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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I am also still awaiting responses from Willis on the following points:
1) Willis said:
“Since there is gravity, the atmophere will have a “dry adiabatic lapse rate”, which means that the temperature must drop with altitude. The atmosphere will warm until the bottom layer of the atmosphere has the same temperature as the surface, and has the dry adiabatic temperature profile above the surface. It will neither gain nor lose energy after that, and will be stable with no bulk motion.”
Ok, you’ve accepted the gravity induced dry adiabatic lapse rate.
And you seem to accept that the warming is from the solar irradiated surface and that the lapse rate is supported by conduction from the surface.
That is then the baseline gravity induced GHE as per N & Z and the Ideal Gas Laws. Nice and stable and set by gravity and atmospheric mass alone.
Then one introduces GHGs which have two effects.
They absorb more energy due to their radiative characteristics.
They then radiate 50% up and out of the system and 50% back down to the surface.
The 50% sent upward reduces total system energy content because it is lost to space. That is a cooling process.
The 50 % sent downward destabilises the gravity induced GHE but in turn provokes more convection and on a water planet energises the water cycle too.
Now, convection and the water cycle are cooling mechanisms (evaporation has a huge net cooling effect of 5 to 1 – see latent heat of vapourisation) so that 50% sent downward must be all or mostly negated unless you can show otherwise and the N & Z data seems to show that the negation is pretty much complete.
Which leaves the (admitted) gravitationally induced GHE firmly in control does it not ?
Checkmate ?
2)
Willis said:
“If there are no GHGs, the surface must radiate (to space, since there are no GHGs) the amount of energy it absorbs. Its radiation is fixed and unchangeable”
You forgot something.
The Ideal Gas Law means that the warmest molecules of air are at the surface.
Those molecules are at a higher temperature than the average for the atmosphere.
Thus they will inhibit upward energy transfer more than would be the case if the atmosphere were at a cooler average temperature throughout.
That will give a higher surface temperature than predicted by the S-B equation.
3)
Willis said:
“That’s why the surface can get hot, because some of the energy radiated by the surface is absorbed by the atmosphere so we’re not emitting to space more that we’re absorbing.”
Which is why the equilibrium temperature rises intead ?
In each case I have quoted Willis’s specific words as he has requested of others several times in this thread.
Ed Fix says:
January 14, 2012 at 7:54 pm
“Carbon dioxide happens to absorb a wavelength of EM near the peak of the earth’s overall S-B radiation spectrum (about 15 micrometers), but it re-emits S-B radiation in a smooth spectrum depending on its temperature only. Just like any other body of matter.”
No it doesn’t Ed. It can only emit at the wavelengths it can absorb, so CO2 emits at 15 microns (it also has some other distinct absorption lines around 2.7 and 4.2 microns, from memory). But it does not emit as a blackbody. Thin gases do not behave as blackbodies (see my earlier posts).
Tenuc says:
January 15, 2012 at 12:49 am
“All matters emit radiation as long as they have a finite (greater than absolute zero) temperature.””
Tenuc, we can and do measure the absorption and emission properties of atmospheric gases. You can find such rsults anywhere on the internet. Atmospheric gases do not behave like blackbodies and only emit at specific, well defined wavelengths. Oxygen and Nitrogen, for example, do not emit in the long wave infrared part of the spectrum. If you want to reconcile this with your citation, just consider that these gases have an emissivity of zero in this spectral region. Thin gases do not behave as blackbodies (see my earlier posts).
The heating of the atmosphere is a purely physical process according to the Ideal Gas Law.
“The Elevator speech”:
Gravity acts as piston compressing the atmosphere.
The atmosphere is then heated by this compression (think of a bicycle pump getting hotter as you pump).
As you get closer to the Earths surface it becomes hotter because the atmospheric pressure is greater (or cooler with increasing altitude and lower pressure).
Convection, evaporation and condensation transfers heat from the surface to upper atmosphere.
Heat radiates then from the top of the atmosphere to space (an infinitely large heat sink).
