A Matter of Some Gravity

Guest Post by Willis Eschenbach

A couple of apparently related theories have been making the rounds lately. One is by Nikolov and Zeller (N&Z), expounded here and replied to here on WUWT. The other is by Hans Jelbring, discussed at Tallblokes Talkshop. As I understand their theories, they say that the combination of gravity plus an atmosphere without greenhouse gases (GHGs) is capable of doing what the greenhouse effect does—raise the earth at least 30°C above what we might call the “theoretical Stefan-Boltzmann (S-B) temperature.”

So what is the S-B temperature, theoretical or otherwise?

A curious fact is that almost everything around us is continually radiating energy in the infrared frequencies. You, me, the trees, the ocean, clouds, ice, all the common stuff gives off infrared radiation. That’s how night-vision goggles work, they let you see in the infrared. Here’s another oddity. Ice, despite being brilliant white because it reflects slmost all visible light, absorbs infrared very well (absorptivity > 0.90). It turns out that most things absorb (and thus emit) infrared quite well, including the ocean, and plants (see Note 3 below). Because of this, the planet is often treated as a “blackbody” for IR, a perfect absorber and a perfect emitter of infrared radiation. The error introduced in that way is small for first-cut calculations.

The Stefan-Boltzmann equation specifies how much radiation is emitted at a given temperature. It states that the radiation increases much faster than the temperature. It turns out that radiation is proportional to absolute temperature to the fourth power. The equation, for those math inclined, is

Radiation = Emissivity times SBconstant times Temperature^4

where the Stefan-Boltzmann constant is a tiny number, 0.0000000567 (5.67E-8). For a blackbody, emissivity = 1.

This “fourth-power” dependence means that if you double the absolute temperature (measured in kelvins), you get sixteen (2^4) times the radiation (measured in watts per square metre, “W/m2”). We can also look at it the other way, that temperature varies as the fourth root of radiation. That means if we double the radiation, the temperature only goes up by about 20% (2^0.25)

Let me call the “theoretical S-B temperature” the temperature that an evenly heated stationary blackbody planet in outer space would have for a given level of incoming radiation in W/m2. It is “theoretical”, because a real, revolving airless planet getting heated by a sun  with the same average radiation will be cooler than that theoretical S-B temperature. We might imagine that there are thousands of mini-suns in a sphere around the planet, so the surface heating is perfectly even.

Figure 1. Planet lit by multiple suns. Image Source.

On average day and night over the planetary surface, the Earth receives about 240 W/m2 of energy from the sun. The theoretical S-B temperature for this amount of radiation (if it were evenly distributed) is about -18°C, well below freezing. But instead of being frozen, the planet is at about +14°C or so. That’s about thirty degrees above the theoretical S-B temperature. So why isn’t the planet a block of ice?

Let me take a short detour on the way to answering that question in order to introduce the concept of the “elevator speech” to those unfamiliar with the idea.

The “elevator speech” is simply a distillation of an idea down to its very basics. It is how I would explain my idea to you if I only had the length of an elevator ride to explain it. As such it has two extremely important functions:

1. It forces me to clarify my own ideas on whatever I’m discussing. I can’t get into handwaving and hyperbole, I can’t be unclear about what I’m claiming, if I only have a few sentences to work with.

2. It allows me to clearly communicate those ideas to others.

In recent discussions on the subject, I have been asking for that kind of “elevator speech” distillation of Jelbring’s or Nikolov’s ideas, so that a) I can see if whoever is explaining the theory really understands what they are saying and, if so, then b) so that I can gain an understanding of the ideas of Jelbring or Nikolov to see if I am missing something important.

Let me give you an example to show what I mean. Here’s an elevator speech about the greenhouse effect:

The poorly-named “greenhouse effect” works as follows:

• The surface of the earth emits energy in the form of thermal longwave radiation.

• Some of that energy is absorbed by greenhouse gases (GHGs) in the atmosphere.

• In turn, some of that absorbed energy is radiated by the atmosphere back to the surface.

