Ned Nikolov has kindly sent me the freshly published 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 highly relevant to ideas and misconceptions regarding theoretical grey body temperature, both for the Moon and Earth. Get it while it’s hot.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, E00H18, doi:10.1029/2011JE003987, 2012
Lunar equatorial surface temperatures and regolith properties
from the Diviner Lunar Radiometer Experiment
Ashwin R. Vasavada,1 Joshua L. Bandfield,2 Benjamin T. Greenhagen,1 Paul O. Hayne,3
Matthew A. Siegler,4 Jean-Pierre Williams,4 and David A. Paige4
Received 30 September 2011; revised 20 February 2012; accepted 20 February 2012; published 4 April 2012.
[1] 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-mm 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
eightfold increase in thermal conductivity (adjusted for temperature) occurring within
several centimeters of the surface.
Citation: 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., 117, E00H18, doi:10.1029/2011JE003987.
Figure 7. Depth profiles of minimum (left curve), average (center), and maximum (right) temperature for the revised
model at the equator assuming a normal albedo of 0.1
6. Summary
6.1. Discussion
[49] The thermophysical homogeneity of the Moon
revealed by Diviner measurements along the equator (and by
extension, globally) is remarkable, though not unexplained.
Ubiquitous mechanical breakdown of surface materials by
micrometeoroids is the dominant surface geologic process,
and the resulting particulate nature of the regolith dominates
over compositional differences in determining its thermal
response. A small percentage of the surface exposes high
thermal inertia material, including blocks, lava flows, and
bedrock not yet pulverized by impactors. Bandfield et al.
[2011] identified small regions of lower thermal inertia as
well, correlated with recent $km-scale impacts. In our
present work, these atypical surfaces are statistically insig-
nificant and we are able to characterize the entire equatorial
near-surface layer with a single set of average thermo-
physical properties.
[50] The Diviner measurements build on Apollo-era
studies by confirming certain characteristics of the near-
surface layer inferred at specific landing sites (and in
returned samples). The increase in density and conductivity
in the upper few cm of the regolith is a ubiquitous feature, as
is the more gradual scale of the transition than inferred by
reflectance.
Full paper here for a limited time. (be quick)
Tallbloke's Talkshop 
Figure I came out with is 0.1 W/sqm/K
Maybe the two results are the same thing, different emphasis.
Wot, praytell, does a forty-dollar percent increase mean?
“a $40% increase “
Thanks Brian, it should have been a tilde symbol rather than a dollars symbol. The journal formatting team go out of their way to make copy and paste a tortuous exercise…
TB,
I hate computer models. They do not show or tell differences in the parameters of the rest of the orb. So this is why averaging is used which changes the whole shape of a planet in the model.
The word “assuming” is also making fools of science when facts should be used.
[Reply] You volunteering to go dig 1m deep holes all over the Moon and stick thermocouples in them Joe? 🙂
Hmmmm…..
Big slingshot between two trees?
🙂
Thanks for presenting this paper with results from the Diviner Orbiter. The two articles represent a tremendous work and it would be a shame if the data is misinterpreted or not fully investigated These two articles do shed light on a number of questions. The major one is:
Personal statement: Lunar regolith does not emit as is requested by the Stefan Boltzmann law. In fact Stefan Boltzmann law is modulated by both geometric form of a surface and of particle size. I have pointed out the former in a thread earlier and the second part of the statement can be proven by earlier work on lunar temperature together with these two Diviner experiment papers. This article directly states that:
“While these data are not yet fully reduced, an initial look shows that emission is indeed peaked towards low emission angels. If present, this directional distribution of emission could be an inherent property of the lunar surface material and therefore affect its kinetic temperature, or could be an observational effect created by anisothermality and/or macroscopic roughness, for example.” (In summary page 11)
Some more opinions on this paper:
A) The article content is not only covering what the title imply. It is also covering a comparison with an earlier temperature model.
B) I should be clear that the Diviner data set does not represent directly measured temperature. It is by itself a model temperatures.
