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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January 8, 2012 11:37 pm

We like tha moon
http://tinyurl.com/djag

Morris Minor
January 8, 2012 11:46 pm

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
January 8, 2012 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…

ferd berple
January 8, 2012 11:53 pm

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
January 8, 2012 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”.

ferd berple
January 9, 2012 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.
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
January 9, 2012 12:06 am

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
January 9, 2012 12:18 am

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.

Brian H
January 9, 2012 12:20 am

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
January 9, 2012 12:23 am

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?

Brian H
January 9, 2012 12:25 am

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
January 9, 2012 12:26 am

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
January 9, 2012 12:28 am

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…
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!

January 9, 2012 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.
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.

Editor
January 9, 2012 12:33 am

… 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
January 9, 2012 12:38 am

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.

Claude Harvey
January 9, 2012 12:59 am

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.”

January 9, 2012 1:08 am

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

Bryan
January 9, 2012 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?
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.

ferd berple
January 9, 2012 1:23 am

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.

ferd berple
January 9, 2012 1:29 am

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

markus
January 9, 2012 1:48 am

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.

ferd berple
January 9, 2012 1:49 am

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

January 9, 2012 2:06 am

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
January 9, 2012 2:07 am

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.

January 9, 2012 2:15 am

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.

January 9, 2012 2:19 am

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.

January 9, 2012 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.

January 9, 2012 2:26 am

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
January 9, 2012 2:30 am

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
January 9, 2012 2:33 am

Thank you, Willis. Very interesting.

markus
January 9, 2012 2:58 am

“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?

lgl
January 9, 2012 3:08 am

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

January 9, 2012 3:10 am

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)

January 9, 2012 3:23 am

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

izen
January 9, 2012 3:36 am

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.
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
January 9, 2012 3:39 am

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
January 9, 2012 3:42 am

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
January 9, 2012 3:43 am

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
January 9, 2012 3:44 am

antwaher = anywhere in my previous comment

markus
January 9, 2012 3:52 am

“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.

January 9, 2012 3:53 am

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.

January 9, 2012 3:57 am

“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.

steveta_uk
January 9, 2012 3:58 am

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.

I assume you are referring to a dead man – since any fool would realize that a living man has an internal heat source that makes your comparison completely irrelevant.
So do you have details of the experiment performed on two dead bodies left out overnight, one with a blanket and one without? If so, please quote a reference.
If not, please apologize for calling Willis “senile”.

January 9, 2012 4:03 am

Bryan says:
January 9, 2012 at 1:15
1. why after 14 Earth days does the dark side never reach absolute zero but stays some 90K above?
—————————–
The Cosmic Background Radiation is about 2.76 K, so you can rule out reaching absolute zero, or 0 K.

January 9, 2012 4:05 am

From David on January 9, 2012 at 12:26 am:

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.

That could be problematic. The Moon is phase locked (aka tidally locked) to the Earth. As it is too solid, hard, and rocky to deform, even if its rotation around its axis could be sped up then it would want to return to the preferred state, with the same face always facing the Earth.
You could try speeding up the revolution of the Moon around the Earth to shorten the day/night transition period on the Moon. With simple Newtonian physics and a two-body problem, for a stable orbit the force of gravitation must equal the centripetal force.
Gravitational force: F=GMm / r^2, F=Force, G=gravitational constant, M=mass of Earth, m=mass of Moon, r=radius of orbit (distance between centers of mass)
Centripetal force: F=mv^2 / r, v=speed (technically scalar component of the velocity).
GMm / r^2 = mv^2 / r – divide both sides by m
GM / r^2 = v^2 / r – multiply both sides by r^2
GM = rv^2
Thus radius times velocity squared equals a constant (G times mass of Earth). Quick and dirty, since it takes about 4 weeks (28 days) for the Moon to revolve around the Earth, a lunar day is around 28 days, we want to shorten that to around 1/28 of current amount, the Moon would have to revolve around the Earth about 28 times faster. To keep it in orbit the radius would shorten by the square of that factor, 28^2=784, current radius divided by 784. The average distance between the centers of mass of the Earth and the Moon (called a lunar distance) is 384,400 kilometers. 384,400/784=490 kilometers, the approximate radius needed for a lunar day of around an Earth day.
However as the mean radius of the Moon is 1,737 km, and that of the Earth is 6,371 km, this method of shortening the lunar day should not be recommended.
So basically we’re stuck with the current length of a lunar day. When we get around to colonizing the Moon, if we’re going to grow plants by daylight then we’ll need something that’ll work with 2 week long on/off cycles. But since algae will get boring quickly, we’ll likely be using artificial lighting as well.

PeterF
January 9, 2012 4:21 am

Willis, thanks for pointing out what impact temperature swings have on the average temperature through the T^4 relationship from S-B. This nicely extends previous discussion here and elsewhere, e.g. at Roy Spencer’s blog (http://www.drroyspencer.com/2011/12/why-atmospheric-pressure-cannot-explain-the-elevated-surface-temperature-of-the-earth/) .
So, you cannot only show the impact of rotational speed of a celestial body to its average surface temperature, but the presence of an atmosphere, be it a “normal” one with GHGs, or a theoretical one completely void of GHGs, will raise average surface temp through smoothing out the temp swings over the surface through redistribution of heat vertically via convection and horizontally via wind from pressure gradients.
Wouldn’t that imply that even a perfect non-GHGs atmosphere would exhibit an adiabatic temp profile? I think it would, however, Roy expects an isothermal atmosphere. This question remains unanswered. Any reasoning from you towards either direction?

January 9, 2012 4:28 am

Nice analysis but you’ve ignored at least 99% of the moon and 99% of the Earth both of which little to nothing is known. Sure vulcanologists etc. have some information about the centre of the Earth but they infer far too much from far too little information.

Bryan
January 9, 2012 4:51 am

Markus says of the Ground Heat Flux
” 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.”
I think you have a different definition of ground heat flux to that used by Gerhard Kramm and Ralph Dlugi.
See Fig 12
http://www.scirp.org/journal/PaperInformation.aspx?paperID=9233

Peter
January 9, 2012 4:54 am

Willis wrote:

But a transparent atmosphere could never raise the moon’s temperature above the S-B blackbody temperature of half a degree Celsius.

Small point, shouldn’t that be average temperature?

DirkH
January 9, 2012 5:00 am

Alexander Feht says:
January 9, 2012 at 3:57 am
“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.”
No, Alexander, try again. Willis talks about the effect that the T^4 term has when the temperature varies drastically, as in the case of the moon, compared to the effect it has when the temperature varies less, as in the case of the Earth. In the case of the drastic variation, a lower average temperature is necessary to allow the planetary body to radiate enough. It’s a mathematical thing.

January 9, 2012 5:02 am

steveta_uk says:
January 9, 2012 at 3:58 am
I assume you are referring to a dead man – since any fool would realize that a living man has an internal heat source that makes your comparison completely irrelevant.

Earth has an internal heat source. Which makes your comment completely irrelevant.

January 9, 2012 5:05 am

“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.”
As I understand it the gravitational pull on the mass of the atmosphere whether containing GHGs or not sets up the baseline lapse rate via compression of the atmosphere. Simply put, the solar energy passing through is slowed down by the compression due to the greater opportunity for collisions between more densely packed molecules.
In principle that is no different from the Radiative GHE because both methods achieve their heating effect by slowing down the flow of solar energy through the atmosphere. Neither scenario is a breach of the Laws of Thermodynamics.
GHGs can try to alter that gravitationally induced lapse rate but in fact changes in the non radiative processes will work as a negative system response.
Additionally, non radiative energy transfer processes can temporarily cause a different lapse rate (either steeper or shallower) from the gravitationally induced one by redistributing energy across the surface but not for long.
The strange thing is that I’m sure that in my schooldays it was the gravitational effect that was termed the Greenhouse Effect and it applied to every planet with an atmosphere whether with or without GHGs.
The term ‘Greenhouse Effect’ has only more recently become identified solely with radiative processes.
As regards the S-B equation that isn’t really relevant because it is only applied after the surface temperature has been set by the combination of the Gravitational GHE (which is fixed) and any net Radiative GHE after the negative system responses to the latter have been played through.
The gravitational effect involves the total mass of the entire planet including atmosphere whether GHGs or not whereas the radiative effect on Earth only involves water vapour plus a miniscule amount of non condensing GHGs. Thus one would expect the radiative component to be far smaller than the gravitational component.
The AGW viewpoint needs to recognise the gravitational component and properly quantify it as compared to the net (after negative system responses) effect of the radiative component and furthermore limit the figure to that attributable to the non condensing GHGs alone.
The condensing GHGs (water vapour) seem to neutralise their own effects via the negative system response of the water cycle and might well deal with the non condensing portion too.
I do not accept the proposition that there can be a positive system response to non condensing GHGs from the water cycle. No evidence has come to light supporting that assumption and with evaporation having a net cooling effect it is implausible to my mind.
Furthermore, adding non condensing GHGs to a transparent relatively non radiative atmosphere such as one containing mostly Oxygen and Nitrogen like Earth’s actually increases the ability of that atmosphere to radiate out to space. Oxygen and Nitrogen cannot do that to any significant degree so in theory they should produce an even hotter surface temperaure. Oxygen and Nitrogen conduct 100% of their energy downward because they cannot radiate to space. In contrast, non condensing GHGs radiate 50% of their energy out to space.

David
January 9, 2012 5:10 am

Willis says…”As a result, while the greenhouse effect has done the heavy lifting to get the planet up to its current temperature,…”
How much of the GHE on earth is actually due to the oceans where the residence time of energy is far far longer then any GHG? Also, although the average albedo of earth is higher then the moon’s, is it higher at laditudes where TSI is stongest?

gnarf
January 9, 2012 5:12 am

Here a nice article showing influence of heat capacity, applied to moon.
You can get average temperatures from 169K to 291K.
The real problem is that averaging temperatures over time and/or space has no meaning. As you say, averaging T^4 and later take the fourth root gives you something more coherent.
If you consider a cold earth with a short temperature range (min and max close from each other) then average temperature is MORE than for a hot earth with a wide temperature range!
In a similar way, if you reduce the number of weather stations and keep only stations close from towns, you reduce the measured temperature range-> you increase the average temperature!

Bomber_the_Cat
January 9, 2012 5:24 am

Willis, I’ve added this to my archive of informative articles. The cooling rate of the moon is useful; I’ve never seen it used to calculate what the earth temperature might be without an atmosphere. As Izen says (January 9, 2012 at 3:36 am), Science of Doom also has an article on Lunar temperatures but from a different perspective. He(she) takes into account various hypothetical heat capacities of the Moon.
Don’t you always find that when you post a straightforward article like this that you get a lot of flack from the anti-science brigade who insists on misreading or misinterpreting what has been said. Well maybe not misreading – some of them don’t appear to have read it.
But take heart from the poem:
“If you can bear to hear the words you’ve spoken, twisted by knaves to set a trap for fools….”
.

cal
January 9, 2012 5:26 am

It always amazes me how rude ignorant people are! About 2 years ago I entered into a discussion on the temperature of the moon on this blog. Armed with just the albedo of the moon and the peak daytime temperature I estimated cooling rates etc to come to a temperature profile that would be consistent with the SB laws. I was met with a barrage of abuse until someone put up the actual figures which were within a couple of degrees of mine (so I was a bit lucky!).
Willis has come at it from the opposite direction and come to the same picture, as one might expect. I think he did a really good job. How anyone can argue with the Physics is a bit beyond me.
A couple of things that Willis did not emphasise.
The profile would be different it there was a liquid surface with a high thermal capacity. This would also flatten the profile just as it does on earth.
I think it is also worth clarifying the reason why the SB equation appears to favour the less dramatic profile. To make it simple: if the surface were at an average of 150K a drop of 50K would take it to 100K and an increase of 50 would take it to 200K. Because of the fourth power law the relative rates of radiation would be 1:16 at the extremes giving you an average of just over 8 over the cycle (assuming a square wave). A constant temperature of 150K would only give you relative figure of about 5 so the temperature would have to increase in order to radiate at 8.5 average. Willis makes this point but uses a formula which may not make it absolutely clear what is going on.
Thanks again Willis. I enjoyed your post as I normally do. Congratulations on not losing your temper (too much!). I would not be so patient.

January 9, 2012 5:31 am

If daylight on earth lasted 14.5 days, instead of 12 hours, there would be huge temperature swings on earth that I would like someone to calculate.
Similarly, if daylight on the moon lasted 12 hours instead of 14.5 days, temperature swings on the moon would be much smaller.
The different lengths of a day on the moon and on the earth probably account for more of the temperature swings than the presence or not of an atmosphere. How much more? Could someone tell me?

Spector
January 9, 2012 5:40 am

Fourth Root of the Mean Fourth Powers
The important thing to keep in mind here is that 304 W/m² is a measure of average energy flow. Thus the ‘characteristic temperature’ calculated by the Stefan-Boltzmann equation is not an average temperature, it is a special average based on the fact that energy flow is proportional to the fourth power (T⁴) of the absolute temperature. Thus the characteristic temperature is equivalent to a fourth root of the mean fourth powers average. This might be considered analogous to an RMS average except fourth powers are involved instead of squares. An average of this type tends to emphasize higher values and thus will yield a higher result than a simple average of surface temperatures. Of course, this only makes sense when using absolute temperatures.

David
January 9, 2012 5:44 am

markus says:
January 9, 2012 at 2:58 am
“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?
————————————————-
Markus, I think this is a good question. Of course the crustal thickness in the oceans is reduced relative to the land, therefore one would assume a higher heat flux. When discussing the affect of a small incidence of energy one must consider that energy is never lost, therfore one must consider the residence time of the material recieving that influx. The law is very simple. At its most basic only two things can effect the energy content of any system in a radiative balance. Either a change in the input, or a change in the “residence time” of some aspect of those energies within the system. The residence time of the earths energy flux into the ocean depths is likely thosands of years, so I suspect it is not properly appreciated.

