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 …
wayne says: January 15, 2012 at 10:33 pm
jjthom, that is hugely appreciated and exactly at the right time. I sure needed that! Hope Willis and others a bit confused also read it. So… N2 does have rotational lines after all… just what I expected! Thanks again.
=======
You need to read the plots and text. O2 N2 etc have mainly rotational “oscillation” this means that the wavelengths absorbed and radiated are in the microwave frequencies. NOT IR e.g. O2 radiates at 2.5mm wavelength CO2 at 4.5 um and 16 um
If you look at the ppt for chapt6 slide 9 provides a satellite down and ground up spectrum. This shows that the satellite see reduction in level when the ground sees increase. Something in the air is turning these wavelengths from outbound to inbound.
This CAN ONLY be GHGs.
Gravity has NO term for wavelength filtering!
From Arnott’s blurb on gaseous IR transfer.
DANGER:
“Water vapor is a very strong ‘greenhouse’ gas. CO2 may very well change the distribution and amount of water vapor, so is both a greenhouse gas, and a lever arm that affects water vapor content. Recall that saturation vapor pressure of water vapor is an exponential function of temperature — a little temperature increase can be important for water vapor.
Looking at the effects of CO2 change in isolation of the bigger picture is dangerous.”
There are a lot of interesting side-issues, but (as Willis has to keep repeating) they really don’t belong in this thread. Things like “does N2 emit/absorb IR?” or “what is the ‘dry adiabatic lapse rate’?” or “can photons go from cool places to warm places without violating the laws of thermodynamics”?
Without some sort of FAQ, these issues will get brought up over and over in any similar discussion by people who have not really thought through the concepts. The same fire has to be put out over and over. With an FAQ, Willis wouldn’t have to snip so many slightly off-topic comments, but could instead direct people to the appropriate place to learn and discuss those ideas.
Otherwise, we might as well start calling Willis “Sisyphus” (I am sure he is tarting to feel that way already). And with that, I think I will go work on other never-ending tasks and leave this thread.
JIsbert says:
It is very important to understand how they add convection: They add it INCORRECTLY. They even tell you this when they say, “Equation (4) dramatically alters the solution to Eq. (3) by collapsing the difference between Ts, Ta and Te and virtually erasing the GHE (Fig. 3).” However, we know in the real world, convection does not drive the atmosphere to an isothermal temperature profile with height; it only drives it as far as the adiabatic lapse rate profile. This is because lapse rates less steep than the adiabatic one are stable and convection is suppressed.
Hence, what they have shown is that IF convection could drive the atmospheric temperature profile to an isothermal profile then the greenhouse effect would be erased. This is in fact well-known. In particular, Ray Pierrehumbert’s book “Principles of Planetary Climate” emphasizes the fact that the temperature at the effective radiating level has to be lower than the surface temperature in order for there to be a greenhouse effect.
So, in the real world, what convection does is to decrease the magnitude of the greenhouse effect (on Earth from something like 60 K, as I vaguely recall it would be in the absence of convection, to the actual ~33 K). However, it cannot eliminate it precisely because convection can only decrease the lapse rate so far.
Willis,
I really don’t mean to nitpick, but your last three statements in your elevator speech were:
• 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.
This implies that back radiation results in the surface being warmer. The word “that” in the third of the three statements has to refer to the back radiation in the second of the three statements. That may not have been what you intended to say, but it is exactly your quote. I would agree with you completely if you had simply left the word “that” out of the last statement, or left the second of the three statements completely out (it is true but irrelevant and leads to a wrong emphasis). What my comment on the heater with insulation showed, was that the heated atmosphere is an effect, not cause. We can argue what words mean, but I am only using what you said.
If you had a giant loss free fan mounted, say 5 km, above a black body under the influence of no external radiation such that it blew upwards, it would create a flow of gas (pick your own) that ascended, cooled (solely due to expansion and some due to radiation if you pick such a gas), descended and then heated, no?
So the energy input to the fan is first converted to potential energy going up, then kinetic energy on the way down, which is converted to heat as it compresses, then radiation as it is absorbed and emitted by the black body surface. Energy is conserved as all the energy into my loss free fan is converted to IR.
Is this what would happen in THIS thought experiment?
