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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It isn’t called a gravitational CONSTANT without good reason. Joel Shore and others make the same mistake.
Gravity is a continuous renewing process which replenishes itself over time. No one knows why or how, not even Einstein, but we must live with it.
So it is NOT a transient effect and the result is PERMANENT all other things being equal.
Without that effect the Ideal Gas Law would not be a Law.
Only rarely does something leave me speechless. What does this mean? I really, truly have to say “nothing”, but I’m willing to have it explained to me.
In the meantime, permit me to explain it to you as I understand it, which is really pretty well.
Gravity isn’t a “continuously renewing process”. Gravity is an interaction between two massive objects that results in a force of attraction between them. Within irrelevant corrections associated with relativity or things like “dark” matter or energy, the form for gravitation is:
F_{12} = – G M_1 M_2 / r_{12}^2
It is always attractive and acts along the “right line” connecting two point-like masses. Spherically symmetric masses behave like (produce the same gravitational field as on the outside of) a point mass at the origin with the same total mass. Hence this field describes the force of gravity near the surface of the Earth.
Near the surface of the Earth (inside the atmosphere) variation with “height” varies the radius r_{12} by a trivial fraction — the Earth is 6400 km in radius, and most of the atmosphere is contained within 32 km of the surface, a variation of around 0.5%. For that reason, one makes little error by assuming that “Near Earth” gravity is a constant field, producing a force of the form:
F = mg
where g = G M_earth/R_earth^2
Gravity has (and pay careful attention here) nothing whatsoever to do with the Ideal Gas Law. I really mean that. Nothing whatsoever. Gravity is not mentioned anywhere in the derivation of the IGL. It plays no role. It is irrelevant. The gravitational force between gas molecules is so tiny as to be completely ignorable, and besides, it doesn’t have the right form to lead to an IGL if that were the only source of interaction. The IGL is derived using a hard sphere interaction or no interaction but a presumption of equilibrium and hence equipartition.
Gravity is constantly being proposed as a source of heat in discussions on this site, usually (AFAICT) by people who are really pretty clueless about what gravity is, what it does, what energy is, where it comes from (in the context of gravity) and so on. I will provide you with a single example of how to use gravity “correctly” as a source of energy delivered to the Earth from outside of the Earth, and one that shows you how people use it incorrectly.
Correct usage is templated by the killer asteroid. It begins far away, where its (negative) potential energy is very small. It falls toward the Earth, being pulled downward by the force of gravity. This force speeds it up. Speeding it up increases its kinetic energy. From the point of view of energy conservation, as its kinetic energy increases, its potential energy decreases, which is in fact the case, becoming more negative (negative and larger in magnitude) is such a way that the total mechanical energy (sum of kinetic and potential) of the asteroid remains constant.
For those unfamiliar with “kinetic” and “potential” energy, think of this as your checking and savings account. Kinetic energy is energy of motion, like your checking account contains money that can easily be mobilized. Potential energy is energy stored in a field interaction that can be freely transformed into kinetic energy, much as your savings account can receive money from checking or vice versa. Moving money back and forth doesn’t affect the amount of money you have, but it does change money in one form/venue to money in the other. The only thing the metaphor doesn’t help you understand is that nature exerts force in the direction that favors the transfer of money from savings to checking, forces push in the direction that decrease potential energy.
So, the asteroid falls to Earth, speeding up all the way, hits the Earth and transforms basically all of its kinetic energy to heat. A lot of heat in the case of an asteroid. Less heat in the case of e.g. small meteors. This heat represents an actual gain in the Earth’s energy budget, because it came from outside of the Earth and ended up inside the Earth (including the atmosphere). It remains there, warming things, until radiation (the only way the Earth can lose energy) rebalances the Earth towards dynamical equilibrium with Mr. Sun.
Incorrect usage is, well, everything else. The problem is that the total gravitational potential energy of the atmosphere is very, very nearly a constant no matter how it moves around, up or down in convection, side to side as wind. Gravity produces a force that sometimes opposes motion, sometimes supports it. No net work is done by gravity as gravity acts on the air, and gravity itself is not the source of the free energy that provides the actual pushes that move air around.