I have just been re-reading Hans Jelbring. He does indeed start his model with- Quote “The model planet does not rotate. It neither receives solar radiation nor emits infrared radiation into space.”
With no energy passing through there is no trapping of energy and no Greenhouse Effect.
As such its pretty much irrelevent to what Willis has defined here.
His condition that the atmosphere cannot absorb or emit any radiation requires all radiation to be to or from the surface.
As others have shown the “average surface temperature” is below what Willis called the “theoretical Stefan-Boltzmann (S-B) temperature.”
He is right, all the atmosphere can do is raise the “average surface temperature” up towards the “theoretical Stefan-Boltzmann (S-B) temperature.”
So to Nikolov and Zeller and the elevator speech. But first its important to understand they use a GHG atmosphere,
Quote
“An increase in atmospheric emissivity does indeed cause a warming at the surface as stated by the current theory. However, Eq. (3) is physically incomplete, because it does not account for convection, which occurs simultaneously with radiative transfer. Adding a convective term to (3) (i.e. Eq. 4) dramatically alters the solution by collapsing the difference between Ts, Ta and Te and virtually erasing the GHE”
I thought the elevator speech from
astonerii says:
January 14, 2012 at 3:25 pm
was doing fairly well except maybe for the lapse rate bit, but no comment from Willis.
Perhaps I can give it a try (apologies to Nikolov and Zeller if I get too far off).
The N & Z process works as follows (note it does include GHGs):
The surface loses energy by conduction to the atmosphere.
The majority of this energy rapidly convects to the troposphere.
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 and convected 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 warm (GHGs) atmosphere.
Thats the speech.
The overall temperature seen from space is still the “theoretical Stefan-Boltzmann (S-B) temperature”, unfortunately their section on pressure and energy is contradictory.
They say “Pressure by itself is not a source of energy!” and in the same section ” the atmosphere ……….is in and of itself a source of extra energy through pressure.)
They are confusing correlation with causation, but there are many more questions about how all this works.
However I better stop there as this thread has had lots of snip and delete (it must be rivalling “Realclimate”).
So I must not incur the wrath of Willis for being off subject.
Hail Core says:
January 14, 2012 at 1:40 am
I have talked with one engineer who is working infrared warmer manufacturer company. They have tried to warm air with infrared warmer and they have never managed to do so. They have even set tens of radiators to work at same time (hundreds kilowatts), no measurable results in air temperature. So the claims that infrared radiation warms atmosphere can’t be correct
————
The observation about IR radiant heaters sounds correct but your interpretation is wrong.
1. Over the short distances within a room you are not going to see much absorption and therefore only a small temperature rise.
2. The absorption band for IR radiation matches room temperature at around 25C. It does not match the temperature of a radiant heater. Typically these operate around 800C. Again this means only a small fraction of the heater output is absorbed.
anna v says:
January 15, 2012 at 2:47 am
Dear Willis
Transparency is in the eye of the beholder. For transparency to work in your argument the atmosphere should be transparent to all electromagnetic frequencies, which is not possible for matter as we know it. To have heat capacity, the molecules must have kinetic energy and interact by scattering, the scattering happens because of exchange of photons, photons are electromagnetic radiation at some frequency, even if very low..
I want to elaborate this.
What is black body radiation? why do bodies at a given temperature radiate even if not a perfect black body?
In a solid the atoms and molecules are on a three dimensional grid, vibrating about their position there with three degrees of freedom. As they vibrate they move in the left over electric fields of each other (Wan der Waals forces are related), motion in electric fields generates radiation and this radiation gets out of the solid at the frequencies where the solid is transparent and thus the solid cools because energy is lost.
In gases there is the continuous scattering of molecules in the fields of each other, and again radiation is induced which leaves and cools the gas.
Quantum mechanics modifies this picture by having photons mediate the interactions, sometimes off shell, some times on and leaving taking some of the energy of the interaction away.
Thus one cannot have matter as we know it of a given temperature not radiating in some frequencies.
‘Energy is radiated by the atmosphere back to the surface’.
