Debate Thread: Miskolczi semi-transparent atmosphere model

I readily admit most of the equations in this go WAY over my head given the time available to review the article; but if I understand the concept correctly it’s based on an analogy I’ve always wondered about.
If I put a pot on the stove and turn up the heat until it is ready to boil, but without enough energy to make it boil, there isn’t really any change I can make to the contents of the post (presuming I don’t replace the water by a large percentage) to change that temperature. For example if I add a pinch of salt to the water I may raise the boiling point but the water will remain at the same temperature – because the overall heat available to the pot hasn’t changed.
As I’m sure you can guess the pot represents the earth, the flame the sun and the air our universe. The heat put into the pot is sapped by the universe at a constant rate.
Thus if I next add a bunch of noodles to the water what happens… well if the noodles are cooler then the water I’ll see a temporary drop in the temperature of the pot, however over time if I did nothing the equilibrium temperature of the pot would return to the same level.
Similarly if I added hot noodles the reverse would apply the overall temperature might briefly increase but because only so much energy was being added to the system the original equilibrium would eventually be restored. – (of course this isn’t a valid question on the temp of the water increasing since we aren’t claiming global warming is coming from outside our system) which leads to the actual experiment…
Finally I could have had 2 pots one with noodles and one without and in the end the temperature of the water in both pots should reach the same equilibrium point – they might need slightly different time frames to do so but the contents of the pot, so long as the contants remain primarily the same do not significantly change the equilibrium temperature of the pot’s contents.
To truly mirror our system I would need to pot to reach equilibrium with the noodles in a bag, and then slice open the bag (CO2 in the earth is represented by the noodles in the bag) and would have to see a sustained temperature difference once the bag was opened to defeat his energy model.
In other words this theory appears to pass the common sense test, but maybe I’m way off…

nice overview here.

Interesting that the resignation of a Scientist from NASA over perceived ‘muzzling’ of his work is not newsworthy if that work goes counter to prevailing AGW sentiment, but perceived ‘muzzling’ of a scientist due to views that are not counter is front page news.

Re: Robert Wood (11:22:24)
Agreed, the statement was in only the higher level “Thesis” section. Overall I would say Dr. Miskolczi is taking a much more “holistic” approach to atmospheric dynamics than others have in the past.
I think folks should be mindful of how the whole “global warming” thing started back when it was used as a lever to support the large scale adoption of nuclear power over coal. Then once the environMENTAL group put the kabosh on nuclear, it was kept as a lever used against fossil fuel energy in general.
It isn’t as if someone did years of research and discovered that CO2 was causing warming, it came about from the opposite direction. People with a certain world view wanted there to be warming from CO2 and so they have built various ways of validating the idea. And that is why there is so much “push back” from the AGW crowd. It is because we aren’t invalidating some scientific conclusion, people who find no evidence of AGW are basically invalidating the world view of these people which is something very personal and some personality types experience that as adversarial on a personal level. Their conclusions are a closely held part of them and to criticize those conclusions is to criticize them personally. That is why they lash back with personal attacks against those would would question them … becuse they feel personally attacked.
AGW has no basis in science. It is a religion. And when you invalidate someone’s religion, they can become extremely defensive. You have to approach it as you would trying to tell a devout Christian about evolution.

Nuts – typo! That should read …”true” climate scientists…

Re: Crosspatch

AGW has no basis in science. It is a religion. And when you invalidate someone’s religion, they can become extremely defensive. You have to approach it as you would trying to tell a devout Christian about evolution.

I fail to see why people who know evolution exists because they’ve seen it in action/nudged it along a bit cannot simultaneously pray for rain and believe in a higher power. I have been known to darken the doorway of a Christian church myself a time or three, and I can envision the dinosaur in the poultry.
Re the Miskolczi paper, I’m still wading through but found that Ken Gregory gives a pretty good cheat sheet version for the people that are not math majors.

Dr. Mikolczi’s theory appears to be correct; or at least to be more correct, than the classical theory with its simplifications from a 100 years ago.
Newton said that: “Force is proportional to the derivative of Momentum”. Or F= d(mv)/dt. Or F = mdv/dt + vdm/dt, mathematically.
Since mass m is = to a constant –> that vdm/dt =0, since the derivative dm/dt of a constant, is zero. And then Newton’s equation simplifies to F=mdv/dt. It was widely adopted, since in produced (almost) correct answers for 3 centuries.
Then a physicist said F != mdv/dt; Newton said F= d(mv)dt and that is correct. He really says that F = mdv/dt + vdm/dt and the vdm/dt term is not always = 0. Mass sometimes is a variable.
This “simplification correction” is called The Theory of Relativity.
It led to E=MC**2 and changed the World. It was merely a “simplification correction”.
Dr. Mikolczi shows where “simplification” was in error, and he provides a “simplification correction” Thinking about it, in hindsight, the “simplification correction” should be as obvious as Einstein’s correction was. After the fact, of course.
The atmosphere is obviously not infinite, for one thing. Secondly, the atmosphere extends all the way to the Earth’s surface. There is not some “discontinuity”, some piece of vacuum between the atmosphere and the Earth’s surface, as the “simplification” postulates.
The atmosphere is a gravitationally bound atmosphere that varies in pressure from the surface to the edge of space. Therefore, It can and does support a convection mechanism, and can use convection to move Energy about.
The atmosphere is connected to an effective infinite source of H2O at one end, and the effective infinite Vacuum at the other end.
These were all neglected in the “‘simplification” from 1928. I don’t know what kind of atmosphere that the simplification described, but it obviously doesn’t describe the reality of Earth and its atmosphere.
How could that be even marginally correct?
These changes make all the difference. It allows some continuity equations that allow for ground and near ground temperatures converging and equal, in equilibrium. Convection as an energy mover process due to gravitation. And a constant optical depth via the limitless H20 pool, at least until the Oceans dry up.
Dr. Mikolczi theory is already confirmed by existing measurements. These measurements of existing thermal profiles more correctly agree with Dr. Mikolczi calculations, and is the measured reality. Versus the “as received” warming theory that was first suggested more than a century ago.

Swampie:

I fail to see why people who know evolution exists because they’ve seen it in action/nudged it along a bit cannot simultaneously pray for rain and believe in a higher power.

I agree with that 100% and believe that many do (including me).
The underlying point was, though, that some people will always call for people who question their world view to be put on trial. It has been that way since before the time of Copernicus.

Mark Nodine:
I’m glad to see that the observed decrease in RH in the mid- to upper- troposphere is being met with a real and ready model created by an expert. As the middle troposphere at 400 mb cools markedly it helps the warmer and damper lower troposphere continue to regulate its preferred temperature range. IOW, the real GHE is at the surface and its warming is both cooling and drying the middle troposphere.
It’s as though the lower atmosphere not only saturates H2O but as it saturates it acts as a barrier to more H2O rising higher, thus drying the middle troposphere. And with more energy retained near the surface, the middle altitudes cool. But with the middle altitudes cooling they offset some of the surface warming, bringing the system back to its preferred thermal constant.
It’s notable that according to the climate models this cooling was only expected at higher in the tropopause and stratosphere, which have warmed slightly since Pinatubo. Maybe that’s b/c the climate models also wrongly modeled a constant RH across all altitudes (another oversimplification recently identified by other researchers). Likewise the air over Antarctica has also been found to be drier than expected, hence being markedly less prone to warming.
It might also reflect upon the paleo record where , with both CO2 & WV lagging behind the temperature rise. The paleo WV record (proxied via light oxygen) tracks much more consistently with interglacial temperatures than CO2 ever has!
IOW this validates the inability of CO2 to drive temperatures past a certain saturation point. Since CO2 can only contribute so much before effect and metaeffect saturate, temperatures might continue to climb for other reasons.
http://i32.tinypic.com/28h3dqh.jpg
http://i27.tinypic.com/25fuk8w.jpg

From the Climate Audit forum: http://www.climateaudit.org/phpBB3/viewtopic.php?f=4&t=161.
There’s 286 posts in response to the thread, and it may be useful to reference. The conversation over there has mostly been centered around the math/physics. Because they are currently disecting that side of the debate over there, and because it seems that the CA responders seem to know what they’re talking about, we can still be useful and use his description of the atmosphere and determine if his predictions about a compensating (through a decrease in water vapor), saturated greenhouse effect can be indepently confirmed in observations.
David Stockwell has also made several posts on the topic, giving the clearest description of Miskolczi’s theory I’ve seen: http://landshape.org/enm/category/audits/miskolczi/.
His posts were made in a relevant order, so start at the bottom and read up.
Also relevant to this debate is how Miskolczi’s theory effects paleoclimate interpretation. Here is Miklos Zagoni’s (a Hungarian physicist) powerpoint presented at the ICCC, entitled “Some paleoclimate consequences of Dr. Miskolczi’s new greenhouse theory”: http://www.heartland.org/newyork08/PowerPoint/Tuesday/zagoni.pdf
There are other paleoclimate consequences of this theory, including the attribution of the cause of the Paleocene-Eocene Thermal Maximum (http://en.wikipedia.org/wiki/Paleocene-Eocene_Thermal_Maximum#Methane_release).