C) The article honestly describe the problems to get data to fit into the SB law which is the base for temperatures measured in all 9 channels.
D) To get measured to fit the SB law a number of methods are undertaken such as data removal and ad hock introduction of adjustments. See “Selecting Best Fit Model Parameters”.
E) To introduce such parameters and get a good fit might remove the important question from the agenda. This is a very a complex system to master, both the real matter on the surface of moon, the construction of the measuring equipment and the interpretation of the measured data.
I wish the authors or anybody luck with the continued treatment of the vast Orbital diviner Data sets. for sure it will be very valuable to study for a long time for many reasons. It might be interesting to known about early lunar temperature results and how they were modelled. See: C. J. Cremer, Lunar Surface temperatures from Apollo12.
Lunar surface temperatures from Apollo 12
Hans
Thanks Ned for that paper. Much appreciated.
Big thanks to Ned for making the paper available to us… 😎
Hans says:
April 11, 2012 at 8:36 am
“…B) I should be clear that the Diviner data set does not represent directly measured temperature. It is by itself a model temperatures.
C) The article honestly describe the problems to get data to fit into the SB law which is the base for temperatures measured in all 9 channels.
D) To get measured to fit the SB law a number of methods are undertaken such as data removal and ad hock introduction of adjustments. See “Selecting Best Fit Model Parameters”.
E) To introduce such parameters and get a good fit might remove the important question from the agenda. This is a very a complex system to master, both the real matter on the surface of moon, the construction of the measuring equipment and the interpretation of the measured data…”
Yes, Hans, using any of the ideal laws of physics, like SB, in the real world is fraught with difficulty and many assumptions have to be made to get even an approximate result. These heuristic models then often fail in regard to the dynamic of the system observed which have moving bodies and a non-homogenious heat sources. In addition, because models have to be tailored to the specific enviornment of the object being observed, results have little or no relevance if applied to different bodies with different dynamics.
Will the real temperature of the moon please stand up and be counted… 🙂
Explain why I can closely match the Diviner result with SB law? The only extra factors in there are conductivity and something probably to do with surface roughness (not a major effect).
I think the nature of the surface interaction is widely misunderstood, is counter intuitive. This is why I have so much trouble following most of the arguments which have been going on.
Something I have not made clear is earth temperature is very close to the upper SB limit, well above the much lauded 33K too low. This suggests very little is strange about earth. The question then is what is it about “surface” conductivity on earth.
Maybe if I say, earth, moon, most things appear perfectly reflective from the outside, albedo is unity and does not appear in SB might give a clue. Jumping into internal details or different references gives a different view of things, as it would.
Tenuc: The findings from the DIVINER data plus modelled surface characteristics are consistent with he Apollo mission in situ direct thermocouple data. Correctly done, models are useful and informative, and can be relied on with a high degree of confidence if the parameters are not to many, and are well constrained. For the Moon, this is OK. For Earth, it’s highly problematic.
But what we can say about Earth is that if it had never had an atmosphere, it would have a similar ‘grey body’ temperature to the Moon, notwithstanding the differences its axial tilt, greater internal heat, faster rotation and bigger diameter would make.
It is notable that the Moon has a higher (and stable) average equatorial temperature at a depth of a few centimetres or more. I hope Vavasada et al will be publishing a further paper with a modelled temperature for the whole of the Moon below the surface regolith. This may give some insight into the relative rates of cooling of the Earth’s rocky and sandy surfaces compared to the ocean, and thus the contribution the ocean really makes to the Earth’s average surface temperature.
Tanuc,
He is a real gem, an article from Chinese lunar temperature measurements. They differ very much from the Orbital diviner data but both are OK in their own way. It seems clear that the SB law cannot be applied directly when measuring temperature with a radar reciever, or can it?
http://www.europlanet-eu.org/outreach/index.phpoption=com_content&task=view&id=305&Itemid=41
>TB: “But what we can say about Earth is that if it had never had an atmosphere, it would have a similar ‘grey body’ temperature to the Moon, notwithstanding the differences its axial tilt, greater internal heat, faster rotation and bigger diameter would make.”
