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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Hi Willis –
Not an attempt at refutation, rather clarification.
Anna v and others have politely hinted that non-GHG’s are sources of radiative emission at wavelengths other than IR. Whether or not this is a significant source of cooling in your hypothetical world, it is still important to not confuse people.
From my own non-expert understanding of QED, there are infinite paths to electronic excitation. To me, that means nitrogen could obtain kinetic energy via surface collision and then acquire the additional (precise) energy (from whatever means) to undergo electronic excitation – a condition ripe for photon emission to space – and subsequent net surface cooling.
bi2hs
Robert Brown says:
.
Robert: The issue is not a binary one of “Does the radiation from the surface get absorbed at all from the surface or does it not?” Rather, what you want to imagine is photons likely getting absorbed and subsequently emitted several times before the energy escapes the atmosphere. (In essence, a sort of random walk.) And, the question becomes at what altitude in the atmosphere the photon has a good probability of being able to successfully escape to space. It is at this “effective radiating level” where the average temperature of the atmosphere has to be ~255 K. Currently, that level is at ~5 km and hence the temperature at the Earth’s surface is obtained by extrapolating down from that level to the surface using the average tropospheric lapse rate, which is about 6.5 K per km: 255 K + (6.5 K / km)*(5 km) = 287.5 K.
What happens as you add greenhouse gases is that the effective radiating level increases while, to first order, the lapse rate (which is forced by convection to remain around the appropriate adiabatic lapse rate) does not change. So, as an example, let’s say you add enough greenhouse gases to increase the level to 6 km. In that case, what happens is that you have a radiative imbalance because the temperature at 6 km is colder than 255 K and hence the Earth + atmosphere is emitting less energy than is being absorbed from the sun. As a result, the Earth + atmosphere will warm until the new effective radiating level at 6 km is 255 K. And, the new temperature at the surface will now be 255 K + (6.5 K / km)*(6 km) = 294 K.
This is, of course, a simplified picture in many ways including:
(1) The level at which the radiation can successfully escape to space is in fact a strong function of frequency, so the “effective radiating level” is just an average value. To do quantitative calculations, you really need to use a line-by-line radiation transfer code.
(2) The lapse rate actually is expected to change a bit with warming: In the tropics, the appropriate lapse rate is generally the moist adiabatic lapse rate and this is a decreasing function of surface temperature. This effect is called the “lapse rate feedback” and it is a negative feedback that is included in all of the climate models. There are variations in the strength of this feedback from model to model; however, fortunately, because the physics involved is closely related to the physics of the water vapor feedback, models that have a stronger (negative) lapse rate feedback also have a stronger (positive) water vapor feedback and, hence, it turns out that the variability of the total of these two feedbacks from model to model is much smaller.
Nonetheless, to first order the picture you want to have in your mind is that the greenhouse gas concentration controls the level in the atmosphere at which the temperature has to be 255 K…and, in particular, that this level rises as the concentrations increase. The average temperature at the surface is then obtained by simply extrapolating using the average environmental lapse rate of ~6.5 K per km.
Perhaps it would be helpful to invent an even simpler model to develop some thinking.
What if you had a black body sphere, per Willis’s description, evenly exposed to radiation from every direction. It is infinitesimally thin but surrounded by some magic insulating material that is transparent to all radiation wavelengths, a solid. This magic insulation provides us with a black body surface that has radius B. The magic stuff has radius M.
By conduction, the magic stuff equilibrates to some constant ‘lapse rate’, really a temperature gradient that goes from Tb K at the surface, at distance B from the center to 3K at distance M from the center. The only transport mechanism is conduction so it seems that there must be a gradient like you would get from any insulation. Magic stuff has some energy content that implies, since no new energies are involved, that the black body has given up some of its energy to the magic stuff but the overall energy content, when equilibrated, is exactly the same.
I only pose this because, for me, it brings up the intriguing possibility that the incoming radius is impinging on a sphere of radius B but the outgoing energy might just be coming from some sphere of radius between B and M, we’ll call it X, since the volume of the contained energy available for exit is larger than the volume that was available for incoming.
If this is true then the outgoing flux value measured at X has to be less than the incoming flux value at B since there is more area to transit the same energy. Could this provide for a change, up or down on surface temperature?