• As a result of absorbing that energy from the atmosphere, the surface is warmer than it would be in the absence of the GHGs.

 OK, that’s my elevator speech about why the Earth is not a block of ice. Note that it is not just saying what is happening. It is saying how it is happening as well.

I have asked, over and over, on various threads, for people who understand either the N&Z theory or the Jelbring theory, to give me the equivalent elevator speech regarding either or both of those theories. I have gotten nothing scientific so far. Oh, there’s the usual handwaving, vague claims of things like ‘the extra heat at the surface, is just borrowed by the work due to gravity, from the higher up regions of the atmosphere‘ with no mechanism for the “borrowing”, that kind of empty statement. But nothing with any meat, nothing with any substance, nothing with any explanatory value or scientific content.

So to begin with, let me renew my call for the elevator speech on either theory. Both of them make my head hurt, I can’t really follow their vague descriptions. So … is anyone who understands either theory willing to step forward and explain it in four or five sentences?

But that’s not really why I’m writing this. I’m writing this because of the claims of the promoters of the two theories. They say that somehow a combination of gravity and a transparent, GHG-free atmosphere can conspire to push the temperature of a planet well above the theoretical S-B temperature, to a condition similar to that of the Earth.

I hold that with a transparent GHG-free atmosphere, neither the hypothetical “N&Z effect” nor the “Jelbring effect” can possibly raise the planetary temperature above the theoretical S-B temperature. But I also make a much more general claim. I hold it can be proven that there is no possible mechanism involving gravity and the atmosphere that can raise the temperature of a planet with a transparent GHG-free atmosphere above the theoretical S-B temperature.

The proof is by contradiction. This is a proof where you assume that the theorem is right, and then show that if it is right it leads to an impossible situation, so it cannot possibly be right.

So let us assume that we have the airless perfectly evenly heated blackbody planet that I spoke of above, evenly surrounded by a sphere of mini-suns. The temperature of this theoretical planet is, of course, the theoretical S-B temperature.

Now suppose we add an atmosphere to the planet, a transparent GHG-free atmosphere. If the theories of N&K and Jelbring are correct, the temperature of the planet will rise.

But when the temperature of a perfect blackbody planet rises … the surface radiation of that planet must rise as well.

And because the atmosphere is transparent, this means that the planet is radiating to space more energy than it receives. This is an obvious violation of conservation of energy, so any theories proposing such a warming must be incorrect.

Q.E.D.

Now, I’m happy for folks to comment on this proof, or to give us their elevator speech about the Jelbring or the N&Z hypothesis. I’m not happy to be abused for my supposed stupidity, nor attacked for my views, nor pilloried for claimed errors of commission and omission. People are already way too passionate about this stuff. Roger Tattersall, the author of the blog “Tallbloke’s Talkshop”, has banned Joel Shore for saying that the N&Z hypothesis violates conservation of energy. Roger’s exact words to Joel were:

… you’re not posting here unless and until you apologise to Nikolov and Zeller for spreading misinformation about conservation of energy in their theory all over the blogosphere and failing to correct it.

Now, I have done the very same thing that Joel did. I’ve said around the web that the N&Z theory violates conservation of energy. So I went to the Talkshop and asked, even implored, Roger not to do such a foolish and anti-scientific thing as banning someone for their scientific views. Since I hold the same views and I committed the same thought-crimes, it was more than theoretical to me. Roger has remained obdurate, however, so I am no longer able to post there in good conscience. Roger Tallbloke has been a gentleman throughout, as is his style, and I hated to leave. But I did what Joel did, I too said N&Z violated conservation of energy, so in solidarity and fairness I’m not posting at the Talkshop anymore.

And more to the point, even if I hadn’t done what Joel did, my practice is to never post at or even visit sites like RealClimate, Tamino’s, and now Tallbloke’s Talkshop, places that ban and censor scientific views. I don’t want to be responsible for their page views counter to go up by even one. Banning and censorship are anathema to me, and I protest them in the only way I can. I leave them behind to discuss their ideas in their now cleansed, peaceful, sanitized, and intellectually sterile echo chamber, free from those pesky contrary views … and I invite others to vote with their feet as well.