Bill Illis
January 9, 2012 5:45 am

The darkside of the Moon does receive reflected sunlight and thermal radiation from the Earth. It is estimated to be about 0.095 W/m2 so a tiny amount, but enough to raise the Moon’s darkside temperature about 32C above the cosmic background radiation level. That still leaves lots of unaccounted for energy in the Moon’s darkside temperature.
Converting some of this data from W/m2 to Joules/second/m2 helps some in the understanding. There are accumulation rates and rates of energy loss. The numbers for the Moon are different than the Earth but not that much different.

Owen
January 9, 2012 6:22 am

Willis,
I love your work and the uncomplicated way you present it so even people like myself can understand what you are talking about. Anthony Watts has the best climate site on the internet because of contributors like yourself. Thanks for sharing your thoughts and ideas with the world.

January 9, 2012 6:22 am

I no longer bother studying long-winded theoretical articles that miss the most basic reality. The lack of real understanding, in this article, of the thermodynamics of the atmosphere is well brought out in the admission at the end:
“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.”
Those who respect the Standard Atmosphere (which my Venus/Earth temperature comparison confirmed as the equilibrium state of the atmosphere), are not so easily flummoxed by the supposedly “incredibly complex system”. The stability is clearly, even obviously, due to the weight of the atmosphere itself, in hydrostatic condition and thus exhibiting a stable, negative vertical temperature lapse rate with altitude throughout the troposphere. That stable thermal condition predominates over all other atmospheric processes, conditions or mechanisms, including the difference between night and day. Clouds and water vapor don’t rule, the hydrostatic condition does (transient and local deviations like temperature inversions notwithstanding).

David
January 9, 2012 6:30 am

I thought the lunar discussion was very good, and credit to Willis for the article. Didn’t feel it followed through though when the greenhouse subject came into the piece. Why is the average higher with greenhouse warming? Explaining that in terms of the still constant energy emission would have polished it off nicely.

Alan D McIntire
January 9, 2012 6:30 am

gnomish says:
January 9, 2012 at 3:43 am
“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.”
There are different averages here. Bigger temp swings do not change average radiation, but radiation is not proportional to temperature, it’s proportional to the 4th power of temperature.
.
16 16 16 16 and you get temp 16^0.25 16^0.25 16^0.25 16^0.25 = 2 2 2 2 for an average of 2.
Take the same radiation and distribute it
31 31 1 1 and you get temps of 31^0.25 31^0.25 1^0.25 and 1^0.25 = 2.36 2.36 1 1 with and
arithmetical average of 1.68, a 16% drop in average absolute temperature .
Another point that could be addressed- in the real universe nothing acts like a black body when radiation is constantly changing, as on all rotating planets. A blackbody at earth distance would absorb and radiate 1368 watts at the equivalent of the equator at noon, for an equivalent temperature of 394 K, and would radiate at 2.7 watts- the temp of the “big bang” at night. For real bodies you need to also apply Newton’s law of heating/cooling.

January 9, 2012 6:35 am

Alexander Feht says:
Alexander I cannot see what you are referring to even I (uneducated save for a high school diploma) can see throughout that he is comparing the moon and the earth without an atmosphere the only atmosphere he really goes into detail about is the imaginary one he introduces in the thought experiment I think you are letting a strong dislike for Willis get in the way of reading his posts objectively.

January 9, 2012 6:46 am

I do not think that Lunar gravity is sufficient to hold an atmosphere. Increasing rotational speed only makes it worse. Apart from that the above thoughts will work (?).

January 9, 2012 6:59 am

So the moon should be absorbing more energy than the Earth..
You are absolutely right!, but it is not only about “temperature”:
Prof.Piers Corbyn uses the Sun-Moon-earth relation in his forecasting method:
http://www.weatheraction.com/
Richard Holle too:
http://research.aerology.com/aerology-analog-weather-forecasting-method/

Joules Verne
January 9, 2012 6:59 am

@Willis
You state that actual measured average temperature of the moon is -77C.
That’s the predicted S-B temperature. The actual average temperature measured by Apollo missions is -23C. The raw data for the thermal conductivity experiments deployed by Apollo 15 & 17 is available somewhere on NASA website. I tracked it down once. It’s public. The gist is that at any depth in the regolith of more than about 50cm the temperature is a constant -23C. This of course is the average of the surface temperature. Both experiments were at mid-latitude locations.

Joules Verne
January 9, 2012 7:03 am

@Willis
Also, broadband average albedo of the moon as measured by CERES satellite is 0.137 not the 0.11 you cite. Not a huge difference but it does make the S-B temperature several degrees higher.

izen
January 9, 2012 7:10 am

@- Stephen Wilde says: January 9, 2012 at 3:23 am
“Why ignore gravitational compression of the atmosphere ?
Isn’t that what sets the adiabatic lapse rate independently of the effect of greenhouse gases ?”
The adiabatic lapse rate is set by gravitational compression and atmospheric mass independently of the surface temperature.
Which is why the temperature can vary between day and night with little variation in surface pressure or lapse rate…
It simplifies these ‘thought experiments’ if you envisage a superconducting surface that is isothermal. The oceans on Earth go some way towards this with the transfer of energy from the equator to the poles via solid/liquid/vapor phase changes and currents.

Joules Verne
January 9, 2012 7:13 am

From David on January 9, 2012 at 12:26 am:
“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…”
Not even close. The moon reaches 75% of its maximum daytime temperature just a few hours after sunrise. The ocean is what makes the huge difference. Until one completely understands the difference between how water and rocks heat and cool nothing about the earth’s climate will be clear. Everything becomes clear after that. One of the most crucial facts to understand is that the ocean cools primarily through evaporation not radiation. If the ocean doesn’t cool by giving off longwave thermal radiation then it wont’ be warmed that way either. Therefore greenhouse gases that produce downwelling longwave radiation have little effect on the ocean. It’s an entirely different story over dry land where longwave emission is the primary means of cooling. Once you accept that all the observations start making perfect sense. Anthropogenic CO2 is largely a land-based phenomenon. The earth is largely a water world. Thus CO2 plays a more limited GHG role than it would over a world not covered by an ocean.

Brian H
January 9, 2012 7:20 am

Willis, since comments on your “Estimating Cloud Feedback From Observations” post have long been closed, I’ll draw your attention here to this very pertinent paper, that says, amongst other things:

The rate of ascension, and the parcel temperature, is a function of the
quantity of latent heat released and the PV work needed to overcome the gravitational
field to reach a dynamic equilibrium. The more latent heat that is released, the more
rapid the expansion/ascension. And the more rapid the ascension, the more rapid is
the adiabatic cooling of the parcel.

The violent positive feedback generation of tropical thunderstorming, derived ab initio from thermodynamics! With, as you posit, major negative feedback consequences for surface temperature increases.

Cathy
January 9, 2012 7:24 am

Ah! The beautiful and very different male brain.
I so often notice that WWUT posts that dive headlong into abstract theories replete with abstract equations and (yikes!) math . .
rarely entice the (ahem) gentler sex to weigh in.
Vive la difference. (Are we allowed to say that anymore?)
Love you guys.

darkobutina
January 9, 2012 7:58 am

Advice to Willis: Leave discussion on Greenhouse Theory to scientists who are qualified to discuss the problem!
Darko Butina, UK

Brian H
January 9, 2012 8:21 am

Just noticed, my link is to the same paper mentioned by Bryan, above. Lots going on in it, and Tallbloke, your mod, is hosting a conversation between the authors and Gilbert, author of the “Pot-Lid” hypothesis, which integrates virial theory (Potential gravitational energy and kinetic energy trade off 1:1) with hydrostatics, which introduces a “leak” in the KE side of all the energy required to vaporize the water in a given air parcel.
Miskolczi has been strongly invited to weigh in.

Kelvin Vaughan
January 9, 2012 8:23 am

David says:
January 9, 2012 at 12:26 am
An excellent post showing the importance of T^4 in regulating the temperature of the Earth (and other heavenly bodies).
I have a heavenly body and I’m hot stuff!

January 9, 2012 8:24 am

Willis,
As always a very thought provoking thread.
One of the main points of interest that I’ve previously not thought about (until this thread) is the idea that the swings in the Moon’s surface temperature as it rotates would be less extreme if the Moon rotated faster? If that is so, does anyone, NASA for example, have a computer model that has been validated via a scale model of an instrumented rotating sphere receiving a net surface radiative flux of ~300 W/m2? Even if the experimanetal flux had to be somewhat less than ~300 W/m2 flux of the earth/Moon surely we could conduct this type of rotating sphere in a vacuum subjected to a constant radiative flux experiment? It wouldn’t have to be that expensive an experiment surely (compared with the LHC)? Anthony are you reading this?
If this rotating sphere experiment showed that the difference in lit/unlit surface temperature extremes reduced when the speed of rotation of the sphere was increased then wouldn’t we then be in a position to have proven that when modelling the Earth we must allow for the fact that the earth rotates (which the GCMs don’t appear to do but rather instead rely on scaling the incident heat flux by the factor of 4 ratio of flat disk to sphere surface area?). When the Earth rotates presumably the ‘dark side’ is also subject to less ‘solar wind’ than the ‘lit side’?
Another (frivilous) thought. If it’s so cold on the dark side of the Moon, does that mean if we colonised the Moon that we could could have self sustaining super-conductors when on the dark side and that we could replenish our energy supplies using those high efficency PV cells whenever our habitat rotates into the sunlit side of the Moon again?
KevinUK
A fellow senile CAGW skeptic.

Brian H
January 9, 2012 8:31 am

Cathy says:
January 9, 2012 at 7:24 am
Ah! The beautiful and very different male brain.
I so often notice that WWUT posts that dive headlong into abstract theories replete with abstract equations and (yikes!) math . .
rarely entice the (ahem) gentler sex to weigh in.
Vive la difference. (Are we allowed to say that anymore?)

How terribly sexist! i’m not sure which one should be most offended, though.
By all means, step in and join Pamela Grey, Aussie, and Kim. And others. But please, no tortured obscure haiku?!? Satori is rare and not to be routinely relied on in science. 😉

Brian H
January 9, 2012 8:35 am

Paraphrasing Hawking: Unified Field Theory is easy. The real mystery of the universe is women!
8-0 !

January 9, 2012 8:35 am

Willis
I am not sure if this is in anyway on topic as it is something that I do not understand and hence the reason I am raising it here. A guy called Bill Illis posted this link on another thread
http://img40.imageshack.us/img40/4605/greenhousebylatitudec.png
now if I understand this it shows there is no so-called greenhouse warming in the tropics. In fact, given the amount of heat energy received in the tropics it may well be that the atmosphere acts to cool the surface in the tropics. However, given that this relatively large and thermodynamically important part of the earth does not seem to exhibit greenhouse warming, what, if anything does it say about the concept of average temperatures?
I apprecate that I may well be mixing apples and pears but this is something that has been bugging me ever since I saw it
also given your day job and other calls on your time if this is just too daft to deserve a response so be it
kind regards

Tom_R
January 9, 2012 8:38 am

>> son of mulder says:
January 9, 2012 at 3:42 am
but on a clear night the air will cool quicker than the surface. <<
The surface will cool quicker than the air, which is the reason we can have frost form at air temperatures above freezing.
Your point about a difference between air temps and surface temps is still valid.

A. C. Osborn
January 9, 2012 8:40 am

Isn’t it great how the GHGs prevent such wide swings in temperature as experienced by the moon, except of course in deserts, where it doesn’t do a very good job.
I wonder why that is?

Steve Keohane
January 9, 2012 8:42 am

Cool Willis! It is nice to get a description of the effects of rotation on absorption/radiation.
This line fascinates me: In fact, anything that reduces the variations in temperature would raise the average temperature of the moon.
If I apply this to the earth, bodies of water, high RH%, low altitude, all stabilize the local temps by minimizing day/night cycling. I then have to wonder about the effects of long-term LOD Δs, even a few seconds could accumulate a gain or loss in the mean temperature over centuries.

LarryD
January 9, 2012 8:44 am

The Moon’s orbit is inclined, so it never lacks insolation even when the Earth is between it and the sun. As a little reflection will show, since that is when the moon is full.
Even during the full lunar eclipse, the moon receives some insolation, because the Earths atmosphere refracts some light onto it.

