Guest Post by Willis Eschenbach
Since at least the days of Da Vinci, people have been fascinated by perpetual motion machines. One such “perpetuum mobile” designed around the time of the civil war is shown below. It wasn’t until the development of the science of thermodynamics that it could be proven that all such mechanisms are impossible. For such machines to work, they’d have to create energy, and energy cannot be either created or destroyed, only transformed.
I bring this up for a curious reason. I was reading the Jelbring hypothesis this afternoon, which claims that greenhouse gases (GHGs) are not the cause of the warming of the earth above the theoretical temperature it would have without an atmosphere. Jelbring’s hypothesis is one of several “gravito-thermal” theories which say the heating of the planet comes from gravity rather than (or in some theories in addition to) the greenhouse effect. His thought experiment is a planet with an atmosphere. The planet is isolated from the universe by an impervious thermally insulating shell that completely surrounds it, and which prevents any energy exchange with the universe outside. Inside the shell, Jelbring says that gravity makes the upper atmosphere colder and the lower atmosphere warmer. Back around 2004, I had a long discussion on the “climateskeptics” mailing list with Hans Jelbring. I said then that his theory was nothing but a perpetual motion machine, but at the time I didn’t understand why his theory was wrong. Now I do.
Dr. Robert Brown has an fascinating post on WUWT called “Earth’s baseline black-body model – a damn hard problem“. On that thread, I had said that I thought that if there was air in a tall container in a gravity field, the temperature of the air would be highest at the bottom, and lowest at the top. I said that I thought it would follow the “dry adiabatic lapse rate”, the rate at which the temperature of dry air drops with altitude in the earth’s atmosphere.
Dr. Brown said no. He said that at equilibrium, a tall container of air in a gravity field would be the same temperature everywhere—in other words, isothermal.
I couldn’t understand why. I asked Dr. Brown the following question:
Thanks, Robert, With great trepidation, I must disagree with you.
Consider a gas in a kilometre-tall sealed container. You say it will have no lapse rate, so suppose (per your assumption) that it starts out at an even temperature top to bottom.
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
I say no. I say after a million collisions the molecules will sort themselves so that the TOTAL energy at the top and bottom of the container will be the same. In other words, it is the action of gravity on the molecules themselves that creates the lapse rate.
Dr. Brown gave an answer that I couldn’t wrap my head around, and he recommended that I study the excellent paper of Caballero for further insight. Caballero discusses the question in Section 2.17. Thanks to Dr. Browns answer plus Caballero, I finally got the answer to my question. I wrote to Dr. Brown on his thread as follows:
Dr. Brown, thank you so much. After following your suggestion and after much beating of my head against Caballero, I finally got it.
At equilibrium, as you stated, the temperature is indeed uniform. I was totally wrong to state it followed the dry adiabatic lapse rate.
I had asked the following question:
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
What I failed to consider is that there are fewer molecules at altitude because the pressure is lower. When the temperature is uniform from top to bottom, the individual molecules at the top have more total energy (KE + PE) than those at the bottom. I said that led to an uneven distribution in the total energy.
But by exactly the same measure, there are fewer molecules at the top than at the bottom. As a result, the isothermal situation does in fact have the energy evenly distributed. More total energy per molecules times fewer molecules at the top exactly equals less energy per molecule times more molecules at the bottom. Very neat.
Finally, before I posted my reply, Dr. Brown had answered a second time and I hadn’t seen it. His answer follows a very different (and interesting) logical argument to arrive at the same answer. He said in part:
Imagine a plane surface in the gas. In a thin slice of the gas right above the surface, the molecules have some temperature. Right below it, they have some other temperature. Let’s imagine the gas to be monoatomic (no loss of generality) and ideal (ditto). In each layer, the gravitational potential energy is constant. Bear in mind that only changes in potential energy are associated with changes in kinetic energy (work energy theorem), and that temperature only describes the average internal kinetic energy in the gas.
Here’s the tricky part. In equilibrium, the density of the upper and lower layers, while not equal, cannot vary. Right? Which means that however many molecules move from the lower slice to the upper slice, exactly the same number of molecules must move from the upper slice to the lower slice. They have to have exactly the same velocity distribution moving in either direction. If the molecules below had a higher temperature, they’d have a different MB [Maxwell-Boltzmann] distribution, with more molecules moving faster. Some of those faster moving molecules would have the right trajectory to rise to the interface (slowing, sure) and carry energy from the lower slice to the upper. The upper slice (lower temperature) has fewer molecules moving faster — the entire MB distribution is shifted to the left a bit. There are therefore fewer molecules that move the other way at the speeds that the molecules from the lower slice deliver (allowing for gravity). This increases the number of fast moving molecules in the upper slice and decreases it in the lower slice until the MB distributions are the same in the two slices and one accomplishes detailed balance across the interface. On average, just as many molecules move up, with exactly the same velocity/kinetic energy profile, as move down, with zero energy transport, zero mass transport, and zero alteration of the MB profiles above and below, only when the two slices have the same temperature. Otherwise heat will flow from the hotter (right-shifted MB distribution) to the colder (left-shifted MB distribution) slice until the temperatures are equal.