But I digress, my point is that passions are running high on this topic, so let’s see if we can keep the discussion at least relatively chill …

TO CONCLUDE: I’m interested in people who can either show that my proof is wrong, or who will give us your elevator speech about the science underlying either N&K or Jelbring’s theory. No new theories need apply, we have enough for this post. And no long complicated explanations, please. I have boiled the greenhouse effect down to four sentences. See if you can match that regarding the N&K or the Jelbring effect.

w.

NOTE 1: Here’s the thing about a planet with a transparent atmosphere. There is only one object that can radiate to space, the surface. As a result, it is constrained to emit the exact amount of radiation it absorbs. So there are no gravity/atmospheric phenomena that can change that. It cannot emit more or less than what it absorbs while staying at the same temperature, conservation of energy ensures that. This means that while the temperature can be lower than the theoretical S-B temperature, as is the case with the moon, it cannot be more than the theoretical S-B temperature. To do that it would have to radiate more than it is receiving, and that breaks the conservation of energy.

Once you have GHGs in the atmosphere, of course, some of the surface radiation can get absorbed in the atmosphere. In that case, the surface radiation is no longer constrained, and the surface is free to take up a higher temperature while the system as a whole emits the same amount of radiation to space that it absorbs.

NOTE 2: An atmosphere, even a GHG-free atmosphere, can reduce the cooling due to uneven insolation. The hottest possible average temperature for a given average level of radiation (W/m2) occurs when the heating is uniform in both time and space. If the total surface radiation remains the same (as it must with a transparent atmosphere), any variations in temperature from that uniform state will lower the average temperature. Variations include day/night temperature differences, and equator/polar differences. Since any atmosphere can reduce the size of e.g. day/night temperature swings, even a transparent GHG-free atmosphere will reduce the amount of cooling caused by the temperature swings. See here for further discussion.

But what such an atmosphere cannot do is raise the temperature beyond the theoretical maximum average temperature for that given level of incoming radiation. That’s against the law … of conservation of energy.

NOTE 3: My bible for many things climatish, including the emissivity (which is equal to the absorptivity) of common substances, is Geiger’s The Climate Near The Ground, first published sometime around the fifties when people still measured things instead of modeling them. He gives the following figures for IR emissivity at 9 to 12 microns:

Water, 0.96

Fresh snow, 0.99

Dry sand, 0.95

Wet sand, 0.96

Forest, deciduous, 0.95

Forest, conifer, 0.97

Leaves Corn, Beans, 0.94

and so on down to things like:

Mouse fur, 0.94

Glass, 0.94

You can see why the error from considering the earth as a blackbody in the IR is quite small.

I must admit, though, that I do greatly enjoy the idea of some boffin at midnight in his laboratory measuring the emissivity of common substances when he hears the snap of the mousetrap he set earlier, and he thinks, hmmm …

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January 16, 2012 10:11 am

“Same energy applied to higher mass results in a smaller temperature increase”
And if the higher mass is pressurised as compared to the lower mass ?