This is not consistent with the 2nd law of Thermodynamics. Heat flows from hot to cold.
Willis accepts that the Ideal Gas Law ( IGL) calculates the observed lapse rate. The IGL assumes all the small molecules in air behave the same. There is no GHG/non-GHG split. Why is the GHG radiation theory needed?
It is needed so that CO2 can be said to cause warming
The comment by Geoff Sharpe, which I agree with, is off topic and be snipped.
I dislike the snide patronising snips by the author. Please get a proper moderator
Wow – the word ‘Snip’ appears over 100 times on this thread – free and open debate or censorship?
“And if you believe a man like Tallbloke, who censors scientific opinion that he disagrees with, you are an idiot. -w.”
Have we not witnessed Willis doing exactly that over and over on this thread?
How many comments like mine didn’t even make it past moderation?
Hi Willis,
“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.”
Sparse, essential, logical, what is there not to like. Congrats!
Alex
@bananabender et al.
I have already commented on the fallacy of the adiabatic compression of an atmosphere.
The nonsense is still surfacing in this thread, so I have to repeat myself (before Willis wakes up and starts shouting at us all again for not doing what he wants us to do).
Adiabatic compression cannot warm an atmosphere in any lasting way.
– When a gas is compressed adiabatically its temperature is raised as long as no heat escapes from the gas.
– In the real world, near-adiabatic compression usually only happens when a gas is compressed very quickly, as, for example, in a bike pump.
– If you hold the gas compressed, heat will gradually escape by conduction/convection/radiation and the temperature will fall until it reaches ambient temperature again. A compressed atmosphere will just leak heat to its surroundings and return to ambient temperature.
A gas is not hotter just because it is denser. If it were, liquified gases would not be possible.
How can gravity apply continuous work compressing the atmosphere?
When does it decompress? (If a gas decompresses it loses heat (because of the work it is doing in expanding) and its temperature falls).
In other words a one-off compression will not permanently raise the temperature of an atmosphere.
Furthermore, unlike the piston of a bike pump, gravity is not doing work on the atmosphere, in the same way that a ball rolling down an inclined plane or just falling to earth is not having work done on it by gravity.
There is therefore no adiabatic heating of an atmosphere as a result of gravity.
NB: The air of an adiabatic (‘katabatic’) wind, which is forced downwards by circulation and topography and so warms and dries out (the infamous ‘Föhn’ in the Alps)
has work done on it as a result of its motion.
@anna v
Exactly so…
Anna, may I intercept?
That is a very, very needed clarification, believe me, and well stated!
Would you also generally agree with a general view that a gas’s gray body radiation is weaker as compared to solid and liquids at the ratio of the distance between the molecules, therefore weaker electric field? Without explicit knowledge on that aspect that seems the most logical view I have gathered. That would put air’s gray body radiation at about two+ magnitudes less than something like water. I am also assuming that also a gas can absorb gray body radiation in about the same ratio (Kirchhoff’s).
And please, one more, could you clarify what is meant by “on shell / off shell”? (electron shells of course)
Stephen Wilde:
January 15, 2012 at 3:18 am
Stephen, thanks, but let’s just drop it. I think Willis got my point. (but lets say an apology later would not be rejected☺)
Willis Eschenbach says:
January 15, 2012 at 3:17 am
Now, my understanding may be wrong, and my proof may not apply to Jelbring. But since not one person has stepped forwards to say that they understand and can explain Jelbrings hypothesis, we don’t know, do we?
Willis, thank you for your more fully fleshed out thoughts on my contention, and your recognition that you could be wrong. I will email your full comment to Hans Jelbring and together we will offer a considered reply in due course.
LazyTeenager says:
January 15, 2012 at 4:20 am
Incorrect.
Almost 100% of IR radiation will be absorbed by the CO2 and water vapour in only a few metres of air.
The wavelengths of IR radiation at both 25C and 800C are similar and both will be absorbed.
The reason why there is no heating is because the absorbed radiation is converted to kinetic energy which results in convection. Gases can only be heated in confined spaces.