Bart says:
January 15, 2012 at 1:28 pm
What, there has to be thermal exchange between two adjacent objects?
Not if they are at the same temperature there isn’t. And at equilibrium, there is no temperature differential across the surface.
This is not unphysical at all, other than that it is happening only in our thoughts. You do understand what a “thought experiment” is, don’t you?
Thanks,
w.
Willis,
I appreciate the great length of the replies and how some of the misunderstandings can make you feel crazy. You are doing a great job overall, even though I disagree on some individual points.
I have tried to respond to make you understand where N&Z and Jelbring went wrong. Making an elevator speech for N&Z and Jelbring is not necessary. Both make the erroneous assumption that somehow the adiabatic lapse rate determines a temperature. It does not. It only determines a gradient, and even that requires enough mixing to prevent conduction from reducing the lapse rate, and in the limit, approaching to near isothermal. The greenhouse gas (and or aerosols) are needed to raise the location of average outgoing radiation leaving to space (to match the level of absorbed solar radiation), so that a fixed absolute level of temperature is determined at that effective altitude, and the adiabatic lapse rate does the rest.
However, your elevator speech also fails when you state it is absorbed energy, radiated by the atmosphere back to the surface, that warms the surface in the presence of a greenhouse gas. In order to warm the surface, you have to have net heat transfer. For a warmer surface than atmosphere, the heat transfer will be from surface up. This is true if it is radiation or conduction combined with convection. It is true that energy can be transmitted from the atmosphere to the ground by radiation, but more energy is radiated up than down, and it is the NET energy transfer that is the heat transfer. The back radiation is not the cause of the ground heating above the non-greenhouse case, it is a result of the ground being warmer than otherwise as stated above, and the presence of a partial insulation of radiation.
This is in some ways similar to the way an insulation layer on an electrical heater of constant power slows heat transfer out, resulting in a hotter heater to get the power out. Back conduction is not heating the heater surface, it is only slowing the escape rate at the previous temperature. It is not energy going into the insulator and then partially conducting back to the surface, but it is causing the surface to accumulate extra temperature due to energy not being removed as fast, and the increase eventually raises surface temperature so the energy is removed fast enough. However, the atmosphere is different in other ways, as convection can still carry power out. That is where the lapse rate and set temperature at a particular altitude come in. The surface accumulates extra solar heat energy and convection and some radiation transfer carry the excess heat upwards until the adiabatic lapse rate is reestablished at the new level. This then determines the ground temperature as long as the lapse rate is the adiabatic (wet) lapse rate.
Stark Dickflüssig said @ur momisugly January 15, 2012 at 1:13 pm
Nope, I can’t see the word “untrue” in my response. I asked for a reference. Quantum events, such as the emission of photons, are probabilistic and that implies a gas molecule has some probability of absorbing/emitting outside of its characteristic emission lines, that probability is vanishingly small. In the limit (an infinite number of seconds away) then all molecules will have emitted all available photons. I see no mention of this in the first link you provided, merely the bald, unsupported statement.
I’m not sure what this has to do with Willis’s thought experiment.
Spiny Norman says:
January 15, 2012 at 1:53 pm
My friend, it is a thought experiment. No gas is perfectly transparent, although there are many gases that are very close.
So it is not a real gas, but it is very close to one, and we are ignoring the slight differences by imagining, say, that argon gas were perfectly transparent. But the composition doesn’t matter for our purposes.
As to the value as a hypothetical, many thought experiments have no known correlate in the physical world, including the famous “gedanken” experiments described by Einstein. Contrary to your claim, these can be very important and can reveal hidden truths, despite being as non-physical as my planet surrounded by a sphere of evenly spaced suns to bathe it in uniform light.
w.
Willis Eschenbach says:
January 15, 2012 at 12:29 pm
Once again, you claim to understand Huffman.
EB> I think I’ve explained it better than you have explained the GE. Your elevator speech
EB> explains nothing. It’s a hypothesis without an experiment, or better yet, a hypothesis
EB> with a counterexample in the data of earth and venus as explained by Huffman.
Once again, you fail to explain it in a clear, concise manner as requested.
EB> You are being purposefully obtuse IMO. I won’t speculate as to why.