It’s an interesting argument. Here’s my elevator speech version.
• Suppose we have an isolated container of air which is warmer at the bottom and cooler at the top. Any random movement of air from above to below a horizontal slice through the container must be matched by an equal amount going the other way.
• On average, that exchange equalizes temperature, moving slightly warmer air up and slightly cooler air down.
• Eventually this gradual exchange must lead to an isothermal condition.
I encourage people to read the rest of his comment.
Now, I see where I went wrong. Following the logic of my question to Dr. Brown, I incorrectly thought the final equilibrium arrangement would be where the average energy per molecule was evenly spread out from top to bottom, with the molecules having the same average total energy everywhere. This leads to warmer temperature at the bottom and colder temperature at elevation. Instead, at thermal equilibrium, the average energy per volume is the same from top to bottom, with every cubic metre having the same total energy. To do that, the gas needs to be isothermal, with the same temperature in every part.
Yesterday, I read the Jelbring hypothesis again. As I was reading it, I wondered by what logic Jelbring had come to the conclusion that the atmosphere would not be isothermal. I noticed the following sentence in Section 2.2 C (emphasis mine):
The energy content in the model atmosphere is fixed and constant since no energy can enter or leave the closed space. Nature will redistribute the contained atmospheric energy (using both convective and radiative processes) until each molecule, in an average sense, will have the same total energy. In this situation the atmosphere has reached energetic equilibrium.
He goes on to describe the atmosphere in that situation as taking up the dry adiabatic lapse rate temperature profile, warm on the bottom, cold on top. I had to laugh. Jelbring made the exact same dang mistake I made. He thinks total energy evenly distributed per molecule is the final state of energetic equilibrium, whereas the equilibrium state is when the energy is evenly distributed per volume and not per molecule. This is the isothermal state. In Jelbrings thought experiment, contrary to what he claims, the entire atmosphere of the planet would end up at the same temperature.
In any case, there’s another way to show that the Jelbring hypothesis violates conservation of energy. Again it is a proof by contradiction, and it is the same argument that I presented to Jelbring years ago. At that time, I couldn’t say why his “gravito-thermal” hypothesis didn’t work … but I knew that it couldn’t work. Now, I can see why, for the reasons adduced above. In addition, in his thread Dr. Brown independently used the same argument in his discussion of the Jelbring hypothesis. The proof by contradiction goes like this:
Suppose Jelbring is right, and the temperature in the atmosphere inside the shell is warmer at the bottom and cooler at the top. Then the people living in the stygian darkness inside that impervious shell could use that temperature difference to drive a heat engine. Power from the heat engine could light up the dark, and provide electricity for cities and farms. The good news for perpetual motion fans is that as fast as the operation of the heat engine would warm the upper atmosphere and cool the lower atmosphere, gravity would re-arrange the molecules once again so the prior temperature profile would be restored, warm on the bottom and cold on the top, and the machine would produce light for the good citizens of Stygia … forever.
As this is a clear violation of conservation of energy, the proof by contradiction that the Jelbring hypothesis violates the conservation of energy is complete.
Let me close by giving my elevator speech about the Jelbring hypothesis. Hans vigorously argues that no such speech is possible, saying
There certainly are no “Elevator version” of my paper which is based on first principal physics. It means that what I have written is either true or false. There is nothing inbetween.
Another “gravito-thermal” theorist, Ned Nikolov, says the same thing:
About the ‘elevator speech’ – that was given in our first paper! However, you apparently did not get it. So, it will take far more explanation to convey the basic idea, which we will try to do in Part 2 of our reply.
I don’t have an elevator speech for the Nikolov & Zeller theory (here, rebuttal here) yet, because I can’t understand it. My elevator speech for the Jelbring hypothesis, however, goes like this:
• If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest air at the top and the warmest air at the bottom.
• This also is happening with the Earth’s atmosphere.
• Since the top of the atmosphere cannot be below a certain temperature, and the lower atmosphere must be a certain amount warmer than the upper, this warms the lower atmosphere and thus the planetary surface to a much higher temperature than it would be in the absence of the atmosphere.
• This is the cause of what we erroneously refer to as the “greenhouse effect”
Now, was that so hard? It may not be the best, I’m happy to have someone improve on it, but it covers all the main points. The claim that “gravito-thermal” theories are too complex for a simple “elevator speech” explanation doesn’t hold water.