“Niche Modeling” has discussed Miskolczi’s new equations too:
http://landshape.org/enm/category/audits/miskolczi/
The physics and mathematics are often beyond my ken, but this type of discussion allows some of it to sink in. It sure would be nice to have some credible experts who could explain it all to the rest of us.

Climate models showing Enhanced Greenhouse Effect achieve the enhancement by assuming positive feedbacks to temperature increase (such as “relative humidity is constant”). Actual observation of the climate, such as the response to the 1998 El Nino, show that temperature responds as if negative feedback effects were dominate — the temperature rapidly returns to the previous value after the driving event disappears.
Miskolczi’s theory seems to predict this from first principles.
So while this doesn’t prove that Miskolczi’s theory is correct, the observations do falsify EGE. If this were a scientific debate, EGE would have been discarded long ago and alternative theories (like Miskolczi’s) would be actively sought and tested against observation.
However, when I look at the material on RealClimate (for example), I see argumentation that looks very much like they started with the assumption that EGE must be right, and whatever it takes to achieve that is assumed true. The bald-faced inversion of logic that this requires is heavily camouflaged with mathsmanship and jargon.
It reminds me of an old professor of mine in solid state physics: He was able to prove conclusively that superconductivity couldn’t exist above 16 deg K – he submitted this masterpiece for publication just 3 weeks before the first high-temperature superconductor discovery was announced. To his credit, he withdrew the paper. Today (if he was using the RealClimate playbook) he might try to claim that 77K superconductivity was “consistent” with his theory.

BillSheldon (10:38:38 ) :

If I put a pot on the stove and turn up the heat until it is ready to boil, but without enough energy to make it boil, there isn’t really any change I can make to the contents of the post (presuming I don’t replace the water by a large percentage) to change that temperature.

You probably don’t want to take your analogy to this point. The boiling point is at a phase change. The temperature stops rising because, even before the bubbles appear, the exchange between the two phases has started.
It’s hardly apt to treat the atmosphere the same way.

I add a pinch of salt to the water I may raise the boiling point but the water will remain at the same temperature – because the overall heat available to the pot hasn’t changed.

True even in a glass of water at room temperature (assuming the resulting reduction of salt crystals to ions doesn’t itself appreciably change the heat balance).

To truly mirror our system I would need to pot to reach equilibrium with the noodles in a bag, and then slice open the bag (CO2 in the earth is represented by the noodles in the bag) and would have to see a sustained temperature difference once the bag was opened to defeat his energy model.

Maybe I’m totally misreading what you are saying but opening that bag would be the same thing as releasing more CO2 into the atmosphere.
Think of releasing more as taking a blanket out of a knapsack on a cold night an wrapping yourself with it. Let’s ignore the fact that this type of blanket blocks convection instead of radiation because energy loss is still energy loss. The blanket was probably at the same temperature as you but your skin temperature will now rise to a new equilibrium. CO2 blocks radiation but the idea is roughly the same.
—
It seems to me that the major argument in AGW is that CO2 heating causes more water vapor. Now there are some problems with this. RH depends on the temperature and it’s the raised temperature which is causing the problem. So the only real test of AGW theory would be to show that the temperature (or humidity) SHOULD HAVE BEEN SOMETHING ELSE!
But there’s really no way to predict what the measurements should have been. The next best hope would be to show a correlation between CO2 rise and temperature. The AGW’ers however are stuck with the fact that nature swamps any change so drawing any correlation is nigh impossible.
Nature is likely far more diabolical. There MUST be one or more negative feedback mechanisms in place. I can’t believe the Earth’s atmosphere is neutrally stable (picture a kid’s marble on a flat plate). The only way to achieve POSITIVE stability is with negative feedback (picture the same marble in a mixing bowl). If it weren’t positively stable, it would have runaway long ago at the slightest change in parameters such as the sun getting ever so slightly brighter or more CO2 occurring because of a volcanic eruption.

DAV (15:42:40) :

Maybe I’m totally misreading what you are saying but opening that bag would be the same thing as releasing more CO2 into the atmosphere.

Erratum: sentence should have read: “Maybe I’m totally misreading what you are saying but opening that bag would NOT be the same thing as releasing more CO2 into the atmosphere.”

In response to RICO: Temperatures in the past were also strongly
influenced by the location of continents and seas.
http://www.geosc.psu.edu/Courses/Geosc320/Campbell_Cont_Drift_Climate.pdf –
– A. McIntire

Robert Wood (15:56:11) : “Rico, The gross (large) variations in the Earth’s cl;imate are due to eternalities, such as passing through cosmic duist clouds, precession of the equinoxes, variations in the Sun etc. ”
Given the paleoclimate record, none of those things seem likely. Do you have any evidence to back up what you say?

Michael Hauber (16:17:39) :

Why do they throw all those letters in the equations without defining most of them? Is there some list somewhere where I can find out what ‘P’ is? Is this supposed to be common knowledge if you’ve done a ‘climate 101′ course?

It’s an all too common practice in practically every field. One of the reasons is that some things are so common it becomes background to the author. It becomes almost the equivalent of Internet abbreviations and idioms. The one distinguishing characteristic though is that it’s really hard to do a search for ‘P’ or ‘K’ and still get something relevant.
To answer your last question: I seriously doubt that anyone can.
You may (or may not) find this helpful. The book refers to the K and Psi operators. Anyway, they seem to be used in the same way. My guess: Psi is probably being transliterated as P. Short-Wave Solar Radiation in the Earth’s Atmosphere: Calculation … . CAUTION: not light reading IMO.
I came across the book by Googling “K P0 P radiative model”

I have always said it is a thermodynamic / heat transfer problem.
Physicists tend to be long winded. I dare say that a solution can be had and integrated over the entire planet with potentially different boundary conditions over each one. I’m also not sure that Kirchoff is the guy to invoke in this case. For practical solutions I would turn loose some good Mechanical Engineers with experience in Thermodynamics and heat transfer. That would surely give the physicists gas though.

Robert Wood (17:40:29) : Ah, Rico, what do I do with you?
A little data might help. And then an explanation consistent with those data. Take the Permian/Triassic period, for example. The data indicate that lots and lots of species died. The data indicate that large amounts of volcanic activity occurred around the same time. The data indicate that the climate got cold for a while then much warmer for a very, very long time. All of those events are hard to explain on the basis of “externalities”. The same could be said for the more recent K/T boundary. The evidence there suggests that a large celestial object impacted the earth, followed by a period of intense volcanic activity, leading to a prolonged period of climate change. That again is hard to explain on the basis of “externalities”.
So… what’s your data? Or do you just have explanations independent of data? If it’s the latter, what do I do with you? Lol!

I hate to sound facetious, but if Real Climate trashes Dr. M’s theory, then the good doctor is probably right.

OT but Chaiten has graduated, inconspicuously, but VEI 6 and still ticking.
These calderas being uncommon and their eruptions infrequent we are still due a couple more sixes this century.

If the lid or blanket is acting as GHG, then 90% of the lid or blanket would be equal to a big hole. Lets say the lid is made of chicken wire. then some of the water vapor would condense on the wire and fall back into the pot. Therefore the heat transfer through the wire would be slower and at the same time the falling water would lower the temperature of the pot.

So, Rico, where’s you’re data proving runaway greenhouse? Your position seems to be that it is the only explanation which makes sense. Where’s your proof that warm periods are “more easily explained on the basis of gas concentrations in the atmosphere”.