Well Willis you asked – and my elevator speech – I will stick to simple concepts and laws and not use any maths…
Errors
• Assumption that non-GHG gases (transparent to radiation) are somehow incapable of being at a temperature above absolute zero. You seem to think that only the GHG molecules have any heat content (kinetic energy)? Obviously FALSE
• Ignoring conduction – you happily accept that GHG can warm other gases in the atmosphere by ‘collision’ with non GHG but for some reason do not accept that the surface molecules warm the atmospheric molecules by collision. Obviously FALSE
• Confusion of ‘atmospheric heat content’ with ‘atmospheric temperature’ . Obviously FALSE
Elevator speech – without mentioning radiaiton
1. Atmospheric temperature is a measure of the sum of the kinetic energy of all the gas molecules in the volume being measured.
2. If the number of molecules in the volume with the same kinetic energy increases the sum of the kinetic energy of all the gas molecules in the volume is higher – therefore as in (1) the temperature is higher.
3. Pressure is a measure of the number of gas molecules in a volume. Pressure increases toward the bottom of the atmosphere due to the weight of molecules above. Therefore, there are more molecules in a given volume at the bottom of the atmosphere. If all molecules in the atmosphere have the same kinetic energy then as in (1) and (2) the temperature is greater at the bottom where there are more of those molecules in a volume than at the top. Pressure is also proportional by temperature as the gas molecules collide and ‘jostle for space’. (This is Charles’ Law – one of the gas laws)
4. The molecules at the bottom of the atmosphere are given kinetic energy by collision with the high energy vibrating molecules of the surface then in turn they collide with other gas molecules transferring the kinetic energy upward from the surface
5. As the molecules at the bottom of the atmosphere increase in kinetic energy raising local pressure and temperature that volume of atmosphere expands (Charles law) becomes lighter and moves higher (Archimedes principle)
6. As the gas rises higher and expands the pressure caused by the atmosphere above it reduces the number of molecules in that volume reduces and therefore the number of molecules with a particular kinetic energy in the volume reduces so the temperature reduces. (see 1 and 2)
7. As the process from 4 -> 6 operates cooler air is drawn in to replace the rising hotter air and a convection current starts. Indeed, convection is a simple term to describe the process 4 -> 6.
8. Convection is a warm air current that takes sensible heat from the hot surface upward in the atmosphere until the expansion cools the volume to the level of the ambient atmosphere. As the planet is rotating Coriolis forces affect the currents of both rising warm air and inflowing cooler air moving the heat energy from the equator to the poles.
I believe that the above describes how the atmosphere will warm from the surface to the top with a lapse rate that is directly due to the gas laws. Indeed convection is the major heat transport in the atmosphere to the tropopause (which literally means the place at which atmospheric convection currents stop ).
Now it is postulated (firmly) by Willis that the gases Nitrogen and Oxygen ‘cannot radiate heat’ therefore the atmosphere will continue to warm by conduction of sensible heat and convection. But according to the Willis postulate never cool as it can only heat up. However, if we add some gas molecules to the mix that can radiate heat energy – say CO2 molecules, all of a sudden we have gas molecules that will radiate the kinetic energy that they have obtained by collision with Nitrogen and Oxygen. So CO2 instead of warming the atmosphere actually is one of the gases that is essential to cool the atmosphere.
I could go on with the effect of water vapor from the surface but I believe we have reached your basement floor. 🙂
I’ve been wondering about the assertion that N2 and O2, being non GHG’s, can neither absorb nor radiate IR radiation. I considered a scenario of a cloud of N2 in space, of sufficient mass to be gravity bound into a ball. Let’s say this ball of gas becomes heated, either by gravitational compression or by the application of energy from some temporary external source.
The question I would like to pose to anyone interested, is if this gas ball cannot radiate IR, then in what way can it loose heat into space? If there is no way for the gas to loose energy, then the only conclusion is that it must remain at that temperature for ever. This is of course, an absurd conclusion to reach.