Bart
January 16, 2012 10:13 am

Willis Eschenbach says:
January 16, 2012 at 1:22 am
“Am I alone in finding your assumption patronizing, sexist, condescending, and unworthy of Martin A?”
No, you aren’t. But, the puritanical streak runs deep in America, and resurfaces periodically to leech the fun out of everything.
Paul Dennis says:
January 16, 2012 at 1:22 am
“The answer is that statement (1) is right and statement (2) wrong. Statement (2) is wrong because the conclusion in statement 2(a) is wrong. “
The answer is that statement (1) is wrong because it is impossible for a spherical geometry. You are claiming there is no lapse rate. I do not think you will find many people who agree.
“The seemingly paradoxical truth is that the average kinetic energy of all molecules does not decrease with height even though the kinetic energy of each individual molecule does decrease with height”
Cannot at the same rate and satisfy the fact that there is no source and no sink in the atmosphere (Laplacian = 0). You must take the geometry into account.
OzWizard says:
January 16, 2012 at 2:12 am
“You do agree that paradoxes cannot exist in REALITY, don’t you?”
There is no paradox. The twin who accelerated away slowed his rate of time relative to the twin he accelerated away from. When he decelerated to get back, he matched his rate of time back to the twin on the ground, but by then, his twin was already older. That’s all there is to it. This is no conjecture. The experimental confirmation of the effect is mountainous.
Stephen Wilde says:
January 16, 2012 at 3:02 am
“That reversal cannot take place while the atmosphere remains in place so there is a continuing conductive exchange between atmosphere and space and, finally, I think I can say that you have been wrong all along.”
It is a dynamic equilibrium. And, it has to be taken account of in the “free body” decomposition. Willis refuses to recognize that, so he is indeed wrong. The only question is, how significantly wrong is he?
Joules Verne says:
January 16, 2012 at 7:02 am
“No, Stephen. Willis happens to be right at least in the isolated case of saying there is no energy entering or leaving a transparent atmosphere when the temperature at the lowest level of the atmosphere is the same temperature as the surface.”
No, Joules, Stephen is right here. There is an interface, and a balance which exists as long as the surface and atmosphere is in contact. Take away the atmosphere, and there must be a reaction.
“It cannot raise the surface temperature above the S-B temperature.”
You are once again repeating the mistake of reversing Kirchoff’s law. SB does not limit temperature, it limits radiation.

Bart
January 16, 2012 10:18 am

steveta_uk says:
January 16, 2012 at 9:10 am
Sorry, again you’ve either got your dimensions wrong, and don’t mean “energy”, or else this is simply inverted. Same energy applied to higher mass results in a smaller temperature increase.”
Try: The denser mass should gain a higher temperature for the same energy flux input. Eventually, the flux balances, but not before it has left behind a deeper deposit of energy.

don penman
January 16, 2012 10:26 am

steveta_uk
It is not the same energy being given to the denser atmosphere and the less denser atmosphere as you say but it is a constant flow of energy that is being given to both by the Sun or the surface,in the end the denser atmosphere will have more energy than the less dense atmosphere.

January 16, 2012 10:45 am

Right Willis, you agree that there is a dynamic equilibrium between surface and atmosphere so that there is a continuing conductive energy exchange between surface and atmosphere at equilibrium.
Previously I think you said that once equilibrium was reached all such exchanges would stop.
Now lets take the next step.
The atmosphere takes energy from the surface via conduction to its maximum capability. What N & Z seem to be suggesting is that such capability is set by pressure and density so as to allow greater collisional activity at greater densities.
Once the atmosphere has taken what it can then that energy is removed from the in/out radiative flux and has to be made up via a cooler surface radiating less out until the S – B balance is restored.
But meanwhile the energy in the conductive exchange between surface and atmosphere hasn’t gone away. All that energy is still present in the air above the surface and for there to be a dynamic equilibrium the surface has to give up as much conductive energy to the air as it receives from the air.
So the surface has to be warm enough to supply BOTH the outgoing radiation to satisfy S – B as regards the radiative energy exchange AND the upward conductive energy to balance what is coming back down from the air.
That sounds like it requires a higher surface temperature than one would expect from the S – B equations.
Or not ? Over to you.

January 16, 2012 10:50 am

Whoops, Bart has reformatted his post and now I see that it is he who supports the dynamic equilibrium point rather than you, Willis.
Anyhow despite that see if you can still follow my logic.

Bart
January 16, 2012 10:50 am

Bart says:
January 16, 2012 at 10:18 am
steveta_uk says:
January 16, 2012 at 9:10 am
“Try: The denser mass should gain a higher temperature for the same energy flux input. Eventually, the flux balances, but not before it has left behind a deeper deposit of energy.”
Let’s try again: The denser mass should gain more heat energy for the same energy flux input. Eventually, the flux balances, but not before it has left behind a deeper deposit of energy. This creates a different boundary condition at the surface/atmosphere interface than would otherwise be the case.
I haven’t read the full exchange, so I’m not taking sides. Merely trying to facilitate the discussion.