Once again, I won’t believe you understand it until you can explain it.
EB> The only thing Huffman (and I) have noticed is the correlation. You are discarding that
EB> data in favor of your speculation about GE theory. Once you or I get a hold of a reasonable
EB> sized planet that we can experiment with at our leisure we can settle our disagreement.
EB> Until then I’ll respectfully disagree with you.
beng says:
January 15, 2012 at 2:34 pm
The dry adiabatic lapse rate is NOT caused by GHGs, beng, it exists whether the gases in question are GHGs or not. The dry adiabatic lapse rate is given by g / Cp, which is gravity divided by specific heat. There is NOTHING IN THERE about GHGs.
w.
Willis says:
It is a little more confusing than that because the adiabatic lapse rate represents a stability limit on the actual lapse rate…That is, lapse rates greater than this are unstable to convection whereas lapse rates less than this are not. An atmosphere with no GHGs will not be able to cool significantly through radiative emission…and hence some, such as Roy Spencer for example, have argued that it will end up with an isothermal profile or a lapse rate less than the adiabatic one. (I have no strong opinion either way on this.)
However, your point is basically correct for our Earth that does have some GHGs: The troposphere is strongly warmed from below (by both solar radiation absorbed at the surface and GHG absorption) and cooled from above. As a result, the lapse rate would, in the absence of convection, exceed the adiabatic lapse rate and this sparks convection which reduces the lapse rate down to the appropriate adiabatic lapse rate. And, as I noted, to the first approximation, this average lapse rate does not change with the addition of GHGs (although to a better approximation, it is expected to decrease slightly).
Willis simplified steady state model shows that the force of gravity on a non-“greenhouse” atmosphere has no effect on surface temperature and with no convection there is very little energy transfer by other than radiation. Think about the perfect gas law. (PV)/(nT)=constant. Pressure (P) is the result of the gravitational attraction between the mass of the planet and the mass of n molecules of gas. Now take two planets with the same mass but with different number of molecules of gas. P/n will be the same for both so there should be no change in T. Now what should we expect when we increase the input radiation. The surface temperature will increase and conduction will transfer some of that energy (not much) to the atmosphere. That slight increase in atmospheric temperature will increase the volume but not the pressure because there has been no change in n. The surface will soon radiate as much energy as it receives.
Leonard Weinstein says:
January 15, 2012 at 3:09 pm
Thanks, Leonard. It is frustrating, and likely I snipped some stuff that folks thought was the next Theory of Relativity … I struggle with how to do this as does everyone, and if so they are welcome to repost it, but if it was nonsense when it was snipped, it has not changed in the interim.
I have said before that the lapse rate doesn’t mean that the surface has to be warmer than the atmosphere.
It means that the atmosphere has to be cooler than the surface.
In other words, as you point out, the lapse rate does not determine the surface temperature. It is the other way around, the surface temperature determines the starting temperature for the lapse rate.
Leonard, without wishing to pick on you but because it is a good example, let me use this to show why it is so important to quote my words. In general, and particularly for an elevator speech, I think about my words hard and I pick them carefully. What I said was:
• As a result of absorbing that energy from the atmosphere, the surface is warmer than it would be in the absence of the GHGs.
I did not say what you reported. You claim I said the absorbed energy “warms the surface”. I very carefully did not say that, for that specific reason. I’ve been caught in what I see as a meaningless semantic argument before.
So I carefully went around that trap, by making the indisputably true statement that “the surface is warmer than it would be in the absence of the GHGs”. In my own common parlance I call that that “warming the surface”, but there are folks who want to argue it’s somehow not real warming, so I avoid that terminology in favor of the terminology I use.
Folks, please take the message here. Leonard did not understand, nor did he correctly report, what I had said. As a result he was arguing against a position I HAD NOT TAKEN. An unfortunate waste of time for all concerned.
Please, please, QUOTE WHAT I SAID THAT YOU THINK IS WRONG. Be as specific as you can, so we can all understand what it is that you are arguing against.
I am happy to defend my own words.
I cannot defend your interpretation of my words.
Quote what you disagree with.
w.
Willis, I’d like to congratulate you on providing, possibly unintentionally, one of the finest BS filter posts we’ve seen on this site.
