The Moon is a Cold Mistress

Guest Post by Willis Eschenbach

I’ve been considering the effect that temperature swings have on the average temperature of a planet. It comes up regarding the question of why the moon is so much colder than you’d expect. The albedo (reflectivity) of the moon is less than that of the Earth. You can see the difference in albedo in Figure 1. There are lots of parts of the Earth that are white from clouds, snow, and ice. But the moon is mostly gray. As a result, the Earth’s albedo is about 0.30, while the Moon’s albedo is only about 0.11. So the moon should be absorbing more energy than the Earth. And as a result, the surface of the moon should be just below the freezing temperature of water. But it’s not, it’s much colder.

Figure 1. Lunar surface temperature observations from the Apollo 15 mission. Red and yellow-green short horizontal bars on the left show the theoretical (red) and actual (yellow-green) lunar average temperatures. The violet and blue horizontal bars on the right show the theoretical Stefan-Boltzmann temperature of the Earth with no atmosphere (violet), and an approximation of how much such an Earth’s temperature would be lowered by a ± 50°C swing caused by the rotation of the Earth (light blue). Sunset temperature fluctuations omitted for clarity. DATA SOURCE

Like the Earth, averaged over its whole surface the moon receives about 342 watts per square metre (W/m2) of solar energy. We’re the same average distance from the sun, after all. The Earth reflects 30% of that back into space (albedo of 0.30), leaving about 240 W/m2. The moon, with a lower albedo, reflects less and absorbs more energy, about 304 W/m2.

And since the moon is in thermal equilibrium, it must radiate the same amount it receives from the sun, ~ 304 W/m2.

There is something called the “Stefan Boltzmann equation” (which I’ll call the “S-B equation” or simply “S-B”) that relates temperature (in kelvins) to thermal radiation (in watts per square metre). It says that radiation is proportional to the fourth power of the temperature.

Given that the moon must be radiating about 304 W/m2 of energy to space to balance the incoming energy, the corresponding blackbody lunar temperature given by the S-B equation is about half a degree Celsius. It is shown in Figure 1 by the short horizontal red line. This shows that theoretically the moon should be just below freezing.

But the measured actual average temperature of the lunar surface shown in Figure 1 is minus 77°C, way below freezing, as shown by the short horizontal yellow-green line …

So what’s going on? Does this mean that the S-B equation is incorrect, or that it doesn’t apply to the moon?

The key to the puzzle is that the average temperature doesn’t matter. It only matters that the average radiation is 304 W/m2. That is the absolute requirement set by thermodynamics—the average radiation emitted by the moon must equal the radiation the moon receives from the sun, 304 W/m2.

But the radiation is proportional to the fourth power of temperature. This means when the temperature is high, there is a whole lot more radiation, but when it is low, the reduction in radiation is not as great. As a result, if there are temperature swings, they always make the surface radiate more energy. As a result of radiating more energy, the surface temperature cools. So in an equilibrium situation like the moon, where the amount of emitted radiation is fixed, temperature swings always lower the average surface temperature.

For confirmation, in Figure 1 above, if we first convert the moment-by-moment lunar surface temperatures to the corresponding amounts of radiation and then average them, the average is 313 W/m2. This is only trivially different from the 304 W/m2 we got from the first-principles calculation involving the incoming sunlight and the lunar albedo. And while this precise an agreement is somewhat coincidental (given that our data is from one single lunar location), it certainly explains the large difference between simplistic theory and actual observations.

So there is no contradiction at all between the lunar temperature and the S-B calculation. The average temperature is lowered by the swings, while the average radiation stays the same. The actual lunar temperature pattern is one of the many possible temperature variations that could give the same average radiation, 304 W/m2.

Now, here’s an oddity. The low average lunar temperature is a consequence of the size of the temperature swings. The bigger the temperature swings, the lower the average temperature. If the moon rotated faster, the swings would be smaller, and the average temperature would be warmer. If there were no swings in temperature at all and the lunar surface were somehow evenly warmed all over, the moon would be just barely below freezing. In fact, anything that reduces the variations in temperature would raise the average temperature of the moon.

One thing that could reduce the swings would be if the moon had an atmosphere, even if that atmosphere had no greenhouse gases (“GHGs”) and was perfectly transparent to infrared. In general, one effect of even a perfectly transparent atmosphere is that it transports energy from where it is warm to where it is cold. Of course, this reduces the temperature swings and differences. And that in turn would slightly warm the moon.

A second way that even a perfectly transparent GHG-free atmosphere would warm the moon is that the atmosphere adds thermal mass to the system. Because the atmosphere needs to be heated and cooled as well as the surface, this will also reduce the temperature swings, and again will slightly warm the surface in consequence. It’s not a lot of thermal mass, however, and only the lowest part has a significant diurnal temperature fluctuation. Finally, the specific heat of the atmosphere is only about a quarter that of the water. As a result of this combination of factors, this is a fairly minor effect.

Now, I want to stop here and make a very important point. These last two phenomena mean that the moon with a perfectly transparent GHG-free atmosphere would be warmer than the moon without such an atmosphere. But a transparent atmosphere could never raise the moon’s temperature above the S-B blackbody temperature of half a degree Celsius.