Willis Eschenbach says:
These two different interpretations of what the adiabatic lapse rate is due to have been bugging me for a while: Is it due to the work done by expansion of a parcel of gas as it moves upward or is it due to the change in gravitational potential energy…or are they two sides of the same coin?
I finally worked through it last night and the answer I got is that it is due to both. I.e., there are contributions due to both the fact that the gravitational potential energy decreases with height and the fact that the parcel of gas does work on the gas around it by expanding.
The DALR is not an equilibrium condition. The condition for hydrostatic equilibrium is a different equation. (It determines the relationship between pressure and density with height.) The DALR is a condition for stability, i.e., lapse rates steeper than the adiabatic lapse rate are unstable to convection and lapse rates less steep than the adiabatic lapse rate are stable and convection is suppressed. This is, of course, why we see lapse rates less than the adiabatic lapse rate in parts of our atmosphere (such as the stratosphere).
Stephen Wilde says:
January 16, 2012 at 3:02 am
“In fact there is a constant conductive energy exchange between surface and atmosphere as long as there is an atmosphere.”
No, Stephen. Willis happens to be right at least in the isolated case of saying there is no energy entering or leaving a transparent atmosphere when the temperature at the lowest level of the atmosphere is the same temperature as the surface.
The problem for Willis is that he doesn’t seem to understand that all matter with a temperature above absolute zero radiates. So that transparent atmosphere is constantly losing a small amount of energy to space via radiation and this is replaced by conduction from the surface.
And it is that conduction from the surface which establishes the temperature gradient from surface to space. Gravity can only raise the temperature while it is reducing the volume of a gas. The volume of the atmosphere is not being reduced. Gravity and pressure are in equilibrium. What gravity does is create a pressure gradient and a temperature gradient follows it. It cannot raise the surface temperature above the S-B temperature. It just redistributes the heat capacity making it greater at the surface and lesser at TOA but has no effect at all on total energy in the column. Nikolov et al seem to believe gravity somehow increases the total energy in the column and it simply does no such thing.
hi Willis, you snipped my post of 5.06am on 14th, for not beig an elevator pitch, when in fact it is a 3 sentence pitch on the temperature profile of your ideal planet. It may be whollly wrong, but WUWT? Sorry i didn`t notice earlier, i am travelling in scandanavia and nly accessing by kindle. I have no dog in the fight, but just liked your challengeenough to have a go.
Capo says:
January 16, 2012 at 3:13 am
“Tallbloke:
“No Willis, before we can move on to a discussion of the science, you need to acknowledge that Hans Jelbring defined his model planet as one which does not radiate to space,…”
That means that Jelbrings model is not “based on first principles of physics” in contradiction to what Jelbring says. Every body with T>0 radiates, so where’s the sense in this assumption?
If this is one of the assumptions, the conclusion would not belong to real, but a phantasy world.”
The outer shell of Jelbring’s object has T=0, . . . .I think. What is going on inside of the object is an extension of the hypothesis that every body with T>0 radiates. The deal here could be there is some level of opaqueness of any gas whether it be full frequency or partial frequency may not matter. I hypothesized above a GHG-free atmosphere and found it to be warmer than the average radiation the surface of the planet receives. . . .not unlike the greenhouse formula suggests. But a GHG-free atmosphere may be impossible and so-called greenhouse gases may not matter and what you see from space is simply just a mix of the signature of different frequencies of transparency so that any “shell” TOA with a T>0 will radiate in unique ways.
Your comment I think is good but there is no evidence it is correct.
It seems a lot of stuff is colder on its outer shell than it is internally and it radiates according to its outershell and not at the temperature of the nuclear fusion thingy temperature in its core. Is that a violation of first principle physics?
I don’t agree Joules.
Willis doesn’t realise that all matter vibrates with kinetic energy if it is above absolute zero so that there can never be a zero exchange between surface and atmosphere. There can be a zero NET exchange but his view of the consequences of that is incorrect.
Even in a non GHG atmosphere there is a constant exchange of conductive energy between the surface and atmosphere.
N & Z do not say gravity is the direct cause. They say gravity is involved but the source of the heat is additional collisional activity when more densely packed molecules are irradiated under pressure.
Wow – I’d completely failed to understand that there are two kinds of temperature – that the part that follows the S-B law IS JUST THE RADIATIVE PART OF THE TEMPERATURE! Meanwhile, the CONDUCTIVE part of the temperature doesn’t do any radiating at all!