In particular, there are a number of individuals who I previously read with interest who have exposed their shallow understanding of various physical mechanisms. I shall in future read their output with a deal more caution.
And thanks in particular to the interjections of some real experts.
And a final note to those who believe all matter must radiate until it reaches absolute zero. Considier a single N2 molecule out in space. Is it radiating? For that matter, does it have a temperature? If so, in which frame of reference is this temperature defined? Does it appear “hot” to one observer, and therefore appear to be radiating, while appearing “cold” to another observer in a difference frame of reference?
PS. Clearly my previous post is off topic, so I expect to be snipped. And deservedly so!
Willis says:
“The atmospheric lapse rate is a result of the kinetic/potential tradeoff for all molecules. It does not require bulk convective motion for the lapse rate to exist. As Tim says, at equilibrium the atmosphere will be isentropic, rather than isothermal.”
Perhaps through most of the atmosphere.
But if the atmosphere is not losing energy to space via radiation it will be warmer than the average temperature.
The daily pulses of energy would push the system warmer because so little would be conducting down to the surface to be radiated away. Common air is one of the best insulators around.
Also anything that does conduct down would be largely replaced by convection within a few hours.
This would work exactly like that well insulated passive solar water heater system where the storage is placed higher than the collector and the water gets far warmer than average day where it is placed does. In fact it often gets warmer than the day ever gets because of no loss due to convection it gets as warm as you can make a greenhouse get (which is a lot warmer than most greenhouses because hardly anybody goes beyond dual glazing in greenhouses)
The atmosphere at the bottom at night you would have this tight little temperature gradient inversion layer. It would likely be measured in inches due to the lack of weather and non-existent convection.
We currently see these inversion layers at night where the surface cools faster than the atmosphere. When the sun comes up convection dominates because of the need to replenish heat lost by the atmosphere due to radiation which make up virtually all of the atmosphere cooling. At that time the gradient is the least steep and evaporation kicks to lower the gradient as well.
It seems clear that’s the case and the only question is a number for it as its all been sucked up into universal CO2 theories. If its the entire number then perhaps Jelbring is right because it would be consistent with Robert Brown’s comment: “Can gravity ever act as an energy source that releases heat in a gas? Sure. It is the primary source of heat in stars as they form, right up to where they “ignite””.
Gravity would not need to be a continuing source of heat as this heat would never be lost. It would just be there. Its also interesting how Jelbring has correlated this with mulitple planets based upon the masses of their atmospheres. Kind of reminds me of how climate science pooh poohed the mid 20th century warming and ocean oscillations until they could no longer hide from them. Akasofu’s and Easterbrook’s charts of the direction of the climate system made a lot more sense too in how they matched temperature oscillations in time with the PDO.
So I would like my question answered about what the surface actually is radiating rather than depending upon calculations dependent upon proxies to tell me. Seems most of the controversy here is in the idea that surface radiation is cranking all that gravity induced heat to space and gravity then has to replace it. I think not! I tend to think the theory would have to fail if it had to do that. And a reread of Jelbring has led me to believe he never claimed that.
Joel Shore says:
January 15, 2012 at 3:29 pm
Joel, I’m not talking about the earth. I’m talking about the dry adiabatic lapse rate. It is a consequence of gravity and is specified as DALR = g / Cp, where g is gravity and Cp is specific heat of the atmosphere at constant pressure.
So what is confusing about that? The dry adiabatic lapse rate is not affected by GHGs. If it were, there would be a “GHG” term in the equation.
All those other things you speak of, environmental (actual) lapse rates, rates affected by GHGs, they are all real. But they have nothing to do with the DALR. It is g / Cp, and nothing else.
Finally, I think (sadly) that Dr. Roy is wrong about the eventual distribution at equilibrium being isothermal. That would put the maximum total energy (kinetic plus potential) at the top of the atmosphere. I see no reason why that uneven energy distribution would be favored over the even energy distribution reflected by the normal lapse rate. I see no reason why the normal lapse rate would not obtain.