Almost all — and by “almost” I mean 0.9999… with many nines of it — of the energy that actually moves air around, moves it up and down and sideways — comes from one place and one place only. Mr. Sun. The sun warms the surface, the surface warms the air, the air expands (reducing density), and experiences a buoyant force as colder denser air seeks to displace it. It rises (increasing gravitational potential energy) as colder air falls in behind it (decreasing gravitational potential energy) in a near-zero-sum game whose source of energy was the heat that warmed the air packet and altered its density, not gravity. If there were no external heating, no inhomogeneity in density, there would be no net buoyant force and the air would stratify, unmoving, at which point gravity would do no work whatsoever, not even balanced work on chunks of air.
In order for gravity to release energy that appears as actual heat, in other words, some mass has to go downhill (because just rolling a ball downhill is also an example of the good paradigm). Sure, rolling something down hill gives you energy, but you can’t roll the same ball downhill twice without first pushing it back up to the top, and to do that requires a source of energy that is not gravity. Gravity can store energy (energy from somewhere else) and release it later, but it cannot act as a source of energy unless all of the mass ends up at the bottom of the hill when you are done, and once it gets there nothing happens until something else pushes it up once again.
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” — fusion kicks in — as a source of non-gravitational free energy. Brown dwarfs and black dwarf stars are stars whose primary source of heat is a slow gravitational collapse that is literally “squeezing” gravitational energy out in the form of blackbody radiation, a process that can take billions of years. Jupiter’s surplus heat may come from a similar process, because Jupiter is not that far away from the mass range that would have caused it to be a brown dwarf instead of a gas giant. But the Earth? It is tiny. Its atmosphere long, long ago equilibrated so that solar heating is the only meaningful source of energy, with tiny corrections from the internal heat of the Earth bleeding out through the surface, from the tides, from radioactivity, even from magnetic induction (it is a conducting ball spinning in the Sun’s magnetic field, which means that it is very weakly being magnetically “braked”, a process that releases an impressive number of Joules in a year but that is utterly irrelevant as far as being a thermally significant source of heat).
So please — can we stop speaking of gravity as a source of heat? Seriously, and permanently? Gravity is not a source of heat in the Earth’s atmosphere. Not ever. No, no, no. Gravity is not irrelevant — it is the reason that there is a lapse rate in the thermal gradient of the atmosphere — but it provides no energy to the processes that maintain that gradient. That energy has to come from somewhere else, and there is only one somewhere else and it is a million miles across, 93 million miles away, and converting over 4 million metric tons of mass to energy every second some tiny fraction of which makes its way, after meandering around inside it for 100,000 years, to the Earth.
I still do not understand the N&Z paper any more than Willis does — it seems to imply that gravity is providing heat and that PV = NkT is somehow relevant to the process, but the former, as I make clear above, is nonsense and the latter is equally irrelevant — the lapse rate may have something to do with the structure of dynamic equilibrium in an atmosphere, but it isn’t providing heat or altering the way heat is absorbed or emitted per se. It only becomes important along with differential outgoing radiation, radiation with different temperatures in different bands, which is the “atmosphere warming effect”, a.k.a. “the greenhouse effect”, no matter how you dress it up and no matter that it has nothing to do with the way greenhouses actually function.
I’m still working on plausible non-greenhouse sources of warming, or ways that the “simple” greenhouse effect is not so simple — differential warming or cooling due to differential lateral transfer of heat, differential warming or cooling due to modulation (or internal feedback of) albedo. Until I understand what N&Z are trying to assert as a hypothesis I will reserve judgement, but so far I don’t understand what they are trying to assert.
rgb
[COMMENT: Robert, many thanks for this post. For those unfamiliar with him, Robert is a physicist who teaches this stuff for a living. I would strongly recommend that anyone who believes that gravity can do ongoing work or be the source of ongoing heat read this post two or three times. -w.]
@Robert Brown
What’s missing from the whole scenario is “work”.
This Wikipedia entry from thermodynamics sums it well:
In the case of our model planet, the atmosphere gravitationally attracted to the spherical mass would be a static system unless perturbed by an energy input of some kind. The atmosphere would essentially be like a layer of paint on the sphere, static and unmoving.