January 9, 2012 8:51 am

Darko,
http://wattsupwiththat.com/2012/01/08/the-moon-is-a-cold-mistress/#comment-858507
Instead of appealing to authority and claiming that Willis has nothing to add that hasn’t already been said already in ‘Slaying the Sky Dragon’ (not all of us have forked out our hard earned dosh to read it) would you actually like to point out what is wrong in Willis thread here instead? I know that will take more work, but hey that’s sort of the whole point of this blog. You appear to have the scientific training/qualificatins to do so, so why not ‘fill your boots’?
Just out of interest what was the ‘major scientific discovery’ your team discovered? Did it involve applying the scientic method? If so, how did the scientific method assist you in your ‘major discovery’? Who subsequently confirmed your discovery. Did you make all your data and analytical methods i.e. code available to third parties in order that they could confirm or rufute your discovery/findings? What difference did your ‘major discovery’ make to the way we lead our day to day lives?
I’m asking these questions after Googling ‘Darko Butina’ which returned the following link
http://www.chemomine.co.uk/DB-exec-summary.htm
If thats you I’m not sure I’d call discovering an anti-migraine drug a ‘major scientic discovery’. Did your team get a Nobel Prize for that?
KevinUK

R. Gates
January 9, 2012 9:08 am

Nice general analysis Willis, and for the most part I think you’ve pinned down the importance of the greenhouse atmosphere of Earth in terms of keeping it far warmer than it would be otherwise. Thank god you didn’t say it was gravity and the ideal gas law!
In your calculations, as other have pointed out, you’ve forgot to mention that the Earth emits more energy in LW from the surface than it receives in SW solar at the surface, which of course is not true in the case of the moon, which pretty much emits exactly back what it gets from the sun. Of course, you of all people should not forget the incredible heat sink that the ocean is for our planet and the effects the ocean has on maintaining temperature at night. I also think you might be a bit off in your calculation as to how fast the Earth would cool at night without an atmosphere. Precise Measurements have been made of the moon’s rate of cooling of the lunar surface during a lunar eclipse, and it is somewhere around 30C an hour at peak. (see http://www.diviner.ucla.edu/blog/?p=610). So, if you stripped away the Earth’s atmosphere (and took away the ocean) I think it might not cool quite this fast, but certainly faster than the 4 to 6C or so an hour that you calculate. The backradition from the greenhouse atmosphere really slows down the rate of surface cooling at night far more than you seem to calculate, as without it, there is nothing at all to slow the LW from going right back into space.

Joe
January 9, 2012 9:21 am

I’m not sure I agree with the Q.E.D. conclusion. To get there you have to assume an atmosphere made up of an imaginary material. I’m not convinced that a contradiction built on a imaginary basis is all that helpful.
In other words, your conclusion that this material that has mass and conductivity but no insulating property results in a perpetual motion machine does not invalidate any real world scenario as the properties of this fictitious material are what created the contradiction in the first place.

January 9, 2012 9:25 am

“The adiabatic lapse rate is set by gravitational compression and atmospheric mass independently of the surface temperature”.
Yes.
“Which is why the temperature can vary between day and night with little variation in surface pressure or lapse rate…”
No. Solar insolation (or lack of it) varies the temperature at the surface and upsets the adiabatic lapse rate. Convection then starts (or stops) in order to restore the adiabatic lapse rate.
But convection cannot go further than restoration of the adiabatic lapse rate because it is set independently by gravitational compression and atmospheric mass independently of temperature.

DonS
January 9, 2012 9:32 am

Willis, you gotta stop raking that stick along the picket fence around the yard where all those watch dogs lie. All that yapping is keeping me awake. Sorta like economists: ask ten of them a question and you’ll get twenty answers, every one of which you can take to the bank.

January 9, 2012 9:37 am

On the Climateect blog, back in Mid August 2011 and Oct. 16-17, I realized for the first time how the “Toy” model, ( i.e. Constant temperature, Solar insolation divided by 4, and no day-night considerations ) was so simple a model, that it was distorting a lot of thinking. In the Toy, the Greenhouse effect can only be supported by an atmosphere with GreenHouse Gases (GHGs). But in the real world, with a day and night, temperature changes, and terratons of H20 in three phases, there are so many ways to trap heat in non-thermal mechanisms.

There are heat trapping mechanisms in the daily cycle of the earth’s heat flow. I have been lumping them all as GHE (Green House Effect).
GHE certainly includs
1 — back radiation from GHGs, of which CO2 is only one and not the most important one. Agreed?
The following heat trapping mechanisms are also in play.
2 — Heat Capacity of water and air in the ocean and atmosphere.
[2b – Heat Capacity and Thermal Conductivity of Rock and soil]
3 — Heat of Fusion as water turns to ice.
4 — Heat of Vaporization as water vapor condenses into water.
5 — Adiabatic physics of the atmosphere.
6 — Thermal conductivity of the air and water in the ocean.
[7. and an albedo that changes as a function of time of day and season]
Here I make an observation that I invite your comment:
The Toy model [no day-night, only average insolation] is a static, single temperature model, and as such the contribution of 2 through 6 are zero. The whole answer is in 1, the GHGs.
But in [a day-night model such as ] Postma’s model, which I find far more realistic than the Toy, Temperature MUST vary by Lat, Long, h, and Time. Heat is trapped by all mechanism 1 through 6. and as a result, the contribution of the GHG to GHE might be smaller that implied by the Toy model.
Here is my crucial set of questions:
Does GHE include A) 1, the back radiation? or B) all heat trapping mechanisms 1 through 6.
If A), what then do we call 2, 3, 4, 5, and 6?
If B), then what are the units or dimensions of GHE to capture its strength? [with so many factors?]
Rasey Oct.1719:27 with links to prior points of discussion.

For instance, to the question why the lunar night side is not at abolute zero, it is largely because the lunar rock is warmed in the daylight and that warmth is conducted at a decay rate several meters down. At night, that subsurface heat reservoir is conducted back to the surface at a rate probably not too different from the theoretical SB emmision rate.
Frankly, I think any serious discussion of Greenhouse Effect and Global Warming that uses an average temperature, without day or night, to be fatally flawed. The Toy model is good for one thing: to give a MAXIMUM GHG contribution to the GHE. Once you introduce all the other heat trapping mechanisms (invisible to SB physics) the contribution of GHGs to GHE must be smaller, perhaps much smaller.

January 9, 2012 9:48 am

The UTC presentation covers this nicely, but I will try and rephrase it : (
Willis uses the average S-B temperature of -18˚ C ( 255 K ) which is wrong because it is incorrectly calculated using a cross section instead of properly integrating over a hemisphere. The correct number is over 100˚ C colder. A black body is considered massless and rotation of a black body will in no way change the average absorption or emission.
Adding a transparent atmosphere increases the black bodies square meter emission area while at the same time the absorption sphere area stays the same.
What I am trying to say (poorly) is that with an atmosphere there will be a point above the surface radius where the absorption and emission are exactly equal to the S-B calculations. Above that altitude the temperature will be colder than the S-B number and below that point the atmosphere will be warmer than the S-B number with the surface warmer than the atmosphere.
Increasing the volume and density of the atmosphere will increase the temperature at the surface and decreasing the volume and density of the atmosphere will lower the temperature at the surface (keeping everything else constant of course). The Ideal Gas Law will calculate the temperatures accurately.

January 9, 2012 9:57 am

If balancing the energy budget, does the Moon “suck” or “emit” energy, relative to earth, and which would be the predominant wave lengths of such a transfer?

darkobutina
January 9, 2012 10:00 am

Replay to Kevin-UK
The only reason that I have commented on the article by Willis is that I have great respect for the blog site and have found some great articles by the specialists in their own fields. However, the field of radiation and heat balance is so complex that it really should not be open to ‘let us all join in for our thoughts’. The topics of that nature can only be properly addressed in the scientific journals, and believe me, there are lot of journals there that have not been ‘contaminated’ by the proponents of imaginary global warming. I would highly recommend to type in Google scholar names “Gerhard Kramm and Ralph Dlugi” published in Natural Sciences in 2011, which will give you a free PDF file to read. Also, I believe that Alan Siddons has contributed in the past to this blog site – that is the guy who knows this area – check the archives or Google his name. Since it seems that Willis did some reading on the topic, I think that he would contribute much more by summarising what the separate chapters in the book were saying about greenhouse gasses, rather than to venture into this field with his own ideas.
As to the major discovery that I was part of, it did drastically improve the quality of life of millions of people in the last 20 years, since this was the first effective drug for treatment of migraine. Just ask any migraine sufferer how miserable life can be. Since drug discovery is one of the most regulated sectors, each country has its own independent regulatory bodies, one in US is called FDA, and they use their own experts in field of biology, chemistry, toxicology and statistics and check all the original data that the company has produced in ten years of the research. That is the normal way that all experimentally based sciences, outside the so called ‘climate sciences’ operate.
Darko Butina, UK

January 9, 2012 10:03 am

Bill Illis says:
January 9, 2012 at 5:45 am
“The darkside of the Moon does receive reflected sunlight and thermal radiation from the Earth.”
I believe you mean the nearside. When the darkside is also farside, it of course does not receive radiation from the Earth. That said, a 32K increase in nearside night temperatures is highly significant, since it is close to the 43K temperature measured in the lunar polar and other areas that exist in permanent shadow. Next step: to see whether the farside has even cooler minimum temperatures in permanent shadow.

Lars P.
January 9, 2012 10:07 am

Willis, the flat world model that is used to calculate the average does not make sense. As you correctly say the radiation changes with the 4th power of the temperature, so temperature cannot be averaged in a linear dependency, it does not make sense.
If we would have a planet with 50°K on the sunny side and 10°K on the dark side the averaged temperature would be 30°K which is not what the planet radiates.
sigma*50**4+sigma*10**4=2*sigma*Taverage**4
If we compute the temperature of equivalent radiation will result 42°K. So 42 is the average temperature between 10 and 50 in terms of equivalent radiation (btw. “Answer to the Ultimate Question of Life, the Universe, and Everything is 42”) .
The same for the moon, if the sunny side is 60°C (333°K sic) and the cold side -175°C (98°K) the equivalent radiation temperature is 280°K which is +7°C
So the model where the sun’s radiation is divided through 4 and spread over the whole earth is leading to wrong results.
Averaging temperature as an arithmetic mean is leading to nowhere – it is a fictive value of no physical meaning.
Thanks for the posting, let me know if you see things differently or I got my calculations wrong.

cal
January 9, 2012 10:18 am

Honorable says:
If daylight on earth lasted 14.5 days, instead of 12 hours, there would be huge temperature swings on earth that I would like someone to calculate.
Similarly, if daylight on the moon lasted 12 hours instead of 14.5 days, temperature swings on the moon would be much smaller.
The different lengths of a day on the moon and on the earth probably account for more of the temperature swings than the presence or not of an atmosphere. How much more? Could someone tell me?
—————-
Both poles are without sun for much more than 14 days and yet the temperature does not drop to anywhere near the level on the dark side of the moon. This is mainly due to the movement of warm air from the tropics which maintains the tropopause at about 200K. The existence of this relatively stable layer of the atmosphere quite close to the ice surface (it is only about 6500 metres at the poles and the ice surface is close to this height in many places) means that further cooling is not possible. So if you are asking for a calculation for the earth as it is with an atmosphere then this is an indication of what you might get. Contrary to your guess the atmosphere is the main determinant of temperature swings but the actual calculation which would have to model air flows in response to a 14 day cycle is beyond my ability and (I would suggest) a bit pointless.

stumpy
January 9, 2012 10:20 am

Very interesting post. A few points though, what impact does the ocean have on night time cooling rates, surely it would change the earths behaviour from the moons. Secondly, how would the albedo change without cloud cover in a clear atmosphere, surely the earth would obsorb more energy and thus have a higher average temperature. Also, the earth constantly emits heat as its core cools – I a negligiable affect day to day for us, but how signficant does it become in a clear atmosphere i.e. does it determine a minimum surface temperature at night (for example higher than the moons as its cold through) which increases the average? Just some thoughts, all things that people should already have assessed before they got all hung up on co2!
Diurnal change in temperature, convection of heat and the earths thermal mass has been something that should be considered for a long time but often neglected when considering the earths climate. In climate models I understand convection is a secondary calculation after the heat trapping of GHG’s and therefore all of the warming affect is applied to GHG’s and their affect is overstated as a result.

gbaikie
January 9, 2012 10:22 am

“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. ”
A man is engine creating 100 watts- in one hour: 360,000 watts.
A dead man isn’t going to be kept warm with a blanket.

Roy
January 9, 2012 10:23 am

Willis,
As ever an excellent and interesting post, taking a different look at things.
Your approach here may solve a different question, the Faint Early Sun Paradox. You discussed this in your previous post on the thunderstorm thermostat http://wattsupwiththat.com/2009/06/14/the-thermostat-hypothesis/ in which you summarise the question as:
“In contrast to Earth’s temperature stability, solar physics has long indicated (Gough, 1981; Bahcall et al., 2001) that 4 billion years ago the total solar irradiance was about three quarters of the current value. In early geological times, however, the earth was not correspondingly cooler. Temperature proxies such as deuterium/hydrogen ratios and 16O/18O ratios show no sign of a 30% warming of the earth over this time. Why didn’t the earth warm as the sun warmed?”
Following the approach of this post, it is not the temperature that needed to warm 30% over 4 billion years, but the average radiation, which would need to rise from about 180 W/m2 to 240 W/m2. Or via Stefan Boltzmann from about -36C to -18C.
The length of day 4 billion years ago was around 7 hours ( http://www.ptep-online.com/index_files/2009/PP-16-02.PDF) rather than 24, so with only 3.5 hours warming and 3.5 hours cooling, the diurnal range would be perhaps only around quarter that at present. So cutting 3/4 of the cooling effects of temperature swings form the ancient Earth means that it would have around 12C less ‘swing cooling’ than we’ve got today. So it would be around -24C rather than -36C.
So given a 30% dimmer sun, the ancient earth is about -24C rather than -18C today before atmospheric effects. Nothing too paradoxical about that.