But you can see why such an elevator speech is like garlic to a vampire, it is anathema to the “gravito-thermal” theorists—it makes spotting their mistakes far too easy.
w.
scf says:
January 21, 2012 at 1:37 am
“Having read Willis’ comments, and Jelbring’s comments about Willis’ comments, I am quite surprised. How on earth is it possible that Jelbring has such a weak grasp of physics?”
Please, point out exactly what part is weak in my paper insteaed of using general degrading statments about my understanding in physics. Willis behavior in this respect has been outstanding and what I consider him to be is not printable. The results in the article stands and falls by applying 1:st law of thermodynamics and 2:nd law of thermodynamics. Are these 2 laws familiar to you? Just tell me which one is wrong or point to any other fault IN THE ARTICLE. Zeroth´s law is not applicable in this case since gravity is involved and it makes the constant energy per any equal mass within the insulated sphere constant. This is equivalent to the adiabatic temperatuer lapse rate of -g/Cp. To avoid the sill PM argumet I confirm that a system that has reached maximum entropy cannot include a PM so I agree with you on that point. The treated atmosphere only contain ideal gases and no perpetuum mobile.
Willis and you seem to share the same problem. You don´t understand my paper and still you know that it is wrong by adding unspecified circumstances. Just read it and comment line by line what is wrong. Don´t forget to comment on observational evidence that support the model results which primarily are observed temperture lapse rates on other planets that support the model result. That includes observed temperature lapse rates on Venus, Mars, Titan, Jupiter, Neptun and Uranus.
Willis Eschenbach;
I am not impressed by a fit with four visible free parameters plus selection parameters. That has no evidentiary value at all.>>>
I, on the other hand, am not impressed with an accusation that isn’t true. Go back and take a look at the equations yourself Willis and count the g_d d_mned parameters. Equation 7 is actually two equations on a single line, and further, it is an interim step. Each of the two equations expressed in Equation 7 has 2 variables. You cannot possibly be suggesting that we count up the variables in two different equations and accuse N&Z of having four variables in a single equation, can you? Oh wait. You just did.
The purpose of the TWO equations shown in Equation 7 (which should be expressed as Step 7 for clarity) are to explain the transformation that leads to Equation 8, which is their FINAL equation, and which contains TWO variables, from which the surface T of 8 planets is then calculated.
So, your harsh criticism of N&Z being nothing more than curve fitting based on four free parameters is falsified simply by reading what they said instead of reading what someone else SAYS they said. Are we skeptics seeking the truth? Or rabid confirmation biased critics stooping to half truths and omitted facts to support our position?
Willis Eschenbach;
People, please pay attention to this interchange. Hans Jelbring asserted categorically that “Any surface radiation power exceeding 100 W/m^2 is bull.”>>>>
People, please pay attention to Hans Jelbring’s entire comment where it becomes clear that English is not his first language and that he struggles in several places to articulate clearly what he means. Rather than going all attack dog on his choice of words, how about cutting the guy some slack and asking for clarification?
Hans Jelbring,
Any surface radiation power exceeding 100 W/m^2 is bull regardless if it is from equatorial, midlatitude or polar regions during days or night. Just show how this fantasy power radiation changes between day and night in polar regions as an exsample.>>>
Hans, could you expand on this statement for clarity? Your wording suggests that the surface of the earth never exceeds radiance of 100 w/m2 which just isn’t correct. Is this what you meant? Or were you referring to net radiation? Or some sort of averaged number over time? We don’t understand exactly what the 100 w/m2 you are speaking of here actually refers to.
OK, jae, let’s provide some empirical evidence (and in the process, hopefully we’ll depoliticize this argument).
We’ll consider a different system, that has NO politics associated to it, and yet has (essentially) similar physics. That system is a cryogenic tank, also called a “dewar”, also called a “thermos flask.”
In its simplest form, a cryogenic tank is insulated by a layer of vacuum (say 1 cm thick). Of course, heat can be carried across that gap by radiation. NASA engineers (among others) would like to reduce that radiative heat flow, so that spaceships can hold liquid oxygen/hydrogen/helium longer.
Weird-sounding engineering idea: Fill that one centimeter vacuum gap with ten (or more) ultrathin, aluminized, lightly crumpled, sheets of plastic film (typically ordinary mylar), with each mylar sheet having a thickness of only 0.001 cm (or less), such that the thickness of each sheet is tiny compared to the thickness of the vacuum gap, and in particular, such that the net thermal resistance of all the mylar layer’s together is negligible.
Now a photon traversing the vacuum gap is absorbed (by an ultrathin mylar sheet) and reemitted … absorbed (by a sheet) and reemitted … absorbed (by a sheet) and reemitted … (analogously, as infrared is absorbed (by CO2) and reemitted … absorbed (by CO2) and reemitted … absorbed (by CO2) and reemitted … ).
