated differently.”

    Correct. And even more so a planetary body covered by liquid water thousands of feet deep has to be treated VERY differently than one covered by rocks.

  24. Harriet Harridan says:

    Thank you TB. Satisfied customer. Who is going to break the news to Willis Eschenbach? 🙂

  25. Hans says:

    I just noticed that NASA states that the Black-body temperature of moon is 270.7 K. (Moon fact Sheet). Such a number has little physical meaning because of the big difference between lunar day and night temperatures (which follows from moon having n atmosphere).
    Whatever way NASA they have gotten their number I certainly have much more confidence in the temperature curve in the head showing an average lunar (equatorial) surface temperaure of 213 K.

    NASA got it by calculating 1367.7/4×0.89 = T^4

    (Not a clever approach but obviously a standad regardless if there is any atmosphere or not)

  26. David Springer says:

    tallbloke says:

    March 28, 2012 at 4:35 pm

    “Dave, I don’t think Ned Nikolov is struggling with anything. His method gets very close to the actual measured average.”

    He’s struggling with straw man. Where does NASA say the predicted mean temperature of the moon is 255K?

  27. tallbloke says:

    Dave, I think I’m beginning to see why you disagree with N&Z.
    Maybe you’ve misunderstood what they mean by the term ‘grey body’.

    I think their definition is the correct one.
    The incorrect one is the one the radiative theorists have been deluding themselves (and us) with for all these years.

    You may disagree.

  28. adolfogiurfa says:

    @Tallbloke: …which is calculate for a perfect black body of negligible heat capacity.
    And, as there is nothing with “negligible heat capacity” the SB equation it´s either a phantasmagoric entity or a nice mathematical exercise.

  29. tallbloke says:

    I bet there’s a lot of frantic webpage re-writes going on right now. 😎

  30. Hans says:

    tallbloke says: March 28, 2012 at 4:35 pm

    “Being at the same distance from the Sun as the Moon, the Earth’s grey body temperature would therefore be the SAME AS THE MOON’S.”

    Don´t be so sure. The surface composition matters and it is not for sure that earth´s surface would look like moon´s even without water. Agree that you express a fair assumption.

    Mars with a thin atmosphere (only 7 mbar) and no water has a Bond albedo 0.25 and moon has 0.11. Mars actually has water frost on the north pole and carbon ice on the south pole to be honest which should affect the Bond albedo)

  31. David Springer says:

    @tallbloke

    “Therefore, even without getting into complex arguments about lapse rates, radiative-convective coupling in models or gravito-thermal effects in the atmosphere, we can say that in a very real sense, Nikolov and Zeller’s hypothesis that pressure (in concert with the throughput of solar energy) is responsible for the enhancement of Earth’s surface temperature over that of an airless grey-body is at least 3/4 correct.”

    If by that you mean they are right for the wrong reason then I’d tend to agree. I’ve said long before Nikolov et al came along that the primary role of the atmosphere is in providing enough surface pressure for water to remain liquid through a range of 0-100C. After that non-condensing gases in the atmosphere can be ignored in first approximation of climatic conditions. Water in all its phases makes the weather. Non-condensing atmosphere just makes the weather possible through enabling the water cycle.

  32. steveta_uk says:

    I’ve just digitised the above graph (by eye) to get 24 hourly readings, and the simple mean ff the numbers is 211. Given the value on the graph is 213 then this is pretty close.

    But that’s using a simple arithmetic mean which is meaningless when applied to a temperature series.

    Using exactly the same data, and deriving a mean temperature using a 4th power law (as you must do to compare with SB) I get 284.8.

    Surprise-surprise – using the correct sums, you get a figure 74 degress higher! Which isn’t far off the supposed 95K discrepency, and may be far closer if I had the real data rather than my eyeballed estimates.

    I really really really think this is simply about misapplying sums, and nothing more.

  33. tallbloke says:

    http://history.nasa.gov/conghand/stations.htm

    “the average temperature of the Moon (not-withstanding the tremendous day-night variations) is not far from the average temperature of the Earth.”

    There will be a Talkshop prize for the best collection of NASA Moon average surface temperature guesses. 🙂

  34. David Springer says:

    tallbloke says:

    March 28, 2012 at 4:50 pm

    Dave, I think I’m beginning to see why you disagree with N&Z.

    Maybe you’ve misunderstood what they mean by the term ‘grey body’.

    I think their definition is the correct one.
    The incorrect one is the one the radiative theorists have been deluding themselves (and us) with for all these years.

    You may disagree.
    —————————————————-

    The grey body I described is the one that is used with the S-B formula. A blackbody has an emissivity of one. A gray body is a blackbody with an emissivity less than one and greater than zero.

    http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

    A body that does not absorb all incident radiation (sometimes known as a grey body) emits less total energy than a black body and is characterized by an emissivity < 1;

    You have no choice about using a different definition if you expect to use the S-B law. If you do you’re creating what’s called a straw man argument. This what Nicolov et al are doing.

    [Moderation note] The man’s name is Nikolov.

  35. adolfogiurfa says:

    In any case the tomb of global warming should be erected on the moon with the following epitaph: “Here lies Global Warming, which suddenly died when the Decline could not be hidden” 🙂

  36. Ned Nikolov says:

    The curve shown above is an average of all Diviner equatorial measurements taken over a course of a year or longer. It represents the mean diurnal variation of surface equatorial temperature on the Moon.

  37. Ned Nikolov says:

    The above Moon equatorial temperatures are discussed in detail in this upcoming paper by Vasavada et al. (2012):

    Vasavada, A. R., J. L. Bandfield, B. T. Greenhagen, P. O. Hayne, M. A. Siegler, J.-P. Williams, and D. A. Paige (2012). Lunar equatorial surface temperatures and regolith properties from the Diviner Lunar Radiometer Experiment. J. Geophys. Res., doi:10.1029/2011JE003987, in press.

    http://www.agu.org/pubs/crossref/pip/2011JE003987.shtml

    The data are from Fig. 9a in this paper.