The proof of this is trivially simple, and is done by contradiction. Suppose a perfectly transparent atmosphere could raise the average temperature of the moon above the blackbody temperature, which is the temperature at which it emits 304 W/m2.

But the lunar surface is the only thing that can emit energy in the system, because the atmosphere is transparent and has no GHGs. So if the surface were warmer than the S-B theoretical temperature, the surface would be emitting more than 304 W/m2 to space, while only absorbing 304 W/m2, and that would make it into a perpetual motion machine. Q.E.D.

So while a perfectly transparent atmosphere with no GHGs can reduce the amount of cooling that results from temperature swings, it cannot do more than reduce the cooling. There is a physical limit to how much it can warm the planet. At a maximum, if all the temperature swings were perfectly evened out, we can only get back to S-B temperature, not above it. This means that for example, a transparent atmosphere could not be responsible for the Earth’s current temperature, because the Earth’s temperature is well above the S-B theoretical temperature of ~ -18°C.

Having gotten that far, I wanted to consider what the temperature swings of the Earth might be like without an atmosphere. Basic calculations show that with the current albedo, the Earth with no atmosphere would be at a blackbody temperature of 240 W/m2 ≈ -18°C. But how much would the rotation cool the planet?

Unfortunately, the moon rotates so slowly that it is not a good analogue to the Earth. There is one bit of lunar information we can use, however. This is how fast the moon cools after dark. In that case the moon and the Earth without atmosphere would be roughly equivalent, both simply radiating to outer space. At lunar sunset, the moon’s surface temperature shown in Figure 1 is about -60°C. Over the next 30 hours, it drops steadily at a rate of about 4°C per hour. At that point the temperature is about -180°C. From there it only cools slightly for the next two weeks, because the radiation is so low. For example, at its coolest the lunar surface is at about -191°C, and at that point it is radiating a whopping two and a half watts per square metre … and as a result the radiative cooling is very, very slow.

So … for a back of the envelope calculation, we might estimate that the Earth would cool at about the lunar rate of 4°C per hour for 12 hours. During that time, it would drop by about 50°C (90°F). During the day, it might warm about the same above the average. So, we might figure that the temperature swings on the Earth without an atmosphere might be on the order of ± 50°C. (As we would expect, actual temperature swings on Earth are much smaller, with a maximum of about ± 20-25 °C, usually in the desert regions.)

How much would this ±50° swing with no atmosphere cool the planet?

Thanks to a bit of nice math from Dr. Robert Brown (here), we know that if dT is the size of the swing in temperature above and below the average, and T is the temperature of the center of the swing, the radiation varies by 1 + 6 * (dT/T)^2. With some more math (see the appendix), this would indicate that if the amount of solar energy hitting the planet is 240 W/m2 (≈ -18°C) and the swings were ± 50°C, the average temperature would be – 33°C. Some of the warming from that chilly temperature is from the atmosphere itself, and some is from the greenhouse effect.

This in turn indicates another curiosity. I’ve always assumed that the warming from the GHGs was due solely to the direct warming effects of the radiation. But a characteristic of the greenhouse radiation (downwelling longwave radiation, also called DLR) is that it is there both day and night, and from equator to poles. Oh, there are certainly differences in radiation from different locations and times. But overall, one of the big effects of the greenhouse radiation is that it greatly reduces the temperature swings because it provides extra energy in the times and places where the solar energy is not present or is greatly reduced.

This means that the greenhouse effect warms the earth in two ways—directly, and also indirectly by reducing the temperature swings. That’s news to me, and it reminds me that the best thing about studying the climate is that there is always more for me to learn.

Finally, as the planetary system warms, each additional degree of warming comes at a greater and greater cost in terms of the energy needed to warm the planet that one degree.

Part of this effect is because the cooling radiation is rising as the fourth power of the temperature. Part of the effect is because Murphy never sleeps, so that just like with your car engine, parasitic losses (losses of sensible and latent heat from the surface) go up faster than the increase in driving energy. And lastly, there are a number of homeostatic mechanisms in the natural climate system that work together to keep the earth from overheating.

These thermostatic mechanisms include, among others,

• the daily timing and number of tropical thunderstorms.

• the fact that clouds warm the Earth in the winter and cool it in the summer.

• the El Niño/La Niña ocean energy release mechanism.

These work together with other such mechanisms to maintain the whole system stable to within about half a degree per century. This is a variation in temperature of less than 0.2%. Note that doesn’t mean less than two percent. The global average temperature has changed less than two tenths of a percent in a century, an amazing stability for such an incredibly complex system ruled by something as ethereal as clouds and water vapor … I can only ascribe that temperature stability to the existence of such multiple, overlapping, redundant thermostatic mechanisms.

As a result, while the greenhouse effect has done the heavy lifting to get the planet up to its current temperature, at the present equilibrium condition the effect of variations in forcing is counterbalanced by changes in albedo and cloud composition and energy throughput, with very little resulting change in temperature.

Best to all, full moon tonight, crisp and crystalline, I’m going outside for some moon-viewing.

O beautiful full moon!

Circling the pond all night

even to the end

Matsuo Basho, 1644-1694

w.