Rico:

Robert Wood (15:56:11) : “Rico, The gross (large) variations in the Earth’s cl;imate are due to eternalities, such as passing through cosmic duist clouds, precession of the equinoxes, variations in the Sun etc. ”

Given the paleoclimate record, none of those things seem likely.

For starters theoretical variations on Milancovitch cycles are the best explanations available to explain gradual onset of ice ages and the relatively sudden interglacials, even the stadial/interstadial cycles during the interglacials. Not perfect, but close, which Robert mentioned “precession of the equinoxes.”
There are other problems with pinning the blame mostly on CO2 during the interglacials: There are discontinuities where CO2 & temperatures quite literally detrend from each other. This is important because CO2 can only drive so much temperature increase, it requires feedback from an increase in humidity to really drive temperatures upwards.
In the paleo record there are instances where water vapor unlocked during interglacial periods rises and falls in a pattern unrelated to CO2 levels. Both water vapor and CO2 levels lag temperature increases as well (again CO2 alone can’t cause such intense warming, only water vapor can).
http://i30.tinypic.com/izon5h.jpg
Look the graphic over. It’s very peculiar to see CO2 levels plateau while light oxygen (water vapor proxy for the drier ice ages & humid interglacials) tracks along. And when CO2 levels dropped precipitously, temperatures did not, but water vapor levels followed the temperature trends.
I wouldn’t say the light oxygen trend is conclusive, but it demonstrates how CO2 levels can’t be conclusive either when CO2 level have at times decorrelated while another variable was correlated. FWIW the Earth is verging on the end of a Milancovitch peak, which bears upon the data shown above.
A recent study found that the Antarctic is much drier than previously modeled, so the odds of a huge austreal thaw have fallen. That leaves Greenland, and the biggest problem in Greenland is soot deposition that heats the snow, esp. on the peripheral glaciers (the downstream terminus of glacial runoff). There are pictures of blackened ice bergs that demonstrate how intense the soot problem is in Greenland, it’s impressive. The same is true of the all sesquicentennial ice loss – up to 90 percent of it has been from sootfall.

I too would like to compliment Nike Stokes on a well-reasoned, thoughtful, and collegial discussion in Niche Modeling.
Nick Stokes (16:31:30): 1. The whole theme of the analysis as something that undermines current AGW practice is wrong. Dr Miskolczi’s modelling is of a gray-body atmosphere (no spectral lines or shapes).
If I read the material correctly, Dr M’s simulations *did* do a line-by-line analysis, which would take into account spectral lines/shapes.

So, Eli, are we getting a ‘cooling year that shows a significant drop from best curve fit’?
==========================================

Crosspatch writes:

People with a certain world view wanted there to be warming from CO2 and so they have built various ways of validating the idea.

The theory was first proposed in a quantitative way by Svante Arrhenius in 1896. He thought global warming would be a good thing.

AGW has no basis in science. It is a religion. And when you invalidate someone’s religion, they can become extremely defensive. You have to approach it as you would trying to tell a devout Christian about evolution.

I’m a devout Christian who has never had a problem with evolution. In fact, most devout Christians don’t. I find your ad hominem attacks on AGW “believers” to be no more credible than your attacks on Christians. If you disagree with AGW theory, why don’t you try arguing against the theory, rather than attacking the people who hold it?

DAV posts something which illustrates a common misconception:

The only way to achieve POSITIVE stability is with negative feedback (picture the same marble in a mixing bowl). If it weren’t positively stable, it would have runaway long ago at the slightest change in parameters such as the sun getting ever so slightly brighter or more CO2 occurring because of a volcanic eruption.

You’re assuming that any positive feedback must run away, which is not true. For something like water vapor amplification of CO2 warming, the series converges. It doesn’t diverge.
A series like 1 + 1 + 1 + 1… will run away to infinity.
A series like 1 + 1/2 + 1/4 + 1/8… will never achieve 2, though it will get increasingly close to it.

Well, BPL, on this earth temperatures have not been rising for the last seven years, and humidity fails your test recently, too.
===============================

BPL, do you have some proof of AGW? I mean, besides the fact that it’s a “consensus”, the “debate is over”, “we’re at a tipping point”, and “if we don’t act now, we’re all doomed?” Anything at all scientific? We’re all ears.

As a garden variety engineer I appreciate the noises Miskolzci makes re: “infinite atmosphere”, “boundary conditions”, and correcting the “optical depth”, all of which seem pointed at rehabilitating Beers-Lambert as apt, but feel that case is hopeless.
His Kirchoff-related arguments are more useful:
The law established through revisions by a number including Planck and Einstein, that for a body in thermal equilibrium emissivity=absorptivity. These are dimensionless contants of proportion to an ideal black body, absorbing all incident radiation, whose wavelength of emission is strictly controlled by its temperature.
Solids can intelligibly be called gray bodies, as analogous to the ideal, having a temperature controlled curve of emission which is displaced with respect to temperature.
Representative empirical emissivities:
Asphalt 0.99
Green leaves 0.94
Snow 0.85
Water 0.58
Polished metals 0.3 to 0.4
These materials will progressively emit at higher temperatures than the ideal, as analogies between them an the ideal progressively weaken.
Gases’ emissions, on the otherhand, are subject to both temperature and pressure. An infinite number of curves are needed to describe their emissivities at various pressures and temperatures.
At 25 degrees C and 1 Atm CO2 has an emissivity of 9*10^-4, or 1000 times smaller than snow. This is true at 300ppm or 3000ppm.
At 600 degrees C its emissivity rises to 0.07, possibly important on Venus, but not here.
What Miskolzci seems to imply re: Kirchoff, is the recognition that absorbtion, e.g., at 15um by CO2, when not instantly followed by emission along the wavefront, is rapidly followed by the sharing of the kinetic energy gained with the molecules enviornment, other molecules.
The energy is not stored for emission by the CO2 molecule, and need not be emitted at 15um when that molecule next does so. The temperature of the gas is an average and individual molecules can vary widely emitting randomly as their preferred energy drops permit.

I’ve gathered together a set of links about Miskolczi’s paper
He gets Kirchoff’s law flat wrong (it is about absorbtivity and emissivity of the same body, not between systems, and btw, it is a function of wavelength, almost everything has a absorbtivity of ~.9 and more in the IR, but not in the visible), his virial argument is wrong and more. It’s not worth 80 comments, and lord knows it is not worth the >300 at the CA BB.

Gary, Kirchoff’s law applies to any region of the atmosphere in which a temperature can be measured (basically described as being in local thermodynamic equilibrium). This is true up to about 100 km.
You also are confusing absorbtivity with absorption and emissivity with emission. Go read what Nick Stokes says on this in CA BB or Niche Modeling.

Gary do you agree or disagree that absorptivity and emissivity are properties of a material determined by the composition of the material, the temperature of the material and the wavelength of light emitted or absorbed.

I am fascinated about the inconsistency displayed by the AGW supporters, relative to Miscolczi. They nit-pick M’s thesis at length, while they can offer no comparable thesis of their own. Where is the exposition of the physics behing “positive water vapor feedback?” Steve McIntyre has been asking this question for over 2 years, first as an IPCC reviewer and then periodically on his CA blog. IPCC is silent. The radical AGW crowd is silent. The silence is deafening. It appears that this putative feedback can only be shown somehow through GCMs. But those models have to be based on some physical principles, right? (wrong?). And the fact that those models are doing very poorly at modeling atmospheric temperatures (and even surface temperatures over the last 10 years) indicates that WHATEVER assumptions are incorporated in the models are erroneous. Where’s the beef?

Hi, the “action” has moved to the Climate Audit Bulletin Board, all ~600 posts of it. As to the physics behind a positive water vapor feedback, try the fact that water vapor pressure increases exponentially with temperature (more precisely exp(-Hvap/RT).
The issue is that when nits are basic assumptions they are boulders in a theoretical calculation, and that is what is being criticized about Miskolczi’s paper. He has at least two basic assumptions which are a) unjustified and b) wrong.

“As to the physics behind a positive water vapor feedback, try the fact that water vapor pressure increases exponentially with temperature (more precisely exp(-Hvap/RT).”
LOL. While this is true, it is not the type of “feedback” that is at issue here. Don’t we need some W/m^2-type feedback? And if we had this type of feedback, why don’t temperatures in the tropics get above 33 C?