  38. tchannon says:

    Tallbloke
    “They could add in a term for the heat retention in the regolith of the Moon’s surface. What I find interesting is that it makes so little difference.”

    That is in the wave shape, the exponential decay nightside.

    If I understand correctly, regolith has no overall effect because it is symmetric, heat and cool are equal and opposite.

    As I pointed out recently nightside is where the fun things happen, which seems to have been missed by the mainstream, including trolls on a quick visit here. The asymmetry caused by day convection / night inversion is part of an ATE but whether this holds as important over a wide range of atmospheric masses is another matter. Critically gravity is a necessary part of this.
    I also pointed out that GHG might reduce this effect by bridging an inversion.

    For reference

    The earlier N&Z post is
    https://tallbloke.wordpress.com/2012/01/17/nikolov-and-zeller-reply-to-comments-on-the-utc-part-1/

    and image

  39. Steven Mosher says:

    TB, you still dont get it.

    download and read through the sensor code used to create temperatures from raw data ( voltage) at the sensor. Having worked on codes like this I will tell you that any sensor aimed at earth uses radiative physics.Yes, the physics that says C02, water vapor, etc all obey known laws that cause a slowing in the rate of cooling. The engineers who design radars use this physics and it works. The engineers who design IR sensor use this physics and it work. That’s were I learned it. Yup, you want to build star wars devices? you need to apply radiative physics.
    The engineers who design cell phones use this physics and it works.
    If you have no atmosphere then you don’t need to account for the ways in which an atmosphere modulates EM. as in duh. Heck, you can even build a radar to see through the ground if you understand the physics. But you steadfastly refuse to understand the physics of radiative transfer. Yet you use a wifi connection. does it work? you know what physics have to be applied to design and build these systems? thought not.

    [Reply] Did you see the phrase, ‘airless celestial bodies’ in my comment you are responding to Mosh? Yes you did. When using MSU’s to measure the temperature of airless celestial bodies, the radiative physics of water vapour and trace gases like co2 and how the greenhouse models fail to properly integrate convection is irrelevant. Such dodgy models are not required for measuring the temperature of airless celestial bodies. the simple well known radiative physics of Solar irradiance hitting regolith through no atmosphere does the job fine.

  40. Hans says:

    Good to know about the temperature curve!
    Especially:
    •Lunar daytime temperatures require albedo dependene on solar incidence angle
    •Lunar nighttime temperatures require graded structure in upper cm of regolith
    – the albedo increase with solar incidence angle.
    – are determined by pulverization through micrometeoroid impacts
    (These requirement are not/o9r much less applicable to earth conditions since there is an atmosphere on earth)
    /HJ

    Paper in Press
    JOURNAL OF GEOPHYSICAL RESEARCH, doi:10.1029/2011JE003987

    Lunar equatorial surface temperatures and regolith properties from the Diviner Lunar Radiometer Experiment

    Key Points•LRO Diviner reveals radiative and thermophysical properties of the lunar surface
    •Lunar daytime temperatures require albedo dependene on solar incidence angle
    •Lunar nighttime temperatures require graded structure in upper cm of regolith

    The Diviner Lunar Radiometer Experiment onboard the Lunar Reconnaissance Orbiter has measured solar reflectance and mid-infrared radiance globally, over four diurnal cycles, at unprecedented spatial and temporal resolution. These data are used to infer the radiative and bulk thermophysical properties of the near-surface regolith layer at all longitudes around the equator. Normal albedos are estimated from solar reflectance measurements. Normal spectral emissivities relative to the 8-μm Christiansen Feature are computed from brightness temperatures and used along with albedos as inputs to a numerical thermal model. Model fits to daytime temperatures require that the albedo increase with solar incidence angle. Measured nighttime cooling is remarkably similar across longitude and major geologic units, consistent with the scarcity of rock exposures and with the widespread presence of a near-surface layer whose physical structure and thermal response are determined by pulverization through micrometeoroid impacts. Nighttime temperatures are best fit using a graded regolith model, with a ~40% increase in bulk density and an eight-fold increase in thermal conductivity (adjusted for temperature) occurring within several centimeters of the surface.

  41. Steven Mosher says:

    you might also be aware that the moon does not radiate from the surface. It radiates from below the surface. The earth of course radiates from the ERL. you know how that is measured right TB?

    [Reply] Yes Mosh. However, the ERL is irrelevant in a discussion about grey-body temperature, because grey-bodies don’t have atmospheres for ERL’s to exist in.

  42. Hans says:

    tchannon says: March 28, 2012 at 6:49 pm
    “If I understand correctly, regolith has no overall effect because it is symmetric, heat and cool are equal and opposite.”

    This is not the major problem but an important observation. The temperature curve does not fit a cosine decline and rise as they should. The rise and fall of temperature is extremly symmetric but not as a cosine curve. This made me think that the curve was a simple modelling. This is a challenge to the validity of the SB law, especially if the temperature curve is OK which it probably is.
    There are some valuable comments above.

  43. wayne says:

    It took a while to write this so if someone else has already hit on this, apologies in advance.

    I like to mess with the numbers personally. If the numbers don’t make sense then a lot of words, just doesn’t seem to mean much. Nikolov and Zeller have given us a quite amazing equation…
    SB = 5.6704e-08
    alb = 0.11
    emiss = 0.955
    2/5 * √√( (1364*(1-alb)) / (emiss*SB) )
    …. that computes to 154.8 K for the perfect gray body mean temperature. But we don’t live in a perfect universe so let’s rearrange this equation to see if we can gain any insight into the more realistic 213K that Diviner is showing.

    2/5 * √√( (1364*(1-alb)) / (emiss*SB) ) can be rearranged to
    √√( (1-alb)/emiss ) * 2/5*√√( 1364/SB ) giving us the same answer, 154.8 K.

    the 2/5*√√( 1364/SB ) is a constant for both the Earth and moon so let’s just get the number for simplicity from this point onward… 157.5, that’s our number that only depends on the TSI at this distance from the sun. But that leaves another term, √√( (1-alb)/emiss ), and this ratio is all that seems to matter. To get the 213 K that the Diviner is reporting you need this term to be equal to 1.352 for 1.352*157.5 is the 213K.