Question: What happens to the heat leak from the vacuum gap? Does the gap insulate the tank better, or worse? (analogously, does CO2 make our atmosphere insulate better, or worse?)
Answer: As discovered by NASA in the 1960s, the thin-layered vaccum tanks — called “multilayer superinsulation tanks” insulate heat flow orders of magnitude better than tanks without superinsulation. That is why every cryogenic tank manufacturer in the world now uses superinsulation.
So that is one more “Elevator Answer” to Willis’ question. Adding CO2 to the Earth atmosphere has effects similar to adding superinsulation to a cryogenic tank. In both cases, thermal conductivity is reduced, with the (desired) result that NASA’s spaceship tanks retain their cryogen longer, and with the (similar, but sobering) result that the Earth’s surface warms to a higher temperature from the sun’s solar input.
Ultrashort Elevator Answer: CO2 acts as a multilayer superinsulator.
The point being, there’s essentially zero doubt (among scientists and engineers) regarding multilayer superinsulation; both theory and empirical observation agree that multilayer superinsulation just plain works.
And this is yet another reason why there’s essentially zero doubt (among scientists and engineers) regarding the GHE in general: the GHE just plain works
I said early on in this thread
“The isothermal/adiabatic distribution for an isolated ideal gas in a gravitational field has long been debated.
For the isothermal distribution we have Maxwell, Boltzmann and Clausius.
For the adiabatic distribution we have Loschmidt, Laplace and Lagrange.
The smart money must be with the isothermal advocates but I would not regard this as a debate of which was settled and of historical interest only.
Here for instance is a member of the physics department of the University of California making a very up to date case for the adiabatic distribution.
http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.4990v3.pdf”
Its a pity that Willis who last week was with the adiabatic camp, now thinks to hold such a position is only held by “ignorant” people.
This is an overreaction which has more place on a Deltoid thread than here.
However anyone who makes the adiabatic distribution for an thermally isolated ideal gas in a gravitational field a cornerstone of their theory about the real adiabatic atmosphere is needlessly going against the orthodox physics.
A bit like Claes Johnson and photons.
Its much better to stay within the orthodox framework of physics when addressing a general problem such as the Earths Climate.
Then separately argue the case for the existence or otherwise of photons or whether an adiabatic distribution for isolated ideal gas in a gravitational field is appropriate.
Bart;
Bart says:
January 21, 2012 at 3:21 am
And, in another forehead slapping moment, I suddenly realized I do not even have to argue that SB violation is possible.>>>
You NAILED it!
Well, until the last sentence…
Bart;
And, adding more IR emitters to the Earth’s atmosphere will tend to cool, rather than heat, it.>>>>
Nope. You should get to the same surface temperature, or close to it.
By opening up more pathways for emission to space, you don’t actually cool anything provided that you consider the whole surface and the average of T^4 of that surface. I think it easier to explain by going the other way. Take a system with a given number of pathways and shut some of them off. Does the temperature rise? One would think so, but not by nearly as much as one would think.
As soon as you shut some of the pathways off, that forces energy that otherwise would have escaped to be recirculated by other means. But the over all temperature does NOT need to rise (or more accurately, it doesn’t need to rise as much as one would think) to re-establish equilibrium. Because the energy is not being forced to re-circulate, it must also have the effect of re-distributing energy about the planet. Shut off some pathways, and there is no other possible result but that net energy flow from the tropics to the poles increases. The result is, because P varies with T^4, is that the coldest parts of the planet experience the most increase in T, which in turn results in a planet of more uniform temperature.
Equilibrium still requires that emission to space match absorption. By shutting off some channels, we force the emission to be spread around more than it would otherwise. Equilibrium however still arrives at the exact same w/m2 being emitted because absorption didn’t change. We get a cooler tropics and a warmer high latitudes, but the average of T^4 remains identical. If we fall into the trap of averaging T instead of T^4, we will get an average of T that is higher than it was before we shut some of those channels off.
Your main thought process howevere is correct. Shut down some channels, or create some new ones, and you redistribute flux in terms of what frequencies and how much escape from where. But the surface temperature simply “evens out” until equilibrium is established again. But change in net energy balance? There isn’t any.
A Physicist: “With regard to thermodynamics and transport theory (which is broadly what this WUWT topic is about), an historically recent and very broadly applicable framework regards thermodynamics and transport theory as (essentially) the study of the geometry of flow on manifolds, specifically the study of Hamiltonian dynamical flows on manifolds that are equipped with a symplectic structure.”
That’s beyond what vestigial mathematical skill remains from the last math course I took, over forty years ago. But, since you appear to be conversant in these matters, perhaps you could point out where I am wrong in understanding the above-identified Velasco et al. paper to reason from Hamiltonian dynamics to a conclusion that at equilibrium an ideal gas in a gravitational field will exhibit a non-zero temperature lapse rate. Or maybe you could point out the equation at which that paper or the Román et al. paper on which it depends went off track. Those papers are discussed in this thread: http://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/.