January 9, 2012 11:51 am

Yes – This must be one key factor in resolving the Faint Sun paradox. The negative “climate feedback” from BB radiation is highly temperature asymmetric to any change in radiation DS. So DT =DS/(4*sigma*T^3). Changes to surface radiation are mostly due to 3 things – 1) Solar radiation 2) Albedo 3) Greenhouse gases. The unique feature of the Earth is that it is 70% covered by liquid water which acts to regulate the greenhouse effect AND changes Albedo through cloud formation. There is geological evidence of liquid oceans on Earth 4 billion years ago when the sun was 30% less bright. This can only be possible if somehow the Earth self-regulates its temperature through water. One simple modle of how this could occur for “water worlds” like Earth is the following.
Let’s assume that there are simple relationships both for low clouds and net greenhouse effects upon incident solar energy. Defining x = S0/342 as the normalized solar flux on a Water World relative to that incident on Earth today and taking albedo of water as 0.1 we make the following (arbitrary) assumptions.
1. Low Cloud Cover is assumed to be driven through evaporation only by solar heating: Total cloud cover (CC) is assumed to be CC = 0.4*x. The albedo for low convection clouds is taken simply as 0.5 so. This results in a planet albedo which varies as 0.1+0.2*x. This value is chosen so that the planet albedo today is 0.3 (about the same as that on Earth).
2. The net total normalised greenhouse effect g is assumed to depend inversely on x. Water evaporation and high clouds at low x yield a high g value which the decreases as higher forcing drives evaporation leading to a lower lapse rate and more direct latent heat loss to the upper atmosphere. Today g is 0.3 and the (arbitrary) proposal is that g depends inversely on increasing x so g= 0.3/x. Therefore would therefore imply that 4 billion years ago g was 0.45.
Then the global Energy balance is simply:
(0.9-0.2x)S0 = SU(1.0-0.3/x), where S0(now) is 342 watts/m2
–> SU = ((0.9-0.2x)x*342)/(1-0.3/X)
–> Tsurf(x) = T(now)*4th root(SU(x)/SU(now))
The result of this simulation can be seen here
The objective of all this is just to show HOW a water covered planet could self regulate its temperature, and it also has something to say about climate feedbacks. IPCC GCM models assume net positive feedbacks with radiative forcing. They all average around 2 watts/m2/degC If such feedbacks are assumed to be true then the Earth would have boiled off its oceans long ago as solar radiation increased by 30%. Even more contradictory is working backwards from current average global temperature of 288K
We fix the current temperature to be the observed 288K and work backwards by subtracting DT from solar forcing every million years. It is here that we see the basic problem of assuming linear positive feedback. If the temperature falls enough so that 4sigmaT^3 = F then we get a singularity. (a href=”http://clivebest.com/blog/wp-content/uploads/2011/09/hindcast.png”>You can see this calculation here.
In the context of this simple model positive feedbacks would appear to be ruled out.

Philip Peake
January 9, 2012 10:23 am

Willis says: 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.
I know what you mean, but have to take issue with the terminology. GHG never provides “extra energy”, it might act as a reservoir of energy and *return* some of that energy.
On a planetary scale, even this effect is liable to be small. The thermal (energy) capacity of gas is very low compared to rock, so even if you were to take the energy accumulated in the entire atmosphere and apply it to the surface of a planet the effect would be small (and one-time … at least until it had heated up again.
As for energy transfer, from warm areas to cold, if we think about a non GH gas, the only way it can be warmed is through conduction — contact with the planetary surface (since by definition radiation passes straight through it). This is going to limit how fast the gas can acquire energy, and since the same applies to it delivering energy (physical contact and conduction) the effect is going to be small.
Then consider the volume of gas required (GH or not) to make any significant difference, and the fact that you would need a constant supply of warm gas making contact with the ground, and the velocity of the winds required to distribute sufficient energy to make a significant difference by this mechanism.

gbaikie
January 9, 2012 10:32 am

“ferd berple says:
January 9, 2012 at 1:49 am
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.” ”
This referring to permanent shadowed craters, which can get to 20 K.
But you correct there is average surface temperature difference as you go poleward,
a difference is not as extreme. But very significant.

R. Gates
January 9, 2012 10:34 am

gbaikie says:
January 9, 2012 at 10:22 am
A dead man isn’t going to be kept warm with a blanket.
______
Actually, that depends on how long he’s been dead. The decomposition of a body can generate a lot of heat, and wrapping that dead body in a blanket certainly alters the rate at which the decomposing body loses heat. This doesn’t even take into account the added activity of the maggots etc. that will want to have a nice meal and generate even more heat under that blanket.
But in comparing the Moon as a “dead” body and the Earth as a “living” body, it certainly is true that the Moon generates far less (but not zero) LW radiation than does the Earth, and furthermore, most don’t realize that the Earth’s surface generates more LW energy than it absorbs in SW energy.

gbaikie
January 9, 2012 10:49 am

“Kasuha says:
January 9, 2012 at 2:07 am
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.”
The air would warmed from hot surface. Any simple gas wall heater [no fans] shows that.
[Hot poisonous gas heats an heat exchange before being vented and warmed
metal {heat exchanger} heats the air in the room]
“- 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.”
Whatever.
“- 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.”
Any heated surface regardless of color will radiate same amount of heat [roughly].

PaulR
January 9, 2012 11:03 am

A. C. Osborn says:
January 9, 2012 at 8:40 am
Isn’t it great how the GHGs prevent such wide swings in temperature as experienced by the moon, except of course in deserts, where it doesn’t do a very good job.
I wonder why that is?

Because the most powerful green house gas is water vapor, and the relative absence of water and water vapor is exactly what makes a desert.

gbaikie
January 9, 2012 11:06 am

“* 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?”
The Moon’s day and orbit around earth about 28 days. [It’s tidal locked- always has one side facing the Earth].
The Moon orbit is such that not all orbits cross earth’s shadow. Nor does the Moon’s shadow
blocks the sun on earth with every orbit [fairly rare].
Related: during lunar eclipse
http://www.diviner.ucla.edu/blog/?p=610
Measures cooling of surface when earth is blocking the sunlight.

January 9, 2012 11:14 am

@cal: I get your point but poles might not be such good examples to the extent that when it is day, it is the equivalent of a permanent sunrise (i.e. the sun does not do so much warming). What would happen at the equator if days lasted 14.5 days followed by an equally long night. I would not be surprised if temperature would rise to 60 degrees, but that is a pure guess.
Finally, your interesting pole argument does not clarify what would happen on the moon if days lasted 12 hours instead of 29 times longer.

January 9, 2012 11:20 am

“gravity doesn’t add energy to the atmosphere on an ongoing basis.”
It doesn’t need to.
It just slows down the flow of solar energy through the system by increasing density at the surface to produce more opportunities for molecular collisions before the energy is released back to space.
The result is an accumulation of solar energy within the system at the surface so that a higher surface temperature can be achieved.

R. Gates
January 9, 2012 11:22 am

PaulR says:
January 9, 2012 at 11:03 am
A. C. Osborn says:
January 9, 2012 at 8:40 am
Isn’t it great how the GHGs prevent such wide swings in temperature as experienced by the moon, except of course in deserts, where it doesn’t do a very good job.
I wonder why that is?
Because the most powerful green house gas is water vapor, and the relative absence of water and water vapor is exactly what makes a desert.
______
Indeed, the absence of water vapor allows for the wide swings in temperature in a desert, but try taking out all the GH gases, such as CO2, CH4, and N2O above a desert and see what happens. Despite the belief of some, you would not get much “graviational” or “ideal gas law” warming from the nitrogen and oxygen left. The temperature drop would in fact be similar (though not identical) to what the Moon experiences during a Lunar eclipse when the Earth’s shadow passes over the sunlit moon and during the course of the eclipse the temperature drops 100K. Nitrogen and Oxygen won’t stop the LW at all.

Spector
January 9, 2012 11:23 am

As an example of Fourth Root of the Mean Fourth Powers averaging, the maximum and minimum temperatures on the graph of Figure 1 appear to be about + 90 and -190 which have a simple average of -50 degrees C. These are equivalent to absolute temperatures of about 363 and 83 degrees K. If these values are then raised to the fourth power we have 17,363,069,361 and 47,458,321 having an average value of 8,705,263,841 and the fourth root of this is about 305 degrees K or about 32 degrees C.
This is the type of value that an average energy flow S-B characteristic temperature would return. We do not have to use the S-B constant to convert these values to energy because that constant would be removed by division when the average is converted back to temperature.

gbaikie
January 9, 2012 11:24 am

“Here a nice article showing influence of heat capacity, applied to moon.
You can get average temperatures from 169K to 291K.
The real problem is that averaging temperatures over time and/or space has no meaning. As you say, averaging T^4 and later take the fourth root gives you something more coherent. ”
The mistake is that cooler something is, the more work can be done.
Simply if surface can only be heat to say 123 C from solar energy then
if surface is 120 C then less energy is absorb compare to radiated.
So a 10 C surface can absorb far more energy than a 120 C surface.
Something with large heat capacity could take days of sunlight to reach 10 C.
Something with low heat capacity could takes hours to get to 120 C.

January 9, 2012 11:28 am

Are there any forbidden to mention wavelengths?…just thinking about, as IR and visible light are not the whole spectrum.

Bart
January 9, 2012 11:31 am

izen says:
January 9, 2012 at 3:36 am
“But as the point is made above, that atmospheric effect of energy distribution can never raise the temperature ABOVE the S-B limit.”
This misconeption seems to be repeated time and again. It is bass ackwards. The temperature can go above the S-B “limit” (of which, there isn’t one), the radiated energy cannot in equilibrium. Kirchoff’s Law:

Kirchhoff’s Law has another corollary: the emissivity cannot exceed one (because the absorptivity cannot, by conservation of energy), so it is not possible to thermally radiate more energy than a black body, at equilibrium.

gnomish
January 9, 2012 11:38 am

Alan D McIntire says:
January 9, 2012 at 6:30 am
“There are different averages here. Bigger temp swings do not change average radiation, but radiation is not proportional to temperature, it’s proportional to the 4th power of temperature.”
hi alan. i know you’re trying to be some kind of helpful, but radiation is not temperature; averaging radiation does not average temperature. measuring radiation is not the same as measuring temperature (it’s a proxy, mmk?) furthermore, the word average MEANS what it does and not something whimsical that changes with the consensual breezes.
all of which really substantiates my main point that if one can’t use the language = words that by definition have definitions – you won’t be doing logic- and reason will exceed the grasp of gobbledegook.
if you want to have temperature and radiation mean the same thing- lose one of the words.
but the distinguishing characteristic of my rant is that logic can not be done without the cognitive tools- and temperature is not heat, it’s not radiation, it’s not average radiation, it’s not a function of gravity, either.
i mean- this is the first thread i’ve even seen where somebody noticed that submerging a heat source in a conductive fluid *maybe kinda sorta might* work to refrigerate it instead of heat it or insulate it.
.

gbaikie
January 9, 2012 11:39 am

“honorable says:
January 9, 2012 at 5:31 am
If daylight on earth lasted 14.5 days, instead of 12 hours, there would be huge temperature swings on earth that I would like someone to calculate.
Similarly, if daylight on the moon lasted 12 hours instead of 14.5 days, temperature swings on the moon would be much smaller.
The different lengths of a day on the moon and on the earth probably account for more of the temperature swings than the presence or not of an atmosphere. How much more? Could someone tell me?”
It’s difficult to give simple answer, but I like challenges.
The earth does have a long nite- longer than the Moon’s.
Every year the region of earth within the arctic circle enters
a 6 month long nite.

January 9, 2012 11:43 am

DirkH says:
January 9, 2012 at 5:00 am
Willis talks about the effect that the T^4 term has when the temperature varies drastically, as in the case of the moon, compared to the effect it has when the temperature varies less, as in the case of the Earth. In the case of the drastic variation, a lower average temperature is necessary to allow the planetary body to radiate enough. It’s a mathematical thing.

Oh, it’s “a mathematical thing”… Really. So, what’s new or interesting about this? Anyone who ever saw Boltzmann’s formula or knows what the fourth-power means, understands that the loss of heat by radiation quickly increases with the increase of temperature. So what? Why are we being treated as preschoolers here?
I don’t agree with Darko — popularizing science, even doubting the established science, is good and useful. Amateurs made more breakthroughs in science than professors and doctors ever dreamed of. But this particular amateur doesn’t explain anything new, complex or interesting.
P.S. Couple of people here propose a weird argument about “dead man under a blanket.” Be it known to them that plants are protected from freezing by blankets, though, last time I checked, plants had no internal sources of heat (unless you burn them). Thermal insulation is just that, an insulation — it keeps cold out even if there is no heater inside. Being a Siberian, I remember how much longer after sunset the warmer air is contained in a log cabin covered by deep snow (without any fire or people heating it yet), compared to any structure open to elements.

Richard Sharpe
January 9, 2012 11:44 am

I think you should just have gone with: The Moon is a Harsh Mistress

coldlynx
January 9, 2012 11:46 am

“But a transparent atmosphere could never raise the moon’s temperature above the S-B blackbody temperature of half a degree Celsius.” need to be clarified.
This is why:
A transparent atmosphere would be heated by convection with moon surface. The warm gas will raise due to density decrease. And heat the entire atmosphere by convection.
And what will a transparent moon atmosphere be cooled by?
Only by convection with the same moon surface. The problem is that a cooling atmosphere from below get stable. That is an inversion. A inversion will prevent warm air to decend to the surface and be cooled by surface radiation. Next day will the same surface heat a little bit warmer atmosphere than the day before.
It will not take long until this ideal moon atmosphere would reach a average temperature nearly as warm as the moon highest temperature. How close depend on the atmospheres heat capacity and length of day and night.
This only because the surface heat and cool an atmosphere, which have to obey the gas laws.
When You mention the moon temperature do You mean the moon surface temperature or the temperature of a fictive moon atmosphere?
Do I have to remind You that we do measure air=atmosphere temperature on earth. Not surface temperatures. They are very often close to each other but that is mainly due to convection=wind.

