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Discussion > The Moon and 255K

Well, I said I'd do it. Then I went a bit cold on the idea, surely that 255K thing is not used in any way by the consensus folks, nowadays? No point in arguing with an outdated meme. But over the weekend I found myself in the Science Museum in Paris. This one:

Naturally I chanced upon an exhibit of climate change. There beside the veeeerrry convincing radiation bit (a lamp shines on a thermometer in the open and on one in a closed insulated box under glass in CO2, which turns out to be hotter!) was the old 255K again. The Earth is supposed to be at 255K average and it is at 288K, and all of the difference is down to GHG. At least they were willing to share the responsibility with all the GHGs, not just CO2.

So I conclude the meme I thought irrelevant is still alive. still being quoted. It's wrong though. Let me explain why.

The 255K is derived from the total insolation received by the Earth averaged over the area of the Earth. The sun pumps out 1366 watts/sq m. That only hits one side, and it is represented by a disc of the same radius of the Earth. The surface area of the Earths is four times the area of that disc by elementary geometry. So say each square metre receives 341.5 watts. Stick it in the Stefan-Boltzmann equation with an albedo of 0.7 and you get 255K for the 'average temperature of the earth's surface as a black body with an albedo of 0.7'.

The 288K is derived from the various efforts to establlish an average global temperature by measurement. You have a lot of thermometers, you take max and min from them daily over a period of time, you interpolate for areas poorly covered, you weight, you adjust, you juggle, and you get an average global temperature of 15 degrees C. 288K. Seems reasonable enough, given a good methodology, and the various temperature series agree whether ground- or satellite-based.

Now, in comes the moon. You'd think that as it is the same distance from the sun as the Earth is, it would have the same temperature, except for the albedo difference. So it should be at 270K, for albedo 0.12. Except that the Diviner data show an average temperature at the Lunar equator of 206K. Which means the average temperature of the Moon over all latitudes must be somewhat less than this. It should be 270K, and it is less than 200K. What went wrong?

What went wrong firstly was our basic assumption that we could average the insolation figure by dividing it by the factor of the insolation disc vs the total surface area of the sphere. You can't do that, because the areas of the sphere receiving the full whack of sunlight radiate most of the heat. The areas in the dark quickly dump any retained heat from the surface rock until they reach a temperature at which the wattage of any radiation is very small indeed. The fourth power law of Stefan-Boltzmann bites hard. So we really are not getting insolation over a quarter of the area and radiating it over the whole sphere. You can't apply an arithmetical average. Secondly, we naively assumed that the rate of rotation of the planet was of no significance. It is. The slow rotation of the moon allows the dark areas to quickly reach that low radiation regime and sit in it for the best part of fourteen days. The temperatures go to extremes on the lit and unlit sides, and extremes here means extreme difference in the S-B radiation. If the planet were revolving quickly the average would tend towards the assumed figure, but it would take infinite rate of rotation to achieve the fabled 255K.

So, we should not be using 255K. But all is not lost, we can adjust our method to take the fourth power law into account, and the rate of rotation by assuming some reasonable value for heat retention in the surface and calculating heat flow. We will end up with a figure lower by some margin than 255K, and we will have left behind the idea that this can be expressed as solely a radiative problem.

The next question is what will we compare our new 'ought to be' figure with to reach some conclusion about the temperature rise which can be ascribed to greenhouse gases. Well, the 288K average global temperature, of course. That is a figure arrived at by averaging thermometers. It is in fact not a surface temperature. It is measured at 1.25m to 2m above the surface. Except for sea temperatures. It will never match a figure obtained by radiative analysis. They just are not the same thing at all. You can't take one from the other and end up with a figure for greenhouse warming. The approach just is not valid. The only thing you could do would be to compare the apparent temperature of the Earth measured by radiative means from space. But all that will tell you is that the heat radiated matches the insolation, once you have corrected for albedo and emissivity. It tells you nothing about the greenhouse.

Feb 4, 2013 at 1:06 PM | Registered Commenterrhoda

Yes, like the word 'greehouse' itself, the simple SB explanation causes more problems than it solves.