I’d strongly suggest you do some reading on physics and dimensional analysis, and try to understand the different between energy and force, because you are seriously confused about this stuff, and keep repeating exactly the same errors in the odd belief that somehow we’re going to end up understanding you.
JJThoms, thanks for your viewpoint. I was not looking for IR, just ANY radiation from this post’s non-GHG atmosphere and a reference and that chaper and anna v provided.
Is this correct? http://tallbloke.wordpress.com/2010/07/27/nasif-nahle-nails-the-radiative-physics-of-co2/ Considering the data obtained by many researchers on this matter, the total emissivity of the carbon dioxide is low. It is 0.0017.
This value is very important for calculating the amount of energy that the carbon dioxide absorbs and emits each second. Given the specific heat capacity of the carbon dioxide at its current density and temperature, which is of the order of ~871 J/Kg K, the carbon dioxide is not the cause of any change of the Earth’s climate.
“What two forces are acting for particles in any orbit? I only count one — gravity!”
Plus escape energy makes two.
In fact ANY energy in a molecule causes movement that counts as a second force interacting with gravity.
Are you getting lost in semantic detail and losing the bigger picture ?
No, I’m not getting lost at all.
Newton’s Second Law is (popular version):
F = ma = m dv/dt
On the left hand, one requires a second agent (Newton’s Third Law) acting on the mass m, exerting an actual force of nature. There are four known forces of nature — gravity, the weak nuclear force, electromagnetism, and the strong nuclear force. The nuclear forces are very short range and completely irrelevant to the cooling or heating save insofar as they conspired to create a heavy charged nucleus for atoms. Gravity is enormously weak but is ubiquitous — it is the force that binds big collections of mass together, planets and stars and galaxies and clouds of interstellar gas. Note well that it requires an entire planet to create a force acting on us that a thin surface layer of electromagnetic forces in the molecules of the chair I’m sitting in (further structured by quantum theory and the Pauli exclusion principle) to oppose it so that I don’t fall down towards the center. Basically we “are” electromagnetism — electromagnetic forces mediate the binding of electrons to nuclei to make atoms, bind atoms together to make molecules, bind molecules together to make us, and along the way mediate light and sound and thought, not to mention the computers and network that make us part of a collective consensual superorganism as we exchange information.
Note well that there are four forces and “escape energy” is not one of them. In fact, calling an energy a force is the kind of mistake that I spend a whole lot of time bopping undergraduates upside the head for. They are not the same. They don’t even have the same units. Conflating the two leads one only to error.
Note that the error is a deep error, a really serious error. It isn’t just a matter of speaking differently. It is a fundamental lack of understanding. You cannot add or subtract an energy and a force. It is, quite literally, akin to adding a length to a volume, or a length to a time. Imagine a carpenter trying to add three seconds to the length of a one meter board section he is trying to cut. What the hell does that mean?
Energy arises from taking Newton’s Second Law — the dynamical principle for one of the versions of classical physics — and making it time independent. The calculus is:
F = m dv/dt = m dv/dx dx/dt (chain rule) = m v dv/dx (because v = dx/dt).
Thus
F dx = m v dv
and integrating between matching end points in the units of both sides:
\Delta W = \int F dx = \int m v dv = \Delta 1/2 m v^2 = \Delta K
That is, “The work done by the total force acting on an object equals the change in its kinetic energy”, where the latter is defined as K = 1/2 m v^2.
This is the “Work-Kinetic Energy Theorem” in one dimension. With a bit of work (all of which you can read and follow in my online book) you can make this three dimensional. If one applies it to “special” forces (where the laws of nature are in general special) such that the work done between two points by the force is independent of path, such forces are called conservative forces and one can transform the WKE theorem into the Law of Conservation of Mechanical Energy by defining the potential energy to be the negative of the work done by a conservative force. For Newton’s Law of Gravitation
F_r = – GM m/r^2
and Coulomb’s Law (the electrostatic force law, part of Maxwell’s Equations) one can do the integrals for the potential energy once and for all:
U = – G M m /r
for gravity (for example).