    So 1.352 has to equal the √√( (1-alb)/emiss ) term and we really don’t seem to know either the albedo or emissivity that I know of but the ratio of the two by (1-alb)/emiss has to be close to 1.352²² or 3.34. Lets just round that to 3.3333 or 10/3 for simplicity. You could also say this is √√( (1-0) / 0.299 ) that is the same 1.352 ratio or an albedo of zero and an effective emissivity of 0.299, later on this below.

    If you take this same approach with the Earth you need a number for √√( (1-alb)/emiss ) that ends up with our mean surface temperature around 288.2 K per standard atmospheres.
    The moon is giving
    √√(10/3) * 157.53 = 213 K so
    √√(34/3) * 157.53 = 289 K for the Earth (or close).

    So what is this 10/34 ratio between the moon and the Earth… it’s about 0.294 (note 0.299 above)… wait, that is Earth’s albedo if you allow the entire adjustments in this √√( (1-alb)/emiss ) ratio to be if you assume the emissivity of each to be one.

    I have no final answer to why these numbers jibe so well to the same number our satellite measurements are showing but maybe someone else can add a little insight into this ratio.

    PS: by √√( (1-alb)/emiss ), you quickly see that if the albedo goes up and the effective surface emissivity goes down (think !clouds), then in reality little has changed in this overall term, so the temperatures also do not change much (or perhaps none at all!). Don’t you love the strange symmetry in physics!

  44. Hans says:

    Steven Mosher says: March 28, 2012 at 6:55 pm

    “TB, you still dont get it.
    download and read through the sensor code used to create temperatures from raw data ( voltage) at the sensor. Having worked on codes like this I will tell you that any sensor aimed at earth uses radiative physics.Yes, the physics that says C02, water vapor, etc all obey known laws that cause a slowing in the rate of cooling.”

    As a former boss of a radar station in the military service I can assure TB that the “sensor code used to create temperature from raw data” has nothing to do with radar performance. It is a model that has to be validated by itself.

    “Yes, the physics that says C02, water vapor, etc all obey known laws that cause a slowing in the rate of cooling.”

    No, it does not. The absorbed solar power has to be emitted seen over a season (or locally a day)That is the basic law which has to be followed regardless of the composition of the atmosphere. An approximate steady state is at hand. The Greenhosue Effect is mainly produced by the atmosphere as such (which is modulated by water vapor content but not by carbon dioxide)

  45. Hans says:

    Wayne,

    Look at Hans says: March 28, 2012 at 4:44 pm

  46. wayne says:

    After spitting all of that (yuk!) math at everyone, if someone took the time to really understand the logic in that flow, a simple calculator and a piece of paper will do, you should come up with a epiphany.

    That is, any talk of albedo without emissivity is pointless, any talk of emissivity without albedo is pointless, ignoring either or blindly assuming albedo as zero or emissivity as one (climate “science”) is totally pointless and wrong from the get go. For it’s the ratio of the two that matters, much like the physics variable of GM, we don’t know the gravitational constant or the actual mass of solar system bodies very well but we DO very accurately know the multiplication of the two, the GM.

    We need a variable in climate science that is the “(1-albedo)/emissivity”. It seems we know the combined ratios pretty well and temperature related but a lot of times we are just guessing on the exact figures on either. And, in reality, they both probably change in tandem, a change in one causing an opposite change in the other, or that is how I see it after digging on this subject for a while.

  47. wayne says:

    Hans: “Look at Hans says: March 28, 2012 at 4:44 pm”

    Right Hans, that’s the huge problem in assumptions that climate science seems to be infested with. The figures I gave above are so simple to calculate, no higher math, but it is sure easy to get so much closer that the oversimplicity that NASA used that you pointed out. Being in the US, I have to ask… and how many billions are we spending for this junk science results? Give me a job NASA, I can come up with better science for song! 😉

  48. tchannon says:

    A few minutes of fiddling and this is close enough for initial purposes

    This is an overlay of the DIVINER plot and the output of a very simple SPICE simulation, exactly valid for thermal but fun to figure out the values and topography.

    I suspect the regolith actually behaves more as a lossy line of some kind. In this case I split the time constants, which gives closer to the wanted regolith curve.

  49. tallbloke says:

    David Springer says:
    March 28, 2012 at 5:07 pm

    @tallbloke

    “Therefore, even without getting into complex arguments about lapse rates, radiative-convective coupling in models or gravito-thermal effects in the atmosphere, we can say that in a very real sense, Nikolov and Zeller’s hypothesis that pressure (in concert with the throughput of solar energy) is responsible for the enhancement of Earth’s surface temperature over that of an airless grey-body is at least 3/4 correct.”

    If by that you mean they are right for the wrong reason then I’d tend to agree. I’ve said long before Nikolov et al came along that the primary role of the atmosphere is in providing enough surface pressure for water to remain liquid through a range of 0-100C. After that non-condensing gases in the atmosphere can be ignored in first approximation of climatic conditions. Water in all its phases makes the weather. Non-condensing atmosphere just makes the weather possible through enabling the water cycle.

    Well, I think it is important to recognise the role of the ocean, and the role of pressure on it. But in my own view, it goes further than that. The ocean is forced by the pressure on it to rise to a temperature at which its surface can emit as much energy as it absorbs from the Sun. What is that temperature? 290K

    To what extent is that temperature responsible for the 288K average surface temperature?

    Good question.

    Nearly all of it is my guess.

  50. mkelly says:

    Steve Mosher says: “…to understand the physics of radiative transfer.”

    First let us restrict ourselves to radiative HEAT transfer. Radar is not thermal radiation (heat). Radar and other EM can have slip distance, bounce off the ionsosphere, get ducted do to inversion layers etc.