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Morris Minor

No… the moon is cold because its solid surface has a relatively high emissivity. The Earth is warmer because its gaseous atmosphere has a low emissivity (very low if it was only nitrogen and oxygen). According to Trenberth et al. the atmosphere emits195 W/m2 wheras the Earths surface emits 40 W/m2 by radiation. (102 W/m2 is transported by convection to the atmosphere where it is then radiated to space). Greenhouse gases increase the emissivity of the atmosphere. Therefore the GH gasses effectively cool the Earth!…

Matt

Well, it took me seconds to come up with a very different albedo figure for the moon at various space/physics sites (0.12 not 0.07); and it seems the same may be true about the stated temperatures…

ferdberple

If a non GHG atmosphere did not radiate EM energy, it would be a perfect insulator. In space N2/O2 would never cool.
In contradiction to the notion that N2/ O2 do not absorb / radiate EM radiation, here is their absorption spectra. As can be seen, both N2 and N2 absorb EM radiation. N2 has quite a broad spectrum. So if neither radiate, then the atmosphere is going to get very hot from absorption of EM radiation by N2 and O2, and this heat will conduct to the surface..
http://www.coe.ou.edu/sserg/web/Results/Spectrum/n2.pdf
http://www.coe.ou.edu/sserg/web/Results/results.htm

tokyoboy

The nuance of the first line of the Haiku is apparently a bit different…….
I may translate it into “Oh beautiful full moon!” from the original “Mei-getsu ya”.

ferdberple

Compare the spectra of H2O with CO2 and N2. Which one is most unlike the other two? If climate science is to be believed, you would think N2 would be most unlike the other two. Imagine the surprise I got when I took the time to check.
http://www.coe.ou.edu/sserg/web/Results/Spectrum/h2o.pdf
http://www.coe.ou.edu/sserg/web/Results/Spectrum/n2.pdf
http://www.coe.ou.edu/sserg/web/Results/Spectrum/co2.pdf

wstannard

I must diagree with Willis’ theorem as so well written above. I have tried to give an alternative view on the Greenhouse effect here…
http://wstannard.wordpress.com/the-greenhouse-effect-2/the-earths-energy-balance/
I hope I have written this as well as Willis writes. My conclusion is that there is no greenhouse effect that warms the planet. There appears some misunderstanding of the S-B equation (the Earth is not a blackbody) and the fact that the most of the radiation from the Earth is emitted by the atmosphere, not the Earth’s surface!
I would be interested in further comments.

Matthew

Isn’t there also the issue of radioactive decay warming the Earth but not the moon? I imagine that would account for some of it.

Whence the warming at night to maintain a smaller range? From what energy source? I suspect the real reason Venus varies so little over its long day/night cycle (1K, or thereabouts) is that the radiative “short-circuiting” by such a dense and high-CO2 atmosphere is almost perfect. On Earth, not so much, but some. I.e., energy from the dayside is being transferred radiatively by CO2 to the nightside.
You heard it here first!
>:)

Mike G

Can you equate rates of heating and cooling on earth and moon, when earth’s surface is mostly water? Surely you have to leave the oceans in place when the atmosphere is removed for your thought experiment?

Also, or moreso, probably, by H2O ↔ H2O radiative transfer. Doesn’t work so well in the low-humidity deserts, whether Saharan or Antarctican, of course. There, CO2 is on its own, and is too sparse to achieve much.

David

Wow… as an aside, imagine if we could increase the Moon’s rotation to about the same as Earth’s – perhaps by a deliberate glancing meteor blow. The faster rotation would reduce the temperature swings to about the same as Earth’s, thank to the calculations above…
Then we could terraform the Moon. One speculative proposal is here: http://www.lunar-union.org/planetary-engineering/terraforming_moon.html. If this is combined with a faster rotation then it would be much better.
I am amazed at the information on that other website that points out that Titan, with a surface gravity similar to the Moon’s, has an atmospheric pressure about the same as Earth…
An excellent post showing the importance of T^4 in regulating the temperature of the Earth (and other heavenly bodies).

pat

will do some mooning tonite too, willis
we were promised our first hot day of summer today in my part of australia, but it didn’t live up to the predictions:
9 Jan: Sydney Morning Herald: Dan Cancarrow: Brisbane has hottest day of the summer
The city hit a high of 33.8 degrees at 1.21pm, exceeding last month’s average of 27.6 degrees and the summer’s previous maximum of 32.9 degrees…
Last month’s average maximum was almost two degrees (1.9) lower than the city’s long term December average of 29.5 degrees.
http://www.smh.com.au/queensland/brisbane-has-hottest-day-of-the-summer-20120109-1pqqi.html
***how precise is 249km? is there a miles equivalent that rounds off?
9 Jan: Ninemsn: AFP: Species lag in climate change shift
Fast-track warming in Europe is making butterflies and birds fall behind in the move to cooler habitats and prompting a worrying turnover in alpine plant species, studies published on Sunday say…
The papers, both published by the journal, Nature Climate Change…
A team led by Vincent Devictor of France’s National Centre for Scientific Research (CNRS) found that from 1990 to 2008, average temperatures in Europe rose by 1C.
This is extremely high, being around 25 per cent greater than the global average for all of the last century.
***To live at the same temperature, species would have to shift northward by 249km, they calculated…
The data derives from observations made by a network of thousands of amateur naturalists, amounting to a remarkable 1.5 million hours of fieldwork.
???The study was not designed to say whether these species are suffering as a result of warming, which is one of the big questions in the climate-change saga.
However, the risk of population decline is clear, the authors say.
Species that lag behind a move to a more suitable habitat accumulate a “climatic debt”.,,
The second study looked at 867 samples of vegetation from 60 mountaintop sites across Europe in an assessment of the hottest decade on record.
Seen at local level, there was little apparent change during the 2001-2008 study period.
But when the picture zoomed out to continental level, it was clear that a major turnover was under way…
(Michael Gottfried, a University of Vienna biologist) “Many cold-loving species are literally running out of mountain. In some of the lower mountains in Europe, we could see alpine meadows disappearing and dwarf shrubs taking over within the next few decades.”
The research was the biggest plant-count of its kind in Europe, gathering 32 researchers from 13 countries.
http://news.ninemsn.com.au/technology/8400117/species-lag-in-climate-change-shift
obviously a “we have the numbers” ploy…even if it ain’t CAGW’s fault!