This is true. When the local lapse rate exceeds the DALR, the atmosphere overturns until the DALR is restored. However, some people (including Dr. Roy, I fear) have the stick by the wrong end. They think that overturning is the cause of the lapse rate. In fact, the definition of the lapse rate specifies that it is the rate that happens in still air, so convection cannot be the cause of the DALR.
w.
The atmosphere would be in motion and not isothermal for the following reasons:
I don’t know what the topology of this imagined planet with a transparent atmosphere is, but I would have to assume eventually a non-smooth surface at some arbitrary scale. With planetary rotation and differences between polar and equatorial insolation, any atmospheric state would be unstable, and particulates would always be present in the atmosphere, if from nothing else, bombardment from other cosmic bodies. The largest source of particulates eventually becomes the planet surface. Thus the atmosphere would contain particulates and thus not remain uniformly transparent, and would be heated by the same process as the surface, and the suspended atmospheric particulates would radiate back to the surface, raising temperatures above the S-B temperature. And the atmosphere would be turbulent.
In effect the surface area of the planet is enlarged by suspending some of it in a third dimension above the planet. Because the incoming radiation is of a different, higher temperature blackbody spectrum from the reradiated IR, the opportunity for scattered radiation to be absorbed on a second or subsequent collision with either another particle or the surface is magnified, and unlike water vapour clouds, the albedo of dust, especially from extraterrestrial origin is low. Thus the likely equilibrium temperature of an optically and IR transparent atmosphere would be higher than a water dominated atmosphere such as found on Earth.
So even without a GHG, a “transparent” atmosphere would have the same effect, at some arbitrary particulate level.
Thus the elevator explanation is the same, except that “particulates” (I like “dust”!) replaces “GHGs” (or synonyms).
Absorption spectra of gases discussed in detail:
http://www.patarnott.com/atms749/pdf/GrantPettyDeathPhotons.pdf
If it doesn’t absorb it doesn’t radiate
I’m pretty sure I made a mistake analyzing Ferd Berple’s comment. That won’t, however, stop me rom trying to analyze Willis’s “Elevator Speech.” Willis said:
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.
Although not explicitly stated, I infer from the third and fourth bullets that “the energy radiated by the atmosphere back to the surface” is the source of the increase in surface temperature. My question then is: “What stops the process–i.e., what stops the surface temperature from increasing without bound?”
For example, consider the surface temperature in the presence of an atmosphere that is greenhouse gas free. I assume the surface temperature will eventually stabilize at some temperature T0 > 0. Now add a greenhouse gas to that atmosphere. According to Willis’s elevator speech, (a) the surface will radiate energy (IR and non-IR), (b) some of the surface IR radiation will be absorbed by the greenhouse gases in the atmosphere, (c) the greenhouse gases will radiate some of their absorbed energy, (d) a portion (backradiation) of that “re-radiated” IR energy will reach the surface, and (e) the backradiation will increase the surface temperature.
OK, so far so good. For a moment, let’s assume that this produces a steady-state surface temperature T1 > T0. Applying this assumption, we now have a surface temperature of T1. Since T1 > T0 > 0, the surface will radiate energy (both IR and non-IR). As before, some of the Isurface radiated IR energy will be absorbed by the greenhouse gases in the atmosphere and a portion of that absorbed energy will be “backradiated” to the surface. If as occured when we first introduced greenhouse gases into the atmosphere, “greenhouse gas backradiation” raises the surface temperature from T0 to T1, why won’t greenhouse gas backradiation raise the surface from temperature T1 to T2? And once a surface temperature of T2 is reached, why won’t the process repeat raising the surface temperature to T2; to T3, etc?
Although there may be many ways to limit the surface temperature, I can only see one way. Specifically, if the amount of IR surface radiation eventually decreases to zero there will be no greenhouse absorption of surface radiated IR energy and no IR backradiation of IR energy radiated by the surface. This will occur if the surface temperature approaches infinity because as the surface temperature approaches infinity, the amount of blackbody radiation in the IR band decreases.