  51. wayne says:

    Tim, that SPICE overlay is very intriguing !! As Hans knows I am working on and off on an expanded per latitude band simulation of energy transfers, a ‘K&T’ by latitude so to speak, and I sure could use whatever equation you used to mathematically create that curve. You say it is as if it is a ‘loss line’ but it’s been years since I’ve dealt into electronic circuit calculations. Any help there, maybe a link, or speak a bit more on the parameters used to so closely match that curve? I’m trying to do the same for Earth on a per latitude basis as that curve of the moon’s diurnal temperatures.

  52. tallbloke says:

    Heh. Never a dull moment, article updated

    UPDATE: 21.10 GMT
    Well, at least I was right about one thing; the empirical data is the most important. I’ve just had an update via email to say the latest empirical estimate of mean temperature for the Moon is 192-197K. This figure pretty much splits the difference between the old 255K and Ned and Karls theoretical figure of 155-157K. Karl says they will be working a regolith heat retention term into their equations.

    So this makes it easier to understand the falloff in temperature of around 20K through the lunar night, and the curves at dawn and dusk. It also means the Earth’s ‘greenhouse effect’ is around 91-97K. Which more or less matches a dry adiabatic lapse rate of 9.1K/km in a 10km high troposphere, so at least the numbers are starting to make good sense. I’ll do the necessary corrections to the figures in the article as everyone digests the new information. TB

  53. Doug Cotton says:

    This is not new analysis. Alan Siddons published similar in May 2009.

    http://www.globalwarmingskeptics.info/attachment.php?aid=63

  54. Hans says:

    tallbloke says: March 28
    “Karl says they will be working a regolith heat retention term into their equations”

    Does that mean the SB law is partially abandoned?

  55. Hans says:

    TB says:
    “…curves at dawn and dusk. It also means the Earth’s ‘greenhouse effect’ is more like 62-67K rather than the ~97K…”

    Whatever about 33 C depends on the atmosphere and the rest on the unrealistic assumption that we remove all oceans and change the earth´s Bond albedo from 0.30 t0 0.11 for no good reasons.
    We certainly don´t live on a planet with a surface looking like the lunar one.

  56. Anything is possible says:

    Tb says @10:25pm

    “It also means the Earth’s ‘greenhouse effect’ is more like 62-67K rather than the ~97K implied by the earlier estimate. Which more or less matches a moist adiabatic lapse rate of 6.7K/km in a 10km high troposphere, so at least the numbers are starting to make good sense. ”

    That works for Venus too :

    Multiply the amount of radiation required for a black-body temperature of 195K, by a factor of 1.91 to allow for Venus being closer to the Sun, and that equates to a BB temperature of 229K.

    Factor in an adiabatic lapse rate of 7.9K/km into a troposphere 65km high, and it comes out at 229+(7.9*65) = 742.5K, which is pretty darned close to the observed surface temperature…..

  57. tallbloke says:

    AIP: Good spot!

    Except I got my figures wrong. So it’s the dry lapse rate times the troposphere height which matches the GE not the moist lapse rate. Even better…

  58. Hans says:
    March 28, 2012 at 7:30 pm | Reply w/ Link

    tchannon says: March 28, 2012 at 6:49 pm
    “If I understand correctly, regolith has no overall effect because it is symmetric, heat and cool are equal and opposite.”

    This is not the major problem but an important observation. The temperature curve does not fit a cosine decline and rise as they should. The rise and fall of temperature is extremly symmetric but not as a cosine curve. This made me think that the curve was a simple modelling. This is a challenge to the validity of the SB law, especially if the temperature curve is OK which it probably is.

    The curve isn’t cosine because we’re dealing with T^4 and N&Z’s proper calculus integration of true local effect.

    Beware regolith effect. It is NOT symmetrical at all. If you apply N&Z math to day flux minus regolith effect (put in an estimate) and night non-flux plus regolith effect, you can prove there is a huge asymmetry to the temperature effects. It is this asymmetry which is raising the mean lunar temperature higher than the N&Z calculations for grey-body with zero regolith effect.

  59. Doug, you are right. Alan Siddons did spot this before we did with N&Z here. However, Nikolov and Zeller have done what Alan failed to do: nail the maths. This is like the difference between estimating planetary positions from observed patterns, and using Newton’s calculus.

    And just as Newton’s calculus proved Kepler’s and Copernicus’ heliocentric system, so Nikolov & Zeller are proving the greenhouse gas stuff is medieval science. It doesn’t fit the real figures. N&Z’s math does, within reasonable allowance for regolith.

    And more. Nikolov & Zeller are indeed challenging the sacrosanctness of the Second Law of Thermodynamics as currently stated. But to vindicate their challenge, one has to go and study the work of Graeff – another Nobel-standard scientist, still unrecognized except for a few here and a few others. https://tallbloke.files.wordpress.com/2012/01/graeff1.pdf

    The Second Law is up for revision. Not abolition, but serious revision. And Graeff has done it. James Clerk Maxwell would be proud of him. Without this revision, Climate Science is lame right from the start. Even before the bad IPCC maths.

  60. Ned Nikolov says:

    To disperse any confusion about latest figures regarding the magnitude of Earth’s atmosphere GH effect – we can say for sure now that, at the equator, the GH effect is 299 – 213 = 86K. Since equator is the location with the least GH effect expected, we can safely conclude that the current theory underestimates the GH effect AT LEAST by a factor 2.6.

    Based on latest analysis of Diviner data and NASA model results, the overall atmospheric GH effect averaged over the entire planet appears to be 90K – 96K.

    A clarification about the 250-255K figure being used for the Moon’s emission temperature.
    255K is the temperature estimated by the standard SB formula assuming Earth’s albedo of 0.3. Moon’s actual albedo is much lower than that since the it has no clouds. The effective albedo of the Moon surface accounting for Sun’s angular effects is about 0.126. So, it makes no sense to think (and use) 255K as Moon’s effective temperature! Using the correct lunar albedo in the standard SB equation produces ~ 270K, which is 56K higher than lunar equatorial temperature and some 72K larger than the most likely Moon true mean temperature.