Add external energy (our solar light source for example), and the surface warms, and the atmosphere roils, parcels of atmosphere are lifted and returned to the surface as they cool.
Think lava lamp.
Work is being done in the lifting, and in the lifting the adiabatic lapse rate applies. Rising (expanding) air cools, sinking (compressing) air warms. That’s a product of work due to the external energy input.
Shut off the energy, and the model planet goes back to steady state equilibrium with the atmosphere clinging like paint again.
Like you, I can’t see any way “that gravity is providing heat and that PV = NkT is somehow relevant to the process”.
Willis Eschenbach says:
January 14, 2012 at 3:14 pm
As I said to someone else who wanted to abuse me because I don’t understand Huffman, if you’re such a dang expert, where’s your elevator speech on the Huffman Effect?
—
No abuse intended Willis. I don’t see how someone can read Huffman and not understand. It’s about as simple as it gets. This is the only post you’ve made that’s left me scratching my head. I’ve enjoyed all the others.
. I’m happy to disagree and hope you are as well 🙂
Take Care.
Eric
To avoid confusion, I’m NOT stating that the GHE is a chemical reaction, that is simply an analogy. What happens is the GHGs become well mixed in the atmospheric profile due to pressure and heat. Hence, the GH effective radiating altitude gets set very high even with low concentrations. Because the atmospheric profile is changed very little by adding additional GHGs, that altitude does not increase if things like additional CO2 are added. It is that height that determines the overall GHE.
Willis Eschenbach says:
January 15, 2012 at 2:50 am
(I Hope I got that formatting right and people know who said what)
Actually, Kwik made a mistake even within these lines when he said: ” it looses its energy (via conduction)…”
The rising air doesn’t loses much energy from conduction because air is such a poor conductor. Mostly the air rises “adiabatically”, neither gaining nor losing energy. The air GAINS gravitational energy and LOSES internal energy (ie it cools off).
What’s the temperature of space ?
Given the model world Willis postulates, it seems evident he is correct. Since the gas molecules cannot absorb or emit radiation at these frequencies, they can only heat or cool by conduction or expansion. Initially you get convection, but eventually the air near the surface is at surface temp and the temp of the air smoothly decreases with altitude. All the molecules at any given altitude all have the same temp (or very, very nearly so) so conduction ceases. Convection ceases. The atmosphere no longer absorbs any energy from the surface, so it is now irrelevant. Willis wins. Since Jelbring seems to postulate the same simplistic world it would seem he loses.
Move one step closer to reality with a rotating world illuminated from one direction and you no longer have an equilibrium case. Conduction and convection will not cease, and the atmosphere can indirectly radiate by warming the surface on the dark side by conduction. The air thus being cooled can moderate the peaks of temp (again by conduction) when that side is sunlit again. Since radiation is related to the fourth power of temp, clipping the peaks reduces a disproportionate amount of radiant energy. This reduces the total radiation of the surface, thus raising its average temp from what it would be without a transparent atmosphere.
So Willis is right for Willis’ world. All models are simplifications, but I think he went one simplification too far when trying to show GHG are required to raise the surface temp.
[snip – site policy violation, fake name edited also – Anthony]
[snip – in your previous comment (under a different handle) you used the F-word, and it was caught by our spam filter. If you have something to say, put your name on it, otherwise don’t comment again. I have no tolerance for people who abuse site policy from the comfort of anonymity – Anthony]
motion in electric fields generates radiation and this radiation gets out of the solid at the frequencies where the solid is transparent and thus the solid cools because energy is lost.
In a solid the radiation gets out at the surface, and comes out at the frequencies where the solid is opaque — you have it exactly backwards. Atoms or molecules absorb or emit symmetrically, or nearly so (the laser is an example of an exception, but requires special preparation and states that line up “just right” with an external driver). The whole point of blackbody radiation is that if a solid is a “perfect absorber” — a black body — it is also a “perfect emitter” in all frequencies and hence generates a BB spectrum if it has a given temperature as derived by Planck, subject to his quantization hypothesis.