Clear presentation, very poor physics.
The surface of the Moon is colder than the surface (and lower layer of the atmosphere) of the Earth for the same reason a man without a blanket, during a cold night, is colder than a man under a blanket.
Both Moon and Earth radiate into the space as much heat as they receive from the Sun. The only difference is that the heat exchanging surface of Earth is the upper atmosphere (which is cold), while on the Moon it is… well, the surface of the Moon.
Build a dome on the Moon, fill it with air, and it will be soon warmer inside than outside. The heat exchanging surface in this case will be the shell of the dome, not the ground surface inside the dome.
I think Mr. Eschenbach should write less and think a bit more before writing.

… the greenhouse effect has done the heavy lifting to get the planet up to its current temperature,…
What a lovely way of putting it! Thank you Willis.

richard

This means that the greenhouse effect warms the earth in two ways,
does he mean slows down the cooling.
Moon gets hot without greenhouse gases and cools rapidly at night time,
Earth does not get so hot and cools down slowly.

Willis Eschenbach

Matt says:
January 8, 2012 at 11:49 pm

Well, it took me seconds to come up with a very different albedo figure for the moon at various space/physics sites (0.12 not 0.07); and it seems the same may be true about the stated temperatures…

You’re right, Matt, I used a number from my memory, and it is slightly larger. NASA states that the lunar Bond albedo is 0.11. It makes only a trivial difference. Instead of 318 W/m2, it makes the lunar calculated radiation 304 W/m2. Doesn’t change my discussion or my points in the slightest. I’ve updated the head post with the correct figures.
w.

Willis Eschenbach

tokyoboy says:
January 8, 2012 at 11:53 pm

The nuance of the first line of the Haiku is apparently a bit different…….
I may translate it into “Oh beautiful full moon!” from the original “Mei-getsu ya”.

Reading Basho always makes me wish I could read Japanese.
Many thanks,
w.
[I’ve updated the head post to reflect your translation. —w.]

Willis Eschenbach

ferd berple says:
January 9, 2012 at 12:01 am

Compare the spectra of H2O with CO2 and N2. Which one is most unlike the other two? If climate science is to be believed, you would think N2 would be most unlike the other two. Imagine the surprise I got when I took the time to check.

ferd, the N2 is the most unlike the others because the line strength is many, many orders of magnitude weaker than that of the others.
In addition, at least from what you show, N2 only absorbs in a narrow window, and in that window (according to your citations) N2 absorbs 10 orders of magnitude less than CO2.

Claude Harvey

Five-hundred-thousand years of reconstructed history of the earth’s surface temperature demonstrates that atmospheric temperature is controlled by a chaotic system which is bounded by a relatively narrow band of temperatures we define as “Warm Periods” and “Ice Ages”. It has remained in that defined band of temperatures despite horrific asteroid bombardment, cataclysmic volcanic disruptions, enormous variations in cosmic radiation and significant variations in solar energy input as the earth perpetuates from circular to elliptical orbits about the sun every 100,000 years or so. So, what exactly is the mystery here? We’re on the long, slow, and slippery slope to another Ice Age by fits and starts with the Roman Warming Period probably marking the apex of our current cycle. To quote Willis’ previous great story, “Everything else is turtles on top of turtles.”

Willis Eschenbach

Alexander Feht says:
January 9, 2012 at 12:30 am

Clear presentation, very poor physics.
The surface of the Moon is colder than the surface (and lower layer of the atmosphere) of the Earth for the same reason a man without a blanket, during a cold night, is colder than a man under a blanket. …

Clear presentation, very poor reading skills. I said nothing comparing the moon without an atmosphere to the earth with its current atmosphere. So you are railing against a position I did not take.
Alexander and others, listen up. If you disagree with something I said, QUOTE MY WORDS THAT YOU DISAGREE WITH. Otherwise, you may end up like this example, where you are attacking a straw man and abusing me for something I NEVER SAID.
I’m perfectly serious here, folks. If you do not quote what you object to, you may get no answer from me at all. I’m tired of people who jump on my case without bothering to reveal what I said that has them in such a snit. And yes, Alexander, I’m looking at you.
If you think I’m wrong, well, I might be wrong, I’ve been wrong before. But my friends, how about before you conclude that I’m wrong, you ask about whatever it is I said that makes you think I’m wrong? Then I can clarify my words, or I can admit I’m wrong, or I can show why I don’t think I’m wrong. QUOTE MY EXACT WORDS so we can all understand what you are objecting to, and we can discuss it.
w.