January 9, 2012 11:47 am

So in an equilibrium situation like the moon, where the amount of emitted radiation is fixed, temperature swings always lower the average surface temperature.
You betcha, as I showed slightly more quantitatively as the reposted topic of another thread. One that is actually almost directly applicable to the moon — much more so than the Earth.
The greater the temperature inhomogeneity over the surface, the greater the cooling, because T^4 goes up with T faster than it goes down with T. It’s really that simple.
rgb

gnomish
January 9, 2012 11:55 am

“The result is an accumulation of solar energy within the system at the surface so that a higher surface temperature can be achieved.”
stephen – which is heavier, a pound of feathers or a pound of lead?
stephen – which is hotter?
stephen – btw- how thick is this surface? how much depth can you pull out of this superficiality? how profound can shallow be?
sure would be nice if people used words – which have definitions – so everything isn’t confabulated into one long loud munch painting.
a surface has no thickness, gravity has no temperature, pressure has no volume and sounds without definitions are grunts, not words.

January 9, 2012 12:00 pm

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.
Sorry, I’m reading and commenting as I go. This is consistent with observations in the very dry, windless desert. To quote the Wikipedia article on Deserts, in hot deserts the daytime peak temperature can be 45C and the minimum temperature right before dawn can be 0C or even cooler. That is dead on your estimate, allowing for the fact that even in the desert there is stratospheric water vapor acting as a GHG to block a little of the heat — along with CO_2 of course.
Your estimate is of enormous consequence, in other words. It suggests that there is almost no greenhouse effect active over hot, dry deserts. Not CO_2 GH. Not H_2O GH. Not CH4 GH. They radiatively cool almost as fast as the dark side of the moon!
Almost no is not the same as no, but this points out the enormous importance of water vapor as a GHG. I’m guessing that it forms a critical aspect of glacial epoch stability — when all that water is bound up in glaciers and it is really cold all the time near the poles, I’m betting that it is always dry all of the time in all of the upper latitudes. Dry air just doesn’t trap a lot of heat at night, no matter what the hell the CO_2 levels are.
I’ve suggested — repeatedly — that direct measurements of the rates of radiative heat loss in the middle of geographically large deserts would provide us with more or less a direct measurement of the actual heat trapping of the greenhouse effect in the absence of water vapor. Your back of the envelope calculation shows why it is so important. We’re talking about a tiny effect compared to raw vacuum, not a big effect, and that includes the cooling of the thermal ballast of the lower atmosphere as well.
rgb

gbaikie
January 9, 2012 12:02 pm

“I do not think that Lunar gravity is sufficient to hold an atmosphere. Increasing rotational speed only makes it worse. Apart from that the above thoughts will work (?).”
I have strong bias towards not changing the Moon [or Mars]. Because i think the Moon as it
is better in many ways than earth. But with that said.
If want “milder climate” on the Moon, you could use water.
First water is very abundant in our solar system, even compared to our water world Earth.
There easily 1000 times more water than we have in earth oceans, which is “accessible”.
The Moon itself is very water poor- compared to Earth. As is Mars. But the Moon does
have concentrated quantities of water in it’s permanently shadowed polar craters. This
amount is on order of billions of tonnes. Which is tiny compare to our amount of water.
A billion tonnes is 1 cubic kilometer- so that amount is fair size lake. Or each square kilometer
of deep ocean has about 3 cubic km of water and earth has 510 million square miles and 70%
of area is deep ocean.
So, anyhow to answer question 10 meter depth of water is roughly equal our atmosphere. So
one could pools of waters 10 meter deep and these wouldn’t varying much in day and nite cycles.

January 9, 2012 12:04 pm

Let’s consider two superconducting spheres, one with a radius of one and the second with a radius of two. They are the exact same distance from the sun and they have the identical average solar insolation per square meter of 100 W per square meter and they radiate at 100 W per square meter. Their surface temperatures are identical.
Now let’s place the smaller sphere inside the larger sphere. The outer sphere 4π(2R)^2 has 4 times the area of the inner sphere. As a result the outer sphere has no change in insolation or radiation. The inner sphere now has 400 w per square meter insolation and correspondingly higher temperature.
A planets atmosphere acts in effect like like an outer conducting sphere, The bigger the atmosphere the higher the internal spheres temperature. It is just that simple.

January 9, 2012 12:09 pm

Overall, good article, but you are off by a factor of two in twelve hour cooling of the middle of a hot desert. It often is 45C, around 4C/hour. Not a lot of greenhouse effect when there isn’t water vapor to help.
The rest of the article is dead on the money. The earth almost certainly self-organizes to increase the efficiency of heat loss as it warms by increasing the (surface integrated) delta T. This adds to its overall stability (provides negative feedback) — within limits.
rgb

cal
January 9, 2012 12:13 pm

honorable says:
January 9, 2012 at 11:14 am
@cal: I get your point but poles might not be such good examples to the extent that when it is day, it is the equivalent of a permanent sunrise (i.e. the sun does not do so much warming). What would happen at the equator if days lasted 14.5 days followed by an equally long night. I would not be surprised if temperature would rise to 60 degrees, but that is a pure guess.
Finally, your interesting pole argument does not clarify what would happen on the moon if days lasted 12 hours instead of 29 times longer.
Your second point is easier to answer than the first where, as I tried to explain, the enormous winds that would inevitably sweep round the globe would be difficult to model. However it would be pretty safe to say that the presence of the atmosphere would dramatically reduce the temperature excursion compared to the moon.
In the second case one can more easily estimate the effect since the moon is a much simpler system. One can see from the graphs that Willis has provided that the temperature drops precipitously once the day ends. Nothing changes in this respect if the day is only 12 earth hours long. However, after 12 hours, just before it can reach its current absolute mimimum it would start to warm again. It is difficult to judge exactly how low the temperature would reach before it started to rise again but my guess is that it would only be about 20 degrees more than it is with a 14 day night. The warming cycle is more difficult to guess since the shape of the upward curve on the temperature plot is due to the fact that the sun is oblique for several days whereas in the 12 hours scenario it would only be a couple of hours so one cannot just read the rate of rise off the graph. My guess would be that it would reach a temperature at least as high as the current moon surface after 3 or 4 days and then decline. But I could be wrong. One could argue that at peak sun the surface has to radiate as much as it radiates at peak sun on 14 earth day cycle therefore the temperature has to be the same. The reason I have gone for the slightly lower temperature is that the surface would start warmer so would be radiating more in the early hours. There is also a thermal capacity issue which I can only guess at. If I am right this would make the total excursion between -160 to +60. Still much larger than the earth.
Still not quite sure why you are asking the question!

don penman
January 9, 2012 12:24 pm

If we give the moon an atmosphere that does not have greenhouse gas then the atmosphere will have zero radiation or emissions and the moons surface will radiate all the energy received from the sun at the top of atmosphere into space.The atmosphere contains some of the received energy from the sun but it cannot radiate it to space, my point is that we can’t ignore the non-radiation of the atmosphere in calculating the amount of radiation sent out into space.The energy radiated at the planet surface would be some average of the emissions at the surface and that at the atmosphere which would be lower than the amount received at the top of the atmosphere until an equilibrium at a higher temperature was reached.

January 9, 2012 12:25 pm

Willis, I too appreciate the choice of Title. The Moon is a Harsh Mistress is a favorite SF and Political novel.
In that it is a story about:
Ecology, Politics, Economic Freedom, Manners,
And a growing collection of people, organized by computer, attempting to overthrow the “Authority”, it is a story that well suits the “Battle in support of CAGW Skepticism.”
It has a place on my “Read many times” bookshelf. TANSTAAFL!

gbaikie
January 9, 2012 12:26 pm

KevinUK says:

“One of the main points of interest that I’ve previously not thought about (until this thread) is the idea that the swings in the Moon’s surface temperature as it rotates would be less extreme if the Moon rotated faster?

Another (frivilous) thought. If it’s so cold on the dark side of the Moon, does that mean if we colonised the Moon that we could could have self sustaining super-conductors when on the dark side and that we could replenish our energy supplies.”
Any rotation of planet in terms of heat can thought of as means of transporting heat to the night side of planet. So superconductor transporting electricity or heat to the nite side is similar.
As for the nite side of the Moon. It’s very easy to warm a building in a vacuum. It is also very easy to keep a building cool. So lunatics aren’t going wasting a huge amount energy, that earthlings do on heating or cooling their homes. With LED lighting there would not be much energy use to keep the lights on.
So, we left with industrial processes that need a lot energy. One could go to location on the Moon and get constant solar energy [high elevation] at lunar poles.
One also can use nuclear energy on the Moon. The Moon is perfectly safe place to store radioactive waste. And there is little reason to have much in terms of containment, a complete nuclear meltdown is not important other than wrecking the facility.

January 9, 2012 12:34 pm

ferd berple says:
January 9, 2012 at 1:23 am
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.

No Fred, Willis is right CO2 is 10 orders of magnitude greater than N2 as I have pointed out here several times. Your mistake is to compare one rather weak CO2 band with the solitary band for N2. In fact there are many CO2 bands, between 4 and 5 microns there are ~21,000 lines with the strongest band at ~10-18, by contrast there are ~100 lines in the same range due to N2, peaking around 10-28. There are ~1000 lines due to H2O in the same range up to 10-21. That wavelength range isn’t particularly relevant to GHE however because it’s not in the Earth’s emission band, between 12 and 18 microns CO2 has ~20,000 lines peaking around 10-19, H2O has ~500 lines up to 10-21, N2 has no lines at all!
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.
The joke appears to be on you.

January 9, 2012 12:45 pm

From gnomish on January 9, 2012 at 11:55 am:

stephen – which is heavier, a pound of feathers or a pound of lead?

In a federally funded study of the effects of climate change on the quality of feathers and lead emissions (per the funding request), from a fixed height of 6 feet, 100% of survey participants agreed that a pound of lead dropped on their bare heads was heavier than a pound of feathers. From 2 meters, 100% found a kilogram of lead to be heavier than a kilogram of feathers.
This study remains unpublished due to incompleteness of the American/metric equivalence portion, as all participants refused to be hit with slugs of lead.

January 9, 2012 12:57 pm

Interesting post. Incidentally I know the moon orbits and keeps one face to the earth. But interestingly the idea that it has an axial rotation as opposed to just an orbit is widespread, even to a report on the BBC a few days ago. Maybe I should not be surprised by the BBC, but otherwise it’s a common mistake even in scientific discussion.

gbaikie
January 9, 2012 1:01 pm

“P.S. Couple of people here propose a weird argument about “dead man under a blanket.” Be it known to them that plants are protected from freezing by blankets, though, last time I checked, plants had no internal sources of heat (unless you burn them).”
Plants do generate heat, as does all life [including reptiles or microbes].
Though mammals generally run much hotter.

January 9, 2012 1:03 pm

Usually “cold mistresses” are deceitful as they really are engaged in a urgent search for heat 🙂

jae
January 9, 2012 1:37 pm

Willis said:
“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.”
Yes, but the atmosphere is not transparent, and I don’t know anyone who says it is (looks like a straw man to me). Remember that the “S-B theoretical temperature of approx. -18 C” represents that average equilibrium radiation coming from about 5,000 KM! NOT FROM THE SURFACE AND NOT THROUGH TRANSPARENT GASES. Adjusting for lapse rate, that makes the surface about 15 C. That can be called a greenhouse effect, if one prefers to do so, but I don’t think that it is mostly due to radiation.
I don’t have near enough time to read all the comments you get and give, but to my knowledge you (or nobody else) still have not countered the points made over and over again by Harry Dale Huffman and the authors of a previous post, points that clearly demonstrate that atmospheres on planets all have positive effects on temperature and that those effects are not affected much, if at all, by the types and amounts of gases in those atmospheres.

old engineer
January 9, 2012 1:44 pm

Willis-
Thanks for another thought provoking post.
Unlike Brian H @ January 9, 2012 at 8:31am, I loved the Haiku. Perhaps if Brian H were more widely read, he would have known that the Haiku is to the Japanese as the sonnet is to the English, and that far from being obscure, Basho is one the most famous of the Haiku poets.

Septic Matthew
January 9, 2012 1:54 pm

Joules Verne: One of the most crucial facts to understand is that the ocean cools primarily through evaporation not radiation. If the ocean doesn’t cool by giving off longwave thermal radiation then it wont’ be warmed that way either. Therefore greenhouse gases that produce downwelling longwave radiation have little effect on the ocean.
What exactly does the downwelling longwave radiation do to the surface of the water?

Agile Aspect
January 9, 2012 2:13 pm

“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.”
The -18 C surface is at roughly 40km above the Earth. Your assumption that the temperature calculated using the Stefan-Boltzmann and the Sun’s flux at the TOA is the temperature of the surface you happen to standing on is false.

gbaikie
January 9, 2012 2:14 pm

Willis Eschenbach
“So give me Huffman’s claims in three sentences, just reading his stuff makes my head hurt. What has he said and why is it important?”
I believe Huffman is overstating his point.
But I think gravity does have an affect.
Gravity from point of view can have all the effect in this universe.
Energy is all about gravity, as in, no gravity basically no energy in this universe.
But in terms affects on greenhouse effect, I think has some effect.
But this effect isn’t quantified enough, as far as I have seen.
An obvious problem is what meant.
But keeping it simple, gravity affect how fast gas molecules would travel.
And gravity is buoyancy. No gravity- no mixing of gas/fluids.
More gravity more mixing.
So you can’t simply ignore gravity- not if you want
a complete theory.

nano pope
January 9, 2012 2:19 pm

So what is preventing the Earth from reaching 90C each day? Albedo, the shorter day, what exactly is cooling our planet?