  61. tchannon says:

    I am away with network connection outage and computer playing stupids, meantime a curved ball comes in, mean temp is different? Don’t like it, says there are things going on.

    Note sure where to start here.

    Lucy, there is no asymmetric effect but I’d better clarify what I mean. Heat is put into something following some law, symmetric means it comes back out by the same law. Applies eg. to a direct heated solid.

    wayne, I decided to play a little more, simplify even more and get some values in there. Output is not very neat (old software) but will do here

    What I found is I needed to reduce TSI by 5% but given this is crude, so what. The Diviner plot says for equator, not the Lunar mean. I’ve ripped it down to the simplest possible.

    What freaks people is flux, they don’t get it because it is alien in human experience but some know current sources are a bit head banging.

    A little side project I have on is correcting a temperature dataset where the meteorologists involved didn’t understand and got it wrong. Fortunately I have been able to reverse what they did and fix it up. The result is very pertinent to regolith, soil temperature. Can’t see the daily profile but day data gives annual. All that happens with depth is an amplitude change, plus of course a phase shift. I can see no wave shape change. In this case two depths plus a standards change to different depths. Not finished yet so I can’t say much more.
    Main point here is this is data hands on.

  62. wayne says:

    Thanks so much Tim! Boy your fast, and that now jogs my memory, the nighttime linear slope is the linear cutoff ‘leakage’, of course, of course, ding, and the daytime is just the cosine half-wave input. That should get me close enough to develope the algorithm. Yo’ the man!

    After viewing the Koorin data that Earth’s nighttime ‘leakage’ will not be perfectly linear for there is a tailing off of the sensible and latent + radiation for about the first half of the night, then just radiation, which is nearly perfectly linerar in the few degree cool off (just for the long term mean, no short term weather).

  63. Hans says:

    Lucy Skywalker says: March 29, 2012 at 12:50 am

    “The curve isn’t cosine because we’re dealing with T^4 and N&Z’s proper calculus integration of true local effect.”

    I am talking about the cosine depending on the solar irradiation when moon rotates.

  64. tallbloke says:

    Ned: Thanks for the clarification and apologies for getting figures mixed up earlier. I think we’re nearly there. I’ll have another go round on trying to make the figures in the article consistent with what you’ve updated us with today.

  65. Ned Nikolov says:

    Rog,

    With these new Diviner data and some detailed NASA model output I got from Dr. Vasavada for Moon’s latitudinal temperatures, I was able to make the necessary correction to the analytical integral formula for calculating Moon’s mean temperature. The math is vey elegant and the final expression can be reduced to an amazingly simple formula. This new gray-body formula not only produces the correct Moon temperature, but also leads to a new and physically more robust relationship between the atmospheric enhancement factor (NTE) and pressure across planets …

    It’s always a good sign when additional data make a theory more solid, not less. This means the theory has deep physical roots …

  66. Hans says:

    Ned Nikolov says: March 29, 2012 at 1:08 am

    “To disperse any confusion about latest figures regarding the magnitude of Earth’s atmosphere GH effect – we can say for sure now that, at the equator, the GH effect is 299 – 213 = 86K. Since equator is the location with the least GH effect expected, we can safely conclude that the current theory underestimates the GH effect AT LEAST by a factor 2.6.
    Based on latest analysis of Diviner data and NASA model results, the overall atmospheric GH effect averaged over the entire planet appears to be 90K – 96K.”

    It is very unfortunate to use the word Greenhouse effect for anything else than the differens between OBSERVED average temperature and OBSERVED average IR emission temperature on one and the SAME planet that actually has an atmosphere. In that way the concept GE can be comprehended and furthermore its cause can be traced to one dominating physical processes (in atmospheres which are dense) which is an equalization of total energy per mass unit (according to the second law of thermodynamic applied to energy as it should be and not temperature). GE on earth is about 33 K, That is a part of the ATE you are calculating.

    Your use of this concept as above increase confusion. You have to clearly state that ATE (or what you want to call it) and what you unfortunately call GE above include different bond albedos for moon and earth and other physical processes such as surface structure and even unknown processes. The task of science is to understand the physical processes at hand and as far as possible isolate them. Your point about ATE is well found and should be described as well as possible. Different albedos should not be hidden in a new or old concept. The impact of albedo on surface temperature is well known and understood since at least 100 years.

  67. Hans says:

    Nikolov says: March 29, 2012 at 8:34 am

    Ned,

    To find a mathematical expression that fits observational data is one thing. Trying to understand the fit can be called a hypothesis. A verfied hypothesis can be called a theory.
    With the the updated knowledge at hand will you please express what the N&Z theory tells to avoid future confusion.

    “It’s always a good sign when additional data make a theory more solid, not less. This means the theory has deep physical roots …”

  68. Harriet Harridan says:

    Ned Says:

    “The math is vey elegant and the final expression can be reduced to an amazingly simple formula. This new gray-body formula not only produces the correct Moon temperature, but also leads to a new and physically more robust relationship between the atmospheric enhancement factor (NTE) and pressure across planets … ”

    Really looking forward to that Ned. Any chance of a sneak preview? ……… 🙂 Or, maybe a guest post on the blog…?

  69. Tchannon
    to clarify. Yes agree the flux is symmetrical. No break with Conservation of Energy. Heat in = heat out re regoliths, just a delay / inertia factor in operation.

    However, the resultant temperature adjustments, loss by day and gain by night, are highly asymmetrical. Small loss by day, huge gain by night, overall the mean lunar temperature is raised above what N&Z formula predicts if regolith effect is not taken into account.

    This simply follows from N&Z maths.

    IOW, allowing for regoliths means that the gap between theoretical figures and empirical data can now pretty well be closed. Therefore N&Z is upheld, the IPCC use of the S-B equation is not.

