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 have been over this already upthread, but I want to be sure interested readers late to the game understand the principles that I am elucidating.
SB can fail to hold in at least two ways:
A) the energy distribution is skewed or non-uniformly distorted from the Planckian distribution by non-radiative, or at least non-uniform, energy dissipation mechanisms
B) the spatial distribution of radiation can be altered
On the first score, pro-GHG commenters have held that emissivities of common surface constituents have been analyzed, and bulk emissivities have been measured near unity. BUT, those measurements were carried out in particular environments which are non-representative, e.g., in the laboratory or in placid weather conditions in calm waters. Worldwide energy dissipation mechanisms and radiative conditions are hardly represented here.
Moreover, the measurements are typically not of the entire spectrum, but of selected bands, e.g., those performed by Niclòs et al – 2005, which looked at “four channels placed in the 8–14 μm region”. Overall emissivity is then extrapolated based an an assumed Planckian distribution. So, skewing or non-uniformity in the distribution would not be detected, and the claim of near unity emissivity becomes significantly a circular argument.
On the second, the spatial distribution can be altered particularly by absorption characteristics of neighboring masses. The angular dependence of emissions in the aforementioned reference is attributed to surface roughness of the waves. Imagine how it would vary with larger waves or choppy seas! Or, if measurements were done on land, with local flora and landmasses. The effective emissions must be scaled to what they would be for an equivalent perfectly smooth, flat plate to match SB conditions. There is no indication in this article that such scaling has been done, but the nosedive the curves take after 70 degrees suggests the integrated area loss could be substantial, and this is in calm conditions.
So, in sum, SB has not been demonstrated to be applicable, and it is a thin reed upon which to base the entire GHG argument.
“It is not akin to a single pressurisation. It is akin to continuously renewed pressurisation and every time anything moves or is prevented from moving by a denser object work is being done and heat energy produced.”
For the avoidance of doubt I am NOT suggesting that it is the interaction of mass with gravity that causes the dry adiabatic lapse rate.I think that misinterpretation was placed on my words previously.
Instead it is the effect of gravity in creating greater density at the surface which then causes more collisional activity, more conversion of radiation to conduction and a slowing down of energy flow through the system.
The increased density at the surface amplifies the initial miniscule gravitational effect.
Ed Fix says:
January 14, 2012 at 7:54 pm
Willis Eschenbach says:
January 14, 2012 at 5:48 pm
…you claim that non-GHG gases radiate in the IR, so you’ll have to rebuild the parts of your theory that depend on that incorrect claim.
Willis, you’re conflating absorption with emission. Any body, solid or fluid, emits electromagnetic radiation with a spectrum determined by the S-B relationship. A body’s transparency spectrum is independent of its emission spectrum. They’re separate processes.
…
http://wattsupwiththat.com/2012/01/13/a-matter-of-some-gravity/#comment-864675
========
This is the problem I’m having with trying to answer here, you can’t have it both ways, either everything above absolute zero emits ir or it doesn’t. If hot air doesn’t then it’s defying this world’s physics.
Hot air radiates out heat which is thermal infrared, which is thermal energy on the move by radiation. If it can’t get hot by absorbing thermal infrared (spectrum), then one of the other methods of getting hot must be in play; by transfer in conduction or convection, or by pressure or whatever.
Bart says:
January 15, 2012 at 10:12 am
In my thought experiment in the head post, at equilibrium there is no heat exchanged between the surface and the atmosphere. In addition, there is no atmospheric circulation. Remember the heating is even and constant, so why would heat be flowing into and out of the atmosphere?
w.
Paul Dennis says:
January 15, 2012 at 12:55 pm
“There is no conduction of heat through the atmosphere since the surface and atmospheric column are all at the same temperature.”