John Billings
January 9, 2012 2:32 pm

Physics demands, requires and wants equilibrium. That means that the heated side of the moon, once in the shade, will expend its heat until it is the same temperature as the body around it ie. space, ie. about 3 degrees Kelvin. These laws are universal across the whole… universe. The moon has no internal source of heat to disrupt this.
The Earth is incomparable for a variety of reasons. It has internal heat, it has an atmosphere that acts a a restraint on both ends of the scale, and it has oceans that are a ‘dampener’ on heat – oceans take far longer to warm up and cool down than land does.
So I really don’t see where this well-meaning article is trying to take us. The moon and earth are fundamentally different. They cannot be compared. The moon is a cold rock that will forever be trying to radiate its excess sunny side heat into space according to the laws of physics so that everything is the same, with no impediment provided by atmosphere, oceans etc. End of story.

nano pope
January 9, 2012 2:35 pm

Oh, and Harry Dale Huffman isn’t the one claiming heating by atmospheric mass, that sounds like Nikolov Zeller. Harry emphatically states that is wrong (perpetual motion like) in the link below, and also sums up his argument fairly succinctly. You asked for three sentences though, so here’s three from that comment.
“Keeping it simple, the atmospheres must be like sponges, or empty bowls, with the same structure (hydrostatic lapse rate), filled with energy by the incident solar radiation to their capacity to hold that energy. In short, compressing the lower atmosphere doesn’t heat it, it merely allows it to retain more heat energy per volume than the lower-pressure levels above. All of the energy is provided by the Sun. The pressure distribution simply dictates vertical temperature distribution, which constitutes the structure, or energy-retaining form, of the “bowl” I likened the atmosphere to.”
http://theendofthemystery.blogspot.com.au/2010/11/venus-no-greenhouse-effect.html?showComment=1325125898177#c5729196180038388134

January 9, 2012 3:02 pm

The main difference between Earth and Moon is the core heat. The amount of thermal energy under the surface of the Earth (ie down to the core) is several orders of magnitude greater than that in the oceans, let alone the atmosphere. This has a stabilising effect on Earth’s temperatures, especially between day and night and between summer and winter. I have explained this in far more detail on this page of my site: http://climate-change-theory.com/explanation.html

Tim Folkerts
January 9, 2012 3:07 pm

Willis,
Not that you need my help, but I agree with pretty much 100% of what you have said here. I haven’t had time to read every word carefully in the thread, but everything I have read from you seems spot on.

Septic Matthew
January 9, 2012 3:07 pm

Willis: This, in spite of the fact that satellites can measure the ocean’s surface temperature from space by measuring the very longwave radiation from the ocean that this credulous gentleman says does not exist.
Thank you for the response.

gbaikie
January 9, 2012 3:09 pm

“nano pope says:
January 9, 2012 at 2:19 pm
So what is preventing the Earth from reaching 90C each day? Albedo, the shorter day, what exactly is cooling our planet?”
The sun has a max heat at your distance from it.
The moon at same distance can reach more than 90 C.
One way say it is moon has 1360 watts per square meter of sunlight.
And earth below our atmosphere has about 1000 watts per square meter.
Moon reaches a surface temperature of about 123 C
The earth reach a surface temperature of about 180 F [ 82 C]
Convert 123 and 82 into Kelvin:
396 K and 355 K
cube 396 times it by .0000000567
and get 1394 watts per square meter of sunlight.
cube 355 K times it by .0000000567
And get 900 watts per sq meter.
Earth get more than 900 watts, but air convection takes heat away from surface.
And if you wonder why I say earth can get to 82 C, I am talking about surface
temperature not air temperature in the shade- which how we measure temperature
on earth.
90 C or 363 K
is 987.4 watts per square. If stop most of the air convection losses, you should
be able to get 90 C on the earth surface at noon and a clear sky. higher elevation
should make this easier.
The other element is earth radiate heat gained into space.
So what stops us from getting 90 C air temperature?
Well that would generally mean the surface temperature was as hot or
hotter, and therefore the whole planet would radiating roughly 4 times as much energy
as it got from the sun. It can radiate the same energy as it received from the
sun.
So on small scale if limit conviction and conduction of heat during noon on clear day
you get 90 C. But it’s not noon everywhere nor is it daylight.
In other words the heat is spread out. And though it might possible to get 90 C
not possible on earth to get 120 C from sunlight regardless of how stop heat loss-
need more solar power per square meter [not have 300 or so watts blocked by
our atmosphere].

John Billings
January 9, 2012 3:16 pm

You can’t have a GHG-free atmosphere, not on Earth anyway. CO2 is a GHG and is a natural component of all that goes on, given off by plants in the dark. Likewise methane, naturally emitted by decomposition.

kuhnkat
January 9, 2012 3:20 pm

Sorry if I am repeating other’s points, I don’t have time to read them all.
1) thank you for demonstrating why it is STUPID to compute an average temperature of the earth by dividing the incoming energy over the whole surface. Can we throw out the ridiculous comparison between a bare ball and the earth as we know it now??
2) emissivity is also important. The earth has a much lower emissivity due to the atmosphere, about .7-.8 including the earth underneath it!!!
3) you totally ignored conductivity and thermal mass of the totally transparent atmosphere. Effect will be low admittedly, but will still be there. you also completely ignored the the thermal flows in the surface.
4) I believe vacuum is a great insulator don’t you?? On the moon we have large areas convered by dust and VACUUM!!! That’s right, there is no air to fill the spaces in the dust particles so we end up with a very nice INSULATOR compared to the ground down here!!
5) Sloppy.

David
January 9, 2012 3:24 pm

Willis Eschenbach says:
January 9, 2012 at 10:30 am
David says:
January 9, 2012 at 5:10 am
Willis says…
”As a result, while the greenhouse effect has done the heavy lifting to get the planet up to its current temperature,…”
How much of the GHE on earth is actually due to the oceans where the residence time of energy is far far longer then any GHG?
None, as I understand the greenhouse effect.
——————————————————————————————————–
Willis, please understand that of course I do not literally mean GHE, when I refer to the oceans; except in the context of thermal capacity. At its most basic only two things can effect the energy content of any system in a radiative balance. Either a change in the input, or a change in the “residence time” of some aspect of those energies within the system. (You may henceforth refer to this as David’s law. (-;) There is a fairly exact correlation between residence time of energy and thermal capacity. As the ocean thermal capacity is thosands of times that of the atmosphere, it appears logical that it is a more effective GHLiquid, then any GHG; your thoughts in this regard are welcome aand requested.
Also, although the average albedo of earth is higher then the moon’s, is it higher at laditudes where TSI is stongest?
Willis responds…”The earth albedo varies by location, by time of day, and by time of year, so it’s hard to answer your question. Where the TSI is the strongest (tropics) the albedo is part of the dynamic system keeping the earth from overheating, This means albedo also varies by temperature. It is higher where the temperature is highest, which in turn is where the TSI is greatest, so the answer to your question is generally yes, at least in the tropics.” W. ———————————————————-
At first glance this does not appear logical to me. In general the oceans are a blackbody, absorbing whatever radiation reaches the surface with little reflectivity. The NH has a great deal of landmass north of the tropics, as well as year round snow and ice in the artic, antarctic as well as tremendous winter albedo beyond year round ice. Additionally the incident angle of sunligh creates ever greater reflectance as one moves further from the tropics. A further factor is the poles appear to have a great deal of consistent.cloud cover as I look at the global map on the right side of WUWT home page. For these reasons I would have to see actual meauserment to accept your assertion here, as I suspect that the tropics. especially the southern tropics have the lowest albedo as well as the greatest TSI, especially in January when the earth is thee million miles closer to the sun and TSI is close to 100 W/m2 greater then in July. Your thought here are appeciated as well.

Alan D McIntire
January 9, 2012 3:26 pm

clivebest had the basic idea for feedbacks, but got them backwards. Current albedo is 0.3
so we get (1- 0.3)* 342 watts =239.4 watts. With a sun 70% as luminous as at present, and with a surface covered with oceans and no clouds, we would have received
0.7 (sun)* 1 (no clouds)* 324 watts, same as now. albedo wasn’t 0.45 back then, it was closer to zero.

January 10, 2012 1:40 am

Alan – that’s right. Albedo reduces for lower incident radiation . As the Earth’s ocean surfaces get heated, the Earth starts to “swet” – producing clouds which reduces the Albedo. The second assumed mechanism at work is that the H2O greenhouse effect increases at lower solar radiation levels ( by higher humidity in upper atmosphere). As more convection clouds form – this leads to more rain out from the atmosphere and a drop in upper atmosphere humidity.
The overall idea is that there is a balance point which is a play-off between the two effects Albedo and GHG. Water covered planets have an infinite sink of water available to maintain this balance over a wide range of solar radiative forcing levels. This has nothing to do with CO2 which is assumed to be absent in the atmosphere.

Jean Parisot
January 9, 2012 3:26 pm

Is the reference value of 0.11 a visible spatial average or full spectrum, spatial average?

gbaikie
January 9, 2012 3:28 pm

“GHG free atmosphere can warm the planet above it’s S-B temperature. Can’t happen. Violates the Laws of Thermodynamics. ”
Well, I am not convince any atmosphere, roughly with 1 atm with any quantity of greenhouse gases can warm above it’s S-B temperature. You are apparently assuming this could occur.
I am not.
And don’t think Huffman idea can do this either.
Or anything can do this.
Unless warming include huge asteroid strikes or huge, huge super volcano. Supernovas, and huge solar output, also might work.

Peter Spear
January 9, 2012 3:31 pm

I’d like to take the no GHG atmosphere thought experiment a bit further. Since the atmosphere cannot radiate, it can only exchange heat with the surface. Eventually the upper atmosphere would warm through conduction. The lapse rate would be near zero which would shut down any vertical convective heat transport since the warming/cooling due to adiabatic expansion would almost instantly kill any vertical motion. It would be the ultimate in super stable atmospheres. There would be no Hadley cells to transport heat from the equator to the poles. There could be some horizontal transport due to surface temperature differences (day – night and equator – pole) but I would guess that they would be very weak without any vertical motion to drive it. I imagine that the atmosphere, particularly up high would have a very uniform temperature over the entire globe.
Is it the green house gases that give us our weather? With GHG back into our thought experiment atmosphere, there is cooling of the upper atmosphere due to outgoing long wave radiation. This give rise to a vertical temperature gradient (lapse rate) which can drive convective transport. I believe convective transport is the source of almost all of our weather.
As a paraglider pilot who likes good thermals, I certainly appreciate green house gases!
Regards
Peter Spear

Svend Ferdinandsen
January 9, 2012 3:37 pm

Very interesting article with many good points.
Only problem i see is that the Earth albedo is for a great part clouds and with no GHG gasses you would not have clouds. So the albedo would be much smaller hence much more energy absorbed, and the SB average temperature would be more like -5 to 0C.

coldlynx
January 9, 2012 3:38 pm

There is a small difference that have big impact Willis. You write:
“But without GHGs, the only thing radiating is the surface, and the atmosphere is transparent. How can the surface possibly radiate more to space than it absorbs from the sun?”
You are right in that statement regarding the surface. But the ATMOSPHERE will be warmer than average temperature since it is heated more efficient than cooled by convection. Surface will radiate as much as before but with less temperature swing due to the heat capacity of the atmosphere. The difference is where to measure the temperature, surface or atmosphere.

Tim Folkerts
January 9, 2012 3:54 pm

Genghis says: January 9, 2012 at 12:04 pm: “Let’s consider two superconducting spheres … ”
Genghis, you have some good thoughts, but you also make a couple mistakes. With the two concentric shells (separated by a vacuum), you will find that the temperature will be the same for both shells. If the outer shell could transfer energy via radiation to the inner shell and warm it up, that would violate the 2nd law of thermodynamics.
Most of the radiation from the inside of the outer shell will not hit the inner sphere, but will indeed return to some other part of the outer shell itself. If you look more carefully, I am sure you will find both surfaces do indeed radiate 100 W/m^w and are at the same temperature.
(If you add an atmosphere, then the situation could change a bit, and the inner surface could indeed be warmer than the outer shell by an amount related to the lapse rate.)

George
January 9, 2012 4:06 pm

[I]Alexander Feht says:
January 9, 2012 at 11:43 am
P.S. Couple of people here propose a weird argument about “dead man under a blanket.” Be it known to them that plants are protected from freezing by blankets, though, last time I checked, plants had no internal sources of heat (unless you burn them). Thermal insulation is just that, an insulation — it keeps cold out even if there is no heater inside. Being a Siberian, I remember how much longer after sunset the warmer air is contained in a log cabin covered by deep snow (without any fire or people heating it yet), compared to any structure open to elements.[/I]
Some plants can insulate themselves with snow or “blankets”, but that is rare on the surface. They can come back from roots that are below the freeze line in the soil using it as a blanket. The mechanism really is about anti-freeze in the sap. Conifers have the best version of anti-freeze running in the plant family, which explains their hardiness. It is all about keeping ice crystals from damaging the cells.
Dead men don’t care and the embalming fluid might work as an anti-freeze though…

metamars
January 9, 2012 4:12 pm

Hardly any scientists believe that the earth’s core and mantle is producing any energy, other than a modest amount of fission. Unlike a sun, no nuclear fusion can occur. However, I am aware of a theory that does claim creation of energy in planetary bodies, above and beyond any nuclear fission contribution. This theory – subquantum kinetics – has made a number of verified predictions (according to it’s author) See http://etheric.com/LaViolette/Predict2.html. The extension of a mass-luminosity curve to planets, was discovered by Laviolette, and is consistent with his theory of “genic energy”. Not mainstream science, but consider the fact that a Greek physicists says that LaViolette deserves 2 Nobel prizes for his mass-luminosity discovery, and it makes you wonder.
Lance Endersbee has shown that a 21 year moving average of Sea Surface Temperature vs. CO2 at Mauna Loa has a correlation of .9959, while a 1 year moving average is poorly correlated. Meanwhile, Nir Shaviv has shown that solar activity considered as modulated by cloud cover (a function of solar magnetic effects) correlates very well with the short term change in SST (see http://www.sciencebits.com/calorimeter).
This huge gap in timescale between Shaviv’s results and Endersbee’s 21 year moving average results is a mystery, I believe. That’s where LaViolette’s theory may come in. Although I’m not a domain expert, I will say that I don’t expect the heating that Shaviv has studied to take decades to ‘average out’ via various thermal transport processes. However, in LaViolette’s theory, a new source of energy (which he calls ‘genic energy’) is being created WITHIN planetary and solar bodies. Such heat could conceivably take years to work it’s way to the surface of the planet.
Meanwhile, subquantum kinetics has, as it’s governing equations, reaction diffusion equations such that one or more of the ‘substrates’ is electric potential. I will speculatively wonder whether or not the sun’s magnetic effects not only modulate incident radiation on the Earth, but also modulate internal genic energy production within the earth, but via the electric potential substrate which is fundamental in subquantum mechanics.
Some more info on LaViolette’s theories here: http://blog.hasslberger.com/docs/PioneerEffect.pdf . He also has a book out on the subject, now in its 3rd edition. LaViolette has a bachelor’s degree in physics, but a Ph.D. in systems theory. His father was a Ph.D. physicist, who reviewed his work.
See also “Comparison of Subquantum Kinetics to Conventional Physics and Astronomy” at http://www.etheric.com/LaVioletteBooks/SQK-c.html.