Re-run the moon with the thermal inertia equivalent of the earth’s and rotation like the earth’s.
Thanks
JK

Bryan

The SB equation is misused by IPCC style Climate Science.
The Moon is a perfect example of this.
1. why after 14 Earth days does the dark side never reach absolute zero but stays some 90K above?
2.why after 14 Earth days does the Sunlit side never reach its predicted radiative max but stays well below it.
The guilty little secret of IPCC Moon Science is that to get anywhere near realistic temperature figures they have to include a substantial contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.
The guilty little secret of IPCC Earth Science is that they refuse to include a ANY contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.
If they did so they would find little use for the so called greenhouse effect.

ferdberple

Willis Eschenbach says:
January 9, 2012 at 12:55 am
ferd, the N2 is the most unlike the others because the line strength is many, many orders of magnitude weaker than that of the others.
Perhaps you misread the reference? From what I see, N2 line strength is 10-28, CO2 is 10-23, which is 5 orders of magnitude. However, N2 has 10 orders of magnitude wider spectrum (600 cm-1 versus 50 cm-1). In addition, there are 4 orders of magnitude more N2 in the atmosphere than CO2. So, on this basis it is hard to see that N2 absorbs/radiates significantly less than CO2.
In contrast to CO2, H2O line strength is 10-19 which if 4 orders of magnitude stronger than CO2. As well it has a much, much wider spectrum than CO2. The absorption strength and spectra of water so overwhelms CO2 as to make it CO2 a joke when you consider the amount of H2O in the atmosphere as compared to CO2.

ferdberple

correction n2 spectrum is 10 times, not 10 orders of magnitude wider.

Willis Eschenbach

jim karlock says:
January 9, 2012 at 1:08 am

Re-run the moon with the thermal inertia equivalent of the earth’s and rotation like the earth’s.
Thanks
JK

Thanks, Jim. I’m happy to be finished writing this, I need to discuss and answer questions and objections, and I have a day job. However, I do invite you to re-run the moon as you suggested and report your results.
w.

markus

Some goose says;
January 9, 2012 at 12:30
“The surface of the Moon is colder than the surface (and lower layer of the atmosphere) of the Earth for the same reason a man without a blanket, during a cold night, is colder than a man under a blanket”
Bull, say both men don’t radiate heat by themselves, like the earth and moon, then that bloke under the blanket will get no warmth from the atmosphere and will be silly, sorry chilli.

ferdberple

Willis, did your calculations take into account the temperature difference between the equator and the poles? From looking at Figure 1, if you used that for your data it will not give an accurate result because it reflects an average of temperature between the equator and poles. The temperature difference between the lunar equator and poles is greater than between night and day averages.
“Most notable are the measurements of extremely cold temperatures within the permanently shadowed regions of large polar impact craters in the south polar region,” said David Paige, Diviner’s principal investigator and a UCLA professor of planetary science. “Diviner has recorded minimum daytime brightness temperatures in portions of these craters of less than -397 degrees Fahrenheit. These super-cold brightness temperatures are, to our knowledge, among the lowest that have been measured anywhere in the solar system, including the surface of Pluto.”
http://www.sciencedaily.com/releases/2009/09/090917191609.htm

John Marshall

All sounds very convincing. If the moon had an IR transparent atmosphere, ie. no GHG’s, then there would still be a temperature rise due to adiabatic compression as happens on Jupiter with its atmosphere of hydrogen and helium. You cannot ignore this temperature increasing physical phenomenon. It has been understood for over 100 years and is the reason for the Fohne Effect, by which the Chinook supplies warm winds to the Canadian and American prairies and the cause of warm katabatic winds. (not to mention diesel engines and refrigerators).
It is also true that to take the temperature of a system that system must be at equilibrium. The earth, with its turbulent atmosphere never is. To use the S-B equations on a system then, again, that system MUST be at equilibrium which the Earth never is.

Kasuha

I have three points.
– IR radiation is the only way how surface temperature is transferred from solid surface to atmosphere. If a moon had atmosphere that is perfectly transparent to IR, that atmosphere would do nothing with its surface temperature.
– Earth albedo of 0.3 is partially given by clouds and other atmospheric effects. You can’t simply imagine Earth without atmosphere but having the same albedo.
– Albedo of a solid body affects not only its absorption of incoming radiation but also its release of outgoing radiation. It’s not correct to assume Earth absorbs energy according to its albedo and then cools down as fast as Moon does.