Eli, you’ll note that the discussion at ClimateAudit went strangely silent after a clear precedent for using Kirchhoff’s Law in the atmosphere to equate absorption & emission was presented — on p. 3 of Goody & Yung (1989) (a standard textbook on atmospheric radiation) . I will reproduce the relevant quote here:
Since clouds, ground, and atmosphere do not differ greatly in temperature, it follows from Kirchhoff’s laws that emission and absorption are approximately equal to each other. Terrestrial radiation is therefore passed from layer to layer in the atmosphere … The situation differs in the upper atmosphere because Kirchhoff’s laws are not obeyed if the pressure is very low.
If you’d like to read this for yourself the relevant pages are available online here: http://books.google.com.au/books?id=Ji0vfj4MMH0C
This should be compared with Miskolczi & Mlynczak (2004)’s usage of the same law where it is stated (p. 232):
• In the average sense the atmosphere is very close to the radiative equilibrium, and, as a consequence, the zonal and global average upward emittance is about half of the average surface upward flux density. This fact is supported by the recent assessment of the Earth’s annual global mean energy budget by Kiehl and Trenberth (1997). Their estimates of SU and EU are 390 and 195 W m –2, respectively.
• As a consequence of the Kirchoff’s law, within the clear atmosphere the
downward emittance is approximately equal to the absorbed flux density. Based on our data set, the global average clear-sky downward atmospheric emittance is 311.4 W m–2, while the global average of the absorbed radiation by the clear-sky is 311.9 W m–2. This equivalence – for the highly variable atmospheric emission spectra and for global scale – was not shown before with such a high numerical accuracy.
There is no difference, and from what I can see, finally, there is nothing even unusual or controversial about Miskolczi’s usage of the law. So much for “just flat wrong.” All of this talk that “Kirchhoff’s Law can’t be used to equate absorption & emission” is just a clear nonsense.
I’m not even a physicist, so it’s been very difficult for me to resolve this. It came as a huge surprise to me when I saw this quote on p. 3 of the standard textbook. What’s particularly troubling is that our experts don’t seem to have taken atmospheric radiation 101.

Alex Harvey,
I have looked at Zagoni’s slides before, but don’t find them helpful: a PowerPoint presentation can give a sense of the conclusions, but doesn’t present the logical argument. A set of bullet items does not constitute a mathematical proof.
Others (I think at RealClimate) have pointed out that Zagoni, or even an alternative presentation of Miskolczi’s, asserts as an experimental observation what in the original paper is presented as a theoretical derivation: Not in the sense of “here’s what we said would happen and there it is”, but in the sense of “the reason why you should believe this formula is because of data” instead of “the reason you should believe this formula is because of the mathematics”.
Therefore, I am staying to what I understand: I don’t have much insight into the application of Kirchoff’s law (which several sources, including Goody & Young in your own quote, say has limited applicability in gaseous situations); and in the issues where I believe I understand what is at stake, I find Miskolczi’s way of applying theorems (specifically the virial theorem) to be rather opaque.
So, I’ll wait until I hear from him about my detailed questions. I’m interested in his explanation of this paper, not of Zagoni’s presentation.
And keep in mind, that for a theoretical argument to be cogent, every step along the way has to be right. If there is one step of the ladder missing, the argument is no good. That in itself doesn’t prove that the conclusion is false – maybe the weak point can be fixed – but in this case, the conclusion is contradicted by the generally accepted understanding of the greenhouse effect. “Extraordinary claims require extraordinary proof”, which means you don’t get a free pass for missing steps…

– And keep in mind, that for a theoretical argument to be cogent, every step along the way has to be right. If there is one step of the ladder missing, the argument is no good. That in itself doesn’t prove that the conclusion is false – maybe the weak point can be fixed – but in this case, the conclusion is contradicted by the generally accepted understanding of the greenhouse effect.
So you’re saying, if one step in the ladder turns out to be wrong we should throw away the whole ladder? The paper could contain the discovery of several new physical laws — the relationship atmospheric Kirchhoff law Aa = Ed and the general greenhouse equation (eq 21) — but because of your virial objections, we should throw away the whole theory?

Neal,
I am rather astonished to read this.
You say that you’ve studied the first 10 pages. That would mean you understand that eqs (5) & (6) are trivial arithmetical consequences of eqs (1), (2), (3) & (4). You would understand likewise that eqs (1), (2) & (3) are taken from the standard literature so there’s no controversy there either. It’s only eq (4) — the Kirchhoff Law — that people are concerned about. But if eq (4) was valid, we would have a very nice ladder. No, it wouldn’t lead to heaven, but it would lead to some very important conclusions.
“The physical interpretations of these two equations [(5) & (6)] may fundamentally change the general concept of greenhouse theories.” (p. 6.)
Eq (5) says that upward LW radiation is independent of the LW atmospheric absorption processes. That would mean that the classical theory of the greenhouse effect is wrong! It wouldn’t mean Miskolczi’s final conclusion is right (sure, we would need the rest of the ladder for that), but it certainly would mean that the classical theory is wrong. Goodbye IPCC AR4, goodbye Kiehl & Trenberth (1997). Now you can tell me that I’m wrong (maybe I am, after all, I’m not a physicist) but tell me that it’s not important? Okay, that surprises me. No wonder there’s a huge chapter of gaps in our knowledge of global warming theories if the defenders of the consensus don’t even care!
I trust you have read Miskolczi & Mylnczak (2004)? It’s a sort of required reading for anyone studying this work. At any rate, you would note that the virial theorem is not even mentioned in MM2004. Miskolczi had arrived at his revolutionary conclusions as early as 2002. Quoting his resignation letter (written in late 2005 since it’s dated “effective 1st January 2006”):
“More than three years ago I presented to NASA a new view of the greenhouse theory and pointed to serious errors in the classical approach …” http://hps.elte.hu/zagoni/Proofs_of_the_Miskolczi_theory_elemei/image068.jpg
But the idea for the virial theorem wasn’t even born in 2004. Yet in MM2004 you’ll note his conclusion (p. 249):
“Probably the most important consequence of the semi-transparent atmospheric model is the significant reduction in the expected response in the surface upward flux to greenhouse gas perturbations.”
With or without the virial theorem, for heaven’s sake, eq (4) + eq (21) (which is independent of the earlier equations) = a revolution in understanding.

Neal,
– I’ll be interested indeed to learn of Dr. Miskolczi’s response to your detailed questions. I do hope that his responses can be shared. Obviously I can’t answer the questions myself.
– If Eq.(4) and (21) don’t depend on anything coming along before, why not put them upfront?
I don’t have any opinion about the way the paper is structured, but they are definitely independent. Nick Stokes already confirmed the derivation of eq (21). No one else has challenged it, so it’s looking pretty good on the eq (21) front at this point.
– Regarding “There is lack of understanding of the physics of atmospheric infrared radiative transfer, which is impacting the quality of the discussions as well as the outlandish claims by the author that his work requires revaluation of radiative-convective equilibrium models…”: Clearly a reference to this section.”
Frankly the quote suggests to me that the reviewer skimmed the paper, saw some conclusions he didn’t like & rejected it. The whole paper is about IR radiative transfer so that could refer to anything, whereas Miskolczi’s claim about the radiative-convective models is actually on pp. 14-15.
Anyhow I’m sure it would be more interesting to be having this discussion after Dr. Miskolczi responds to your questions. I’m sorry I can’t help you with those questions.

Meanwhile I hope that someone is going to break the silence and explain how it is that Goody & Yung use Kirchhoff’s law to equate fluxes in the atmosphere if it is theoretically invalid to do so.
On the significance, consider the following passage from Kiehl & Trenberth (1997), p. 198:
“Thus, little of the longwave energy that escapes to space represents emission directly from the surface. The atmosphere acts as a “blanket” to this radiation, which produces radiative forcing to the climate system. We define the longwave “radiative forcing” of the climate system as the difference between the top of atmosphere longwave flux with and without the greenhouse absorbers.”
Yet according to Miskolczi’s eq (4), none of the LW energy that escapes to space represents emission directly from the surface. And his simulations confirm this to a correlation coefficient of r=0.997. “…the global average clear-sky downward atmospheric emittance is 311.4 W m^–2, while the global average of the absorbed radiation by the clear-sky is 311.9 W m^–2,” MM2004, p. 232. This would affect climate sensitivity, so I would expect (=hope…) climate scientists to care about it. IPCC2007 derives in large part from the work of Kiehl & Trenberth.
It is not surely a worthwhile exercise for NASA to attempt to falsify this result now?