The faster rotation would make a lot of difference compared to the lunar data.
TB: “I hope Vavasada et al will be publishing a further paper with a modelled temperature for the whole of the Moon below the surface regolith.”
That is what the chinese already have done
Compare with Apollo
From simulation post here
Now tell me what happens if the surface thermal conductivity is high, such as protective atmosphere and presence of water?
A few comments:
1) The most important piece of information from the Vavasada et al. (2012) paper pertaining to our discussion about the SB formula is that the long-term average surface temperature at the lunar equator (the warmest latitude of the Moon) is 213K, or some 57K lower than the global mean predicted by the simple SB equation. Hence, the SB formula cannot be correct!
2) NASA has had fairly accurate models of Moon temperatures for over 10 years now. The Diviner measurements confirm the reliability of these models (see Figures 4 and 9 in the paper).
3) The subsurface (below 0.3 m depth) temperature at the lunar equator is nearly constant at about 250K. However, this does not mean that subsurface temperatures at higher latitudes have the same value! As the surface temperature declines from equator towards the poles, so does the subsurface temperature. Unfortunately, we do not have direct subsurface measurements outside the lunar tropics (the Apollo missions were within 22 degrees of the equator).
tallbloke says:
April 11, 2012 at 1:59 pm
“Tenuc: The findings from the DIVINER data plus modelled surface characteristics are consistent with he Apollo mission in situ direct thermocouple data. Correctly done, models are useful and informative, and can be relied on with a high degree of confidence if the parameters are not to many, and are well constrained. For the Moon, this is OK. For Earth, it’s highly problematic.
But what we can say about Earth is that if it had never had an atmosphere, it would have a similar ‘grey body’ temperature to the Moon, notwithstanding the differences its axial tilt, greater internal heat, faster rotation and bigger diameter would make….”
Exactly, the bolded items in your post is why It’s like trying to compare chalk with cheese! We also have to add to your list the following…
Difference in strength of magnetic field, mass, density, gravity, chemical composition, topography, radio activity… (and probably lots more differences I’ve not thought of or have not even yet even been discovered). The models will never produce results that can be compared, unless we have all the required information to make the necessary tweeks it to fit the new constraints.
Earth without atmosphere, oceans and biomass is a mythical object and perhaps this is another elephant in the room regarding the current cargo-cult brand of IPCC climate science.
Hi Ned,
Figure 7 gives a subsurface equatorial temperature of 240K not 250K. That’s a big difference!
The Moon’s pole’s don’t get any seasonal warmth from axial tilt like Earth does, because iit orbits Earth close to the ecliptic rather tha the equator, so I’d expect the subsurface at high latitude to be quite a lot colder. Is that right?
Hans says:
April 11, 2012 at 4:08 pm
Tenuc,
He is a real gem, an article from Chinese lunar temperature measurements. They differ very much
from the Orbital diviner data but both are OK in their own way. It seems clear that the SB law cannot be applied directly when measuring temperature with a radar reciever, or can it?
http://www.europlanet-eu.org/outreach/index.phpoption=com_content&task=view&id=305&Itemid=41…
Hi Hans, unfortunately URL not working. However, I found a press release on the same site which sounds like the paper you were descbing.
THE FIRST MICROWAVE IMAGE OF THE COMPLETE MOON
“…Dr. Zheng and his team have constructed global brightness temperature maps of the Moon for different frequencies, and separately for day and night times. The results are particularly revealing. On the 37 GHz daytime map, the maria, which appear dark in visible light, become bright in microwave wavelengths to reflect the higher temperatures (due to stronger absorption in the solar visible spectrum).
Geological features like craters and mountains are clearly visible, but the prominent bright areas correlate mainly with the surface abundance of titanium. The correspondent nighttime microwave image is even more striking: The nighttime moon appears dotted by dark (cool) areas that turn out to be associated with hot areas during lunar eclipses. “This enigma will keep the theorists busy for a while!” says, Dr. Zheng.”