Real matter is generally not a perfect absorber, and pure atomic or molecular matter — single species — tend to have specific quantum structure such that they absorb and emit primarily in transitions between specific discrete energy levels. Things are also different when one considers transparency and penetration of real matter, especially for “transparent” fluids. In that case radiation doesn’t come out of “the surface” — it comes out of a (usually exponentially attenuated) depth from the “surface” (if there is one — in the case of the atmosphere the notion of a “surface” is largely artificial with the possible exception of structural interfaces such as the tropopause (which still have some depth, but it is small compared to the overall range of variation). This is quite relevant for BB radiation — the outgoing IR isn’t released from a “surface”, but rather from a rather complicated volume of atmosphere. Remember that no matter how large the CO_2 cross section in the atmosphere, CO_2 is only 0.03% of the atmosphere (and the atmosphere itself is exponentially attenuating) so the “emitting surface” is kilometers if not tens of kilometers in depth. Water is even more complicated, as it forms clouds.
There is a lot I’m still working on understanding in all of this, don’t get me wrong. It’s just that your assertion above is exactly, diametrically wrong regarding the transparency, it is the opposite of the case.
rgb
Just to avoid confusion, I previously posted a comment as’David’, giving a thought-experiment about a ball of nitrogen in space. I have noticed that at least one other person has commented under the name ‘David’. They are not me. I have only posted one comment (so far).
Think lava lamp.
Well said, Anthony, and an excellent example. Or, as I suggested on another thread, consider the rolling turnover a boiling wort when making beer — heat input at the bottom from the flame, heat output at the top from evaporation and convection, heat transport from bottom to top due to differential density and buoyancy such that the temperature of the beer remains in a steady state in between.
In neither case does gravity do net work as the wax blobs rise and fall or as the wort turns over. It isn’t irrelevant. Imagine heating the beer from the top. Hmm, no turnover, no rolling convection, no real boiling — the wort heats and evaporates at the same spot, and conduction would take forever to heat the beer. Try turning a lava lamp upside down and turn it on (heat at the top!) Actually don’t, because the bulb might overheat and start a fire because cooling of the bulb through the liquid would almost completely disappear and the lava lamp wouldn’t “lava” — the wax would melt once, fall, and sit at the cold bottom forever.
rgb
Anna V,
You say “Thus one cannot have matter as we know it of a given temperature not radiating in some frequencies.” Consider a sample of helium gas at standard temperature and pressure (roughly 270K, 1atm). At what frequencies do you think it will radiate? What transitions will cause this? And what are the relevant transition dipole moments?
Willis Eschenbach says:
January 15, 2012 at 12:13 am
willb says:
January 14, 2012 at 8:24 pm
@Willis Eschenbach
Here is my best shot at an elevator speech explaining the N&Z “greenhouse effect”. The N&Z effect works as follows:
• The sun transfers energy via radiation to the earth, warming the earth.
willb, thanks for the elevator speech. First step looks good.
• The surface of the earth transfers energy into the (non-GHG) atmosphere through conduction, heating the atmosphere.
OK
• Earth’s gravity causes an altitude-dependent temperature and pressure lapse rate to form in the atmosphere. The atmospheric temperature and pressure drop as altitude increases with the temperature ultimately dropping to that of deep space (~3K).
Kinda, although it ignores the thermosphere that may not be significant.
Indeed but it’s easier to ignore that. 🙂
If it’s N2 atmosphere it’s not clear why the temperature of deep space is relevant that would require N2 to have a far microwave absorption which I don’t think it does otherwise Penzias and Wilson at Bell Labs wouldn’t have been able to measure the cosmic background?
• Atmospheric gases heated conductively at the earth’s surface then convectively rise through the pressure lapse rate.
Not sure what “through the pressure lapse rate” means, but OK.
• As the temperature of the atmosphere drops towards that of deep space, the rising gases transition through a number of phase changes (e.g. gas => liquid => solid-a => solid-b). At the occurrence of each phase change the atmosphere releases latent heat in the form of radiation.
OK
Not if we consider a N2 atmosphere, if we have a 20ºC surface at 100kPa we’ll hit -60ºC (~210K) at 33kPa based on the dry adiabat, below the triple point so the liquid phase is out of play. To get to the sublimation curve you’d need to get to ~60K which probably wouldn’t happen below 150km, so no N2 snow!