January 9, 2012 4:30 pm

G’morning W.
Being a shift worker my responses can be sporadic.

I don’t understand how this idea is supposed to work. How will the atmosphere get warmer on average than the surface? Where will the energy come from to maintain it at a warmer temperature than the surface? Why will it not warm the surface, if it is warmer than the surface?

I’ll do my best to express my view. The last time I told my late dad “but you don’t understand” I got a very solid clip across the ear with the response “then explain yourself clearly” lol
There is no “extra” energy. But there is energy “locked away” by the atmosphere unable to radiate it away.
At our hypo planet with non-GHg atmo, the highest insolation is at the equator, tapering down towards the poles.
The air nearest the surface at this point will warm, rise and spread only to be replaced by cooler air from aloft. This process continues for 14 days of daylight.
Although the surface cools at night as your post details, the atmosphere cannot cool as quickly due to the temperature inversion phenom. The air nearest the surface will cool to be the same T as the surface but this will cause it to act like a barrier against the still warm air aloft because it is more dense and cannot rise away from the surface as it did when warming.
At the next dawn the process begins again, but this time we have air aloft that is already warmer than it was 28 days ago (due to not being able to radiate) and is suplemented by further warming for the next 14 days.
The key is temperature inversion. This slows down the conductive cooling rate of the atmosphere which (I think) will accumulate heat until it is at a temperature somewhat very close to that of the surface at noon, the warmest part of the day.
The AVERAGE temperature of the SURFACE will still be much the same as that of the planet with no atmosphere as S-B dictates, but the AVERAGE temperature of the ATMOSPHERE will be much higher.
Hence my statement…

“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.

I think commentor coldlynx is saying much the same thing at 11:46am and 3:38pm jan 9th
regards

Bill Illis
January 9, 2012 4:41 pm

One issue is the differing values for how warm or cold the Moon gets.
I’ve seen numbers saying the surface (really rocks and soil) reaches temperatures of 95C in the sunshine period and I’ve seen values of 120C.
These two different values make quite a difference in how I view the issue. If temperatures reach 120C then its temperature is hotter than it should be and its energy accumulation rate is not much different than the Earth. If it is 95C, then it is cooler than it should be and it cools off and warms up much faster than the Earth.
(Note the Earth would be very different if the rotation rate was 27 days times 24 hours. If the surface temperature accumulated energy at the same rate is does now for 13.5 days, the Earth’s surface temperature would approach 150C near the end of the 13.5 times 24 hours day and of course all the water would boil off and the Land surface would be baked so much that much gas would be liberated from it and we would be on our way to a mini-Venus affect).

R. Gates
January 9, 2012 4:46 pm

Robert Brown says:
January 9, 2012 at 12:00 pm
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.
Sorry, I’m reading and commenting as I go. This is consistent with observations in the very dry, windless desert. To quote the Wikipedia article on Deserts, in hot deserts the daytime peak temperature can be 45C and the minimum temperature right before dawn can be 0C or even cooler. That is dead on your estimate, allowing for the fact that even in the desert there is stratospheric water vapor acting as a GHG to block a little of the heat — along with CO_2 of course.
Your estimate is of enormous consequence, in other words. It suggests that there is almost no greenhouse effect active over hot, dry deserts. Not CO_2 GH. Not H_2O GH. Not CH4 GH. They radiatively cool almost as fast as the dark side of the moon!
______
The estimate of 4C an hour for cooling at the surface over a desert on earth is a pretty good one, but probably not realistic for the cooling seen at the lunar surface when the sun sets. Measurements during lunar eclipses indicate peak rates of about 30C an hour or around 100C during the full length of the eclipse (around 4.5 hours). Of course desert areas are not completely devoid of all water vapor in the atmosphere as the relative humidity is just so low, and you do have the other greenhouse gases which also help to keep the desert from cooling anywhere near the rate seen on the moon. If you left the nitrogen and oxygen, but took every greenhouse gas molecule out of the atmosphere above a desert on earth, you’d certainly get cooling at greater than 4C an hour when the sunlight went away. It might not reach the 30C an hour peak rate as seen on the moon, but, it would be higher than 4C an hour, such that the high to low temperature swing would also be greater.

David
January 9, 2012 4:49 pm

Willis, if you could please respond to the cogent thoughts expressed here. David says:
January 9, 2012 at 3:24 pm

jae
January 9, 2012 4:54 pm

Willis, for some reason you ignored most of my comment. Is it that bad??
“So give me Huffman’s claims in three sentences, just reading his stuff makes my head hurt. What has he said and why do you think it is important?”
Was handled wekk by nano Pope above.
To repeat the rest of my comment in slightly different, maybe more understandable?, words:
On this planet, the radiative equilibrium occurs at about 5 km above the surface, NOT AT THE SURFACE. Average T is -18 at 5 km, but it is higher at the surface. The atmosphere is not transparent on this planet or any other one, everyone agrees (that’s why your arguments about clear atmospheres are just “out there”). It can be AND IS hotter at the surface of Earth than the equilibrium radiation at 5 km above it dictates, by an amount determined by the lapse rate, which is determined ONLY by heat capacity and gravity.
We agree that that extra heat constitutes the “greenhouse effect.” What we don’t agree on is WHY it is warmer at the surface than at 5 km. I say Huffman and all the others with EMPIRICAL DATA from other planets with atmospheres (as well as some really simple observations here on Earth) trump the radiation cartoons (which, BTW, don’t accomodate your excellent explanation about why “average radiation” doesn’t mean much).

R. Gates
January 9, 2012 5:26 pm

Bill Illis says:
January 9, 2012 at 4:41 pm
One issue is the differing values for how warm or cold the Moon gets.
I’ve seen numbers saying the surface (really rocks and soil) reaches temperatures of 95C in the sunshine period and I’ve seen values of 120C.
These two different values make quite a difference in how I view the issue. If temperatures reach 120C then its temperature is hotter than it should be and its energy accumulation rate is not much different than the Earth. If it is 95C, then it is cooler than it should be and it cools off and warms up much faster than the Earth.
_______
Beside the distance from the sun, which is of course the same as the earth’s distance from the sun, it is the composition of the lunar rocks and soil and their location on the surface of the moon that are the prime factors determining how warm the surface gets in any region. Heat is conducted down through the lunar soil up to several meters, mainly through conduction. Temperatures on the Moon can go as high as 130C during the lunar day and down to around -170C at night. As experiments have shown that the surface of the moon cools off at up to 30C an hour during a lunar eclipse when the sunlit sides goes into earth’s shadow, and around a 100C drop over the course of a 4 to 5 hour eclipse, we see that the lunar soils are giving up LW rather rapidly in the absence of sunlight. If we know the range of the moon’s temperature is 130C down to -170C, and it can cool at 100C in 5 hours, we see that the moon’s first few meters of rocks and soil (the depth to which heat is conducted during the lunar day) cool pretty rapidly, and the surface devoid of sunlight on the moon reaches its coldest in less than 24 hours.

Bill Illis
January 9, 2012 6:23 pm

R. Gates says:
January 9, 2012 at 5:26 pm
—————————
This is why I think we need to move the discussion down to the Quantum level and in time. The Moon’s rocks are accumulating energy and then giving up energy when the Sun sets at specific rates. These are far, far, far lower than what we expect compared to the radiation coming in and in the absence of solar radiation. The same is true for the temperature of the atmosphere on Earth at 2 metres high, and especially at the tropopause. The numbers are in the range of 0.01 to 0.00001 joules per second versus the Sun’s energy at 1362 joules per second. It is hard to square.

gnomish
January 9, 2012 6:33 pm

“This, in spite of the fact that satellites can measure the ocean’s surface temperature from space by measuring the very longwave radiation from the ocean that this credulous gentleman says does not exist.”
argo does that, right? i don’t think it is possible for a satellite to do that.
get out your ir radiation colormometer and see if you can possibly read the surface of some water. i tried it. you can’t because the vapor layer blocks the transmission. so what you read is a layer of vapor – not any surface, ok?
dunno why you continue to conflate a layer of ATMOSPHERE with a PLANETARY SURFACE. atmosphere is not a surface. infrared radiation is not measuring temperature of any ocean. draw the distinction.
the ocean of water is not frozen. there is no sposedta about it. the layer of atmosphere is warmed by it as well. so the model must be wrong.

Mike Maxwell
January 9, 2012 6:42 pm

kadaka (KD Knoebel): Apropos of what orbit the Moon would need to be in in order to have a 24-hour day: It would be a geostationary orbit, which is to say about 22,200 miles above the equator (26,200 miles from the Earth’s center, some 42,000 km). You can see a derivation of this in the wikipedia article for “geostationary orbit.” I suppose the fact that the Moon is so much more massive than the man-made moons currently in geostationary orbit would alter this some–presumably making the geostationary orbit slightly higher.
But the tides we’d get with the Moon in that orbit would make any sea level rise from global warming look insignificant. The tidal “force” is proportional to the cube of the distance between the two bodies. Moving the Moon from its current 239,000 miles to 22,200 miles would increase the tidal force more than 1200 times. So I think I’ll go with increasing the Moon’s speed of rotation; it may be tidally locked now, but how long would it take to become tidally locked again after having been spun up? A long time, I’m thinking, by which time maybe we can find another asteroid to spin it up. (Guess we’d need to evacuate the Moon that time.)
BTW, the idea of altering planetary orbits to solve climate change problems (or was it terraforming?) comes up in one of Jules Verne’s books, if I’m not mistaken.

TimTheToolMan
January 9, 2012 6:42 pm

Willis makes the mistake…”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.”
If the difference in temperatures between the two objects is large then the conductive effect will also be large. And according to your graph the difference is around 270C. Enormous. Your assumption of the effect of a hypothetical non-GHG atmosphere is flawed on the basis you’re ignoring conduction.

Rosco
January 9, 2012 6:44 pm

The Moon receives in excess of 1200 W/sq m during the day and nothing at night. This radiation heats the surface to over 107 degrees and up to 123 degrees if you believe NASA
Given the Lunar day is some 27 Earth days the surface heats, probably quickly given how the Earth can heat over the course of a summer day, to the maximum temperature associated with the radiative flux of ~1200 W/sq m. During the long lunar night it is no wonder the temperature continues to plunge to low levels.
The tendency to reduce solar input based on geometry of spheres to an average value is nonsense !!
There is no demonstrated mechanism which validates reducing energy input to an “average” value – especially on a planetry scale – the planetry object is either illuminated and heating or not illuminated and cooling.
This rubbish of quartering the solar insolation and using this to calculate temperatures is simply wrong. All the observational evidence says so.
The Earth is fortunate – our atmosphere and oceans distribute thermal energy from equatorial and near latitudes to polar regions and the upper atmosphere.
Before the Earth has a chance to become “overcooked” because the insolation during the day is much more than 170 W/sq m on average – I estimate that at the equator it reaches a maximum of 4 times that and at 75 degrees latitude the maximum summer figure is about 170 W/sq m.
The thing that make Earth habitable are the period of our day (24 hours), the oceans and the fact that at the equator and near latitudes the surface is mostly water and our convecting atmosphere.

Rosco
January 9, 2012 6:54 pm

Surely all that matters is the relationship between the radiation from the Sun and the temperature the SB equation sayis associated with that radiation – averaging over the sphere means nothing except to tell you the average rate of energy loss to balance input.
The quarter of the insolation thingie is incorrect – I cannot understand why it persists when common sense and logic dictate there is no demonstrated mechanism how a sphere illuminated on one side and approximated by a disk can reduce the radiative flux from a distant star – this is like saying that I can reduce the radiation from my heater by keeping my back turned – which is obvious nonsense as I have a overheated front and cold kidneys.

izen
January 9, 2012 6:57 pm

Will says:
“The true surface of the Earth is exactly the same as it’s S-B temperature, -18º C. Also known as the effective emission height. ”
And it is BELOW that ‘true’ surface that the GHG effect creates a thermal gradient that results in the solid surface of the planet that most of us reside on being warmer than the effectived emission height.
On average… -grin-

gbaikie
January 9, 2012 7:15 pm

“The earth is well above the S-B temperature. You get your own opinions, but not your own facts. ”
If Earth had a atmosphere as thin or 1/10 the atmosphere as Mars, would you still chose to measure the Earth temperature as air temperature and in the shade?
What is the planetary standard for measuring S-B temperature?