Day view here…
Night here…
Love the pictures, and perhaps confirmation of Tims 1.3 on his lunar model thread?
I notice there seems to be a spread of the three cooler bands during the night – lateral conduction perhaps?
Full article here…
hxxp://www.europlanet-eu.org/outreach/index.php?option=com_content&task=view&id=305&Itemid=41
(If Han’s link doesn’t work for you, copy URL into address bar and change hxxp to http)
[ usage of colour is dazzling, could switch to greyscale versions if wanted –Tim]
Hi Tim. tried the greyscale versions, but didn;t show the variability as well as the pseudo-colour,
Anyways, as a child of the 60’s I like a bit of psycodelia, it brightens the place up… 🙂
Repy to tallbloke (April 11, 2012 at 7:03 pm)
Rog,
Yes, the modeled subsurface equatorial temperature is 240K. I was thinking about the 0.4 m deep temperatures measured by Apollo 15. These were at about 250K. See Fig. 1 in this paper:
Click to access 3008.pdf
Yes, you are right – the higher latitudes are expected to have colder subsurface equilibrium temperatures.
tchannon says: April 11, 2012 at 5:34 pm
“Now tell me what happens if the surface thermal conductivity is high, such as protective atmosphere and presence of water?”
Tim,
Your model, The Apollo model and the Orbital Diviner (“observed measurment”) model are very equal goog proxies. Does it mean that they support each other relating to equatorial lunar temperatures? The Cremer et al study from 1971 is based on only time series from two physical lunar points (Apollo 11 and Apollo 12).
The problem is that all of them are based on 1) the correctness of the Stefan Bolztmann law and an assumed value of the “conductivity” of the upper lunar soil.
The Orbital Deviner data sets have been been hardly reduced and changed by introducing a amplitude modulation. This is honestly described in the Vasada et al paper “Lunar equatorial surface temperatures and regolith properties from the diviner Lunar Radiometer Experiment”.
The “conductivity” of the lunar soil is also discussed and your guess was as good as the guess of the Vasada et al model. Hence, all three models ended up approximately equal.
What should be discussed is the application of the Stefan Bolzmann law which is not adequate relating to the good data that the Orbital diviner has collected. Their instruments are truly measuring the irradiation (Watt/m^2) sent out from the surface of earth (bolometers).
Your question above is not well formulated. A number of physical processes exist on earth that does not exist on the moon and a number of physical processes exist on the lunar surface that does not exist on earth. There is no need to introduce an undefined model concept named “earth surface thermal conductivity”. It would for example be a function of wind speed and earth´s rotation just to mention two important variables. The Diviner data set is a very good set which should be the basis for discussing what happens on the lunar surface and to find out how electromagnetic radiation is absorbed and emitted from its surface and how that occur. That´s a basic problem.
Ned Nikolov says: April 11, 2012 at 6:16 pm
1) The most important piece of information from the Vavasada et al. (2012) paper pertaining to our discussion about the SB formula is that the long-term average surface temperature at the lunar equator (the warmest latitude of the Moon) is 213K, or some 57K lower than the global mean predicted by the simple SB equation. Hence, the SB formula cannot be correct!
2) NASA has had fairly accurate models of Moon temperatures for over 10 years now. The Diviner measurements confirm the reliability of these models (see Figures 4 and 9 in the paper).
3) The subsurface (below 0.3 m depth) temperature at the lunar equator is nearly constant at about 250K. However, this does not mean that subsurface temperatures at higher latitudes have the same value! As the surface temperature declines from equator towards the poles, so does the subsurface temperature. Unfortunately, we do not have direct subsurface measurements outside the lunar tropics (the Apollo missions were within 22 degrees of the equator).
About 1) “Hence, the SB formula cannot be correct!”. The SB formula can never and should never be used for average values without specifiying the errors introduced by doing so. The SB formula is a fair opproximation of emitted irradiance from a specific point of the lunar surface given that the importance of emitted electromagnetic vawelength is understood correctly. There does not exist any strict lunar surface on the moon, a fact that affect both absorbtion and emission fo photons. The dust layer introduces problems we dont experience on the surface of earth. The solution of these problems have to be admitted and a solution has to be found.