By the same logic as this thread has used, if it is impossible by the laws of physics for the gas to remain at the same temperature for ever, then there are only two conclusions: either the premise that the gas cannot radiate energy into space is false, or there is some way other than by radiation of loosing energy, which I have overlooked.
Willis: thank you. May I then come back with another question, for I’m still having trouble with this.
Your hypothetical atmosphere (by definition not absorbing or emitting radiation within the thermal infrared range) nevertheless has its own mass so must have its own gravitational field (additional to that of the planet itself without an atmosphere).
This, to a second body at a distance, will presumably cause work (again, in addition to that of the planet without an atmosphere), therefore additional heat. This is not caused by conduction or convection – what can be the cause, other than radiation? Where in the spectrum does this radiation (if it be such) lie?
From Stephen Wildes elevator speech (must be a rather slow elevator, or a tall building): January 15, 2012 at 3:36 am
Takes away from the efficiency? How? I can see that this transiently reduces the heat available for radiation, so should transiently reduce temperature, but you seem to argue that the same amount of heat has to be releases, so the temperature must RISE to compensate.
But this simply isn’t so. The temperature would transiently fall, as the atmosphere takes away heat, until is reaches an equilibirum state with the surface, at which point, since there is no possible source of outgoing radiation OTHER THAN THE SURFACE, then Willis’s balance is restored.
I haven’t read all the comments, so excuse me if this point has already been covered, but I am puzzled by some claims implying that a non-GHG, such as nitrogen, cannot radiate energy. Have I understood this correctly? I thought the definition of a non-GHG was that it does not absorb radiant energy passing through it, in other words it is transparent to radiation at all wavelengths. But it does not follow that it cannot radiate energy acquired in some other way. Consider this thought-experiment. A planet-sized ball of nitrogen is heated by a nuclear-powered source at its center, which is ‘switched on’ at T1. Heat is transferred by conduction to the nitrogen in contact with the heat source, and by conduction and convection to the rest of the nitrogen. The temperature of the nitrogen increases, and its volume expands, doing some work against gravity. By doing work, which substitutes potential energy for kinetic energy (heat), the temperature of the nitrogen is lowered by expansion, but it will not, I think, cool down to its original temperature by this process alone. At T2 the internal heat source is switched off and removed. At this stage the ball of nitrogen has a higher temperature and a larger volume than at T1. Unless it can reduce its temperature, its volume is in equilibrium, with gravity balanced by the higher pressure exerted by the gas molecules. Since the ball of nitrogen is in the vacuum of space, and not in contact with any possible recipient of heat, it cannot lose heat, and reduce its temperature, except by radiation. If it cannot radiate, it will remain indefinitely at a higher temperature than the surrounding space (and possibly other distant bodies). But this would violate the Second Law of Thermodynamics. Therefore it must radiate.
What have I misunderstood?
“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.”
Completely and utterly wrong.
The temperature of the atmosphere can be raised (almost infinitely) according to the Ideal Gas Law pV=nRT without any need for (the totally imaginary) Greenhouse Effect. In theory the surface of a planet could even become hotter than the Sun if it had a sufficient atmosphere pressure.
The primary role of the Sun is to provide enough heat energy to keep the atmosphere in a gaseous state and maintain the vapour pressure. The pressure then heats the planet. The surface temperature of every planetary body in the Solar System is a function of the atmospheric pressure and gravity. Mercury and Mars are relatively cool because they have virtually no atmospheric pressure. Jupiter, Neptune, Uranus and Titan are warmer because they have very high surface pressures.
A blackbody is a purely theoretical concept. It is defined as a cavity radiator of zero thickness. The last time I checked the Earth is a 6×10^24kg solid sphere.
Willis Eschenbach says:
January 15, 2012 at 12:28 am
David says:
January 14, 2012 at 9:08 pm
Open question; Surface heat conducts to the non GHG atmosphere, Can non GHG molecues conduct heat to the surface?