• Some of the radiating energy from the released latent heat is directed downward through the gaseous, IR-transparent atmosphere and is absorbed by the earth.
Whoa, whoa, whoa. The atmosphere is GHG-free. How does the released energy radiate anywhere, when the atmosphere has no GHGs, and as a result can’t radiate in the IR? I fear your explanation dies there …
No latent heat either.
The outer planets are gaseous but have high internal core temperatures caused by gravitational compression. On Earth we should expect our atmosphere to be heated constantly merely by the force of gravity. This heating is likely explained using the ideal gas law PV = NkT. We should expect both a temperature and pressure gradient that both increase toward the surface of the earth. The greater the density of the atmosphere the greater the temperature gradient.
Gravity is a force that heats objects by compression without any help from the sun. Otherwise the core temperature of Neptune and Pluto would be closer to absolute zero.
What’s the temperature of space ?
Your choice of “it has no temperature” (a vacuum has no temperature), or 3 K (the vacuum isn’t empty, it contains electromagnetic energy in the form of blackbody radiation leftover from the big bang).
The latter is probably the right temperature to use as far as cooling the Earth via radiation is concerned. Turn off the sun, wait “a while”, and the Earth would cool to 3 K in equilibrium with “space”.
But 3K is close enough to “0 K” that you wouldn’t go far wrong using it instead as a simpler idealization, at least until the Earth cooled to temperatures that were approaching 3 K.
rgb
Do your worst, antiscientific censorship freak.
For those with the question of what a non-GHG atmosphere would be like, I don’t think it’s too hard to envision. The surface will have temp profile similar to the moon — very cold at night & very hot in day. The air just above the surface will follow the surface temp (by conduction), and eventually the entire atmosphere will end up as nearly isothermal (same temp bottom to top) and close to the average of the surface temp. If you take our current solar input, such a planet would have surface temp’s like the moon, and an isothermal atmosphere (only a tiny lapse rate) of approx the moon’s avg temp.
Of course, day/night cycles will cause temperature cycles in the surface/very near air temp profiles, but the GHG-free atmosphere can NEVER IN AVG be warmer than the avg surface temp — that’s the only means of it getting heated (by conduction). And no, not by “compression” – compression is work, which happened only when the planet first formed. A stable, static pressure, no matter how high, is NOT compression. Yes, there are local updrafts/downdrafts, but the net compression is zero for a non-accreting atmosphere.
Robert Brown and Antony,
you are correct in this description of convection and work. However, in Willis’ model, with even heating of the planetary surface there will be no temperature differences and the atmosphere will not convect. Under such conditions I think a uniform temperature distribution will arise, and not a thermal gradient resulting from the lapse rate.
@Paul Dennis – yes, that’s what I was alluding to with the paint layer in equilibrium analogy. We are in agreement
I used to think wuwt was a legible place, instead it turned into comment-erasing freakodrom. WUWT is dead to me as well as many other people i am sure. uoyckuf
REPLY:Oh reverse f-word (misspelled), clever. Comments that don’t meet policy, like fake names and f-words? THAT’s what you are defending? Don’t let the door hit your butt on the way out – Anthony
You say “Thus one cannot have matter as we know it of a given temperature not radiating in some frequencies.” Consider a sample of helium gas at standard temperature and pressure (roughly 270K, 1atm). At what frequencies do you think it will radiate? What transitions will cause this? And what are the relevant transition dipole moments?
So you’re asserting that a container of helium gas, confined inside a perfectly transparent container in intergalactic space, would still be at 270 K after a million years? Or a million seconds?
Yes, I understand your argument, but the helium atoms are not non-interacting and they are made of matter. When they collide (as they frequently will) the charge they are made up of will oscillate and they will still cool. Slowly, perhaps, but you have second order effects to consider. When they collide, the non-interacting energy levels all shift and second order (two-photon) transitions are enabled, are they not?
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With no atmosphere the earth will absorb radiation from the sun and will emit it 100% as LW radiation to space. The earth acts as a black body whose temperature will be as calculated from SB. The near surface temp is zero.