Feb 4, 2013 at 1:24 PM | Unregistered CommenterTheBigYinJames

Many thanks Rhoda for the explanation. I’ve never understood how people who claim that the essential facts of climate science are a simple question of physics can be happy treating a sphere as a disc, averaging temperatures above the ground together with temperatures taken under the sea, and using a figure for albedo that looks like a rough guess. You’ve given a precise form to my vague suspicions.
But it doesn’t answer the question: how could they do that and think they could get away with it? What’s the point of estimating watts per square metre to two decimal places when the initial assumptions are so cockeyed?
It sounds like something dreamed up by the wizards at the Unseen University on Discworld.
(The last time I was at the Palais de Découverte, they had an exhibit on space exporation promising that robots would soon be exploring Mars. It was already five years out of date then)

Feb 5, 2013 at 6:40 AM | Registered Commentergeoffchambers

The Diviner data show conclusively that the 255K average temperature calculation was in error. The mistake in the mathematics that led to this error (Holder's Inequality) had previously been highlighted by Nikolov & Zeller, and others.

My question is - how do "climate scientists" actually use this figure of 255K? Has it been a premise in radiation calculations in GCMs? As we now know that the figure is wrong by about 60K, does this invalidate all IPCC physics and modelling?

Feb 5, 2013 at 9:26 AM | Unregistered CommenterRoger Longstaff

GCMs by nature don't use 'overall' figures, since they model discrete points. I suspect the SB figure has been used as a shorthand explanation to bamboozle the merely interested.

Also note the SB figure is not 'wrong' as such, it's just not very descriptive of actual temperatures. We proved this in the recent modelling threads, that the SB temperature and the 4th root integrated temperatures (which is what we all consider to be a real everyday 'temperature' you can feel and which can affect climate) are not the same.

Feb 5, 2013 at 9:54 AM | Unregistered CommenterTheBigYinJames

Big Yin,

Sometime ago I asked the Met Office to explain the "radiation scheme" in their GCMs. I never got a definitive answer, but it seems to be modelled on "radiative forcings", applied to a baseline. My question related to not only the baseline (average surface temperature) being incorrectly calculated in order to match reality, but the entire radiation model being wrong (as it ignores Holder's Inequality).

It would be good if someone from the Met Office could supply an answer to this.

Feb 5, 2013 at 10:31 AM | Unregistered CommenterRoger Longstaff

On a purely pragmatic basis, if they used the wrong one, they're not going to tell you :) Perhaps this explains the sudden pre-Xmas downgrading of the warming prediction :)

Feb 5, 2013 at 10:43 AM | Unregistered CommenterTheBigYinJames

I think you are joking, but, on second thoughts........?

Please correct me if I am wrong, but we have established that the 255K figure is nonsense; analytically (N&Z), numerically (you, and others) and empirically (NASA's Diviner measurements). If, as you suggest, this figure was used simply to bamboozle the plebs with science then it matters not a jot. However, if it represents the mathematical physics that has been used for all that follows - including GCMs - then the whole subject is shot to hell, and has produced nothing of any value.

I think that I am just re-stating Rhoda's original point here. Is it correct?

Feb 5, 2013 at 11:30 AM | Unregistered CommenterRoger Longstaff

You could be right, but you need to not succumb to the temptation of the belief that Climate Science speaks with one voice - one explanation given by one person, with a specific educational simplicity - could be boll*x, but that doesn't invalidate the rest of it automatically.

It does give you the right to ask the rest of it if they have used the same boll*x, but in the real world you're not going to get an answer.

Feb 5, 2013 at 11:41 AM | Unregistered CommenterTheBigYinJames

Indeed they do not speak with one voice, the invalidity of comparing the S-B number with the thermometer global average is stated quite clearly on Science of Doom.

N&Z reputedly dismiss the relevance of rotation. I think they are wrong to do so.