Incorrect. The column cannot be at the same temperature, because that would require progressively more energy stored in each progressively higher altitude spherical shell, which would be an unstable configuration.
some lecture notes for folks
http://www.google.com/url?sa=t&rct=j&q=line+broadening+stratopshere+c02&source=web&cd=9&ved=0CHEQFjAI&url=http%3A%2F%2Fwww.atm.ox.ac.uk%2Fuser%2Fatmmra%2FB3%2Fhandouts%2FB3clim6h.pdf&ei=KUITT6W1AeOjiQKjzoG7DQ&usg=AFQjCNGnCbFWaBxDm9vzqntHj-L1u2ioQA
http://www.google.com/url?sa=t&rct=j&q=line+broadening+stratopshere+c02&source=web&cd=1&ved=0CCYQFjAA&url=http%3A%2F%2Fnit.colorado.edu%2Fatoc5560%2Fweek4.pdf&ei=0UATT8GPOuLkiALAqd22DQ&usg=AFQjCNEZ4eBWftW0uqM0Iz8R-MqWQ4gUvw
“In my thought experiment in the head post, at equilibrium there is no heat exchanged between the surface and the atmosphere.”
Then, you are thinking of something completely unphysical, and we are arguing how many fairies can dance on the head of a pin.
Bart,
I don’t understand your comment. Can you elucidate please? Thanks.
willb says:
January 15, 2012 at 10:17 am
OK
Doesn’t happen. To liquify nitrogen or oxygen, you need both low pressure and high temperature. No gas spontaneously liquifies at elevation.
Sorry, but your claims just aren’t realistic. Let me suggest the Caballero paper recommended by Robert Brown.
w.
Bart: “The column cannot be at the same temperature, because that would require progressively more energy stored in each progressively higher altitude spherical shell, which would be an unstable configuration.”
Several problems with this claim. First, at higher altitudes the pressure is lower and there is less gas in each shell, therefore its total energy is diminished. Second, it is not unstable. An isothermal column is neutral to convection whereas a temperature gradient in either direction is not – being either stable or unstable according to direction.
However, as I noted above, the upper boundary of an isothermal atmospheric column is unphysical since it allows the gas to escape gravity.
Excellent post, Willis E
Ferd Berple (14 Jan 9:37 am), I like your comment.
With some amplifications to your statement “Since we know that net energy [rate] radiated to space is a function of temperature, we can say that Temperature surface(2) > Temperature surface(1),” your logic seems to prove that the surface temperature of a sphere in the presence of a greenhouse-gas-free atmosphere will be higher than the temperature of sphere in the presence of an atmosphere containing greenhouse gases. If all your assumptions (implicit and explicit) are valid, your arguments seem to disprove Willis’s Elevator Speech.
However, if the contrary is true (i.e., if adding greenhouse gases to an atmosphere increases the surface temperature), then there has to be an error buried somewhere in your logic. I propose three sources of error. Each potential error source requires an amplification to your statement: “Since we know that net energy [rate] radiated to space is a function of temperature, we can say that Temperature surface(2) > Temperature surface(1).”
The amplifications I would like to add to your statement are, (a) the area of surface(1) is equal to the area of surface(2)–this is almost true by definition, (b) the radiation rate per unit area emissivity (i.e., proportionality constant) of surface(1) is the same as the radiation rate per unit area emissivity of surface(2)–if emissivity is a function of gas adjacent to the surface, this amplification is open to debate, and (c) in the presence of an atmosphere (gas) of any kind, the radiation rate per unit area of any surface has the same T^4 monotonically increasing temperature dependence as the radiation rate per unit area from a blackbody (or graybody)–I believe this is amplification is likely to be incorrect.
Consider these amplifications in isolation. First case, (a) the area of surface(1) is greater than the area of surface(2), (b) the emissivity (energy rate per unit area proportionality constant) is the same for both surfaces, and (c) for both surfaces the energy rate per unit area as a function of temperature is the same T^4 (monotonically increasing). In this case, surface(1) may be at a temperature less than surface(2) and still radiate energy at a rate greater than surface(2).