Well a lot of the textbook is available in preview online:
http://books.google.com.au/books?id=Ji0vfj4MMH0C&dq=goody+yung+atmospheric+radiation&pg=PP1&ots=7SeRXY4-6l&sig=PQjWjamOhLkjmHhz4wuMfQ_398o&hl=en&sa=X&oi=book_result&resnum=1&ct=result
See esp. p. 3, & pp. 27ff. If you want to look at eq (4) it is necessary to look at MM2004, pp. 209-232 (i.e. to the end of section 3). Miskolczi makes it quite clear that eq (4) was derived in MM2004, yet the people commenting have generally not bothered to read his earlier paper. In fact, it is not necessary to read M2007 at all. Best of all, MM2004 is a lot easier to follow.

Well Zagoni has scanned some of this and added it to his website here: http://hps.elte.hu/zagoni/Kirchhoff.htm

Neal,
– Eq (21) is derived in Appendix B (where it is called eq B8) and you’ll see in there that it really is derived independently of the other equations. That does, admittedly, make the remark at the top of p. 14 confusing. Nick Stokes followed the derivation of Appendix B through to B8 and agreed that it was valid.
– regarding the significance, again, I’m not saying that the greenhouse effect necessarily disappears on the basis of eq (4) & (5) but it affects climate sensitivity. I would still expect climatologists to care. It might be argued that it is the job of atmospheric physicists is to understand atmospheric physics?
– It also follows that Dr. Pierrehumbert owes Miskolczi something of an apology…

Okay, to get OLR = S_G – E_D + E_U he combines eq (3) & (6). So I have no idea what he means by, “Using the above condition [OLR = S_G – E_D + E_U] for solving Eq. (14) at H=H(τ A) will be equivalent to solving the same equation at H = H(0)” (p. 14). Because on p. 24: “Note, that in obtaining Eq. (28) the Kirchhoff law was not used (see Appendix B).” I suspect he has a brilliant mind that is better suited to thinking laterally than vertically. 🙂

Further, M2007, p. 9:
The popular explanation of the greenhouse effect as the result of the LW atmospheric absorption of the surface radiation and the surface heating by the atmospheric downward radiation is incorrect, since the involved flux terms ( Aa and Ed ) are always equal.
Another statement suggesting that our theoretical understanding of the greenhouse effect is wrong that depends only on the truth of the Kirchhoff law.

Alex Haley,
– I agree that the equation:
OLR = S_G – E_D * E_U
comes from Eq:(3) & Eq.(6), so I don’t have a problem with it (as I don’t see a real issue with the Kirchhof-law question). It must have been too late at night when I checked that question.
– If Nick Stokes wants to buy off on Eq.(21)/(B8), that is his right, but I don’t feel bound by it. I would want to go through more of Goody & Yung to see how these kinds of calculations are usually framed and handled. Unfortunately, probably the most relevant chapter is Chapter 9, which does not seem to be included in anyone’s free preview. (And my copy is thousands of miles away.)
– However, for the sake of discussion, let’s look at the paper from a different angle than the bottom-up approach I’ve taken so far: As Nick pointed out, Eq.(B8) is a stepping stone to Eq.(B11). What I get from this is that he is saying that his Eq.(21)/(B8) formula for radiative loss is maximized when (B11) holds. And then I get the impression that he justifies the actual attainment of the maximum by invocation of some energy-minimum principle. But what is the basis for this principle? As far as I can tell, he says it seems give guidance to calculations that agree with other planetary results, which have reached some sort of steady-state. So on that basis, he wants to conclude that this same principle will apply in the present situation, that it will force the value of the optical depth to be 1.87.
I have doubts about this overall argument:
First, I don’t trust the minimum-energy principle he invokes: I don’t see any reason for it, and I also consider that a minimum is always defined in the context of constraints. One of these constraints is going to be the amount of CO2 in the system. It is not at all clear to me that the climate system can be supposed to be smart enough to generate clouds to make up for the excessive CO2: How does it explore that region of the parameter space in search of a minimum?
Maybe the correct interpretation of the minimum principle is that the CO2 will eventually be flushed out of the system, through ocean absorption and burial.
Maybe the correct interpretation of the minimum principle is that the IPCC is fated to take over the world, and impose a ban on fossil fuels.
I’m being sarcastic, but my point is that there is a gap in logic in saying:
– The fastest way to cool the Earth is to set Optical_Depth = 1.87
=> The minimum principle mandates the fastest cooling
=> OD will find a way to = 1.87, come hell or high water
=> There is no enhanced greenhouse effect.
To me, the gap comes at the point between identifying the possibility of a minimum principle and believing that it will actually be achieved. The Earth is not obligated to support one’s favorite minimum principle.
And by the way, is the optical depth on Mars and Venus equal to 1.87 ? If not, why not?

Oh — and yes the earth is obligated to obey the laws of thermodynamics.

Neal,
– Fair enough, but if you agree with the long-term radiative equilibrium assumption & agree that the energy minimum principle applies to planetary atmospheres in radiative equilibrium, how do you interpret the consequence that the atmosphere system’s “internal energy” must “decrease and approach a minimum value”?
– Why isn’t the critical optical depth of Mars 1.87? Well, it’s Mars, not Earth. 1.87 is the value computed by the LBL method. See Appendix A. Remember, Miskolczi was employed by NASA precisely because he is one of a very select few who know how to calculate optical depths of planetary atmospheres using the LBL method. Meanwhile, 1.841 is the theoretical value. You need to read beyond the first 10 pages. See p. 23, for instance.

Neal,
– I don’t see that your analogy takes you to where you want to be. Your aquarium is a system that is not in equilibrium; the earth-atmosphere is a system that (in the long-term sense) is. So I don’t see the relevance of the fact that it will take some time for your system to reach an equilibrium state (how fast is fast?). The point is, the system has a free mechanism (evaporation & condensation) by which it will, eventually, reach an equilibrium state. Likewise, the earth-atmosphere has a free mechanism (cloud formation) by which it, too, will reach equilibrium. By the way, the fastest way for your system to reach equilibrium (once we look for solutions outside of the physically possible) would be a Star Trek-like atom-for-atom transfer that would instantly move the required volume of water from one side to the other. A similar act of magic might instantly restore equilibrium to the earth-atmosphere system, but I don’t think this is particularly relevant to Miskolczi’s theory.
– Mars, your quote from p. 31 in context is: “On Mars the optical depth has a strong direct dependence on the total mass of the atmosphere and consequently on surface pressure. The average flux optical depth is small, τ_A = 0.175 << τ_A+. In Fig. 13 the simulated OLR / S_U and E_U/ S_U ratios systematically underestimate the theoretical f and f − T_A functions. With the P0 ≈ 0 assumption, Mars does not satisfy the IR radiative equilibrium and the overall energy balance criteria at the surface.” It sounds like he’s saying that his model atmospheres, like the USST-76, are not in radiative equilibrium, but I don’t pretend to know. It’s best to defer this discussion till Dr. Miskolczi responds to your detailed questions. As I said, I haven’t looked at the middle section of the paper in detail and I doubt that my input would be valuable in any case.

Alex Harvey:
– First, the Earth-Sun system is not in equilibrium either: It’s in steady-state (or rather, it WAS in steady-state prior to the radiative imbalance caused by the enhanced greenhouse effect).
– Secondly, the point indeed is that one can imagine all sorts of ways in which a process can happen faster or slower: and the system is simply not obligated to take any of them. But it seems to be key to M’s derivation that the Earth’s atmosphere take the fastest one he has in mind, even though doing so involves some kind of alteration of the water-vapor concentration or cloud cover of the atmosphere – elements that heretofore have not entered the discussion. They appear as a deus ex machina to achieve his magical result of 1.87. To get to his result, it is not sufficient that there be a lowest-energy configuration: the system must “rush” to it. So if you take your own objection seriously, your beef is with M, not with me.
– With all of the context about Mars that you added, I still don’t see anything that explains why the equations he uses to “prove” the 1.87 for Earth don’t apply to Mars equally. To me, that suggests either:
a) He’s not mentioning something essential to his derivation for the case of Earth; or else
b) He’s wrong about the Earth as well.