  70. Hans, you say “GE on earth is about 33K” but this is the fundamental issue that Nikolov and Zeller are disputing, thusly:

    Currently the 33K is calculated from a theoretical grey-body temperature for Earth of 255K, which is 33K less than Earth mean of 288K.

    This theoretical grey-body temperature for Earth is calculated by averaging solar flux evenly over the whole Earth surface and applying the simple Stefan-Boltzmann equation to this average.

    Nikolov and Zeller show that you cannot simply average solar flux and then calculate the resultant temperature (because of Holder’s glaring inequality in this case). You have to take each tiny point, work out the incident solar flux for this tiny point, then calculate the temperature at this tiny point, then integrate the lot. The resultant new formulaic modification of Stefan-Boltzmann gives a temperature MUCH lower than 255K. Whether or not one calls the new difference the greenhouse effect of the atmosphere, the result is the same: some 120K greenhouse / atmospheric thermal effect as calculated without regolith allowance, but allowing for regoliths makes the actual 90-96K data fully plausible.

    There is no wiggle room in N&Z maths. If you follow its logic, its conclusions are inescapable. Plus the data fit well enough, whereas with the old formula, data are wildly adrift.

    It is this inescapable maths that leads to the necessity to re-examine the Second Law of Thermodynamics. One just has to get used to this new situation.

  71. […] Comments Ray Tomes on Miles Mathis: What Causes the …Lucy Skywalker on Empirical results from DIVINER…Lucy Skywalker on Empirical results from DIVINER…Harriet Harridan on Empirical results from […]

  72. Harriet Harridan says:

    N&Z’s equation 6, equation 3 (standard S-B) and the Moon’s mean temp* at 0.126 albedo.


    * Ned: ” ~ 270K, which is .. some 72K larger than the most likely Moon true mean temperature.”

  73. tallbloke says:

    We’ll all have to be patient while Ned and Karl find time to finish ‘reply to comments part 2’

    They have been busy doing real science, now we await the report.

  74. Ned Nikolov says:

    Reply to Hans (March 29, 2012 at 8:43 am):

    Hans,

    You are right – technically, I should not have used the therm ‘Greenhouse Effect’, because it’s conceptually and physically incorrect. I used it just to make the connection to the current mainstream theory. The reality is this, and I encourage you to read our first paper if you have not done it so:

    https://tallbloke.files.wordpress.com/2011/12/unified_theory_of_climate_poster_nikolov_zeller.pdf

    There is noGreenhouse Effect‘ in the sense of a reduction of infrared cooling to space caused by heat-absorbing trace gases as claimed by the current climate science! There is an Atmospheric Thermal Enhancement (ATE), which is entirely due to pressure. Our theory (supported by analysis of inter-planetary data) states that the the full 90-96K difference between Earth and Moon surface temperatures is a result of a Pressure-induced Thermal Enhancement (PTE) unrelated to radiative transfer or cloud albedo. The atmosphere does not reduce the surface cooling to space, instead it enhances the the energy received from the Sun through the physical characteristic of pressure called force. Hence, the composition of the atmosphere is totally irrelevant as far as ATE goes, and changing CO2 concentration cannot affect climate! IR radiative transfer in the atmosphere is a result (product) of temperature set by solar heating and pressure, not a cause for it as claimed by the current theory …

  75. tchannon says:

    Couldn’t find the numeric Diviner data but I have novel plot data extraction software intended for awkward plots as in this blog article. Looks like it is near enough, below is numeric plot overlaid by the original.

    Anyone wants the data, no problem. (not been cleaned), software has given 450 datapoints.

    First plot with the (already improved) model was immediately close

  76. Ned Nikolov says:

    tchannon,

    What’s your email? I can send you the actual data …

    [Reply] Ned, that’s Tim C, so you already have it.

  77. A. C. Osborn says:

    For me there is still the little problem of
    the latest empirical estimate of mean temperature for the Moon is 192-197
    the operative word being “estimate”.
    N&K could still be closer than the “estimate” unless there is a description of how the estimate was arrived at, do they show the maths?

  78. Ned Nikolov says:

    To: A. C. Osborn (March 30, 2012 at 7:24 pm)

    We are working on a paper right now that discusses the math and how the latest mean Moon temperature has been obtained. It’s based on both Diviner data and detailed NASA therm-physical models of the Moon …

  79. Stephen Wilde says:

    Ned said:

    “The atmosphere does not reduce the surface cooling to space, instead it enhances the energy received from the Sun”.

    I agree with that but have a semantic quibble.

    As set out it suggests that somehow the atmosphere ‘creates’ extra energy over and above that which the sun supplies rather than just converting it to kinetic energy.

    I think that a better way of describing it would be to say that the higher atmospheric density at the surface concentrates the thermal effect of the available solar input at the surface.

    In that way one can avoid suggesting that there is a reduction in the rate of surface cooling to space. Instead, the rate of cooling to space from the surface stays the same throughout but the energy delivered by the sun is concentrated just above the surface and declines with height (and reducing density) as observed.

    Still, there is a delay in transmission of solar energy through the system isn’t there ?

    The incoming solar shortwave is more energetic than the less energetic outgoing longwave which implies a conversion process that takes time so I’m not sure that we can escape the slowing down concept altogether.

    I think we must say that the atmosphere slows down the rate of cooling to space but the surface is not involved in the slowing down process because the surface temperature is at the mercy of the density of air molecules at the surface and that will vary with contraction or expansion of atmospheric volume.

    So, if the atmosphere gets warmer due to a composition change then it will expand to reduce density at the surface and weaken ATE and the consequent cooling at the surface will maintain system equilibrium by offsetting the warming of the atmosphere.

    That doesn’t reduce or increase the rate of cooling of the surface, it simply gives the surface a proportionately reduced influence on the whole energy budget.

    The thicker the atmosphere the more it detaches the surface from the energy budget. One could conceive of an atmosphere thick enough to prevent any insolation reaching it at all but the surface will still be very hot because of pressure and density plus downward conduction.