As long as IR backradiation increases the surface temperature, I don’t see how “greenhouse gas saturation” (i.e., the state where the greenhouse gases that exist in the atmosphere are absorbing all the outgoing radiation they can absorb) will stop the temperature increase. This is because backradiation doesn’t stop when greenhouse gases become saturated–i.e., some IR backradiation will exist for both saturated and unsaturated greenhouse gases. And we have assumed that backradiation increases the surface temperature If someone claims that backradiation does not necessarily raise the surface temperature, then (a) I either want to know under what conditions backradiation stops increasing the surface temperature, or (b) how can it be argued (by Willis or anyone) that backradiation for Earth-like greenhouse gas levels will raise the Earth surface temperature.
I think that you have forgotten about things like frequency conversion (where something receives energy at one wavelength and reradiates at a different wave length which is what the earth does) and there is no mention of convection and the evaporation of the atmosphere into free space as a result of convective heat transfer. This boiling of the atmosphere and the Ideal Gas Law explain how a transparent atmosphere in a gravity field still provides a layer of insulation and also transports a part of the energy received through the kinetic motion of the molecules of the transparent gas boiling into space, changing the temperate gradient across the span from far space to the core of the planet so that the 0K point is moved to the top of the atmosphere. Think about it, by adding the atmosphere you have changed the diameter and density of the object under consideration. You need to think about the gradient from free space to the core of the planet, not just the thin film of the solid to air/space boundary. Think also of the boundary or extreme cases say for example a massive or extremely dense planet with a huge gravity well and therefore a very dense atmosphere.
Is the case of a pefectly transparent gas possible? I thought all elements and molecules absord/emit at some point in the spectrum and there can be no zero radiation from a gas except at 0K? The SB equation returns zero only for 0K.
What is the temperature of your array of suns? That means, what is the power spectrum density from those sources? Our sun radiates most in the ultra violet because of a surface temperature of 5000+C. That UV heats the surface of earth which radiates most in the IR because of a temp of around 300K. Both bodies radiate across the entire spectrum with different PSD so the spectrum of the incoming radiation is different to the spectrum of the outgoing.
Also, what is the geothermal heat flux in your thought experiment and for a real planet like earth, how does that flux vary over time, constantly in one direction or randomly as a result of cosmological factors? Don’t forget there are spots with measured geothermal heat flux up to 15Wm-2 in the USA.
And just to be provocative, why are you assuming the energy received at the surface is transmitted outward only? Surely energy is radiated and conducted inward as well? Over an infinite period of time, would not the core of the planet reach an infinite temperature in your simple model?
Sorry, my bad, that last question should read: Over an infinite period of time the planet would not the core of the planet reach the temperature of your array of suns?
A brilliant site for the physics:
http://www.patarnott.com/atms749/
The presentations are clear – from First Course in Atmospheric Radiation: Second Edition, by Grant W. Petty.
Willis Eschenbach says:
January 15, 2012 at 3:08 pm
“Not if they are at the same temperature there isn’t. And at equilibrium, there is no temperature differential across the surface.”
You can have a temperature equilibrium at the surface/atmospheric interface without being in thermodynamic equilibrium. There is no reason the temperature equilibrium is the same as it would be if you took the atmosphere away. In fact, I can assure you, it is not the same. The magnitude of the difference is the only valid point of argument.
We do not know that magnitude. And, we are not going to pin it down through “thought experiments” because the subject is, frankly, too complex for back-of-the-envelope calculations. We need data from experiments which duplicate the exact physical state of the system under study. As far as I can tell from my, admittedly limited, searches, there is no such data available.
Argumentum ad nauseam
A giant thread, which in the end only produced enemies.
WUWT.
“I don’t know if this answers your questions but I’m satisfied that Willis’ reductio ad absurbum approach provides a proof that gravitational effects cannot raise the temperature of the planetary surface.”
It proves that 240 watts of solar flux times 4 does not equal 960 watts per square meter.
240 watts of solar flux times a million also does not equal 960 watts per square meter.
Million sources of 240 watts can not cause temperature higher than -18 C.
The Moon [no greenhouse gases] has temperatures much higher than -18 C
Mars [which does have greenhouse gas, be recieves far less sunlight than the Moon or earth] also is heated during the to higher than -18 C and receives less than 1/2 the solar flux as the earth or the Moon gets.
Some may claim that the earth receives an average solar flux of 240 watts, but you can’t average
the solar flux and expect it to give correct answers.
The only thing averaging the energy from the sun, does is tell you how much something with 4 times the surface area can radiate.