The 255K relies on an albedo of 0.7 That could not happen without ice. Put ice in the 1366 watt stream, even at high latitudes in the absence of tilt, and you will get an atmosphere. Ditto for water. Then you have convection, and horizontal movement, and a probable tendency to equalize temps producing weather. All without any greenhouse. You will surely get cloud (or am I mistaken in the absence of GHE?). You get cloud, you change the albedo. You already have a complex system with non-linear processes. No GHE, no N&Z is required to get to this point. But there IS GHE, and the presence of a big heavy atmosphere even if non-radiative makes a difference too.

Incidentally, it looks like Earth without albedo, rock earth, should be at 270K anyway by the S-B method. So are we looking to justify 288 - 270? Or 288 minus the 190ish of the diviner moon?

Tentative conclusions: There is no way you can compare the Earth, wet, cloudy, icy, spinning, tilted, to a dry rock like the moon. It is just too complicated. You also cannot do an N&Z and pick out a few of those defining characteristics but not all and explain temperature in terms of those alone.

(Also, the common idea in astronomy of a sweet spot distance (or range) from a star for the evolution of life is nonsense too, absent the exact descripton of the planet in question.)

Feb 5, 2013 at 12:24 PM | Registered Commenterrhoda

I think the sweet spot is defined by the existence of liquid water, but as you note, this is dependent on surface temperature which is NOT just a simple function of distance from the sun. Life could quite easily exist on a borderlands area of a rotation locked planet as close as Mercury for instance, or in a vapoury greenhouse-heated planet farther away than Mars.

Feb 5, 2013 at 12:36 PM | Unregistered CommenterTheBigYinJames

What went wrong firstly was our basic assumption that we could average the insolation figure by dividing it by the factor of the insolation disc vs the total surface area of the sphere. You can't do that, because the areas of the sphere receiving the full whack of sunlight radiate most of the heat.
Thank you, rhoda. I was beginning to think I was a voice crying in the wilderness. The argument that "what the sun sees is a disk" is self-evidently fallacious. What you and I would see from space with our eyes is a disk but the sun is not looking at the earth that way and what it sees is half a globe with its warming effect decreasing towards the poles and varying throughout daylight hours.
Simply to look at everything in terms of average insolation or average radiation and, as you then go on to point out, without making allowance for the rotation makes no sense.

Feb 5, 2013 at 1:05 PM | Registered CommenterMike Jackson

If I am not mistaken, the 255K should emerge in models, and not be used, right?

Feb 5, 2013 at 1:10 PM | Registered Commentershub

What the sun sees is a disk is NOT fallacious. If I replaced the moon with a cardboard cutout, it would still be receiving the same total insolation (i.e. number of photons) as the spherical one. The fact that it's actually spherical just means the surface gets fewer of them per square meter and thus the temperature of the surface is lower than predicted by treating it as a disk. To the sun, it looks identical to a disk.

Feb 5, 2013 at 1:36 PM | Unregistered CommenterTheBigYinJames

"If I am not mistaken, the 255K should emerge in models, and not be used, right?"

Sorry Shub - I don't understand your question.

Feb 5, 2013 at 2:07 PM | Unregistered CommenterRoger Longstaff

"So are we looking to justify 288 - 270? Or 288 minus the 190ish of the diviner moon?"

A good question Rhoda. I would count the atmosphere and the oceans together, so the Earth and Moon should be the same (with the same insolation and composition) apart from rotation (and I agree with you that N&Z are wrong about rotation being irrelevant).

I would speculate that the "goldilocks zone" relies upon conditions (insolation and atmosphere) that allow water in all three phases on a planet. I would further speculate that this provides a negative feedback effect that has allowed life on Earth for a billion years. (But that's only for life, as we know it, Jim......) I have been impressed by the N&Z argument that this is controlled only by surface pressure and insolation (with their supporting empirical evidence) but I can not rationalise their explanation for albedo.

Feb 5, 2013 at 4:08 PM | Unregistered CommenterRoger Longstaff

With the danger of getting back to N&Z, I still can't see how a static pressure can cause a raised temperature. Yes, delta P creates delta T, that's how stars form. A static P doesn't maintain a static T though.

An analogy is pumping air into a football. Yes, the increase in pressure raises the temperature of the air inside the football, but leave it standing for a while that temperature escapes through radiation back to ambient. The increased now static pressure doesn't maintain a body heated above ambient.