Martin A
January 16, 2012 10:52 am

Bart says:
January 16, 2012 at 10:13 am
Willis Eschenbach says:
January 16, 2012 at 1:22 am
“Am I alone in finding your assumption patronizing, sexist, condescending, and unworthy of Martin A?”
No, you aren’t. But, the puritanical streak runs deep in America, and resurfaces periodically to leech the fun out of everything.
============================
It is the standard response of a bully when challenged on their bullying to reply:
– It was just a joke.
– The person raised no objection, so what is it to you?
– *If* what I said caused offense, then *you have my apologies*
A real apology is along the lines of “I am sorry; I should not have said that.”

Bart
January 16, 2012 11:02 am

Well, I’ve got to get back to making a living. It is distressing that one camp never wants to take into account the boundary conditions. In every solution to PDEs, boundary conditions are key. It amazes me that so few get it. You really have to wonder what they are teaching in the schools these days.
But, it is futile for me to keep harping on it. If I haven’t swayed any minds yet, I’m not going to. Finis.

shawnhet
January 16, 2012 11:03 am

Willis Eschenbach says:
January 15, 2012 at 10:55 pm
“Shawn, thanks for your thoughts. As you say, despite the fact that I said what I was going to snip, and that I was justified in the snipping, there’s no way to avoid the appearance of censorship.
And since that is one of the several points that I was trying to make by snipping off-topic posts, you are the winner. For your prize, you get to go explain that to Tallbloke.”
Yes, I totally agree. I did not twig that this was part of a larger strategy though.
“Can’t make folks follow requests, that’s for sure. I requested elevator speeches on the Jelbring or N&Z hypotheses, or falsifications of my proof. I tried to snip posts that were off-topic or didn’t answer my request. All people wanted to do was something else, anything else. It’s like herding cats. No, like herding feral cats. No amount of snippage would help. But I suspected that going in. I figured to snip the worst ones pour encourage les autres. But the number of worst ones was overwhelming.”
Personally, I think that the reason that no one can provide simple explanations of how this sort of effect works is that no one has such an explanation(Sorry to be blunt folks, but there it is). From a scientific POV, that’s really the end of it. Maybe at some point, someone will be able to explain this supposed effect, at which point, we can revisit the idea but until then, there’s not much that can be done.
“I figure if I can establish a tradition of judging people’s understanding of a topic by whether they can explain the theory in a clear, concise manner … then who cares if I’m popular? I’m tired of vague handwaving. Boil it down to the elevator speech, then boil it again to half that size, and give us the simplest, clearest explanation possible.”
I agree here completely. this is always a good goal to strive for, but especially, when communicating on the internet where everyone has a different background and breadth of knowledge. I have a hard time not chuckling when someone says I could explain something, but because you are too rude/have already made up your mind/are a member of a vast conspiracy.
Cheers, 🙂

Jim Petrie
January 16, 2012 11:03 am

The entire warmist case depends on positive feedback – on some mysterious tipping point which will trigger a climate catastrophe.
But the immediate feedback is negative – a small rise in temperature gives a big rise in radiative heat loss.
Increasing CO2 increases the rate of plant growth, so CO2 levels will eventually stabilize at a higher level than today – but at a level which is still entirely safe.
Increased water vapor increases clouds. This by and large will have a cooling effect.
Positive feedback is a dangerous and expensive myth

shawnhet
January 16, 2012 11:13 am

Bart says:
January 16, 2012 at 12:10 am
“”The main one being: how can the surface of a planet such as Earth emit more energy than the planet as a whole emits to space?”
And, when did you stop beating your wife?
You have to show it is necessary that more energy be emitted by the planet for non-GHG heating to work before discounting the idea on that basis. SB does not demonstrate it. SB is not a fundamental law – it has loopholes. And, the widespread neglect of these loopholes is just plain sloppy.”
Actually, it is fine with me you want to argue that SB does not apply (for whatever reason). My question is based on what we can observe (ie that the surface emits on average ~390W/m2 while the planet as a whole emits ~240W/m2). You can either dispute that observation or try and explain it. SB on its own appears to explain the radiation of the planet as a whole, but not the radiation at the surface. The currently constituted GHE explains both.
If you have another theory, that’s fine, but I can’t read your mind. I don’t understand how you think it would work at all.
Cheers, 🙂

January 16, 2012 11:20 am

Paul Dennis says:
January 14, 2012 at 11:27 pm
Your redcutio ad absurbum argument is elegant and shows conclusively that in there can be no gravitational effect. End of as far as I’m concerned.

