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 …
jimmi_the_dalek says:
“The completely transparent atmosphere is not Willis’s invention – it is implicit in the models he is criticising. These models claim that all of the GHE can be explained without any mention at all of absorption or emission of radiation by the atmosphere. It follows that their theories should be true for an atmosphere which is completely transparent. Perhaps the authors of these theories do not realise that they have built this into their model, but they have. So it is legitimate to ask how a completely transparent atmosphere would behave. Willis has given the answer, and shown that the ‘it’s all due to gravity’ models are nonsense.”
Nobody does any reading it appears. In a nutshell Willis claims that if the bottom of the atmosphere is warm the surface will emit and since any emission would be in excess of incoming its a violation of the law of conservation of energy.
But if you read Jelbring he says the model receives no external source of radiation and it radiates nothing. “The energy content of the model atmosphere is fixed and constant since no energy can enter or leave the closed space. Nature will redistribute the contained atmospheric energy (using both convective and radiative processes) until each molecule will have the same total energy”
Basically the entire thing is a planet in a bottle with no external interaction and no misappropriation of energy. and in fact it does mention absorption or emission of radiation in the atmosphere, just not from external sources.or to external sources. Instead the only thing allowed is a redistribution of energy already in the bottle. Absolutely nothing you say about Jelbring’s model even approaches corresponding to the description of it in the paper.
The only thing going on here is a mass reading comprehension problem.
Specter says:
“The nominal value for this required flow is usually stated as 239 or 240 W/m². If the surface were emitting energy at a higher average rate, say 396 W/m², then something must be extracting 156 W/m² from the *radiant* energy flow going up in the atmosphere and returning it back to the ground. Only greenhouse gases can perform that function on a continuous basis.”
If you check modtran and UofChicago you will find that at 288k upward radiation by the surface in the absence of greenhouse gases is 347w/m2. Thats a function of the surface albedo. Thats a substantial drop. The way numbers get thrown around in the climate game, myself as an accountant gets really antsy. I see lots of proxies being used and virtually nothing to validate them. Stevenson screen proxies for land surface emissions. 3 foot deep water temperature readings for radiating and evaporating surface films. A weather station network never designed to do this job. A bunch of conspirators massaging the data. Completely ignoring the fact the surface film is pumping out 102 watts in a convection conveyor belt. Gee that couldn’t affect the temperature of the radiating surface. . . .or could it?
I have never ever seen anything in my life like it. And I did some pretty extensive restructuring work with collapsed businesses. I have never seen the gall of some people threatening to erase data while speaking with peer pals to avoid the public inspecting it . . . .then to have it actually disappear! I can’t even imagine how anybody could have faith in any number out there.
Seems to me one heckuva lot of money is being thrown away on a lot of stuf that simply doesn’t need to be done. Perhaps we need better ideas of the surface radiating temperatures and maybe we need it globally. But it seems to me the Cloud 9 guys have run far out in front on this deal from the perspective of understanding the basic underlying principles.
Anna V,
What was the sentence in my post after the one you quoted? Go read it again please.
Ned Nikolov says:
Ned: We have already discussed this; your reply sounds like it will just pretend that all the discussions we’ve had about this don’t exist. 100K of your 33K is just due to the fact that a direct average of T produces very different results for the same value of emitted power depending on the distribution of the temperature across the surface. Nobody but you is claiming that the radiative greenhouse effect raises average temperatures by 133 K. What it does is raise surface emissions from ~240 W/m^2 to ~390 W/m^2. The 390 W/m^2 on the current Earth corresponds to an average temperature of ~288 K as the current temperature distribution is uniform enough that assuming it completely uniform is not a bad approximation.
In the absence of the greenhouse effect, the 240 W/m^2 emissions from the surface would correspond to an average surface temperature of ~255 K or less. A planet without a greenhouse effect will probably have a somewhat less uniform temperature distribution but probably not enough to lower the average temperature that much from 255 K. And, even if it does, this is really not the interesting part of the effect: It is probably best to characterize the temperature of the planet by the fourth root of the average of T^4 instead.
I hope your replies to comments shows that you have learned something from the criticisms of your theory but from what you have been saying so far, I am not at all optimistic that it will.