Feb 5, 2013 at 4:20 PM | Unregistered CommenterTheBigYinJames

Well, the bit of rock in vertical insolation gets 100% of it, and heats so much, and heats the static 'air' so much. You can postulate a static column of air of decreasing temp merely because of the heat transfer from the surface. But the bit at the pole does not heat so much, it's air column is of a different temp profile. In between them you are going to get wind. And vertical movement, and there you go. It cannot remain static, and that is without rotation which would only tend to increase the chaos.

Feb 5, 2013 at 5:33 PM | Unregistered Commenterrhoda

When I said static I was meaning in the macro. Wind cannot account for even localised delta P which would cause a temperature change, remember the difference between a high pressure and low pressure weather event in the atmosphere is measured in the 990-1100 millibar region, so we're talking 1% fluctuations here, nothing that can account for 80K or whatever the difference is.

The point still stands that while compression can cause a temperature change at the time the compression happens, this heat leaks away to the ambient space over time, and pressure alone cannot keep the earth warm unless it was constantly being compressed tighter and tighter.

Feb 5, 2013 at 5:41 PM | Unregistered CommenterTheBigYinJames

I agree that we should not get immersed with N&Z, but their premise is that pressure directly controls the kinetic energy and temperature of the atmosphere, regardless of chemical composition. They infer this from the Ideal Gas Law and Charles' Law. Wether they are right or wrong in this they at least need to be taken seriously as they were the first (IIRC) to identify the IPCC mistake with Holder's Inequality.

But I suggest we stick to Rhoda's 255K question on this thread, and ask - is all IPCC physics and GCM modelling invalidated by the mistake?

Feb 5, 2013 at 5:48 PM | Unregistered CommenterRoger Longstaff

Pragmatist as ever, I say that you won't ever find out. There's more than one reason they don't release the code.

Feb 5, 2013 at 5:53 PM | Unregistered CommenterTheBigYinJames

We don't even need the code - just the documentation of the formulation of the "radiation scheme". As we paid for it I don't understand why we can't see it. Surely documentation exists?

Richard Betts, where are you?

Feb 5, 2013 at 6:37 PM | Unregistered CommenterRoger Longstaff

Well, to be fair, by the same token... the UK taxpayer may have paid for it, but does that mean they have to release it to the worldwide public domain? Why should Russia and China and the US get the results we paid for?

Feb 6, 2013 at 8:18 AM | Unregistered CommenterTheBigYinJames

A fair point, but........

Met Office modelling results are used to compile IPCC reports that spread the CAGW scare worldwide. The reports are used by the EU, and others, who set insane "carbon reduction targets" that are costing us billions and wrecking our economies. My point is that if all of this is based on flawed mathematical physics we all have a right to know.

I have long believed that GCMs have no predictive power at all. Indeed, the IPCC got it right for once when they wrote:

"In climate research and modelling, we should recognise that we are dealing
with a coupled non-linear chaotic system, and therefore that the
long-term prediction of future climate states is not possible.” IPCC
From the 3rd IPCC report, Section “The Climate System”, page 774"

The problem is that everybody seems to have forgotten this and we are all paying a terrible price. Although GCMs have never demonstrated any predictive capability, it is almost impossible to prove that they never will, so the nonsense continues unabated. If, however, a basic mistake in their radiation physics calculations could be identified, then the debate would be over once and for all.

I do not know if the Met Office models are using flawed physics, but as the potential problem is Holder's Inequality, they should be able to publish sufficient information to assure us that that at least their basic mathematical calculations are correct.

Feb 6, 2013 at 9:12 AM | Unregistered CommenterRoger Longstaff

I think you're being naive if you think pointing out a mistake in GCM assumptions would be the end of them, they would just tweak them until the same result was attained. Everyone involved in modelling* knows you start off with the answer you are looking for and adjust all the 'fudge factors' until the model gives that answer.

*I spent many years in the early 90s at a top research labs of a large telco, modelling various network configurations, DSL, fibre etc years before any of it hit the streets.

Feb 6, 2013 at 9:20 AM | Unregistered CommenterTheBigYinJames