Second case, (a) the areas of surface(1) and surface(2) are the same, (b) surface(1) and surface(2) have different emissivities (i.e., different energy rate per unit area proportionality constants) where the emissivity of surface(1) is greater than the emissivity of surface(2), and (c) for both surfaces the rate energy is radiated per unit area is proportional to T^4 (monotonically increasing). In this case, surface(1) may be at a temperature less than surface(2) and still radiate energy at a rate greater than surface(2).
Third case, (a) the areas of surface(1) and surface(2) are the same, (b) the emissivity (energy rate per unit area proportionality constant) is the same for both surfaces, but (c) surface(1) radiates per unit area at a rate proportional to T^4 (monotonically increasing) whereas surface(2) radiates per unit area at a rate proportional to something less than T^4 (say T^3, which is also monotonically increasing). In this case, surface(1) may be at a temperature less than surface(2) and still radiate energy at a greater rate than surface(2).
By definition, we can assume surface(1) and surface(2) have the same area. Furthermore, we can assume that in a vacuum, both surface(1) and surface(2) have the same emissivity and a radiation rate per unit area dependence of T^4. However, it’s harder to argue that in the presence of an atmosphere the temperature dependence of the radiation rate per unit area will be T^4. As I understand it, the blackbody radiation dependence of T^4 applies to
“cavity radiation” emanating into a vacuum from a small hole in an enclosed volume whose inner walls are at a uniform temperature. The T^4 dependence does not apply to cavity radiation emanating into a gas or onto another surface. Similarly, the T^4 dependence does not apply to radiation from a surface in contact with either (a) another surface (e.g., radiation emanating from the outer surface of the smaller of two touching coincident spherical annuluses), or (b) a gas. Somewhere (I forget where) I’ve read or heard that the denser the gas, the greater the deviation from the T^4 rule. If true, there are two implications. First, to compare the radiation rate per unit area properties (and hence temperature) of a blackbody surface in a vacuum to the radiation rate per unit area properties of that blackbody surface surrounded by a gas requires careful treatment of radiation rate per unit area temperature dependence. Second, if in the presence of a gas the radiation rate per unit area temperature dependence is a function of the properties of the gas, then different combinations of gases can produce different surface temperatures. Thus, I believe an error that appears in almost all Earth temperature models is the blackbody (or graybody) radiation assumption of the Earth’s surface in the presence of an atmosphere.
steven mosher says:
January 15, 2012 at 1:26 pm
Very interesting stuff.
Paul Dennis says:
January 15, 2012 at 1:29 pm
“I don’t understand your comment. Can you elucidate please? Thanks.”
The heat equation says that for equilibrium, the Laplacian must be zero. There are no solutions in spherical coordinates which are increasing with altitude. Hence, such a configuration is unstable.
I will ask again … what are the properties of this proposed 100% transparent atmosphere? What is it made of? If its made of a known element, what is that element (or elements)? If its not, and its just a hypothetical substance, what are the properties of that substance that enable it to be 100% transparent (not just 99.99999…%, 100%). I would like to understand whether it has any known correlate in any possible world. If it doesn’t, what is it’s value as a hypothetical? Thanks.
A maintenance elevator story FOR Willis’ QED
He already provided a simple enough argument (an express elevator story) but the following working-through of the history of a liquid planet dropped into a uniformly irradiated environment might help flesh it out a bit:
Assume the liquid is just like water, except that it does not freeze, and its gaseous form is not a GHG. Instead of water, call it fauxter. Assume that the incoming radiation levels are such that the SB equilibrium temperature of the planet Fauxter is below the boiling point of fauxter, and that when it pops into existence, Fauxter is entirely liquid and is colder than the SB equilibrium temperature.
When incoming radiation starts to strike Fauxter’s ocean, the ocean will begin to warm and some of the surface fauxter molecules will transition to vapor. Evaporation will cool the oceans as energy gets pumped into the atmosphere, but the overall effect will be warming. Both the oceans and the atmosphere will gain heat content, and the more the planet warms, the more readily the surface fauxter will transition to fauxter vapor, building the atmosphere.