    What we have here is a sun/atmosphere thermal interaction which is initially dependent on conduction from the surface but the thicker the atmosphere, the more GHGs or the more aerosols the more that interaction becomes taken over by the atmosphere whilst the influence of the surface declines.

    A completely transparent atmosphere would remain reliant on conduction from the surface but even pure Nitrogen has some absorption capability so even a pure Nitrogen atmosphere could theoretically become thick enough to detach the surface from any direct thermal interaction with the sun. Probably that would happen when pressure at the surface causes the Nitrogen to turn into a liquid or a solid.

    The only difference that GHGs make in such a scenario is to reduce the solar interaction with the surface to that applicable at a lower atmospheric density than would be the case without them.

    The logical outturn is that GHGs warm the atmosphere but cool the surface for a zero net effect because they serve only to replace a portion of the sun/surface interaction with a sun/atmosphere interaction.

  80. David Appell says:

    Hans wrote:
    The Greenhouse Effect (GE) simply cannot be defined in a proper way on a planet without an atmosphere since it is a product of the atmosphere.

    Yes, that’s a very good summary of your comment. As I wrote on another post here, the lunar temperature follows from the canonical SB law, applied at each point where radiation is incident (since there is no atmosphere to conduct heat and the lunar surface conducts poorly (but not zero)). Then, directly underneath the Sun the lunar temperature would be

    sigma*T^4 = S(1-alpha)

    which gives a maximum T that agrees with the data. And it predicts the drop in temperature with time, which will go like the 1/4th power of the cosine of the angle of lunar rotation. Then the point is out of the sunlight and the small lunar regolith heat conductance applies, until the point swings back into sunlight.

    The standard SB law explains lunar temperatures very well.

  81. David Appell says:

    I’m posting this here, too, because it’s important: the standard SB law certainly explains the lunar temperature — at least, the part that can be explained by radiative considerations.

    Summarizing Pierrehumbert pp 152-153: The moon has little atmosphere, and low heat conductance of its surface material, so at the point directly facing the Sun, where the temperature will be its maximum, the SB law says

    sigma*T^4 = S*(1-alpha)

    where the solar constant S is effectively that of the Earth’s. With an albedo=0.11 you find

    T=382 K

    which agrees exactly with the NASA data by Vasavada (since we’re not really sure *exactly* what values to take for the solar constant or the albedo).

    As the moon rotates this point will move and the incident radiation on it will vary like

    S*cos(2*pi*t/T)

    where t is time and T is the period of rotation of the moon. So you get a factor of

    cos(angle)^(1/4)

    which is exactly the curve the lunar temperature follows in Vasavada’s data:
    https://tallbloke.wordpress.com/2012/03/28/empirical-results-from-diviner-confirm-s-b-law-was-misapplied-to-moon/

    Then the moon’s rotation takes it around and out of the sunlight after 1/4th of a lunar day, or 6 lunar hours. At that point the temperature is determined by whatever radiation is incident — the cosmic microwave background, galactic cosmic rays, etc — plus the small but nonzero heat conductance of the lunar regolith provides whatever heat it does, essentially a constant — after all, the dark side of the moon does not have T=0.

    So you get the rest of the rest of Vasavada’s curve, though the value of about 95 K isn’t solely calculable by radiative considerations — the surface material properties matter too.

    So the standard SB Law explains the lunar temperature quite well.

    As I explained earlier, both N&Z and Daniel Sweger do their averaging wrong. This shows it.

    It’s astonishing — and sad, really — that commenters here like “Phil” believe the IPCC knows they are wrong about something this basic but is hiding that or repressing it or…something. That’s absurd, and not how science — or scientists — operate.

    [Reply] ‘Standard SB Law’ produces a Moon average of ~255K (if you use Earth’s albedo – a ludicrous fudge), this is what we have been fed for years to support the ‘grey body’ Earth temp. It gets around 270K (also ridiculously high) if you use the Moon’s albedo . N&Z do the job correctly, with properly derived equation, on a rotating sphere not a flat plate, and get the right answer with their new term for regolith heat retention factored in. There will be an official update to their ‘Reply to comments Part 1’ soon. We won’t allow apologists like David to re-write history and we are building a dossier of the official documents stating incorrect figures which proves him wrong in this case.

  82. Hans says:

    March 29, 2012 at 10:27 am

    Hi Lucy,

    Excuse me for a late answer. I appreciate your concern for calculating correctly and also share your opinion to take the Graeff article seriously. I am afraid that my answer will be rather long. My comments in your text for clarity.

    “Hans, you say “GE on earth is about 33K” but this is the fundamental issue that Nikolov and Zeller are disputing, thusly:
    This theoretical grey-body temperature for Earth is calculated by averaging solar flux evenly over the whole Earth surface and applying the simple Stefan-Boltzmann equation to this average.”

    (Correct and this is a fair approximation of earth´s Greenhouse Effect. It is fair because solar energy is distributed around all of earth before IR radiates an energy flux to space both day and nights. The 33 K is a truly a product of the atmosphere as such and its raection in a gravity field. It is the OBSERVED difference between tha average temperature of earth surface and the OBSERVED temperature of earth as seen from space: It is a real temperature difference that cannot be discarded by any theory. On the other hang the total energy content hold by one kg of atmospheric mass is at minimum at the surface and at maximum the higher up in the atmophere you move./HJ)

    Nikolov and Zeller show that you cannot simply average solar flux and then calculate the resultant temperature (because of Holder’s glaring inequality in this case).