Consider, now, a particle in orbit. Only gravitational forces act on it. It has some total mechanical energy (at any instant in time) that is constant:
E = – G M_1 m/r + 1/2 m v^2
In general, for any bound orbit, E < 0. It is a bit involved to transform the kinetic energy into a rotational part plus a radial part, because the latter is generally written in terms of the angular momentum which is a constant of the motion for radial forces (which exert no torque), but it is in my book if you want to learn how. As one adds energy to an orbiting particle (by doing work on it with another force of nature) with a constant angular momentum, one makes the orbit increasingly eccentric, moving from circular to elliptical to parabolic — the first orbit that can actually escape from any radius to infinity.
The condition for the parabolic orbit is:
E(escape) = – G M1 m/r + 1/2 mv^2 = 0
In this orbit, one can find the particle at infinity where U is zero with zero velocity, consistently. The actual trajectory is in fact a parabola, an “infinitely stretched ellipse” in a certain sense. Energies greater than zero lead to hyperbolic orbits and escape even faster. Note that all of the allowed orbits are conic sections — this was a marvellous geometric consequence of the 1/r^2 force law (and is experimentally encoded in Kepler’s Laws). All of this stuff actually drove the Enlightenment and is a wonderful story of human achievement and risk and transformation from a primitive myth-bound magical culture to the scientific and technological society we enjoy today.
From this fairly complete algebraic exposition, you can see that under no circumstances can one call “Escape Energy” a force, or argue that it has anything at all to do with a particle escaping. A particle escapes if the orbit it happens to be in happens to have enough energy to escape, when the only force acting is gravitation and when its trajectory happens to not intersect other objects along the way. There is no “balance” involved. In a radial reduction one can speak of a “balance” between the angular momentum barrier L^2/2mr^2 (which is not a potential energy or force, but which behaves like one in the reduced coordinates of the problem) but you would have to work pretty hard to learn enough to understand that, and in the end it changes nothing because it is not a force, it is just the angular part of the kinetic energy.
This explains 1) in my previous reply in complete detail. To explain 2) is a bit beyond my vacation-day means, as deriving the Maxwell-Boltzmann equation is a pain in the ass and requires that you know a lot of things that you clearly don’t know. I am therefore going to take the lazy way out and just post a link here:
http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
You will note that the key element in its derivation is the Boltzmann distribution. This distribution describes the maximum entropy/maximum ignorance assignment of probabilities of finding a system in any given state with any given energy, as a function of temperature, and in some sense defines the temperature (although there are other definitions, all consistent with this one). You will also please pay careful attention to the figure associated with “distribution of speed”.
As noted above, escape energy is E = 0. For r = R_E and M1 = M_E (the surface of the Earth) solving the escape energy condition yields a speed of around 11.2 km/sec. Objects launched with this speed in a vacuum will go away and never come back. If one goes over to the right (imagine the figure extending out to 15 km/sec on the right) one can draw a line at 11.2 km/sec. All molecules in the MB distribution of temperatures with a speed greater than this line that happen to be on a trajectory that gets “out of the atmosphere” without a collision with another molecule go away. This is how the Earth loses atmosphere, a continuously happening process. There are always molecules that collide just right to have sufficient velocity to escape.
The same general process, BTW, is one way of understanding how the cooling of gases outside of their resonant channels can occur. At any finite temperature some of the collisions of molecules in the gas have enough energy to excite an electron from the ground state to where it spontaneously emits a photon. That photon can then escape, removing a quantum of energy. Even though the average energy of collision may be far too weak to excite an electron, there are always collisions in the MB tails going on, and they slowly bleed energy out of the system.
Now, are other forces involved in getting molecules out of the atmosphere? Sure. Collisions between molecules that keep them in rough local thermal equilibrium. These are basically short range electromagnetic interactions from a classical point of view, although the short range repulsion involved gets a big contribution from Pauli and quantum properties of electrons as fermions. Molecules absorb and emit photons via their electromagnetic coupling with the ambient electromagnetic field, which may or may not be describable by a “temperature” at all (in general not, actually — blackbody radiation is the “Maxwell-Boltzmann” curve for electromagnetic energy or a “gas” of photons, and the radiation field near the Earth pretty much never has the right spectrum and is never in equilibrium.