In this initial phase, incoming radiation exceeds outgoing radiation. The difference is stored both in the rising heat content of the ocean and the atmosphere, and in the increased potential energy of the atmosphere as it gets lifted up through the planet’s gravity well.
Conduction should tend to bring the surface temperature of the ocean together with the near-surface atmospheric temperature. If they are brought fully together then the temperature above would lapse from the ocean surface temperature according to ideal gas law, decreasing with decreasing atmospheric pressure as altitude increases.
This seems to me to be the crux of the issue. The heat content of the atmosphere is all determined by the ocean surface, both through the warming of fauxter into fauxter vapor, and by heat conduction between ocean and atmosphere. If we assume no convection, then the temperature profile from the surface on up just follows the lapse rate, and it is the surface that determines the LEVEL of this profile. The temperature profile can be stepped up or stepped down but the level of the profile is driven from the bottom of the atmosphere, not the top.
This is why atmospheric pressure cannot warm the surface. The causality goes the other way, at least in this GHG-less-atmosphere example. It is surface heat that lifts the atmosphere in the first place and is responsible for the level of the temperature profile going up. That result of the surface temperature cannot in turn be the cause of the surface temperature. The push only goes one way. Atmospheric mass does determine the lapse rate, but not the level of the temperature profile.
Once the ocean surface temperature reaches the SB equilibrium temperature, the system does not gain or lose energy. Solar radiation will still pry fauxter vapor from the ocean, but an equal amount of fauxter should be phase transitioning back to liquid.
The upshot is that atmospheric pressure will not drive surface temperatures above the SB equilibrium surface temperature because the causality goes the other way. It is surface temperature, not atmospheric pressure, that determines the level of the atmospheric temperature profile.
You have now arrived at the Fawlty Towers penthouse. How’s the view?
(Again, for anyone who wants to see it, I put a link on my own blog to Han’s Jelbring’s 2003 paper, “The Greenhouse Effect as a function of atmospheric Mass,” so that Willis will not have to tolerate any link to Tallbloke’s Talkshop on “his” thread. Hopefully he will not again delete this link to my own blog. After all, I put it up at HIS suggestion. For someone who claims to be motivated by the need to fight censorship, Willis seems to have engaged in far more censorship than Tallbloke ever did. Still, very nice post Willis, and your marathon effort in responding to comments is much appreciated.)
I just noticed the point of confusion about the gravitational effect.
It isn’t the process of compression that generates the heat.
It is the increase in atmospheric density at the surface caused by the gravitational compression that generates more collisional activity.That is what N & Z are referring to in their paper so any assertions that they are wrong on the basis of compression not being the cause are missing the point.
Alan Wilkinson says:
January 15, 2012 at 1:36 pm
First, at higher altitudes the pressure is lower and there is less gas in each shell, therefore its total energy is diminished.
Pressure diminishes exponentially. Energy content would increase with the inverse square of the radius.
“Second, it is not unstable. An isothermal column is neutral to convection whereas a temperature gradient in either direction is not – being either stable or unstable according to direction.”
I think you are thinking of a flat geometry. Spherical distribution demands a particular direction for stability.
“However, as I noted above, the upper boundary of an isothermal atmospheric column is unphysical since it allows the gas to escape gravity.”
Good point.
Alec Rawls says:
January 15, 2012 at 1:53 pm
“Once the ocean surface temperature reaches the SB equilibrium temperature…”
Will it do so? How do we know? What is the energy distribution? What is the spatial radiation distribution? Does it integrate to an equivalent SB temperature relationship for an ideal, perfectly smooth blackbody?
It is not a given. SB simply does not, in general, hold in such a situation.
Bart says:
January 15, 2012 at 1:56 pm
Alan Wilkinson says:
January 15, 2012 at 1:36 pm
“Energy content would increase with the square of the radius.”
By which I mean, with constant pressure, but I have made the argument that the pressure and energy density cannot be made to match up due to the different rates of progression of pressure and elemental volume.