Sure.
w
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Thank you Willis, Now I have a folllow up. The second law of thermodynamics, as applied to radiating heat, allows energy to flow both ways, just the net flow of energy is from warmer to cooler, until both systems equalise, the tendency towards entropy is not contradicted. Is this true of conducted heat also?
Now another question Sir. Your statements concerning non GHG I have read. Answering this question will help clairify my understanding. Are you saying that if I am suspended in the vacume of space, and a stream of superheated 8,000 degrees N2 jets by me for 24 hours, at say 10′ away, (nothing but the vacume of space between me and the gas) I will feel nothing and my thermometer will register nothing, but if that stream of gas IS COMPOSED OF CO2 and jets past, again with 10′ of the vacume of space separating me from the gas, I will feel emense heat from the radiating CO2, but none from the non radiating N2?
Willis, back to the science.
It seems so many here were under their breath condemning you for taking a classic consensus climate science and IPCC view of the world in your example. A perfectly radiating planet, in essence massless, with equal light at every point and an atmosphere that can never shed even a watt of energy, that seemed to peeved most. We have heard such a story for years and it is totally meaningless.
But if you insist, you are right best I can tell. The best that planet could do is by conduction heat the entire atmosphere to the same temperature as the surface from bottom to top when an equilibrium was established, even if a gravity caused temperature gradient also was present. By a gravity caused temperature gradient I mean the dry adiabatic lapse rate (DALR=g/Cp) that is not merely a descriptive ratio but has, by some unknown physical process, a tendency for temperatures to sort by themselves, albeit very slowly, warmer deeper in the gravity well matching that ratio.
So, you win, but I don’t see that proving anything. If that enabled natural lapse rate did occur all you would have to do is add the ability for that atmosphere to shed energy. As anna v was saying, just let the N2 be real N2, it does radiate though weakly. In that case you have given the atmosphere the ability to shed that excess energy seen at the top and that gradient would slowly emerge.
But also in that case the N2 can by Kirchhoff’s law also absorb though equally weakly radiation and since there is more density low, more energy would be absorbed near the surface than in the thin gas at top. That one factor would pull the surface above your theoretical S-B temperature though not up to +14°C. Add water at the surface and it seems it would. And I’m not sure that ‘real’ DALR is even necessary, it seems to be strictly from the density, not pressure.
If you see flaws in that let me know.
johndo9 says:
January 15, 2012 at 4:19 am
I have just been re-reading Hans Jelbring. He does indeed start his model with- Quote “The model planet does not rotate. It neither receives solar radiation nor emits infrared radiation into space.”
With no energy passing through there is no trapping of energy and no Greenhouse Effect.
As such its pretty much irrelevent to what Willis has defined here.
His condition that the atmosphere cannot absorb or emit any radiation requires all radiation to be to or from the surface.
As others have shown the “average surface temperature” is below what Willis called the “theoretical Stefan-Boltzmann (S-B) temperature.”
He is right, all the atmosphere can do is raise the “average surface temperature” up towards the “theoretical Stefan-Boltzmann (S-B) temperature.”
So to Nikolov and Zeller and the elevator speech. But first its important to understand they use a GHG atmosphere,
No they don’t. From their abstract:
“the so-called Greenhouse Effect is in fact a Pressure-induced Thermal Enhancement (PTE), which is independent of the atmospheric chemical composition.”
If they did use a GHG atmosphere I think they would be on the right track. The profile of an atmosphere is by and large independent of the chemical composition. Therefore, it is possible to determine the GHE from looking at that profile (which is what they did for other planets). However, you must have some radiating gases that are carried by thermal energy to higher altitudes otherwise you end up with the situation Willis is discussing. If K&Z had specified GHGs were required then I think this entire discussion would be on the right track. The GHE is defined by the pressure distribution as they stated. But, it is if and only if you have sufficient GHGs present.
Maybe a chemist can help with an example. Think of a solution that is stable until you add a small amount of a catalyst. All of a sudden a big change occurs. Only a certain amount of the catalyst is required and, after that certain point, more of the catalyst does nothing. That is what happens with the GHE. The GHGs are the catalyst.