The point, however, is you have to learn a bunch of stuff before you can discuss this problem intelligently where intelligently is just “not using terms in completely wrong, conceptually wrong, ways in discussion”. Ultimately, of course, one wants to have worked through all of the derivations of and relations between the important equations, and worked on it until one understands the whole thing conceptually. Otherwise you will be inventing forces that aren’t, claiming processes that violate the laws of thermodynamics or laws of nature or both, elevating irrelevant processes to importance and leaving out important processes as irrelevant.
One last point, to Anna, if she is still reading. “Transparent” was the term I was addressing. A solid object is not transparent where it emits, it is opaque. An object does not absorb at all where it is transparent. I do believe that you probably understand this, but you are saying it completely wrong, and in a way that is bound to lead to substantial confusion in a discussion of the radiative properties of atmosphere that is indeed transparent in some bands and opaque in others.
There is little to no thermal radiation from a layer of atmosphere that is optically “thin”, that is to say, transparent, in some band of frequencies. The thermal radiation comes from a layer that is optically thick, thick enough to be opaque. So you should be very careful in how you use the term “transparent” when discussing radiation. Willis’ point is that a transparent atmosphere does not directly act to enable cooling. It has to be able to thermally radiate energy and thermal radiation does not (significantly) occur where the emissivity/absorptivity is low (transparent), it occurs where it is high (opaque). This is what confounds elevator summaries of N&Z (at least to me, still, yet) — you cannot have convection heating something on the bottom unless you also remove the heat at the top. The only way to actually remove the heat at the top AFAICT is radiation, and blackbody radiation from the cold top of an opaque atmospheric layer is the greenhouse effect. If you don’t cool up there, you never generate the masses of cooler denser air that displace the warmer less dense air underneath to create the buoyancy force or “lift” that drives convection. Convection requires a hot reservoir (where heat is added) and a cold reservoir (where it is removed) — it cannot occur between two adiabatic energy trapping surfaces.
In fact, the second law of thermodynamics says precisely this same thing. You cannot get work out of a system (including convective work) any more efficiently than you can get it out of an ideal heat engine running between two thermal reservoirs. If those reservoirs are at the same temperature, the ideal efficiency is zero and no steady state motion is possible. One of many, many reasons that denying that the so-called and misnamed “Greenhouse Gas Effect” exists at all is enormously silly. That really is being a “denier”; denying that the laws of nature and the laws of probability are correct is the act of a crank, not a serious person, unless and until they are prepared to present a sufficiently complete and consistent theory to replace, well, all of physics. And even that won’t help you with the laws of statistics that underlie statistical mechanics and the second law.
The logic supporting the GHE as a critical aspect of the overall non-equilibrium processes that describe energy flow into “the Earth” and thence “out of the Earth” is impeccable; based on simple physics and directly supported by the observed spectrum of radiation from the Earth. Denying that it occurs, given the measurements, is literally denying the evidence of our own eyes (in space).
What is at issue is not “The atmospheric effect is a key component of energy flow that determines the warming of the Earth relative to an identical Earth without an atmosphere or with a perfectly transparent dry atmosphere”. That is simply a true statement. What is at issue are things like how this effect is functional on the underlying parameters, both in oversimplified models and in the actual chaotic, heat transport laden, albedo altering, inhomogeneous processes that describe our real atmosphere as opposed to an idealized one dimensional model atmosphere. In particular the feedback/sensitivity and role of the Sun, in particular the relative sizes of natural oscillations compared to responses to increased CO_2.
And even this isn’t an adequate general explanation — understanding the albedo of clouds as a problem in multiple scattering being a good example. Even if all the multiple scattering collisions with photons are elastic and the cloud itself absorbs no energy (other than trapping optical energy in caged motion) as one makes the cloud thicker and thicker, less and less radiation comes through because the random walk of an enemble of bouncing photons carries more and more of them back to the surface (where they become part of the diffuse reflected light. The thicker the cloud, the darker underneath and the whiter on top even without any actual heating of the cloud. And of course, clouds do warm in the sun. The air itself warms in the sun. Everything gets warm in the sun. It’s one of the things that makes clouds so interesting and such a wild card in cooling models.
Joe, I saw your remark in passing, but the thread is now too long for me to even catch up on in less than a day (and I can’t even FIND it in a quick pass through), and there are a million remarks along the way I would like to make about Bad Physics in other places. I only saw the first paragraph in passing looking for ANOTHER reply I wanted to comment on.