Alex Harvey:
Ken Gregory says:
“I think you have misread the paper. OLR/Su = 2/3 is not the general solution. It is the solution for the Earth type atmosphere.
The general solution is OLR/Su = (3 + 2Ta )/5
In the Earth’s case, Ta = 1/6, so the solution is OLR/Su = (3 + 2/6)/5 = (10/3)/5 = 2/3. ie, Su = 3/2 OLR”
Unfortunately, the bottom of page 7 says:
“For the Earth obviously the T_A ~ 0 condition apply…”
So if you believe Gregory, you disbelieve Miskolczi, and vice versa.
So Ken Gregory has addressed my objection, but hardly answered it. Indeed, with allies like Gregory, Miskolczi does not need enemies…

I’ve been thinking about this some more. This quibbling about “fastness” & Miskolczi’s usage of “efficient” is a red herring & a distraction. “The principle of minimum energy requires the most efficient disposal of the thermal energy of the atmosphere.” There is nothing at all odd about this statement of the law. It’s the second law of thermodynamics & I find no substantive difference between this statement and the one at Wikipedia. I feel a decided sense of déjà vu after arguing for 30+ pages at the CA BB about his equally reasonable statement of Kirchhoff’s law.
The argument is much simpler:
A. “long-term radiative equilibrium between the solar and terrestrial radiation…” MM2004, p. 210.
B. second law of thermodynamics
C. therefore, “the internal energy will decrease and approach a minimum value at equilibrium,” Wikipedia’s statement.
It seems your only objection is with point A so you should probably focus on the evidence against this.

Alex Harvey:
I thought of another argument explaining my doubt of the derivation. A Gedanken-experiment, as it were:
– M claims, on the basis of all these principles (conservation of energy, minimum energy, etc.), that the optical depth of the Earth will always be 1.87. So if we dump a lot of CO2 into the atmosphere, the magic number will be achieved by cloud formation at 2 km.
– So now we construct a new Earth, exactly the same as the first – but then we remove all the water.
a) Do all the principles that applied to the old Earth still apply? If not, which ones fail?
b) If we now dump that extra CO2 into the new atmosphere, what will happen to keep the optical depth at 1.87? There is no water available to make clouds.

From the link above above:
We will prove that the equilibrium state is the state with the maximum entropy if we consider the Earth, the Sun and the surrounding vacuum as the system.
Is this not the same as assuming, A. radiative equilibrium; B. 2nd law of thermodynamics; therefore, C. entropy is maximised / energy is minimised?

George Tobin writes:

It’s the planet where increasing CO2 has not resulted in the predicted temperature increase in the troposphere (funny you left that part out) and where the more recent humidity measures also appear to be dropping rather than increasing despite a steady rise in CO2; the planet where the predicted warming (much less the predicted increase in the rate of warming) has not occurred. That planet.

The predicted warming has occurred, the troposphere is warming, and absolute humidity is rising (relative humidity, of course, is not). You’re wrong on all three points. For humidity, here’s an empirical study:
Brown, S., S. Desai, S. Keihm, and C. Ruf (2007), Ocean water vapor and cloud burden trends derived from the topex microwave radiometer. Geoscience and Remote Sensing Symposium 2007, Barcelona, Spain, IGARSS 2007, IEEE International, 886-889.
As I said, precitable water vapor has been going up at about 0.9 mm/decade, consistent with Clausius-Clapeyron.

BPL:
1. “According to the Kirchhoff law, two systems in thermal equilibrium exchange energy by absorption and emission in equal amounts…” [Miskolczi 2007]. In fact, Kirchhoff’s Law states that for a body in local thermodynamic equilibrium (LTE), emissivity and absorptivity must be equal at a given wavelength. Miskolczi confuses emission with emissivity. This can lead to large numerical errors, since emissivity is of course constrained to the range 0 – 1 by definition, but emission can have any nonnegative value, and is typically in the hundreds of watts per square meter for low levels of atmosphere.”
We’ve all heard this objection before, but it is shown above that a standard textbook on atmospheric radiation also uses Kirchhoff’s laws to equate absorption & emission. Therefore, it might be more interesting to begin by acknowledging this fact.

Alex Harvey (05:04:31) :
– “Eliminate the word ‘efficient'”: I believe you’re missing the thrust of M’s argument:
a) He claims there is a minimum-energy state.
b) He claims that the atmosphere will achieve this state as efficiently as possible.
c) “The most efficient cooling of the clear atmosphere requires a total optical depth that maximizes B_o.”
If you eliminate the word “efficient” or replacement words, you have no reason to require that B_o should be maximized, and you have no basis for (B9), B(10) and ultimately “tau = 1.87”. You’ve taken the engine out of M’s argument.
– I looked at your link to Hu’s pages. Since you follow this up with a later query, I will deal with it a bit later. I’m trying to figure out exactly what it is that Hu is trying to show. I’m a bit hampered by the fact that I think his equation (6.5) is wrong: it lacks any dependence on the radius of the Sun, which is important if you’re trying to convert a flux at the Sun to a flux on the Earth. I also think he’s confusing entropy flux (as in (6.4) with entropy change (6.6). But this will take more study.
– “Radiative equilibrium / thermal equilibrium / steady-state”: My point is that these are all somewhat different concepts. A thermal equilibrium is a steady state, but not all steady states are in thermal equilibrium. Radiative equilibrium would be a requirement for a steady state, but not necessarily the other way around (although in most cases it would be true).
– If you drop your pen, the path it follows is dictated by Newton’s laws, NOT by the mere existence of a lowest-energy state. For instance, that lowest-energy state will be the same whether or not the pen is dropped in a vacuum or in a very thick atmosphere; but the path in space-time of the pen will be modified by the absence/presence of air.
– If the existence of a near-infinite supply of water is essential to the equations, please indicate where the chain of equations he has drawn up fails in the absence of water. When you think about that carefully, I think you have to conclude that the argument is no more cogent in the presence of water. Because I think the crux of his argument is: “This cooling process would happen fastest when tau = 1.87. Therefore, the Earth’s atmosphere has to find some way to achieve tau = 1.87.” My answer: “No, it doesn’t.”

Bruce Cobb writes:

BPL, do you have some proof of AGW? I mean, besides the fact that it’s a “consensus”, the “debate is over”, “we’re at a tipping point”, and “if we don’t act now, we’re all doomed?” Anything at all scientific? We’re all ears.

Well, you know, science doesn’t deal in “proof.” That’s for mathematics or formal logic. Science deals in evidence.
The evidence for AGW is that:
1. Carbon dioxide is a greenhouse gas (Tyndal 1859).
2. Carbon dioxide is rising (Keeling et al. 1958 and many others since then).
3. The major source of the new carbon dioxide is human technology (Suess 1955 and many others since then).
4. The temperature trend of the last 150 years is up (Mann et al. 1998, 1999, and many others since then).
5. Other sources for the warming are not plausible.

Alex Harvey writes:

We’ve all heard this objection before, but it is shown above that a standard textbook on atmospheric radiation also uses Kirchhoff’s laws to equate absorption & emission. Therefore, it might be more interesting to begin by acknowledging this fact.

As it happens, Alex, I have my copy of Goody and Yung 1989 to hand. The passage you quote on page 3 runs “Since clouds, ground and atmosphere do not differ greatly in temperature, it follows from Kirchhoff’s laws that emission and absorption are approximately equal.”
You are mistaking a special case for a general law. Yes, if two bodies are at about the same temperature and have the same composition, emission and absorption will be about the same. But this is NOT Kirchhoff’s Law, which states that at a given wavelength or frequency, emissivity and absorptivity are equal for an object in local thermodynamic equilibrium. In fact, if you look on page 39, you find this spelled out in greater detail: “In a constant-temperature enclosure, Iν = Bν, by definition, and, from (2.61) and (2.75),
Bν = Jν = Iν, (2.76)
regardless of the collisions. This is Kirchhoff’s second law, showing that our treatment is appropriately consistent with classical thermodynamics.”
The fact is, Goody and Yung doesn’t deal much with atmosphere modeling, and therefore Kirchhoff’s Law is mentioned only a few times and in an off-hand fashion. For clearer statements about it, try these:
“…there is a very simple relation between emissivity (ελ) and absorptance (αλ)
ελ = αλ [2.5]
This is known as Kirchhoff’s Law and indicates that at the same wavelength, good emitters are equally good absorbers.”
–Henderson-Sellers, A. and Robinson, P.J. 1986. Contemporary Climatology. NY: Wiley. p. 35.
“…the relationship between absorptivity a and emissivity ε is embodied succinctly in Kirchhoff’s Law, which states that:
ελ(θ,φ) = aλ(θ,φ). (6.12)
Note that this equivalence is strictly valid only for monochromatic radiation at a given wavelength λ and when the viewing directions θ and φ are specified…”
-Petty, G.W. 2006. A First Course in Atmospheric Radiation (2nd Ed.). Madison, WI: Sundog Publishing. p. 126.
“A little learning is a dangerous thing/Drink deep, or do not drink, of the Pierian spring.”
-Alexander Pope