“Could I not say that my walls are kept warm due to air temperature? Can not also say the driveway is also kept warm from air temperature?”
The driveway can be warmed by the air, but it can only do so by transferring heat into it.
And air cools as a result.
And this only way any atmospheric gas can cool down.
At night air cools. So air must have warmed surface to cool.
There is about 10 tons of air above every square meter of the earth surface.
When the air at surface cools 1 C, then roughly all the air cools by 1 C.
One has varying lapse rates with changing condition, but air cools at lower
elevation it also cools in higher elevation.
The specific heat of air is 1.005 kJ/kg per K
So 10,000 kg times 1.005 per lowering of 1 C is 10 million watts seconds.
In the absence of a GHE it cannot increase the amount of heat in the Earth system at any given time.
The temperature of air depends upon it’s velocity. Most air is transparent to any photon CO2 might emit, and such photons would not increase the velocity of gas molecules of air.
“OTOH, a GHE can increase the amount of heat in the Earth system at any given time by causing some IR radiation to be absorbed and re-emitted multiple times before the radiation finally gets high enough to radiate to space.”
If GHE gases are interchanging photons many times this has no affect in term of heat in regards to the surface or gases, the only possible significant is if a photon were to be absorbed by surface.
The general “greenhouse theory” seems to be that photon would first start from the surface and possibly be absorbed by CO2 and possible return to the surface or possibly be emitted into space.
That CO2 holds or interchanges photons has no significance in terms of temperature [the gas molecules aren’t caused to move quicker]. And the amount heating cause by photons re-emitted back to the surface, doesn’t seem like much to me- perhaps someone would like to quantify this amount, I could be enlightened.
But regardless of this, the air cools at night, the cooling can only occur by warming the surface, and there is much more energy stored in velocity of air molecule than most land surfaces [which normally cool during each 24 hr night time period- the heat in say, 4″ of dirt, sand, or concrete].
“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.”
The amount energy from the sun is around 1300 watts.
The term: theoretical S-B temperature for earth, I assume is 240 watts per square meter averaged over entire surface.
For our thought experiment what is the theoretical S-B temperature the chosen planet?
Is it 240 watts? Or is the incoming energy 240 [earth receiving 1300 watts]
If latter can we assume that the theoretical S-B temperature is 240 watt [include choice of Bond albedo and time it by that by 240 Watts] and divide by 4. In which case the theoretical S-B temperature is less than 60 watt per meter per sun?
Or is it 1300 watts and one must have earth’s Bond albedo?
Or did you have something else in mind?
Sorry for being late, but there is an essential oversight, apples and oranges. The surface indeed can’t violate stephan boltzman but the inert non-emitting atmosphere can. And secondly the average surface temperatue on earth is not the actual surface temperature. One is the contact temperature of the soil, while the other surface “temperature” is the temperature of the atmosphere on 1.50 meter height in the thermometer house. When the surface cools due to emission during the night, it cools only the lower boundary layer of the atmosphere, if nothing else happens the heavier cooler gas stays put , and a very strong surface inversion emerges. In an iglo for instance the air at the entrance hole can easy be -20C, while the air at the ceiling is +10 +20C, just 1.5 meter higher.
For more cooling of the atmosphere wind and turbulence have to replace the boundary layer and iin case of a radiative atmosphere the emitting lower atmosphere will heat up the surface/actually decreases the cooling rate of the surface while cooling itself. But in a non radiative atmosphere, the majority of the gas stays as warm as it got in day time due to convection. Hence the thermometer house at 1.5 meters can be warmer than the surface.
@joel Shore
I have no idea what you look like, but I picture you with a very robust bone structure and heavily developed exo-skeletal musculature (something like this). Otherwise, I don’t see how you could carry that massive ego around with you…
/dr.bill
Thanks to the continued discussion, a misunderstanding on my part has become clear. I had thought that the gravity was only being credited with creating a thick atmosphere, and the thicker atmosphere is all that was associated with warmer temperatures. So I thought that the paper was only finding a correlation between the density of the atmosphere and its temperature. I had missed that gravity was being credited with continuously creating heat.