In this context it is not enough to say that Velasco et al.’s lapse rate approaches zero as the number of molecules approaches infinity, because Willis’s argument is based on the lapse rate’s being zero at equilibrium even for a finite number of molecules.
Both the GHE and the N&Z paper try to solve a problem in explaining the current avg. temp
of 288K, the first starts from 255K, the other from 154,7K.
What both approaches are neglecting is that the earths surface consist mostly of oceans,
70% area, minimum 3 km deep and a temperature on average of +2C, already 20K higher
than the blackbody temperature the GHE uses when the sun has heated the blackbody.
Ocean surface temperature is on average 290K, just 15K higher than the temperature of the
deep oceans. This warmer layer is ~200m deep in the tropics, reducing to 0m near the
polar circles.
So instead of heating a blackbody from 0K to 255K (255K difference) all the sun has to do
is heat a smal part of the oceans from 275K to 290K, just 15K difference.
This warm ocean then heats the atmosphere, and results in our pleasant 288K average
temperature near the surface.
As background information may serve that the earth radius is ~6370 km, ocean depth
~3km, oceanbed 5 -10 km. The other 6350+ km are hot to very hot, (400K – >5000K)
although it is assumed that allmost no heat is flowing from the hot interior to the oceans
Ocean temps are basically steady since system earth is in radiative balance with the sun.
Ben Wouters
This thought experiment is similar to elevator music. It is there, but not particularly memorable.
I saw one commenter taking a correct approach. He(she) looked at the gas properties, including Prantl number and did an amazing thing, calculated the changing properties with temperature, viscosity, thermal capacity and pressure. I mentioned that isothermal conditions in the tall column of air would require changes in the mixed gas viscosity, perfect insulation and the velocity/energy of the upper most molecules would be greater than the lower. If you take the top and bottom off the tube, what would happen? So it is an unrealistic thought experiment, but maybe a start to a useful one. If that theoretical column was integrated over the entire surface, using the calculations to determine the final temperature, viscosity and pressure of each column, then we would be on to something, but not an elevator description or back of the envelop kinda thing.
There have been a lot of comments mentioning conductivity. About time. Now how about the change in conductivity? CO2 changes the conductivity of a mixed gas. H2O doesn’t have as much impact on the conductivity of a mixed gas. It takes the change in conductive hundreds of years to thousands of years to change climate, in the mean time, Ein to the oceans is never equal to Eout of the oceans. Shouldn’t that be where the problem starts? A ball of water in space over eons absorbing more energy that it emits? Then one fine day it reaches near equilibrium. Gravity does have an impact there. Then add layers of atmosphere one at a time.
The top down approach so far has been problematic, why not start from the bottom up?
I will frankly admit that I haven’t read all the comments, but I see that some people still insist that gravity would still raise the temperature at the bottom of the atmosphere as compared with the top, by means of compression.
If this is the case, the argument wouldn’t be confined to a gaseous amosphere. It would also apply to any solid column – say, a granite pillar – since all solid bodies are at least slightly elastic. To find an easily visualisible model, consider a tall hollow tube filled with tennis balls. The balls have weight, and the balls at the bottom of the tube have more weight above them than those near the top, so they are more compressed. The density of balls, and the pressure they exert on each other through their elasticity, is greater at the bottom.
We assume that the tube is perfectly insulated from the outside world (with respect to heat flow).
Now, does anyone suggest that in equilibrium the balls at the bottom will be hotter than those at the top? If so, what is to prevent heat being conducted from the hotter balls to the cooler ones until the temperature is equalised?
Note that I refer to the situation in equilibrium. If we disturb that equilibrium, say by putting in more balls at the top of the tube, there will be a temporary increase in temperature at the bottom, as the balls there are further compressed, but again the heat generated by compression (which is actually a form of kinetic energy) will eventually be diffused evenly throughout the tube. Does anyone disagree?
If they agree in the case of an elastic solid column, but disagree in the case of a gas, they need to explain the difference. Of course in the case of a gas there will be convection as well as conduction. If the gas were a perfect Newtonian fluid, I suppose that by adding more gas at the top of the column we might set up a perpetual circulation, doing no net work, just as if we drop a perfectly elastic tennis ball we can set up a perpetual bouncing motion. But there are no perfect fluids, any more than there are perectly elastic tennis balls. In any real gas, without any new input of energy, the convection current would eventually come to a halt as its energy is dissipated by friction and converted to heat.
davidmhoffer says:
January 20, 2012 at 8:10 pm
David, you’re pretty close to what I have been saying ever since Ira’s response to the K&Z hypothesis . It’s what I have been calling the maximum GHE. If you look at my comments over the last two weeks you will your description is very close. However, I don’t think your dam analogy is right. More water behind the dam would indicate a warmer climate.