The Moon also effects the climate on Earth in some subtle ways !
Firstly the Moon and the Earth both orbit their common centre of mass, which is about 4000 km outside the centre of the earth. This causes the Earth to shift by up to 8000 km nearer the Sun every lunar month. I found very recently that that there is a clear signal for this effect in the SORCE TIM solar radiation data – see http://clivebest.com/blog/?p=2996 I think this may be the first time anyone has noticed this !
Secondly – there is a very slight effect from extra reflected solar radiation from the full moon on Earth. Thirdly there are tidal effects on the Earth’s atmosphere as well as the Oceans. At the North and South poles these “tides” have been measured by changes in surface ozone.
Finally the moon stabilises the Earth’s rotation axis. It seems likely that without the moon’s stabilising gyroscopic effect the earth’s axis would be more chaotic. The seasons rely on the axis being tilted to the orbital plane of the earth-sun by about 23 degrees. Computer simulations show that the moon’s tidal effect has probably stabilised this tilt over billions of years. By comparison, the axis of Mars seems to be affected by a chaotic effect caused by the influence of other planets in the solar system.

Yet another quality thought provoking post by Willis. Thanx mate.
A couple of things I’m trying to get my head around..
* The moon hides behind the earth for a few days each cycle (is it 7 days?) where it receives no insolation at all. All emission no absorption. Is this reflected in the first graph, if so where?

* Now, I want to stop here and make a very important point. These last two phenomena mean that the moon with a perfectly transparent GHG-free atmosphere would be warmer than the moon without such an atmosphere. But a transparent atmosphere could never raise the moon’s temperature above the S-B blackbody temperature of half a degree Celsius

Yes true and you made this point at an earlier thread, but here is my thought.
If the only thermal interaction between the atmosphere and the surface is via conduction, it is possible to have an average SURFACE temperature of a half a degree (no more than the S-B T) whilst at the same time having an average ATMOSPHERE temperature somewhat higher than the S-B T. No laws of conservation are broken.
The outgoing radiation is still from the surface and it is still the same as the incoming radiation at equilibrium but this doesn’t stop the atmosphere (as a whole) from being warmer.
*

One thing that could reduce the swings would be if the moon had an atmosphere, even if that atmosphere had no greenhouse gases (“GHGs”) and was perfectly transparent to infrared. In general, one effect of even a perfectly transparent atmosphere is that it transports energy from where it is warm to where it is cold.

The question is how much energy is transported. The moon may absorb an AVERAGE insolation of 304Wm2, but at its equator at noon it would receive the full gamut, well over 1000Wm2.
And since warming by conduction is ALWAYS faster than cooling by conduction when a gas is involved, we’d need to work out how much energy is transported.
I contend that the warmth from most of that 1000Wm2 will be transported with strong temperature inversions at night, even more so at the poles.
So if I was standing on the moon with a GHG-less atmosphere, it may be quite cold under my moon boots, but where my body is (up to 2 metres above the surface) I’d say the temperature would be quite warm.
And so it is with our present Earth. All the SB calculations may say an average -18DegC at the surface under my shoes, but this isn’t the same at the 2 metre height when an atmosphere is present, GHGs or not.
I’d appreciate your thoughts.

Willis Eschenbach

Bryan says:
January 9, 2012 at 1:15 am

The SB equation is misused by IPCC style Climate Science.
The Moon is a perfect example of this.
1. why after 14 Earth days does the dark side never reach absolute zero but stays some 90K above?

Because the radiation becomes so small at low temperatures. Note that even after 14 days the moon is still cooling, but quite slowly. At that point it is radiating at only 2.5 W/m2, so very slow cooling would be expected.

2.why after 14 Earth days does the Sunlit side never reach its predicted radiative max but stays well below it.

At mid-day (lunar day) the sun provides about 1368 W/m2. Given the moon’s albedo, that corresponds with a blackbody temperature of about 109° at the surface. The sensors used for the temperature record above are slightly buried in the regolith, so I find the fact that they haven’t quite reached the maximum predicted temperature to be unsurprising.

The guilty little secret of IPCC Moon Science is that to get anywhere near realistic temperature figures they have to include a substantial contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.

I find that the temperature figures that I show in Fig. 1, from NASA data, is quite realistic, and agrees with theoretical calculations. It requires no ground heat flux to make sense.

The guilty little secret of IPCC Earth Science is that they refuse to include a ANY contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.

If you are talking about the earth, as far as I know the ground heat flux is on the order of a tenth of a watt per square metre. I’ve run the numbers myself from a couple of directions, and it’s just not all that large. Even assuming that there are many more deep sea vents than are generally thought, there still isn’t enough heat coming from the inside of the planet to make much difference. If there were, we could sleep on the ground to stay warm …

If they did so they would find little use for the so called greenhouse effect.

Ground heat flux is a couple orders of magnitude too small to be responsible for the Earth’s surface temperature.
Regards,
w.

Neither Moon nor Earth are ideal black bodies; therefore, Boltzmann’s formula cannot be applied directly in both cases. If this is what Mr. Eschenbach is trying to explain, anybody who was paying attention to his physics teacher in the 8th grade of the high school knows that.
As to his answer to my post (senile emotional outbursts notwithstanding) Mr. Eschenbach does directly compare Earth and Moon. There is no other way to understand his words, however one reads them: “The albedo (reflectivity) of the moon is less than that of the Earth. You can see the difference in albedo in Figure 1. There are lots of parts of the Earth that are white from clouds, snow, and ice. But the moon is mostly gray. As a result, the Earth’s albedo is about 0.30, while the Moon’s albedo is only about 0.11. So the moon should be absorbing more energy than the Earth.” And then again, in the next paragraph: “Like the Earth, averaged over its whole surface the moon receives about 342 watts per square metre (W/m2) of solar energy. We’re the same average distance from the sun, after all. The Earth reflects 30% of that back into space (albedo of 0.30), leaving about 240 W/m2. The moon, with a lower albedo, reflects less and absorbs more energy, about 304 W/m2.”.
While these statements are no more than a textbook explanation of the obvious, the general position Mr. Eschenbach takes in his article, from the very beginning, is to compare apples (a non-black body without an atmosphere) and oranges (a non-black body with an atmosphere — and a biosphere to boot). Such a comparison is misleading, since Earth’s and Moon’s mechanisms of heat exchange with the space are completely different.