I was about to argue that the Earth example contradicts Willis’ proof in that the surface temperature can be higher without violating the 2nd law: our surface temperature is higher than S-B though outgoing equals incoming (small variation when catch up is being played for changing forcings).
The difference is the atmosphere above comes into play when it disrupts the outgoing radiation from the surface (no detail – elevator is moving!).
The non-GHG atmosphere won’t disrupt outgoing from the surface so if the surface temperature is higher than the S-B temperature then the outgoing radiation should be greater than incoming – which is a big problem.
I can understand Willis taking the stance he has; there are too many ill explained kook theories doing the rounds on the skeptic side which are quickly embraced as the next ‘final nail’ by the unlearned. That first draft of the Dragon Slayer paper was embarrassing in its claimed 2nd law violation.
dr. bill,
I always pictured joel like this.☺
jimmi_the_dalek says 1/16 9:20:
“PS to Trick above – a transparent atmosphere does not radiate anywhere, even at TOA.”
Jimmi – The transparent GHG-free atmosphere is still made of matter so will thermally radiate/absorb w/space ~3K at TOA. All matter with temperature above absolute zero emits thermal radiation.
Any atmosphere above absolute zero can no longer thermally conduct to space at TOA.
jimmi_the_dalek says:
January 16, 2012 at 11:08 pm
Crispin,
“There is no such thing as a non-GHG atmosphere that does not emit radiation so the thought experiment is not going far.”
On the contrary, the thought experiment shows precisely what it is supposed to, namely that a model in which the radiative properties of the atmosphere do not exist, cannot be correct. So, instead of criticising Willis’s thought experiment, you should be asking Nikolov and Zeller why they omitted these factors.
++++++++++++
Oh, I have no problem imagining impossible atmospheres. It is of course pointless to discuss them because one could simply plonk down additional impossiblities such as changing other physical laws or making Miss Piggy the Secretary of the UN.
BTW thanks Anna V, again.
I am not sure it is entirely Willis’ thought experiment though. I understood he was looking at root of claims made by others. What has emerged after a good deal of discussion is that the postulated atmosphere either could not exist or needs to be restated so that it could exist with different definitions, for example, that is does not absorb IR but can emit radiated energy.
If the idea persists that there is such a thing as a non-GHG gas atmosphere, where non-GHG means ‘not absorbing or radiating or re-radiating energy’ then it is contrary to nature so investigation of black body surface radiation under different gravity-pressure scenarios leads nowhere.
I found the exercise very beneficial, however. For me it lays to rest forever the idea that only certain gases labelled GHG’s heat the Earth. I already knew there is no such thing as a ‘greenhouse effect’ per se but that has a very different explanation. The assertion that the Earth’s atmosphere is primarily heated by CO2 and would be in a permanently frozen state in its absence is bunk. Ergo, the suggestion that building windmills to replace coal-fired power plants will in any way dampen temperature fluctuations upward is sad, unless you are in the windmill business. Et cetera.
re Smokey, January 17, 2012 at 6:25 am :
I don’t want to be disagreeable, Smokey, but that’s my picture of “Phil.dot” you’re parading around there. ☺
/dr.bill
dr. bill,
They’re interchangeable, no?
re Smokey, January 17, 2012 at 6:25 am :
Well, they do seem to arrive and leave together, and they’re pretty much equally obnoxious, but I don’t think Phil.dot is the brighter of the two bulbs. ☺☺
/dr.bill
Willis says: “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.”
That’s a valid statement but it does not invalidate the crux of what N and Z are telling us.
On a planet with spatially variable temperature the warmed atmosphere moving from equator to pole returns energy to the surface. Similarly the ocean gains energy in a warm location and releases it in a cooler location. It’s a feedback loop that raises average surface temperature due to lateral energy transport. The average radiation from the surface will reflect this feedback loop.
All atmospheres possess particulates and molecules that mediate the return of radiant energy to the surface and it appears (in terms of a lack of surface warming after 1998) that the partial pressure or relative concentration of these receptor molecules (above a tiny minimum threshold) is irrelevant. I instance the efficacy of ozone in reversing the decline of temperature with altitude at the tropopause when it is present at about 1ppm.