It’s more like an overflow valve. The dam is full and any more energy just gets kicked out the overflow. It’s more like a V-shaped river. The initial flow of water increases the height behind the dam quickly. However, as the lake grows the same amount of water increases the height less and less. The overflow amount can match this rise and the water level does not increase.
In the atmosphere I think this is due to the fact that CO2 has both a warming and cooling effect. The GHE gets maximized once these two effects become equal. This occurs because the warming effect is a stronger one but diminishes more quickly due to saturation.
PS. I even pointed out that the warming from adding 100 ppm of CO2 would be .005% … which is the increase in mass when you convert O2 to CO2.
davidmhoffer says:
The above is the exact argument made by Alan Siddons, one of the “Slaying the Skydragon” crew. It is an extremely silly argument. Yes, the amount the Earth is emitting as seen from space has to be the same amount it is receiving from the sun in radiative balance…It has to be. However, the amount emitted by the surface of the Earth is not. The radiative greenhouse effect is the only thing that can explain how the surface of the Earth can be at an average temperature so high that it emits ~390 W/m^2 while the Earth as seen from space only emits ~240 W/m^2 and is thus still in radiative balance with what it receives from the sun.
Congratulations on now embracing the arguments of the “there is no greenhouse effect” crew who you once laughed at!
No…The water depth is the analog of the surface temperature. And, while the W/m^2 at the top-of-the-atmosphere is the same as it was, the W/m^2 leaving the surface is not.
The only way that the atmosphere can lower the probability of radiative energy from the surface from escaping to space is radiatively…i.e., by absorbing this energy. So, the only way that the mass of the atmosphere can come into it is in a way that changes the radiative absorption (which it can do to some extent by broadening of the absorption lines of the GHGs).
Response to http://wattsupwiththat.com/2012/01/19/perpetuum-mobile/#comment-871539 wherein David M Hoffer invents a new way to count parameters:
Great…Now all I have to do if I perform a fit of y vs. x with 100 free parameters is break it into two equations, one that defines some intermediate quantity as a function of x in terms of 99 of the parameters and the other that gives the final relation between this intermediate quantity and what I want (y) with 1 free parameter. Then I will have magically gone from a 100 parameter fit to a 1 parameter fit and everyone will be very impressed with my fit. I’ll have to remember that trick!
davidmhoffer says:
January 21, 2012 at 4:07 am
[Willis Eschenbach;
I am not impressed by a fit with four visible free parameters plus selection parameters. That has no evidentiary value at all.>>>]
I, on the other hand, am not impressed with an accusation that isn’t true. Go back and take a look at the equations yourself Willis and count the g_d d_mned parameters. Equation 7 is actually two equations on a single line, and further, it is an interim step. Each of the two equations expressed in Equation 7 has 2 variables. You cannot possibly be suggesting that we count up the variables in two different equations and accuse N&Z of having four variables in a single equation, can you? Oh wait. You just did.
The purpose of the TWO equations shown in Equation 7 (which should be expressed as Step 7 for clarity) are to explain the transformation that leads to Equation 8, which is their FINAL equation, and which contains TWO variables, from which the surface T of 8 planets is then calculated.
This was the same argument Joel tried to use against me back in Ira’s thread. It’s unfortunate that they are willing to discard what may very well be a valid correlation by simply waving their hands.
The two variable are atmospheric pressure and input energy. Those two define the GHE on every one of the planets. I think the non-GHG atmosphere is simply a red herring. GHGs are required, they just have a maximum effect in a gravity field.
This makes a lot of sense when you think about the effective radiation height. The incoming solar energy is what drives the atmosphere to be well mixed … to a point. Lower energy or higher pressure, less mixing. Higher energy or lower pressure, more mixing. The mixing drives the GHGs to a point in the atmosphere that ends up defining the effective radiation height. Once you’ve got enough GHGs to block almost all outgoing radiation you have maxed out the GHE.
The Title of this thread and the whole arguement by mr Eschenbach is a Strawman.
His hypothetical machine is quite impossible and he knows it. You cannot have a perfectly insulated column of air, just as he admits you cannot get any “work” out of downwelling IR.
He also admits that ice can form in the desert at night even though the temperatures are above freezing.
There have been many experiments that show that Cooling occurs, not warming from the night sky and not just in deserts. See Roy Spencer’s Experiment, where he thinks the Air in the Box should fall even lower than 5C lower than the surrounding air temperature and it is DIR that is keeping it from falling that much lower.
Talk about fool yourself with pre-conceived ideas.
http://www.drroyspencer.com/2010/07/first-results-from-the-box-investigating-the-effects-of-infrared-sky-radiation-on-air-temperature/
Richard M says:
Yes, there are 2 variables but there are at least 4 free parameters in their fit.