I need to clarify the last paragraph of my last comment where I said..

And so it is with our present Earth. All the SB calculations may say an average -18DegC at the surface under my shoes, but this isn’t the same at the 2 metre height when an atmosphere is present, GHGs or not.

Should read ” ….at the 2 metre height when a GHG-less atmosphere is present”

A physicist

This seems (to me) to be a outstandingly thoughtful and clearly written post; appreciation and thanks are extended to Willis for his work in writing it.
Obviously these calculations aren’t easy, and very often it happens that simple lines of reasoning, that give a correct result, are evident only after long and intricate calculations have been carried to completion.
This does not mean that the long intricate calculations can be skipped, if only we are clever enough to think of the simple lines of reasoning at the beginning. Rather, both styles of calculation are essential: simple at the beginning (necessarily) and simple too at the end (hopefully), and complicated in the middle stages, where all the difficulties are worked through.
An extended discussion of those complicated middle stages can be found on the American Institute of Physics (AIP) web site The Discovery of Global Warming: Basic Radiation Calculations.
Broadly speaking, the next step in making Willis’ model of the moon’s temperature look more like models of the earth’s temperature would be to “churn” the top layers of moon dust, analogous to the vertical convective transport processes of the earth’s atmosphere; the AIP web page gives a description of how these effects are modeled in-detail.
Recommended.

Just Passing

Thank you, Willis. Very interesting.

markus

“If you are talking about the earth, as far as I know the ground heat flux is on the order of a tenth of a watt per square metre. I’ve run the numbers myself from a couple of directions, and it’s just not all that large. Even assuming that there are many more deep sea vents than are generally thought, there still isn’t enough heat coming from the inside of the planet to make much difference. If there were, we could sleep on the ground to stay warm.”
Am I OK to assume there is no heat transfer, other than the .1 Wm/2, between the oceans waters and the ocean floor, either way?

Willis Eschenbach

Alexander Feht says:
January 9, 2012 at 2:26 am

Neither Moon nor Earth are ideal black bodies; therefore, Boltzmann’s formula cannot be applied directly in both cases. If this is what Mr. Eschenbach is trying to explain, anybody who was paying attention to his physics teacher in the 8th grade of the high school knows that.
As to his answer to my post (senile emotional outbursts notwithstanding) Mr. Eschenbach does directly compare Earth and Moon. There is no other way to understand his words, however one reads them:

“The albedo (reflectivity) of the moon is less than that of the Earth. You can see the difference in albedo in Figure 1. There are lots of parts of the Earth that are white from clouds, snow, and ice. But the moon is mostly gray. As a result, the Earth’s albedo is about 0.30, while the Moon’s albedo is only about 0.11. So the moon should be absorbing more energy than the Earth.”

And then again, in the next paragraph:

“Like the Earth, averaged over its whole surface the moon receives about 342 watts per square metre (W/m2) of solar energy. We’re the same average distance from the sun, after all. The Earth reflects 30% of that back into space (albedo of 0.30), leaving about 240 W/m2. The moon, with a lower albedo, reflects less and absorbs more energy, about 304 W/m2.”.

While these statements are no more than a textbook explanation of the obvious, the general position Mr. Eschenbach takes in his article, from the very beginning, is to compare apples (a non-black body without an atmosphere) and oranges (a non-black body with an atmosphere — and a biosphere to boot). Such a comparison is misleading, since Earth’s and Moon’s mechanisms of heat exchange with the space are completely different.

Thanks, Alexander. You agree (I think) that both my statements are true, since you call them a “textbook explanation of the obvious.”
Nor does either statement depend on the presence or absence of an atmosphere. They are statements that are true because of differences in albedo. They are just statements of how much energy is entering either system.
As to your claims about my “general position”, even I couldn’t say what that might be, so how could you? Let me suggest that you stick to my specific positions, as expressed in my specific words, and leave speculation about my “general position” alone.
I am looking at the moon without an atmosphere to try to get an estimate of the temperature fluctuations of the Earth if it had no atmosphere. It’s called a “thought experiment”. Apples and apples.
I am also trying to understand the different ways that an atmosphere can affect a planet, and how planetary rotational speed affects the average temperature.
So I fail to see the problem. I specified several times I was interested in the effect of, how did I put it … OK, I called it a “perfectly transparent GHG-free atmosphere” on a planet. I’m working towards understanding the vagaries of that as it applies to temperature variations.
All the best, thanks for quoting what I said. As it turned out, both things you quoted me as saying were 100% true. That’s why quoting the words of someone you disagree with is so important—it allows us all to see and agree (or agree to disagree) on the exact issues in question.
w.

lgl

Don’t forget the ocean. Without it there would not be much energy to be backradiated during night.