The denser it is, the greater is the energy that the atmosphere accumulates and the more effective it is in transferring energy. The average temperature as indicated by a thermometer will reflect that. If there is no atmosphere, there is no warmth at two meters and no redistribution.
Given the necessary minimum level of greenhouse gas to facilitate the transfer it is the bulk density of the atmosphere that determines the ‘average’ surface temperature.
That is the novelty and value of the Nicolov and Zeller presentation.
But, none of this is has any great relevance since it is the cloud cover that mediates the incidence of solar radiation changing within the scale of a human lifetime, and this is also a point that N and Z make.
Willis, I want to make a few comments on the manner in which this discussion has been handled.
As for the snips the role of the teacher is to keep the discussion on track and so I see the snips as necessary and desirable. The only pity is that you had to do it yourself. The nice thing was that you indicated where the snips had occurred. That does not seem to happen at Real Climate.
As for the tone of your replies: Well, when you say ‘Good for you’, its disparaging and a teacher who seeks to encourage would not say that. It tends to alienate people. It is useful to discourage the real time wasters and it’s perhaps not so big a deal in the adult world and on a blog like this where some delight in being insulting while adding nothing to the discussion. These types need firm handling because they are thoroughly disrupting. You can mix it with the best of them but a better policy might be to have a third party insist that the comment be cleaned up before its posted.
This has been a very successful post. I’ve read nearly all the comments and learned a lot. And you are a good teacher.
There is nothing quite like a good hypothetical.
Bart,
Then you’re doing the integration incorrectly. The emissivity doesn’t drop below 0.9 until you get to an angle between 65-70 degrees. 90% of the area of the hemisphere is covered by a solid angle of 130 degrees. The emissivity graph doesn’t start until 20 degrees. So conservatively the emissivity between -65 and 65 degrees is greater than 0.96. That means the total emissivity is at least 0.86 if the emissivity were zero for angles outside that range. It’s not. Plot the full emissivity curve as a function of sine(θ) and then integrate.
Bart,
That’s the Laplacian of the temperature, i.e. the kinetic energy, not the total energy. The Laplacian of an isothermal atmosphere is indeed zero. If the temperature were increasing with altitude, you would be correct. Heat would flow downward driven by the temperature gradient. The same thing is true if the temperature decreases with altitude, heat flows upward. There is no thermal equilibrium if there is a difference in temperature. And that’s temperature, not potential temperature.
Anna & others that think a non-greenhouse gas emits thermal radiation:
Yes there is some radiation even from non-greenhouse gases, but it is so small compared to the ground radiation and greenhouse gas radiation that it can be considered zero for the analysis. Keep in mind that a room full of air has a finite probability to all move into one end of the room and suffocate you. I don’t think that would make you worry. When probabilities many orders of magnitude smaller than important details are invoked, you are really grasping at straws.
Thanks to the continued discussion, a misunderstanding on my part has become clear. I had thought that the gravity was only being credited with creating a thick atmosphere, and the thicker atmosphere is all that was associated with warmer temperatures. So I thought that the paper was only finding a correlation between the density of the atmosphere and its temperature. I had missed that gravity was being credited with continuously creating heat.
Which leads, incidentally, to a twenty second demonstration that the system violates the e.g. heat engine or refrigerator statement of the second law of thermodynamics, because gravity, in fact, does not create heat. It can only help move heat created some other way around. In fact, the assertion that it can spontaneously polarize temperatures and maintain that polarization without the input of actual heat is a violation of the refrigerator statement — it doesn’t need help! No cyclic process can have the sole effect of moving heat from a cold reservoir to a hot reservoir. End of story.