About 2) The Diviner Orbital data set show that the former models relating on the SB law is inaccurate in the form that it has been used (about averaging and not knowing the strong influence of lunar dust)
About 3) The Chinese data set temperatures are calculated using a model which is not based on the SB law and the published temperatures differ rather much from the Diviner data set during especially day time. This is very interesting and should be discussed in detail.
Ned Nikolov says: April 12, 2012 at 7:08 am
Hi Ned,
Thanks for the article which is valuable for me.
Ned, thanks for that.
Is there any understood reason why the Apollo data would show a higher subsurface temperature at 20 degrees of latitude than the equator does in the Vavasada model? Is it possible there is instrumental error of 10C or more? Will Vavasada be plotting MSU surface temperatures at those latitudes to help determine the reasons for the discrepancy?
Lots of questions. Sorry. 🙂
The technique of using radar for measuring soil temperature is well developed in China although to measure 37 GHz electromagnetic radiation from lunar surfaces and earth surfaces are quite different tasks. Both are actually comparison between two models measuring temperatures. Details have to be sorted out and understood. As can be seen the two methods don´t get equal results on earth and the moon.
Atmospheric and Oceanic Science Letters,Volume 4, Issue 5,2011
Article: pp. 257–263 | PDF
Validation of Land Surface Temperature Derived from 37-GHz AMSR-E over Northern China
ZHANG An-Zhi
1. Key Laboratory of Regional Climate-Environment Research for Temperate East Asia (RCE-TEA), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
2. Graduate University of Chinese Academy of Sciences, Beijing 100049, China
JIA Gen-Suo
1. Key Laboratory of Regional Climate-Environment Research for Temperate East Asia (RCE-TEA), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
WANG He-Song
1. Key Laboratory of Regional Climate-Environment Research for Temperate East Asia (RCE-TEA), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
ZHAO Tian-Bao
1. Key Laboratory of Regional Climate-Environment Research for Temperate East Asia (RCE-TEA), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
ABSTRACT
A validation study of land surface temperature (LST) obtained from the Ka band (37 GHz) vertically polarized brightness temperature over northern China is presented. The remotely sensed LST derived jointly by the Vrije Universiteit Amsterdam and the NASA Goddard Space Flight Center (VUA-NASA) from the Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) were compared to the daily in-situ top soil temperature/infrared surface temperature observations from eleven/three Enhanced Coordinated Observation stations in arid and semi-arid regions of northern China. The VUA-NASA LST from the descending path exhibited a stronger correspondence to the in-situ infrared surface temperature than soil temperature observations, whereas correlations (R2) of the latter ranged from 0.41 to 0.86. Meanwhile, the ascending overpass LST was generally warmer than the in-situ soil temperature observations at all stations, and the correlation (R2) was between 0.07 and 0.72. Furthermore, the correlation of the descending path was generally greater than that of the ascending path at the same station. The descending path VUA-NASA LST was sensitive to precipitation and presented good agreement with ground temperature dynamics. The analyses demonstrated that the descending overpass LST was reliable to reflect reasonable patterns of temperature dynamics for land surface temperature in the region.
Tenuc says: April 11, 2012 at 8:08 pm
Tenuc,
Many thanks for helping. See also
http://www.lpi.usra.edu/meetings/lpsc2011/pdf/1352.pdf I am going to uset the next two images for discussing lunar temperatures in my next comment.
It is important to have access to the text in the press release so I include it below since it is hard to find on the net. The following comment is especially intriguing:
” The correspondent nighttime microwave image is even more striking: The nighttime moon appears dotted by dark (cool) areas that turn out to be associated with hot areas during lunar eclipses. “This enigma will keep the theorists busy for a while!” says, Dr. Zheng.”