If I recall correctly what you were starting to say — and I probably am not — the way I describe the atmospheric effect completely omits any reference to upwelling or downwelling radiation, and is completely independent of the details of how heat gets in. Given an influx of heat energy that must be lost to keep a planet in “dynamic equilibrium”, the integral of the outgoing flux has to equal dQ/dt in, on average. If the flux is in a BB spectrum at temperature T, you have the ideal case. If it is split up into surface and atmosphere (by any heat-transfer mechanisms) and emitted at a cooler temperature for part of the frequency spectrum, this reduces the net flux UNLESS the temperature (and hence flux) increases at other frequencies. If the surface is warmer than the atmosphere this warms the surface. If it is cooler, it cools the surface (it works the other way, in other words, just as well — I don’t care WHICH of the two bands is the warmer or cooler one.
The details of transfer are irrelevant to the effect and its connection to the measured emission spectrum.
rgb
At last! I’ve found an error in something from Robert Brown!
He said “one can find the particle at infinity where U is zero with zero velocity”.
Of course, this is wrong – if one of your particles has gone to infinity (or beyond) there’s no way you’re going to find it again!
I gave this analogy at Tallbloke’s site and have expounded a bit here:
If you turn on an air compressor and let the tank fill, the tank gets hot. This compression is no different from compression due to gravity. But if you wait a while, the tank cools off. The air pressure is somewhat less after cooling, but still considerably higher than one atmosphere. If one allowed air to accumulate on an airless Earth in, say, the period of a week; the air at the bottom would likewise get hot. But like the compressor tank, it would radiate away the heat, cooling in the process.
Once the air inside the compressor has cooled, the molecules in the compressor will be hitting each other more frequently than the air outside it also. Yet, the compressor and the higher pressure air in it are the same temperature as the air outside the compressor. Also, the air in the compressor is more dense than the air outside it, just as the air in the lower atmosphere is denser than the air above it.
Anything happening at the atmosphere/Earth interface should also be happening on the inner surface of the compressor.
Thanks to Robert Brown for the effort put into that. I will pay close attention to it but in my mind the issue has moved on a bit because I can now see that the effect of gravity is not to cause any heating in itself (except a miniscule portion) but rather to reorder mass so that other processes generate heat energy.
In the current context it is not gravity directly that heats the non GHG atmosphere but the extra collisional activity that occurs when mass is irradiated whilst under pressure.Gravity only sets up the scenario in which that can happen.
Then the important issue would seem to be the role of conduction as compared to the roile of radiation.
This whole issue is a multidisciplinary one and no non specialist can go into every component as deeply as has already been done by many here within their own specialisms.
“Wow – I’d completely failed to understand that there are two kinds of temperature – that the part that follows the S-B law IS JUST THE RADIATIVE PART OF THE TEMPERATURE! Meanwhile, the CONDUCTIVE part of the temperature doesn’t do any radiating at all!”
I think you did the jumbling up there.There is no radiative part of the temperature or conductive part of the temperature. That would be nonsense and I did not say it.
There are two kinds of energy transfer for current purposes. Radiation and conduction. The temperature is the result of the two processes combined.Thus radiation and convection can each contribute seperately to the final temperature.
It is the mass in a non GHG atmosphere that doesn’t do any radiating (except perhaps a trace that can be ignored for present purposes).
If energy is held by mass that doesn’t radiate then it can only be transferred by conduction. Convection may occur later but only after the energy has been conducted from surface to non GHG molecules.
“Once the air inside the compressor has cooled, the molecules in the compressor will be hitting each other more frequently than the air outside it also. Yet, the compressor and the higher pressure air in it are the same temperature as the air outside the compressor. Also, the air in the compressor is more dense than the air outside it, just as the air in the lower atmosphere is denser than the air above it.”
You now need to irradiate with an energy source such as the sun. The denser mass should gain a higher temperature for the same energy input.The greater density and more collisions allows that mass to hold on to more of the solar irradiation in kinetic form hence the higher temperature.
“The denser mass should gain a higher temperature for the same energy input.”
Sorry, again you’ve either got your dimensions wrong, and don’t mean “energy”, or else this is simply inverted. Same energy applied to higher mass results in a smaller temperature increase.