Alex Harvey (05:23:08) : “We will prove that the equilibrium state is the state with the maximum entropy if we consider the Earth, the Sun and the surrounding vacuum as the system.”
More confusion I have about what Hu is doing:
– It’s essentially the foundation of thermodynamics that the equilibrium state is achieved when the entropy is maximized. So I don’t quite see what it is that Hu is actually trying to show.
– When I look at the end of Hu’s page, I get the impression that he’s aiming at (6.9), relating the Earth’s temperature to the Sun’s temperature at the point when the rate of entropy production is minimized. But actually, (6.9) is dimensionally impossible; however, it’s clear that Hu means:
T_earth = T_sun * sqrt(r_earth/(4L)).
– In (6.5) and (6.6), Hu writes a factor of pi*(r_earth)^2 when he really should have 4*pi*(r_sun)^2. When this is corrected, (6.9) becomes
T_earth = T_sun * sqrt(r_sun/(2L)). This answer is inherently more reasonable than Hu’s (6.9), that would suggest that a planet’s steady-state temperature depends strongly on its radius. That would mean that a planet could have an arbitrarily small temperature, even if it’s near to the Sun, provided that you make the planet small enough. That seems pretty unlikely to me!
– The part of Hu’s derivation that you are relying upon, between (6.7) and (6.8) , is the least clear.: “The rate of entropy production is always positive, but there is a T_earth which it is minimized.” First, this is an explicit call for a entropy-production rate-minimization principle (not the same thing as a minimum-energy principle), which might relate to some theorem in non-equilibrium thermodynamics, but doesn’t seem to have much justification here. Secondly, I notice further that (6.8) looks as though it should be the result of differentiating (6.7) – but it’s not! In fact, Hu says “The minimum value of delta_S_dot is achieved (very close to but greater than 0) when the incoming solar radiation is balanced by the outgoing terrestrial energy.” But this point you would get that by using the straight-forward “what would you get for Earth’s temperature if there were no greenhouse effect?” equation. (Except that, as noted before, he gets (6.8) wrong so he gets (6.9) wrong.)
Sorry, Alex, this paper is a real loser:
– 4 out of the 9 equations are flat-out wrong.
– The motivation for minimizing a rate is an explicit call for minimization of a rate, not a call for the existence of a minimum state.
– The final result is in actual contradiction to the cited rationale. Steady-state radiation balance implies my result, not his:
T_earth = T_sun * sqrt(r_sun/(2L))
Alex, this took a lot of time to read, understand, and ultimately de-bug. In the end, this turned out to be a poorly written, poorly thought-out article, and mostly irrelevant to the point. If you cite another article that seems to have those characteristics, I will not give it this level of attention again.

Apologies, Neal. I foolishly supposed that since I got the paper from the NASA/Langley website it would be correct. I certainly didn’t mean for you to analyse the conclusions of the paper in detail. It’s looking a bit like the quality of the science at NASA is falling somewhat.

BPL writes:

…this is NOT Kirchhoff’s Law, which states that at a given wavelength or frequency, emissivity and absorptivity are equal for an object in local thermodynamic equilibrium. In fact, if you look on [Goody & Yung] page 39, you find this spelled out in greater detail: “In a constant-temperature enclosure, Iν = Bν, by definition, and, from (2.61) and (2.75),
Bν = Jν = Iν, (2.76)
regardless of the collisions. This is Kirchhoff’s second law, showing that our treatment is appropriately consistent with classical thermodynamics.”

The other problem (further to my post above) is that several physicists (apparently including Neal J. King above) have assured me that eq (2.76) is an equation relating fluxes.
Therefore, would it be possible for you to explain a little more clearly how an equation relating absorption & emission that is denoted “Kirchoff’s second law” can possibly be adduced in support of your assertion that

Kirchhoff’s Law states that for a body in local thermodynamic equilibrium (LTE), emissivity and absorptivity must be equal at a given wavelength. Miskolczi confuses emission with emissivity.

when to a layperson such as myself (who perhaps hasn’t drunk deeply from the rivers of knowledge) it appears to stand in outright contradiction. Thanks.

And 59,200 for “kirchhoff’s law -absorptivity -emissivity absorption emission” (i.e. with pages containing both words ‘absorption’ & ‘absorptivity’ / ’emission’ & ’emissivity’ deleted).

Alex Harvey writes:

I note that your quotes all came from climatology textbooks rather than physics textbooks.

“A First Course in Atmospheric Radiation” is a physics textbook, son.

At any rate, equally clearly, Kirchhoff’s laws are also used to equate absorption & emission.

Not by anyone competent in the field, they’re not.

Try this: go to Google and type in “kirchhoff’s law absorption emission.” You’ll see there are 73,800 pages returned. Then, if you type in “kirchhoff’s law absorptivity emissivity” you’ll only get 26,500 pages. Now repeat this at Google Scholar and you’ll get a ratio of around 4,000 to 1,000 in favour of matches against ‘absorption’ & ‘emission’. Now I realise that this doesn’t prove anything in itself, but as I start reading the abstracts I find over & over again that “Kirchhoff’s laws are used to relate absorption & emission.”

Try this: Don’t use the number of hits of web pages to prove scientific points. Sturgeon’s Law applies to the internet, you know.
Yes, Kirchhoff’s laws are used to relate absorption and emission if you set the problem up that way. But that is NOT the same as saying Kirchhoff’s Law says absorption must equal emission, which is wrong. You’ve got three quantities related here:
temperature
emissivity (or absorptivity)
emission (or absorption)
For example, if a body, let’s say a patch of gas, is at a temperature of T = 270 K, and has a graybody emissivity of 0.2, its emission will be ε σ T4, or about 60 watts per square meter. Kirchhoff’s law tells you the absorptivity, 0.2, must be the same as the emissivity. But it does NOT tell you the absorption will be the same as the emission! Without intelligence and sufficient technology to hand, an object can’t decide how much energy is falling on it. If our patch of gas has 1,366 watts per square meter falling on it (it’s at noon on the equator, let’s say), it will absorb 0.2 x 1366 or 273 watts per square meter — more than four times what it’s emitting. The absorptivity and emissivity will be the same, but the absorption and the emission will not be the same.

Alex Harvey:
– I didn’t catch where BPL was impugning Dr. Mlynczak. Where was that?

Alex Harvey:
OK, you’re talking about M&M (2004). I haven’t focused much on that, as it doesn’t seem relevant to the questions I have.
As I’ve said before, I don’t have any particular beef with equation (4), whether or not it comes from Kirchhoff’s law.
But I have lots of other beefs with M (2007).
I guess if you’re really curious about Mlynczak’s point of view, why not just send him a note asking what he thinks about M (2007)?

BPL:
I don’t think I can prove anything. I’m just asking questions, and I’m noticing that right now I’ve asked the same question several times & you’re refusing to answer. Is G&Y’s eq. (2.76) an equation that relates absorptivity & emissivity or isn’t it? I’m not asking for a lot of your time here. “Yes” or “no” will suffice. It’s not about intelligence. Your CV suggests you win the IQ contest. There’s no need for the insults. It looks to me that you’ve just said something that’s wrong & are refusing to admit this. But I’m quite happy to be corrected. Thanks.

Alex Harvey:
I would agree that “two systems in thermal equilibrium exchange energy by absorption and emission in equal amounts” and “the thermal energy of either system cannot be changed”. If anything else were happening, these two wouldn’t be in thermal equilibrium.
But I don’t know if there is much point in dragging Kirchhoff’s law into this.