The first microwave image of the complete Moon has been obtained by the Chinese lunar satellite Chang’E-1. Global brightness temperature maps reveal radiation from the surface and deeper layers of the Moon and its diurnal variation. This will help astronomers to determine the detailed heat flow and, thus, the inner energy of the Moon. These exciting new results will be presented by Dr. Yong-Chun Zheng and Dr. Kwing L. Chan at the European Planetary Science Congress in Rome from Monday 20th to Wednesday 22d September.
Chang’E-1 (CE-1) is China’s first scientific mission to explore planetary bodies beyond Earth. The stereo camera, one of the eight science instruments on board the spacecraft, has produced a state-of the-art global image of the Moon with unprecedented image quality and positioning precision. The Solar Wind Ion Detector (SWID) has discovered the acceleration of scattered solar wind protons close to the lunar polar terminator. And now, the Lunar Microwave Radiometer (MRM) made it possible, for the first time, to globally map the Moon in microwave frequencies.
Astronomers know that active radar observations of the Moon cannot provide thermal information, only passive observations in the infra-red and microwave regimes can achieve that. Furthermore, only microwave detectors can sense emission from below the lunar surface (down to tens of meters). Ground-based microwave observations are not the best choice in order to do this, because they cannot “see” the far side of the moon neither can obtain accurate brightness temperature near the limb.
Before CE-1, there was no passive, multi-channel, microwave remote sensing of the Moon from a satellite. CE-1 had a polar orbit and, thus, was able to observe essentially every location of the moon with a nadir view. Thanks to the long lifespan of CE-1 (494-days), the MRM obtained brightness temperature data that cover the Moon globally eight times, during both lunar daytime and nighttime periods. This global, diurnal coverage provides extremely valuable data for studying the lunar regolith (‘dust’ and impact debris covering almost the entire Moon surface).
CE-1 was observing from an altitude of 200 km from the lunar surface, providing spatial resolution orders of magnitude better than any ground-based microwave observation can ever achieve on Earth. Indeed, the sensitivity (0.5K) and dynamical range (20-500K) of the observable brightness temperature obtained by CE-1 is unsurpassed. “No future mission, from any country, has been planned with a comparable program in microwave measurement”, says Dr. Zheng of the Chinese Academy of Sciences.
The CE-1 microwave observations have made several important breakthroughs. MRM passively measured microwave emission in four frequency channels: 3, 7.8, 19.35, and 37 GHz. The higher frequency emission comes from a layer just a little below the surface (a few centimeters), whereas the lower frequency emission can probe depths beyond a few meters. “With such penetrative ability, the microwave data can be used to infer thermo-physical properties of the lunar regolith, as well as, to find out about the variation of regolith thickness across the lunar surface”, says Dr. Chang from Hong Kong University Sci&Tech. Such information is useful for estimating the distribution and amount of helium 3, a promising nuclear fuel for in situ fusion energy production in the future human settlements on the Moon. (Helium 3 originated from the sun and is believed to have been implanted in the lunar regolith by the solar wind).
Using the MRM data, Dr. Zheng and his team have constructed global brightness temperature maps of the Moon for different frequencies, and separately for day and night times. The results are particularly revealing. On the 37 GHz daytime map, the maria, which appear dark in visible light, become bright in microwave wavelengths to reflect the higher temperatures (due to stronger absorption in the solar visible spectrum). Geological features like craters and mountains are clearly visible, but the prominent bright areas correlate mainly with the surface abundance of titanium. The correspondent nighttime microwave image is even more striking: The nighttime moon appears dotted by dark (cool) areas that turn out to be associated with hot areas during lunar eclipses. “This enigma will keep the theorists busy for a while!” says, Dr. Zheng.
A sister orbital probe to CE-1, Chang’E-2, is scheduled to be launched in October 2010.
[…] DIVINER’s results show that the Moon’s actual mean surface temperature is much lower than the estimate derived from the standard Stefan-Boltzmann (S-B) equation: […]
[…] because the results that Diviner produced enabled Dr Ashwin Vavasada et al to calculate an average surface temperature for the Moon’s equatorial band of 214.4K. Tim Channon then built a very neat model to replicate the Vavasada result. Ned […]