And, they are not fitting to the GHG effect. They are fitting to their “surface temperature enhancement”. Only 3 of the 8 bodies that they consider have a very significant radiative greenhouse effect and only for one of those bodies (Venus) is the greenhouse effect that majority of what they define as the “surface enhancement effect”. (For the Earth, the radiative greenhouse effect is ~25% of their total surface temperature enhancement.) Most of the “surface temperature enhancement” is simply due to an evening out of the temperature distribution with no change in the W/m^2 emitted by the surface.
It is strange that people who have not understood the most basic facts about what they have done nonetheless seem to think that they have extremely wise and intelligent opinions about it!
Bart says:
January 20, 2012 at 6:38 pm
KevinK says:
January 20, 2012 at 4:04 pm
“When the energy returns to the surface from the “GHG” you cannot ADD it to the energy arriving from the Sun to produce an alleged “energy budget”.”
Energy is constantly coming in. If some of it is made to hang around longer than instantaneously, before the new batch arrives, then you will accumulate a net offset.
It’s not about increasing energy flow, which is always nearly constant. It’s about impeding that flow so that you keep more close to you.
Hi Bart. Do we not have a similar situation with the effect of gravity creating a gradient of pressure in an atmospheric mass? Because air is compressible, it means the density of the air will be greater near the surface, and energy hangs around longer in denser masses of a given composition than it does in less dense masses of that same composition due to the higher heat capacity.
Thank you, Joe, for this very reasonable question, which I will try to answer concretely.
From the viewpoint of geometric thermodynamics, every conserved quantity is associated to a thermodynamic potential. All systems conserve energy, and the thermodynamic potential associated to energy is called temperature. Some systems (but not all) conserve particle number, and the (less familiar) thermodynamic potential that is associated to particle number is called the chemical potential. Ideal gases are an example of a system that does conserve both energy and particle number.
If we regard the atmosphere as a stack of thin layers, we observe that each layer exchanges both energy and particles with the layers above and below it, and moreover the exchange of particles is associated to work done against a gravitational potential.
So a preliminary accounting of any thermodynamical theory of the atmosphere must ask:
(1) Does this theory account for the temperature potential?
(2) Does this theory account for the chemical potential?
(3) Does this theory account for work done against the gravitational potential?
Unless all three potentials — temperature, chemical, and gravitational — are accounted, the theory is thermodynamically wrong.
With reference to Tallbloke’s page, we find a mistaken implication in the second paragraph:
Mistakenly, the Loschmidt analysis goes on to completely neglect the chemical potential, on the grounds (presumably) that because there is no net exchange of particles, the thermodynamic effects associated to the exchange of individual particles can be neglected.
But since the exchange of individual particles really does occur (and is in fact the mechanism that sustains a pressure-and density gradient), Loschmidt’s analysis is wrong to neglect the chemical potential.
One way to get clear on these matters is to extend the analysis to thermodynamically account (explicitly) not only temperature and chemical potential gradients, but also pressure and density gradients. The result is simply that (at equilibrium) atmospheric pressure and density vary so as to ensure that both the temperature and the chemical potential are uniform.
Ultrashort Elevator Summary: Gravito-thermal theories wrongly neglect chemical potentials.
DavidB says:
January 21, 2012 at 5:34 am
I see that some people still insist that gravity would still raise the temperature at the bottom of the atmosphere as compared with the top, by means of compression.
consider a tall hollow tube filled with tennis balls. The balls have weight, and the balls at the bottom of the tube have more weight above them than those near the top, so they are more compressed. The density of balls, and the pressure they exert on each other through their elasticity, is greater at the bottom.
We assume that the tube is perfectly insulated from the outside world (with respect to heat flow).
Now, does anyone suggest that in equilibrium the balls at the bottom will be hotter than those at the top? If so, what is to prevent heat being conducted from the hotter balls to the cooler ones until the temperature is equalised?
This goes back to the proof I offered Duke.edu physicist Robert Brown up near the top of the thread. he said:
“if A and B are placed in thermal contact, they will be in mutual thermal equilibrium, specifically no net heat will flow from A to B or B to A.” That’s the zeroth law.”
And I pointed out:
Assuming your A and B have at least some dimension, then a thermal gradient across them would mean that the top surface of A will be at the same temperature as the bottom surface of B where they contact. Therefore no heat will flow. Even so, the average temperature of the whole of body A will be higher than that of B. QED.
But add in some adiabatic action – a nice little bit of vigorous vertical mixing – and the temperature gradient reappears. The elevator speech goes thus: “When air moves in a vertical airflow from the top to the bottom it is compressed and thus heats. When air moves in a vertical airflow from the bottom to the top it is decompressed and thus cools. In an atmosphere with a lot of vertical mixing you therefore will see a temperature gradient.”