Exactly like heating two pints of water in a kettle for one minute, compared to heating one pint for one minute in the same kettle. The greater mass will increase in temperature less. Density is irrelevant.
Willis: You wrote in reply to Crosspatch that he must repeat [and keep in mind] a GHG-free atmosphere. It seems to me there is a basic gap in the concept. A gas that does not (meaningfully) intercept/absorb LWIR does no mean it cannot emit such radiation or that it will not cool be emissions of electromagnetic radiation at all. In other words the definition of ‘GHG’ seems to be based on its ability to efficiently absorb certain wavelengths but not all, and that it primarily emits in the same range. It is an unreasonable definition for our purposes. There are materials that do not emit IR as efficiently, or shall we say ‘preferentially’, as well as other materials. But emit they do. So right from the start there is a problem conceptually about the emission of energy in the form of photons, reducing temperature being limited.
Surely this is true: all objects emit IR if they are heated enough. Is it correct to say there is such a thing as an atmosphere that will not emit any IR? I find that unbelievable. Not absorb IR, that is quite different, if you picked carefully.
Create a black planet in space, heat it from within. Give it a very thick atmosphere of gases that have no meaningful absorption of IR. The atmosphere will insulate the plane to some extent, or is it more true to say that if that atmosphere does not absorb IR it will not insulate the planet? When you want to put a gas between the panes of a double-glazed window, do you put in an IR absorbing gas, or on that does not absorb IR at all? The purpose is insulation so do we put in CO2 or Argon? We use Argon because it is such a lousy transmitter of heat. Conclusion, a non-GHG atmosphere can be a good insulator. The base of the atmosphere will be hot from conduction. The temperature will not be S-B in equilibrium state.
The heat conduction coefficient of air or argon varies with density (really, viscosity) so gravity has an effect. http://www.boulder.nist.gov/div838/theory/refprop/NAO.PDF see formula 4.
The insulation is more efficient for any given planet if there is a) more if it, and b) if it is made of gases that are poor thermal conductors that are also dense (argon being one example). Gravity (leading to gas density) matters. That paper explains how density (and viscosity) alter the thermal characteristics of a gas. The GHG-free atmosphere that does not insulate does not exist because it would also have to have no ability to conduct heat. Even Hydrogen has some heat conduction capacity. Convection is a heat transport mechanism that merely complicates the understanding.
“The GHG-free atmosphere that does not insulate does not exist because it would also have to have no ability to conduct heat.”
Conduct to where? If this is a non-radiating (or neglibably radiating to be picky) gas, then being conductive is irrelevant, as the is nowhere for the heat to be conducted to. Above is free space, non-conductive, below is a radiating surface.
The conditions imposed by Willis:
ie. an atmosphere that has no GHG, is inherently impossible in a real world. In the context that he is defining such an atmosphere as an atmosphere that cannot radiate ANY energy in the IR, he is also implicitly not allowing radiation of any form of energy in any other part of the radiation spectrum. This is not possible in a real atmosphere.
Therefore the proof is also impossible.
He is ignoring that gases can lose energy by radiating it at other frequencies. It may have to go through complex transition trains to result in emissions in the visible, microwave, UV, or xray or some other higher frequency but eventually the energy will be radiated away to space. If nothing else real atmospheres contain dust and other solids in the form of particles so small that they do not settle out thanks to constant mixing from weather. Even if the atmosphere was composed of a single gas that in and of itself could not radiate energy at any frequency (microwave to IR) than the entrained dust in that gaseous atmosphere would still radiate away energy in the IR when it was mixed high in the atmosphere.
Like engineering problems that introduce impossible limitations like “infinitely rigid”, or “without mass”, the model might be useful to isolate a single concept but it does not and will not accurately represent the real world physics of the actual object.
In a real atmosphere the temperature profile is determined by the lapse rate. That lapse rate will determine the temperature of the actual radiation surface of the planet, which due to convection will be far above the physical surface. That radiation surface may or may not consist of gas molecules, since real atmospheres contain entrained dust and other complex molecules that do radiate energy to space.
Larry
Okay, I repeated my Elevator speech, with Willis’ comments, and my answers to Willis.
IMO it was not snarky.
I had “kwik says”, “willis says” and “kwik answers” so one could see the sequence of interchange.
Willis snipped the whole thing, so I will leave the discussion.