For the umpty-zillionth time — in a static atmospheric profile (one where the density variation is fixed) gravity is doing no net work on the system. In an atmosphere in thermal equilibrium the temperature of the atmosphere is constant. A lapse rate only exists because the atmosphere is not in equilbrium, and there is differential bulk transport of heat away from the surface that maintains disequilibrium. If the upper atmosphere is not permitted to cool via radiation, this heat transport continues until there is no lapse rate for a superconducting/non-rotating Earth, or it drives lateral transport of heat from warmer regions to cooler ones to increase the net cooling of the planet relative to the initial condition of no transport but yes differential heating. This transport cools the tropics, warms the poles, and produces net warming on average. This transport is the only mechanism I can see so far that affects the actual average temperature, and that not relative to an ideal black body but because it drives the non-ideal (but overall cooler) rotating Earth absorber towards the warmer ideal blockbody by enabling not superconduction of heat but relatively weak transport of heat.
Willis’ thought experiment is dead on the money. Given a superconducting ideal absorber Earth (the baseline for most discussions of GHG warming) and a perfectly transparent non-GHG atmosphere, the atmosphere is completely irrelevant if you block or ignore lateral transport of heat — it warms to a uniform temperature from top to bottom that matches the surface temperature underneath and is as irrelevant to gain or loss otherwise as the other non-radiating matter in thermal contact with the surface just beneath the surface. There is no lapse rate in such an atmosphere. It cannot gain or lose heat anywhere but at the point of contact with the surface, and internally it shares heat until it is driven to a constant temperature.
As for people who are asserting that gravitational potential energy is somehow equivalent to heat, as if a falling body heats up as it moves — OMG. Please, take a short course in thermodynamics. Get a friggin’ physics book and read the thermo chapters. Learn the difference between reversible and irreversible processes. Just FYI, the difference between “heat” and “internal energy” is entropy. Heat flow into a system is always accompanied by the exchange of entropy. This connects it with the Second Law (entropy statement) via Clausius’ Theorem.
To put it in a way anybody can understand, if you drop a rock from rest it doesn’t change temperature at all as it falls, but when it inelastically collides with the ground at the bottom some of its initial potential energy relative to the ground is converted to heat – nearly all of it for a rock much smaller than the Earth. But this conversion is a one way thing. It creates a hot spot where it hits, and the heat then spreads out into the entire system, warming it until it is at a uniform temperature again. It is then not “impossible”, but more or less infinitely improbable that this disorganized kinetic energy in the internal energy of all of the molecules will combine “just right” to kick the rock back up into the sky to its original height.
When you understand that statement, you will begin to understand entropy and why heat will always spontaneously flow from warmer to cooler given a channel between them capable of carrying energy, and why one requires a “Maxwell’s Demon” that can decrease entropy, sort out faster molecules and slower molecules so that detailed balance is not maintained in order to create a hot and cold separation. It isn’t even as likely as the separation of black and white dyed salt grains into nicely separated layers as you shake a container — a lot more atoms, a lot less likely (although on the other hand, nearly zero equals nearly zero on all scales).
In fact, read:
http://en.wikipedia.org/wiki/Maxwell%27s_demon
and learn. It is even relevant to human consciousness and quantum theory, as measurement processes always involve irreversible entropy increases, something that leads to several silly paradoxes and nonphysical “processes” (e.g. “wavefunction collapse”) in the discussion of open quantum systems.
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Bart says:
January 16, 2012 at 11:09 pm
“I have not questioned the SB relationship at all. I have questioned the shallow manner in which it is being applied. The difference between us appears to be, I know how it is derived, and the conditions upon which its successful application depends. You, however… apparently not so much.”
So show me an instance where the correct (IYO) application gives the answer you are expecting under your hypothesis. Again, you are the one claiming that the evidence underlying the current view of the radiative state of the *entire* atmosphere is faulty. If this were true, it should be relatively easy to find some evidence of it. The atmosphere is a very big place.
Cheers, 🙂
RE: Bill Hunter:(January 17, 2012 at 3:23 am)
“Specter says:
“’The nominal value for this required flow is usually stated as 239 or 240 W/m². If the surface were emitting energy at a higher average rate, say 396 W/m², then something must be extracting 156 W/m² from the *radiant* energy flow going up in the atmosphere and returning it back to the ground. Only greenhouse gases can perform that function on a continuous basis.’
“If you check modtran and UofChicago you will find that at 288k upward radiation by the surface in the absence of greenhouse gases is 347w/m2. Thats a function of the surface albedo. Thats a substantial drop. The way numbers get thrown around in the climate game, myself as an accountant gets really antsy. I see lots of proxies being used and virtually nothing to validate them.”