I dont think its the swing of temperatures that affect the average, but the speed of the rotation. i.e. the amount of time the dark side has to cool.
If the moon was fixed, [the] hot side would get to 90, the dark side to -270, with an average of round about where that green line is above.
If the moon rotated at 1000 rpm, my guess would be that the average temperature would be closer to 90 than to -77
caveat – I am not a scientist (IANAS)

Stephen Wilde

Why ignore gravitational compression of the atmosphere ?
Isn’t that what sets the adiabatic lapse rate independently of the effect of greenhouse gases ?

Nice summary of basic science.
Science of doom covered the same topic around a year and a half ago with the useful point that as the thermal capacity and inertia of the surface/atmosphere increases, the maximum temperature falls, but the minimum and average rise while the AMOUNT of energy emitted stays the same.
http://scienceofdoom.com/2010/06/03/lunar-madness-and-physics-basics/
It shows up the warming from atmospheric pressure nonsense for what it is, it is the equalising effect on the temperature range from a energy transporting atmsophere that raises the average temperature.
But as the point is made above, that atmospheric effect of energy distribution can never raise the temperature ABOVE the S-B limit, it needs a GHG effect to do that…

Bryan

Willis Eschenbach says of the Moons temperature record
“it requires no ground heat flux to make sense”
“after 14 days the moon is still cooling, but quite slowly. At that point it is radiating at only 2.5 W/m2, so very slow cooling would be expected.”
I thought you might be interested in a new peer reviewed paper by Gerhard Kramm and Ralph Dlugi.
They calculate the Moons Ground Heat Flux to be 16.2W/m2 – hardly negligible (page 990)
They go on to confirm their previous work that
” the greenhouse theory is a set of merit-less conjectures with no physical support.”
Of particular interest is ;
The energy reservoir diagram Fig 11
The irradiance overlap area Fig 5
On a more humorous note they find further errors in the Halpern et al G&T comment paper
See page 1316
Wrong formula
Wrong units
Which of course leads to silly numbers.
http://www.scirp.org/journal/PaperInformation.aspx?paperID=9233

son of mulder

What is the average value of the earth’s surface (ground) temperature? It is different from the temperature measured by weatherstations which measure air temperature just above the ground. But it is the earth’s surface that emits and receives the Boltzmann radiation, solar and back radiation. Surely a different T. In direct sunlight the earth surface is warmer than the air (eg tarmac gets hot, damp areas less so because of latent heat) but on a clear night the air will cool quicker than the surface. Is there a tendency for the average surface temperature to be higher than the average surface air temperature? I’ve never seen this discussed [anywhere] in the AGW debate.

gnomish

that was my favorite heinlein.
but: ” the bigger the temperature swings, the lower the average temperature.”
an average is an average. extremities don’t change the average by any mathematical process.

son of mulder

antwaher = anywhere in my previous comment

markus

“While these statements are no more than a textbook explanation of the obvious, the general position Mr. Eschenbach takes in his article, from the very beginning, is to compare apples (a non-black body without an atmosphere) and oranges (a non-black body with an atmosphere — and a biosphere to boot). Such a comparison is misleading, since Earth’s and Moon’s mechanisms of heat exchange with the space are completely different.”
Thanks for staying with it Alexander, however, I did not see Willis position as you did. It’s a big universe out there. Haven’t we always quantified our knowledge of it in within physical laws known here on earth. I only saw a comparison between earth and the moon using known physics. Of course you would rather compare apples and oranges by using the analogy of humans and extraterrestrial bodies.
You said;”The surface of the Moon is colder than the surface (and lower layer of the atmosphere) of the Earth for the same reason a man without a blanket, during a cold night, is colder than a man under a blanket.” That didn’t work for me at all.

John Marshall

Kasuha claims that IR radiation is the only heat transfer available between atmosphere and surface. It is not, how about conduction and the one that transfers most heat to the upper atmosphere, convection. Radiation is the smaller part.

“I am looking at the moon without an atmosphere to try to get an estimate of the temperature fluctuations of the Earth if it had no atmosphere. It’s called a “thought experiment”. Apples and apples.” — so says Mr. Eschenbach.
In the article above, I see “Earth without an atmosphere” mentioned once (“In that case the moon and the Earth without atmosphere would be roughly equivalent, both simply radiating to outer space”) — but after that, having stated the obvious again, Mr. Eschenbach continues to talk mostly about the effects of the greenhouse gases and atmosphere (just look over several following paragraphs in the above article). I don’t see here any “thought experiment” comparing our Moon with “the Earth without an atmosphere” (however meaningless such a comparison would be).
One of the main conclusions in the above article is as follows: “This means that the greenhouse effect warms the earth in two ways—directly, and also indirectly by reducing the temperature swings. That’s news to me, and it reminds me that the best thing about studying the climate is that there is always more for me to learn.” Really? My reading skills are developed enough to see that Mr. Eschenbach is talking about atmospheric effects again.
Not to mention that it’s news to me how this can be news to anybody. Let it be, though. I have better things to do.