Anything is possible
January 9, 2012 7:43 pm

Willis : Just a heads-up, but it would appear that NASA’s page on the Lunar Thermal Environment has been updated (and by up-dated I mean completely re-written) since last Friday.
It now gives the average temperature at the Lunar Equator of 206K (-67C) which strikes me as being somewhat at odds with your quoted average planetary temperature of -77C.
http://www.diviner.ucla.edu/science.shtml
A read through of a the Unified Climate Theory thread on Tallbloke’s blog would indicate that this change was made partially at the prompting of a certain scientist with the initials “NN”
We live in interesting times…….. (:-

jae
January 9, 2012 7:56 pm

Willis:
OMG: YOU SAID THIS:
What I and others have been consistently calling the “S-B temperature” in this thread is the temperature the planet would have if it were an airless blackbody. It is the temperature calculated from the S-B equation for the amount of solar energy hitting the planet.””
WOW. Please explain how this relates to the real Planet Earth, sir! I am very confused about this statement. We do NOT have an “airless body!” WTF ARE YOU SAYING, MAN?

Rosco
January 9, 2012 8:16 pm

Surely the “day” side of the Moon is radiating way more than 304 W/sq m – up to almost equal to the solar constant whilst the “dark” side is radiating way less – say even as low as a few watts/sq m if NASA is correct for the minimum temperatures.
These would be the absolute maximum and minimum and there would be variation over the whole sphere.

January 9, 2012 8:25 pm

It is the same thing coldlynx said, with the same problem. You are claiming that a surface can warm an atmosphere to a temperature warmer than the surface. To do that, you’d have to have heat flowing from the cooler object (the surface) to the warmer object (the atmosphere).

I’m sorry I didn’t make myself clear.
I am claiming the equator can warm the atmosphere to a level higher than the higher lattitudes hence the atmosphere will have a higher average temperature than the average temperature of the surface.
The warmest “object” is the equator. Lets forget about averages for a moment.
It is the equator which warms the atmosphere (the most) via conduction. And because the atmosphere is a gas, it rises and spreads when warmed via conduction. However, the reverse, i.e. cooling via conduction, cannot happen as quickly, or as efficiently if you will, due to temperature inversion.
I do not claim the atmosphere will ever get warmer than the surface at the equator at noon, but the average temperature of the (whole) atmosphere will be warmer than the average temperature of the (whole) surface.
Why would the atmosphere…say 100mtrs altitude at the poles… be warmer than the surface at the poles? Because temperature inversion will not allow the atmosphere to cool down to the level of the surface.
The energy comes from the very warm equator via conduction. Is distributed globally via thermals and convection and conduction but it cannot cool as efficiently without radiation, hence the build up.
regards

Rosco
January 9, 2012 8:28 pm

I simply must disagree with this “But a transparent atmosphere could never raise the moon’s temperature above the S-B blackbody temperature of half a degree Celsius.”
Clearly the Moon gets much hotter than half a degree celsius so I find the reference to blackbody temperatures misleading. The radiation from the Sun at ~1367 W/sq m hits half of the sphere of the moon thus the blackbody temperature of this part is ~ 381 K whilst illuminated. As the Moon spins the radiation levels drop very low on the dark side – I’ll say again I see no reason to even consider an average – it is basically meaningless and a tool of the AGW to use to justify their theories.
This clearly demonstrates that probably the most significant feature of the Earth with respect to habitability is the period of rotation followed by the amazing properties of water followed by a freely convecting atmosphere.

Tim Folkerts
January 9, 2012 9:06 pm

Willis,
Here is an interesting thought experiment. Set a large rock out on a sunny day on the moon (or lifeless earth-like object). Once it reaches ~ 100 C, place the rock into a very well insulated container. By reducing convection and conduction and radiation, you could in principle keep that rock very close to 100 C all thru the night. By repeating this process, you could in principle heat an arbitrarily large amount to rock up toward the MAXIMUM daily temperature. As long as the RADIATING SURFACE is at the S-B effective temperature, other parts could be warmed up to a level approaching the MAX temperature with clever insulation.
In a similar way, in principle it could be possible to heat the IR-transparent atmosphere up to a temperature approaching the MAXIMUM surface temperature.
* heat some air by putting it into thermal contact with the hottest part of the ground
* move the hottest air so it is out of thermal contact with the ground
* repeat.
So I can sort of see the argument some are making. It could be possible to get the whole bottom layer of the atmosphere to ~ the maximum surface temperature. (I do think the lapse rate would keep the whole atmosphere from getting this warm
**********************************************
In practice I don’t think this would work without some sort of “compartments” in the atmosphere. The actual atmosphere would warm and rise in the “hot afternoon” areas (but cool as it rose). This would tend to set up a circulation with hot air rising, spreading out at high altitudes, and heading toward the night side, where the air would fall, warming the cool side. The cool air from the night side would “get sucked back” toward the hot side to replace the rising warm air. Only if you could “trap” the hot air in some compartment above the ground (out of thermal contact with the ground as well) (akin to putting the rocks in the well-insulated containers) would this even start to work effectively (at least in my opinion).

Dave
January 9, 2012 9:10 pm

” So in an equilibrium situation like the moon, where the amount of emitted radiation is fixed, temperature swings always lower the average surface temperature.”
Hi Willis,
Seems like a mistake here before you’ve even got started. The moon has thermal mass, so incoming radiation and outgoing radiation only balance in the longer term. Temperature variation is a short-term effect, You can only assume the balance when working in the long-term, so to do so whilst working in the short-term invalidates the analysis.
Regards
Dave

Rosco
January 9, 2012 9:16 pm

I hate to bring up argument four from Radiating the Ocean but I cannot agree with the argument :-
“In addition there are losses of sensible heat (~ 30 w/m2) and evaporative losses (~ 70 w/m2). That’s a total loss of 390 + 30 + 70 = 490 w/m2.
But the average solar input to the surface is only about 170 watts/square metre.
So if the DLR isn’t heating the ocean, with heat gains of only the solar 170 w/m2 and losses of 390 w/m2 … then why isn’t the ocean an ice-cube?”
As I see it the answer is simple – during the day with the Sun vertically overhead the insolation is probably 4 times 170 W/sq m – 1367 W/sq m solar constant (Trenberth) X 51 % heats the Earth’s surface (IPCC). The physics I was taught said the insolation could be calculated by multplying half the solar constant by the latitude of the point of interest at the equinox. So for where I live, 27 S, the maximum insolation in those circumstances would be in excess of 600 W/sq m.
Clearly this would fry us all – although we can get fairly warm here – if it weren’t for the the energy soaked up by evaporating water, a convecting atmosphere and the relatively short day length – ie 12 hours max baking followed by 12 hours cooling.
There seems to be supported by the solar panels I once foolishly bought. They are rated at 175 W per 1.3 sq m. This reduces to ~135 W/sq m which is a reasonable 25 odd % efficiency.
Accordingly I believe the role of the Sun has been downplayed to support AGW theory. Also I refuse to believe 99% of the atmosphere comprised of Nitrogen and Oxygen does not become heated and as such radiate IR and therefore rendering the amount of IR from CO2 negligible – negligible to my way of thinking is less than 1 % and CO2 is way less than that.

Rosco
January 9, 2012 9:31 pm

I think that the oceans are responsible for most of the radiation at night, they warm the air above the surface which begins to convect as the land has lost the “stored heat”. Thus a “land breeze” sets in drawing the cooler air to the ocean to be warmed and humidified and this warmed air helps slow heat loss and provides the radiative effect observed at night – explains why the seaside is always warmer than inland at night and why Palm Trees can grow in Scotland – I’ve seen ’em.
I still think trace gases with low specific heat properties cannot create a large radiative effect and the amount of energy is small compared to latent heat of water – just my opinion but AGW theory seems to be the CO2 tail wagging the water dog.
It’s all a cycle as someone once said.

DeWitt Payne
January 9, 2012 9:56 pm

Hi Willis,
Good article.
The surface temperature of some part of the moon can exceed 120 C (1368 W/m2 for a black body) if the emissivity of the surface for long wavelength IR is both less than 1 and less than the absorptivity for solar radiation. There are a number of substances known to have this property (see the table here: http://www.redrok.com/concept.htm ). Freshly galvanized metal plate, for example, has an absorptivity for solar radiation of 0.65 and an emissivity for thermal IR of 0.13. If we put a sheet of galvanized metal at the lunar equator, it would absorb 0.65 * 1368 = 889.2 W/m2. But to radiate that much energy, it would have to have a temperature of (889.2/(5.67E-7 * 0.13))^0.25 = 1805 K or 1532 C. Of course, that’s more than 1000 C above the melting point of zinc, but you see the point. There’s even a company, Almeco-TiNOX Solar ( http://www.almeco-tinox.com/en/products/solar_absorber/coating_technology ) that makes a coating that they claim has a solar absorptivity of 0.95 and a thermal emissivity of less than 0.04. Now that would get really hot!

Warren
January 9, 2012 10:09 pm

@ Rosco
The “Palm Trees” you see in Scotland are Cordyline australis, they grow in a wide range of climates in New Zealand, from snow level to sea level, this has been discussed previously in WUWT
I have photographs of them from my time in Scotland and Ireland, along with various Hebe spec. that have been grown from stock from New Zealand.
They are not a true “Palm tree”

CRISP
January 9, 2012 10:12 pm

“But a characteristic of the greenhouse radiation (downwelling longwave radiation, also called DLR)……”
The 2nd Law of Thermodynamics: You cannot tranfer heat from a cold body (upper atmosphere) to a hotter body (the earth surface) without doing work. This applies to absolute transfer, not to nett transfer, despite the bullshit being spouted by the alarmists. This is an iron-clad law. There is no getting around it. Any so-called radiative ‘down-welling’ is totally irrelevant to warming. The Greenhouse Theory is based on this nonsensical idea.
You must distinguish between Greenhouse Theory and atmospheric insulation. Two very different concepts.
They have had 100 years to prove the Greehouse Theory – and have utterly failed. Forget it guys. It is bogus. Move on.

January 9, 2012 10:42 pm

Willis
I disagree and here is why.
1. Even in that perfectly transparent atmosphere there is an atmosphere.
2. The temperature of the surface is about 60-90C during the day.
3. Atmospheric molecules would still physically impact the surface of the Earth.
4. The molecules would pick up that thermal energy and pass it on to other molecules.
5. Convection would heat the atmosphere
6. Due to the frequency of collision of molecules it would take time for the atmosphere to mechanically radiate its warmth back to the ground with the ground colder at night.
And thus without an IR at all you have been abel to average the temperature. To what?
The molecules are absorbing energy from a body radiating at 70-90 c and the molecules are incapable of emission in the IR so how do the get rid of their now excess mechanical energy?

izen
January 9, 2012 10:49 pm

@- CRISP says: January 9, 2012 at 10:12 pm
“The 2nd Law of Thermodynamics: You cannot tranfer heat from a cold body (upper atmosphere) to a hotter body (the earth surface) without doing work. This applies to absolute transfer, not to nett transfer, despite the bullshit being spouted by the alarmists. This is an iron-clad law.”
So does The 2nd Law of Thermodynamics: mean that you cannot tranfer heat from a cold body (a coat) to a hotter body (me) without doing work. ?
No point in wearing a coat on a cold morning then…..

coldlynx
January 9, 2012 10:57 pm

Willis You write
“… the surface can never warm the atmosphere to be warmer than the surface is. No matter what the difference in efficiency is, the surface can only warm the atmosphere up to the temperature of the surface. Beyond that it can’t go, you can’t make heat flow uphill. ”
Right. But that is not what I say. (Or try to…, sorry for my english). I say the average atmosphere temperature will be warmer than average surface temperature, and below maximum surface temperature. The “daily” temperature swing will pump up the temperature in the atmosphere to above average surface temperature and below maximum surface temperature.
Just because of how heat is transported. From warm to cold. And warm gases have less density than cold gases.

R. Gates
January 9, 2012 11:25 pm

For those who’d like to watch an actual NASA lecture given to potential future Astronauts headed to the moon, with lots of great detail about the thermal, geological, radiation, environment, I highly recommend:
http://www.lpi.usra.edu/lunar/moon101/mendell/

ferd berple
January 9, 2012 11:33 pm

Isn’t dividing solar output by 4 a form of averaging that will tend to distort the black-body calculations and result in too high a calculated temperature? Isn’t the radiation perpendicular to the sun 1368 W/m2, but as you approach the poles and terminator this drops off COS. Don’t you need to raise this to the 4th power and then average? Similarly, isn’t using a constant albedo also a form of averaging. Surely the moon’s surface is not homogenized. Both these factors would appear to increase the calculated BB temperature above what could be expected without averaging.

Dan in California
January 9, 2012 11:47 pm

Two points. First, Luna’s surface warms rapidly after dawn partially because the thermal conductivity of the regolith is very low. The effective surface depth is thin because it’s not rock or compacted; it has good vacuum insulation between the particles. I haven’t a clue how to quantify this, or whether it would significantly change the thought experiment results.
Second, I was around when the exterior coatings were chosen for the Space Station. That’s another example of a body at the same distance from the sun. The coatings were chosen to have absorption and emission characteristics to keep the structure at about 20C without active thermal control. Turns out that’s not terribly difficult.

ferd berple
January 10, 2012 12:07 am

Rosco says:
January 9, 2012 at 9:16 pm
Also I refuse to believe 99% of the atmosphere comprised of Nitrogen and Oxygen does not become heated and as such radiate IR
It does seem remarkable that the emissivity of N2/O2 would be 0.0000. That would seem imply that N2/O2 would never cool in space. Hardly seems possible.