In this case the situation is very simple: If the Earth is hot enough to have a global average surface radiant energy flow of 396 W/m², then something in the atmosphere must capture an average 156 W/m² from this radiant flow before it gets away. That is because the average energy actually flowing from the whole planet must be the nominal 240 W/m² required by conservation of energy.
There is no reference to temperature. There is no reference here to MODTRAN. The 396 value comes from the Trenberth diagram. Again, no reference to temperature is required as this is a simplified energy balance equation. It is not a temperature balance equation. No atmospheric absorption of solar energy is considered here.
The standard value of 240 W/m² assumes a 30 percent reflection of incoming solar energy and 100 percent LWIR surface emissivity.
Dr Brown says: “it warms to a uniform temperature from top to bottom that matches the surface temperature underneath and is as irrelevant to gain or loss otherwise as the other non-radiating matter in thermal contact with the surface just beneath the surface. There is no lapse rate in such an atmosphere. It cannot gain or lose heat anywhere but at the point of contact with the surface, and internally it shares heat until it is driven to a constant temperature”
But when you introduce a rotating planet the surface is always changing temperature. That combined with the fact in a passive solar water heating system with well-insulated storage above collectors you can create a natural convective loop that warms the water in the tank to well above the average temperature of the surface over periods of days. In fact because outside the system convection exists the water system gets warmer than even the warmest days.
But if you start stripping insulation off of the water storage the temperature you can obtain goes down in this system. You can boost the heat by greenhousing the collectors and eliminate immediate heat loss but some folks just lay out black pipe and get comfortable shower temperatures in the system well above the ambient temperature outside at the peak of the day with a much more economical system.
The system comprises of black copper piping arrayed into a collector. The pipe is insulated as it runs up the hill to the storage tank that is also well insulated. Heat loss at night is primarily through the insulation as even with water conductive heat down the pipe is rather minimal (and water is about 24 times more conductive than air). So that as an analogy it seems logical that the following is true for a non-radiating atmosphere in our world: 1) it would be a lot warmer than the average temperature everywhere with the warmth of the tropics overwhelming the poles; 2) At near equilibrium (true equilibrium would never be reached) Convection would be minimized though not completely eliminated due to the pulsing of ground temperatures as the sun comes up and goes down (convection would be minimized because of the very low heat losses in the system, the surface would get very cold at night but as a system very little; 3) conduction losses to the ground would be measurable but rather insignificant to overall warming that was generated. 4 )as I effectively strip off insulation in the storage vessel (the atmosphere) and introduce radiating gases to the atmosphere the atmosphere would cool in proportion to how much the radiation capabilities of the atmosphere goes up. 5) by adding another .04% of a radiating gas that is .125 efficient I am going to very slightly cool the system. 6) that the moist lapse rate is lower than the dry lapse rate is purely and moreso a function of latent heat transport, otherwise as purely a radiator it would be increasing the lapse rate; and 7) by assumption that the 30 degree greenhouse effect we have today is the residuals in the system from not making the atmosphere’s thermal conductance to space as conductive as the ground. After all these passive water heating systems work in Alaska too at least when the sun is shining..
So Dr Brown I have read your posts with fascination, though a lot of it was over my head. Where have I gone wrong above? This is relevant to me in viewing Jelbring’s model as I have to break through intuition that arises from simple analogy models like that above.
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Trick,
When you (and many others) say “The transparent GHG-free atmosphere is still made of matter so will thermally radiate/absorb w/space ~3K at TOA. All matter with temperature above absolute zero emits thermal radiation.”
the problem is not your physics but your use of the English language. The word “transparent” means “does not absorb”. What you should be saying, in my opinion, is not “transparent gases absorb radiation”, but “there is no such thing as an absolutely 100% transparent gas”. Which is fine, but irrelevant. What you should be asking, as I see it, is whether Nikolov et. al (or Hoffman), by claiming that the GHE can be deduced purely from gravitational considerations, have made an assumption which is equivalent to assuming transparency, because if they have, then they have built a non physical component into their theory.