“The upshot is that atmospheric pressure will not drive surface temperatures above the SB equilibrium surface temperature because the causality goes the other way. It is surface temperature, not atmospheric pressure, that determines the level of the atmospheric temperature profile.”
Do you then see a role for density of the atmosphere at the surface altering the rate of cooling of the surface and thus elevating the equilibrium temperature above S-B ?
Presumably the more fauxter that enters the atmosphere the greater the mass of the atmosphere, the greater the density at the surface due to gravitational compression and the higher the surface equilibrium temperature will become ?
steven mosher says
January 15, 2012 at 1:26 pm
some lecture notes for folks
Steve, are those the same calculations that go into the models? The problem is the models and reality don’t appear to match, which indicates something missing in the calculations. You can either believe the data or the theory?
For example, we have all these planets that don’t match these calculations, we have Miskolczi and his 230 observations that yield a constant optical depth. The point is the theory must be wrong when nature gives different results. Could it be the pot/lid hypothesis? I don’t know, I just try and follow the data and see where it leads me.
So if I pump superheated nitrogen into a metal tank, the nitrogen will not release any heat to the metal walls via infra-red, but by physical contact alone?
Then the metal tank will be heated by the contact with the nitrogen and the tank will release heat to the environment via both infra-red and physical contact with the air surrounding the vessel.
I was not aware that some balls of glowing hot gas can not radiate heat via the infra-red.
It seems counter intuitive.
Is that correct?
****
Paul Dennis says:
January 15, 2012 at 12:55 pm
I think Willis’ model is correct, bar one aspect which is that of the dry adiabatic lapse rate. I think that in the model the atmosphere will rise to a uniform temperature which is that of the planetary surface. This atmosphere is unable to radiate energy because it is composed exclusively of non-GHG molecules. Thus at equilibrium all the energy is radiated from the planetary surface. There is no conduction of heat through the atmosphere since the surface and atmospheric column are all at the same temperature.
****
The earth’s dry lapse rate is caused by GHGs. Dry may mean w/o condensation (adiabatic), but the water-vapor, CO2, etc, are still present. The reason the upper atmosphere cools is because it can radiate w/GHGs, and is exposed to the cold of space. Air near the surface radiates too, but is insulated (and radiated back at) top & bottom by adjacent emitting/absorbing layers. A non-GHG atmosphere, as you stated, has an insignificant lapse-rate & eventually represents the avg surface temp thruout its entire column — it couldn’t be otherwise since non-GHG means it can only radiate heat away at insignificant levels.
Is the non-GHG world “warmer” at the surface than an airless world? It’s kinda apples & oranges, but the air temp right above the surface in the day would be hot indeed from conduction. There might be some wind & shallow mixing. But that air would also cool down at nite (from conduction) to near the bitter-cold surface temp & prb’ly form a strong but very shallow temp inversion. Bottom line is, the non-GHG world would be a cold place averaging well below freezing at earth’s orbit. Doesn’t matter what the surface pressure was — one bar or one-hundred.
I doubt there’s a “real” non-GHG planet out there — CO2, water vapor, methane, NO2, etc, seem to be common atmospheric components at least in our solar system.
Willis & Robert Brown,
I think that the three of us agree that the emissivity of gaseous argon is not strictly zero, and we also agree that it is so small that treating it as zero can make no conceivable difference to your argument. Those (such as Anna V and Spiny Norman) who think that negligible emissivity will change your argument are naive.
Thepompousgit is of course right that in practice the effective emissivity of any real sample of argon would be dominated by various imperfections, such as the container (on earth) or passing dust (in space). But again this doesn’t change the argument.
Oops. In my haste to add my comment, I’m pretty sure I made a mistake. Specifically, in Ferd Berple’s logic, I forgot to include (a) conduciton between the surface and the atmosphere, and (b) more importantly the fact that radiation from the surface can go to both the atmosphere and space. So what I wrote above is likely to be partially correct or flat out wrong. I want to think some more.