With an atmosphere, the earth’s surface absobs radiation from the sun, heats up and emits some energy as radiation, some via conduction and convection and the latter is dominant. the earth’s surface is cooler than the BB temperature as it is transfering heat to the atmosphere. The near surface air is far hotter than the zero atmosphere case simply because it has heat capacity and can receive heat via conduction from the surface
Heat from the surface is carried upwards by convection and radiates out to space. Radiation out balances radiation in and energy is conserved.
Near surface air already has internal energy because of its pressure and its equilibrium temp is a function of it’s own PV and the heat transferred to it from the earth’s surface.
If the pressure of the near surface air is higher then it will have a higher equilibrium temp than the lower pressure air as it has higher internal energy to start with Energy is conserved.
All valuecan be quantified and no radiation effect is needed.
I’m no expert but where I believe Willis is wrong is that he is confusing surface temp and near surface air temp. He is also wrong about an atmosphere without GHGs not being able to radiate to space.
Good riddens. My hit won’t make much difference to you rating, but thats the best I can do. Bye, big oily slave.
REPLY: LOL! Such maturity, and then there’s the big oil barb, heh. OK, we’ve had our fun, you’ve earned permanent troll bin status, all subsequent comments go to the bit bucket. – Anthony
“So it is NOT a transient effect and the result is PERMANENT all other things being equal.
Without that effect the Ideal Gas Law would not be a Law.”
“Only rarely does something leave me speechless. What does this mean? I really, truly have to say “nothing”, but I’m willing to have it explained to me.”
Then I’ll try to put it better.
Within a gravitational field the pull of gravity is a constant force.It is not akin to a single one off pressurisation, it is akin to continuous pressurising. Therefore there is work being done continuously but only as long as there are energetic molecules for the gravitational field to work on.
That is not to deny that all the energy in the molecules comes initially from the sun. Gravity simply governs the distribution of energy within the atmosphere in accordance with the Ideal Gas Law.
With a gaseous atmosphere the Ideal Gas Law applies. A temperature gradient is set up from surface to space with the warmest molecules at the surface.
It is the action of gravity on the molecules of the atmosphere that creates that outcome.
No solar input, no energy to be distributed and no lapse rate.I don’t think that anyone says that the gravity itself is the source of the energy.
The rising air doesn’t loses much energy from conduction because air is such a poor conductor. Mostly the air rises “adiabatically”, neither gaining nor losing energy. The air GAINS gravitational energy and LOSES internal energy (ie it cools off).
Agreed, Tim. Also even if it did lose energy to “something”, what could it be? There are only two choices — other air (mixing and thermalizing via convection and diffusion) and “everything else” via radiation. The former doesn’t help — yes, you are moving heat uphill, but there’s only a certain distance “uphill” you can move it as heat in matter. Sooner or later, you have to remove the heat thus transported, and only radiation removes heat from the Earth altogether. Otherwise you simply heat the air overhead until warmed air at the bottom doesn’t rise any more and you once again have a static lapse rate. That’s the way actual greenhouses work — they trap warmed air so it cannot convect heat away. Sort of.
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To avoid confusion, I’m NOT stating that the GHE is a chemical reaction, that is simply an analogy. What happens is the GHGs become well mixed in the atmospheric profile due to pressure and heat. Hence, the GH effective radiating altitude gets set very high even with low concentrations. Because the atmospheric profile is changed very little by adding additional GHGs, that altitude does not increase if things like additional CO2 are added. It is that height that determines the overall GHE.
This seems correct to me, although somebody (Tim F.?) asserted otherwise. Indeed, I suspect that the Earth is largely insensitive to changes in GHG concentrations, and might even operate the opposite way than expected in some cases. Once you are “opaque” you are opaque, and making it twice as opaque doesn’t really happen. I am actually curious as to whether anybody knows anything concrete about this, as it has bothered me for some time. I’d expect alterations in the outgoing radiation profile due to doubling CO_2 concentration to be, well, almost impossible to detect, as radiation of IR from the troposphere is going to still be radiation of IR from the troposphere. Is the troposphere going to move? Will the adiabatic lapse rate change? Why, exactly, is radiative balance going to change?
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