Agreed as I said above.
What is an interesting physics question is in your model what will the temperature distribution in the non-GHG atmosphere? I think it might be constant throughout with no convection and therefore no adiabatic lapse rate. The atmosphere in this model is effectively a gas column in an adiabatically bound state, heat conduction throughout the column will lead to an equilibrium of constant temperature distribution. I think Roy Spencer may have indicated this to be the case as well in his earlier comment.
I disagree because the system will be unstable to any perturbation so you’ll end up with the dry lapse rate.
Thank you for an elegant disproof of gravitational theorems.
Agreed.

January 16, 2012 11:22 am

Well, Willis, that was a bit over the top given that I’ve already explained that I made an error in attribution due to a change in the formatting of Bart’s post.
I think that your outburst shows a very nasty underlying attitude to the extent that I don’t want to engage with you any further.

JimOfCP
January 16, 2012 11:27 am

Stephen Wilde says:
January 16, 2012 at 8:51 am
“You now need to irradiate with an energy source such as the sun. The denser mass should gain a higher temperature for the same energy input.The greater density and more collisions allows that mass to hold on to more of the solar irradiation in kinetic form hence the higher temperature.”
First, unless the wall of the compressor is at absolute zero, it is radiating in the infrared.
Second, you have to specify the gas. Nitrogen and oxygen are not dipolar and therefore do not interact with infrared radiation. CO2 and H2O are polar and do interact.
So assuming the air inside and outside the compressor wall contain the same % of CO2, the air inside and outside will have the same temperature. Otherwise, the inside would be perpetually hotter than the outside and you could get work done for free, a clear violation of thermodynamics.
http://www.elmhurst.edu/~chm/vchembook/globalwarmA5.html

January 16, 2012 11:31 am

“First, unless the wall of the compressor is at absolute zero, it is radiating in the infrared.”
Have you never heard of conduction ?
This thread is a total waste of my time.

Joel Shore
January 16, 2012 11:33 am

I said:

I.e., there are contributions due to both the fact that the gravitational potential energy decreases with height and the fact that the parcel of gas does work on the gas around it by expanding.

Of course, that sentence should have said that the gravitational potential energy INCREASES with height.

shawnhet
January 16, 2012 11:38 am

gbaikie says:
January 16, 2012 at 12:37 am
““The main one being: how can the surface of a planet such as Earth emit more energy than the planet as a whole emits to space?”
So since earth is colder it will need to emit more photons to equal the energy.
Every grain of sand is emitting photons. Does every atom in rock emit photons?
I would guess, since there more joules of energy on earth then is delivered by the Sun in a second [or nanosecond] and any thing isn’t mostly facing the sky and gases are suppose absorb and emit some of these photons going towards space and things are warming and cooling, that is how.”
I’m sorry to say that I do not understand your post. My question was referring to the fact that the Earth as a whole emits ~240W/m2 while the surface emits~390W/m2. From the POV of my question, it doesn’t matter whether the 390w/m2 comes from the sun or a giant bonfire or gravitational collapse of the planet or microscopic amounts of pressure induced nuclear fusion or whatever. In the case of a Nitrogen atmosphere if the surface emits 390W/m2, then the planet as a whole should based on current theory emit 390W/m2. Since this is not what we observe in the real world, we can either explain what is different about the actual atmosphere compared to a nitrogen one of the same mass and pressure or we can explain how a nitrogen atmosphere would actually produce the difference in emission btw the surface and the planet as a whole. If we can’t do either, then we do not have a useful hypothesis IMO.
Cheers, 🙂

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