Close. One has to ask what drives the “vigorous vertical mixing”. The answer is, temperature difference in the non-equilibrium, open system caused by differential heating. What does the heating? The Sun, of course. It isn’t so much air compressing and heating as it falls as it is air being heated at the bottom and rising (and displacing cooler denser air as it does so). The convective flow actually cools the bottom when it is being heated, without exception, although it does establish the lapse rate. Otherwise you have another of those processes that moves heat from colder to hotter.
The other point is that your elevator speech has nothing to do with either Jelbring or N&Z. The general thermodynamics of adiabatic expansion and its importance in the atmosphere is long known and completely absent from both of their papers. They both assert that something about the atmosphere differentially warms it due to gravity, not that the sun heats the ground, establishes convective flow that moves the heat around (cooling the ground in the process) and that radiative imbalance in GHGs cause differential cooling of the upper troposphere to maintain the energy flow.
Without the rapid cooling of the upper atmosphere that keeps it cold relative to the ground — cooling that is strictly radiation, because sooner or later the Earth has to lose the incoming heat from the sun — the adiabatic warming profile would not exist, and in parts of the atmosphere that profile inverts even as it is (for example, over the arctic in the long arctic night) as further proof that this isn’t an atmospheric compression effect, it is plain old convection.
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Richard M says:
It wasn’t hand-waving at all! I am the ONLY ONE to my knowledge who has even bothered to replicate their fitting procedure. Then I showed how I could change the temperature of the three bodies that have a significant greenhouse effect to essentially eliminate that effect and still get almost as good a fit using their fitting form (even though the data for N_TE was now quite a bit squirrelier since Venus now had a value considerably smaller than Earth and Titan and I made no attempt to change the fitting form or definition of T_sb to optimize the fit)!
I have also explained that there is likely a generally positive correlation between P and their N_TE because as you add an atmosphere to a planet, you will even out the temperature distribution, raising the average temperature. (Higher pressure also tends to correlate with more greenhouse gases and it can also cause broadening of the GHG absorption lines, although I think this is a smaller issue in the positive correlation that they see because, for the most part, their surface temperature enhancement does not really reflect the radiative greenhouse effect.)
Here’s a shorter elevator speech:
If there is a temperature gradient between two parts of a system, net heat flows from the warmer part to the cooler part. If there is net heat flow within the system, it is not in equilibrium.
Wow, so perfectly correct! Two laws of thermodynamics (0 and 2). Done.
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Tallbloke:
Your last argument in response to my ‘tennis ball’ model seems to prove too much. Using this argument you could prove that heat can never be conducted along a metal rod. Suppose one end of the rod is in a fire, and the other end in a bowl of ice water. There is a continuous gradient of temperature along the rod. But if we conceptualise the rod as a collection of infinitely thin ‘slices’, each slice will be at the same temperature as the next one. Therefore, by your argument, ‘no heat will flow’. And yet it does!
Willis,
I’m just a bozo on the bus, so I post with trepidation. I was wondering about something that seems to have been addressed by Crispin above. Starting with a perfectly insulated column of non-GHG gasses initially at uniform temperature and pressure throughout, suppose you cause it to appear on the surface of a planet, and suppose that its gravity does indeed cause a temperature gradient to appear.
Then, suppose you take advantage of the temperature differential at the top and bottom to drive a heat engine, which reduces the temperature differential. And so on. That seems to me to say that at some point, the engine will stop.
My question is this: is Jelbring saying that gravity will somehow add heat to the system, thereby restoring initial heat differential? Is he actually explicitly saying that he is creating a perpetual motion machine, or is that something you have inferred? Could he simply be saying that gravity will cause a temperature differential?
I don’t know enough physics (hardly any, in fact), to venture an opinion and certainly an elevator speech is far beyond my capabilities. But I’d just like to know what Jelbring is explicitly saying and whether you might be addressing a straw man argument. I’m not being in any way antagonistic – this is a genuine and open question asked out of ignorance.
The problem is that GHGs and back radiation does not explain the vertical temperature of the atmosphere. The inescapable conclusion of this is that the GHG model is not capable of explaining our atmosphere and that there is more at ‘play’ than the GHG model would suggest.
Why not? I would have said that this is precisely what they predict, although the observed vertical temperature profile of the atmosphere is due to convection induced by differential heating as a part of the overall greenhouse process. In order to get the greenhouse effect, you need to radiate (in a frequency band) from the greenhouse gases up where the atmosphere is cold instead of down where it is as warm as the surface. That’s all it takes. That is experimentally observed to be the case in the actual IR spectrum as measured by NASA satellites.
The real question is: Why do you think one needs additional explanations at all?