    (The NASA approximation gets really bad when applied to a planet without an atmosphere for several reasons and the black body temperature given in “Moon fact sheet” is a sign of scientific incomepetence or agenda from NASA and other institutions/HJ)

    You have to take each tiny point, work out the incident solar flux for this tiny point, then calculate the temperature at this tiny point, then integrate the lot. The resultant new formulaic modification of Stefan-Boltzmann gives a temperature MUCH lower than 255K.” (Agree for a planet without an atmosphere. Try to do it for earth/HJ)

    Whether or not one calls the new difference the greenhouse effect of the atmosphere, the result is the same: some 120K greenhouse / atmospheric thermal effect as calculated without regolith allowance, but allowing for regoliths makes the actual 90-96K data fully plausible.
    (It can quite easily be figured out what physical processes are involved to generate the temperature difference between the average lunar surface temperature and earth´s surface temperature)

    There is no wiggle room in N&Z maths. If you follow its logic, its conclusions are inescapable.
    (Observational evidence is even more inescapable and there are several obvious reasons why the temperature differnce is as you mention/HJ)

    Plus the data fit well enough, whereas with the old formula, data are wildly adrift.
    (Curve fitting is a mean to reach understanding not a theory. I agree that NASA way of calculating the averate black body temperature on a planet without an atmosphere is scandalous/HJ)

    It is this inescapable maths that leads to the necessity to re-examine the Second Law of Thermodynamics.
    (I disagree about this even if you include the article by Graeff. I am on Loschmidt´s side but that doesn´t disprove the second law of thermodynamics. Both the 1st and 2nd law of thermodynamics is based on energy, not temperature. It should always be applied to energy. To associate the 2nd law to temperature is only working in specifíc physical situations. Look at what I said about the energy content per mass unit above. Net energy can always be moved from a higher energy state to a lower one. That is what happens when DALR is formed in the atmopshere. It also includes that IR radiation can go from a lower temperature to a higher in specific situations AND THAT IS STILL ACCORDING TO THE 2nd LAW. My Karesuando data https://tallbloke.wordpress.com/2012/03/16/hans-jelbring-back-radiation-and-observational-meteorologial-evidence/ shows that this occurs in nature. But it cannot happen at a flux of +300 W/m^2 (back radiation) as IPCC states./HJ)

    One just has to get used to this new situation.
    (Yes, there is a new situation but not exactly the one you believe in. I am writing this comment since you seem to be honest and really wish to get down to basic scientific knowledge/HJ)

  83. David Appell says:

    [Reply] ‘Standard SB Law’ produces a Moon average of ~255K (if you use Earth’s albedo – a ludicrous fudge)

    It does not — again, you are misapplying the SB law, because the lunar surface is not anywhere close to being in equilibrium, while the Earth’s surface is.

    I am not “rewriting history” — I am simply applying physics correctly.

    [Reply] Good to hear. It’s about time someone on your side of the fence did. We have a nice (growing) collection of warmists telling us in many web-pages that the Moons average surface temperature is around 255K. Funnily enough, we haven’t found a single one which says it’s around what the empirical DIVINER data shows it really is – around 192-197K. 🙂

  84. David Appell says:

    [Reply] Good to hear. It’s about time someone on your side of the fence did. We have a nice (growing) collection of warmists telling us in many web-pages that the Moons average surface temperature is around 255K. Funnily enough, we haven’t found a single one which says it’s around what the empirical DIVINER data shows it really is – around 192-197K

    Who cares what other people are saying? They are applying the physics incorrectly too then.

    You keep focusing on the average temperature. What about the temperature at all other times — the entire Vasavada curve? Standard theory explains all of it, even the correct shape — and thus, it provides the correct average. So what is missing in the standard theory?

    [Reply] An exposition of it in the literature.Giving the correct average surface T. Where is it?

  85. David Appell says:

    Then here’s how standard theory gives not just the correct curve, but the correct average too:

    On the sunlight side of the moon, the average temperature will be

    =B*

    where, as usual,

    B=[S*(1-alpha)/sigma]^1/4 = 382 K

    and the angle average is taken from -pi/2 to +pi/2, as in Sweger’s equation 10. As Sweger says, this is 2.7, so

    =(2.7/pi)*B

    The dark side of the moon is whatever it is: radiative + heat conductance, which from the data is approximately

    =95 K.

    Averaging these two numbers gives

    =212 K

    in exact agreement with the data.

    QED

    [Reply] Resubmit with the values you are using for alpha and sigma, and a link to the data used as a source for your handwaving concerning the temperature of the dark side.

  86. David Appell says:

    [Reply] An exposition of it in the literature.Giving the correct average surface T. Where is it?

    It’s too simple to be in the literature. As I wrote, the explanation is in Pierrehumbert’s textbook, Ch 3 pp 152-153.

    If the curve is correct, it follows logically that the average is correct. Nonetheless, I just submitted it in a comment submitted just before this one.

    [Reply] “too simple to be in the literature”. Lol. Look out for a paper from Ned Nikolov and the senior JPL scientist Dr. Ashwin Vasavada soon. 🙂

  87. Hans, thank you for replying at length. I appreciate that you took the trouble. However, I’m not sure what to do now. I can see that I did not make myself clear enough. My bad. Also you made assertions of “evidence” that were not actually backed by anything I could check.

    Please try and follow the next paragraph, which tries to get to the heart of the matter. I’ve written up the whole thing much better on the wiki page … email me if you are interested.

    I did not say anything about disproving the Second Law (the words you used), I said “the necessity for re-examining [it]” and I was actually thinking of Graeff’s statement modifying the Second Law, and his inescapable logic to get there. Now “necessity” arises if one appreciates the physics-maths argument (Holder’s Inequality) for Nikolov and Zeller’s mathematical reworking of Stefan-Boltzmann’s basic equation so as to apply to a sunlit hemisphere. And yes, N&Z’s equation’s predictions match Diviner data (192-197K mean lunar temp) with beautiful plausibility. The nighttime effect of regolith thermal inertia, at less than 1% solar flux, is enough to close the gap completely between S-B calculation and measurement – whereas the current calculation with the simple S-B formula produces 271K which is wildly too high – and there is no physically meaningful adjustment that can be applied to lower it.

  88. […] paper by Vavasada et al which adds a lot more detail to the plot of Lunar equatorial temperature he passed our way recently. This is technical, but worth getting your head around, because it reveals and elucidates matters […]