Neal:
– I don’t think it matters whether we call it Kirchhoff’s law or something else. Miskolczi is calling it Kirchhoff’s law because others have called it Kirchhoff’s law. You seem to be in disagreement with BPL who finds eq (4) to be completely unjustifiable. You have read his responses & you seem to be standing to your position that there is no problem with eq (4). Since he won’t answer my questions about the apparent contradictions, perhaps you can explain what he’s missing?
– On another point I re-read MM2004 section 4 last night whilst trying to understand the argument from the minimum energy principle. If you really have no objection to M2007, eq (4), may I implore you to read MM2004, section 4, pp. 233-248. None of the virial arguments are used at all yet MM arrive at much of the same result.
Consider this, MM2004, p. 241:

According to our estimate, a CO2 doubling would rise the global average surface temperature by 0.48 K, corresponding to a global average primary greenhouse forcing of 2.53 W m–2. The detailed results are included in Table 6. We note, that the direct estimate using the left hand side of Eq. (5): ΔSU=(dSU/dτ)Δτ =A(Δτ/2)OLR will give the same greenhouse forcing. For reference, our estimate is about 1.7 W m–2 (35%) less than the one published by Hansen (Table 1 on page 12754 in Hansen et al., 1998). Hansen et al. (1998) used the correlated k-distribution method for the optical thickness calculations which compares well with LBL results. The reason of the relatively large differences in the greenhouse forcing must be the different method of relating the changes in the total optical thickness to the changes in the fluxes.

I’m feeling very puzzled as to how Martin Mlynczak’s name got onto this paper! I did send him an email as you suggested; I hope he responds.

Alex Harvey:
– I took a look last night at the later discussion on Kirchhoff’s law, and as far as I can tell, the main objection to eqn.(4) is just the claim that it comes from KL. I don’t see that anyone (even BPL) has made a strong objection eqn.(4) in itself. As I said, my point of view is that I don’t find eqn.(4) a problem; but I also don’t see that it really has much to do with KL. Maybe that’s not so different from what BPL is saying, except that I’m not getting too excited about the wording Miskolczi employs around eqn.(4). I only care about whether his equations string together, and for me, the train doesn’t come to a screeching halt until just before eqn.(7).
– OK, I will look at that section of M&M. However, I don’t know that I will be able to come to any conclusion: If it depends on real familiarity with the field and the data, as opposed to ability to follow and interpret a logical & physical argument, it might be out of my scope.
– Well, Mlynczac signed the 2004 paper, but not the 2007. Does that indicate anything? Let me know what he says.

Neal:
The reason I asked you to look at MM2004 is that if you really want to understand the argument from the principle of minimum energy, it is spelt out in far greater detail in this earlier paper. And, as I said, it doesn’t depend on the virial arguments.
– On your first point I suppose yes; the authors are supposing that the reader knows Goody & Yung.
– On your second point I think you are confusing terrestrial graybody optical thickness (τ_T) & atmospheric graybody optical thickness (τ_A). They don’t use (τ_T) in the subsequent equations.
– Not sure about eq (5).
– the 10% of profiles were selected because they were the ones that were in radiative equilibrium in their own right.
At any rate, if you really want to understand where M2007 is going, I think that MM2004 helps. Of course, you may feel that there’s no point continuing unless Dr. Miskolczi responds, which I’d agree is valid. I will probably give up in that event too. 🙂

Alex posts:

On your second point I think you are confusing terrestrial graybody optical thickness (τ_T) & atmospheric graybody optical thickness (τ_A). They don’t use (τ_T) in the subsequent equations.

He’s wrong, of course, and if this is what Miskolczi is saying there’s another mistake by the latter. There’s no distinction between “terrestrial graybody optical thickness” and “atmospheric graybody optical thickness.” What is the first phrase supposed to refer to – something other than the atmosphere? On a planetary scale, only an atmosphere or an ocean can have any optical thickness. An opaque object, like the solid Earth, doesn’t transmit any light.

BPL:
Yes, but have you ever actually tried to measure the earth’s optical depth yourself? That’s fine; neither have I. Anyway, if you read the paper I’m sure you would understand why it’s necessary to distinguish a τ_A and τ_T (and indeed quite a few other τs).
Any chance you’re going to clear up this confusion about Kirchhoff’s laws? My two questions remain unanswered. At least one person has read what you’re saying above & supposed that your only issue with Miskolczi’s eq (4) is that you feel very strongly that he shouldn’t have called it the “Kirchhoff law.”

Alex Harvey:
I don’t think you understand what BPL is saying: The straightforward interpretation of the words “the Earth’s optical depth” has to do with transmission of light through the Earth.
If you’ve never done this before, here is a quick approach:
1) Stand in an open field.
2) Look down.
3) Ask yourself, “Do I see the hot molten core of the Earth below me?”
4) If the answer is “Yes”, then you have untimely gone to an unjust reward. Please take it up with “higher authorities”; and in the meantime, I’d rather you didn’t stay in touch, thank you.
5) If not, you have just done a very crude measurement of the optical depth of the Earth. The answer is, “Just about infinite.”
6) This was a measurement at optical frequencies. The answer will not differ significantly for the infrared.

Neal:
– terrestrial vs atmospheric optical thickness: It’s not about defending the sacred honour of Miskolczi’s paper. I’m just responding to the silly suggestion that I’ve misread the paper when BPL hasn’t read the paper at all. How about we have a “why Miskolczi & Mlynczak (2004) are wrong” page as well? The MM2004 is just as interesting & just as controversial (and I’m sure most will want to say just as wrong) as M2007. MM arive at different measures of the same quantities by using different procedures. To get “atmospheric flux transmittance” they use Tr_A =1 – A. To get “terrestrial flux transmittance” they use Tr_T=OLR/S_U. Since graybody optical thickness is the negative logarithm of atmospheric flux transmittance, they end up with two different quantities, τ_A & τ_T.
– earth’s optical thickness, yes that’s infinity; agreed. But I think deep down you knew I was talking about the earth-ATMOSPHERE’s optical thickness? 🙂

Neal writes:

BPL:
That was my question.
I don’t really have a particular beef with eqn.(4) as such.
I’m not sure it makes sense to attribute it to Kirchhoff’s laws, however.
How does your view differ from mine?

Well, basically, I was objecting to Miskolczi’s apparent statement that Kitchhoff’s Law equated emission and absorption, which Alex has defended to the depth no matter how totally stupid it appears to anyone who has ever actually used Kirchhoff’s Law in a calculation.
E = ε σ T(target body)4
A = α σ T(external body)4
Kirchhoff’s law tells you that α will be the same as ε at a given wavelength for a body in local thermodynamic equilibrium. Alex thinks (and is prepared to defend to the death) the idea that it tells you E is always the same as A. And I can’t seem to get through to him, which is why I stopped replying to his posts directly.
I note that one of his posts says I never read Miskolczi’s paper. Aside from the observation that it’s very unlikely he’s a long-range telepath, I did, of course, read Miskolczi’s paper before critiquing it.

And for “Kitchhoff” read “Kirchhoff.” Never post early in the morning…

Neal,
Miskolczi’s equation (4) is:
AA = SU A = SU(1-TA) = ED
where
AA = Amount of flux Absorbed by the Atmosphere
SU = Upward blackbody longwave flux = sigma Ts^4
A = “flux absorptance”
TA = atmospheric flux transmittance
ED = longwave flux downward
These are simple identity definitions. I do wonder why Miskolczi used the upward blackbody longwave for the amount emitted by the ground when he should have used the upward graybody longwave — he’s allegedly doing a gray model, after all. Apparently he forgot the emissivity term, which is about 0.95 for longwave for the Earth. One more hint that he doesn’t really understand the distinction between emission and emissivity.
Note that he seems to be saying the downward flux from the atmosphere (ED) must be the same as the total amount of longwave absorbed by the atmosphere (AA).
The total inputs to Miskolczi’s atmosphere are AA, K, P and F, which respectively stand for the longwave input from the ground, the nonradiative input (latent and sensible heat) from the ground, the geothermal input from the ground, and the solar input. P is negligible and I don’t know why he even puts it in here unless he’s just trying to be complete. He’s saying, therefore, if you stay with conservation of energy, that
AA + K + F = EU + ED
Now, from Kiehl and Trenberth’s 1997 atmospheric energy balance, the values of AA, K, and F would be about 350, 102, and 67 watts per square meter, respectively, for a total of 519 watts per square meter. EU and ED would be 195 and 350, total 519, so the equation balances.
But for Miskolczi’s equation (4) to be true, since AA = ED, we have
K + F = EU
That is, the sum of the nonradiative fluxes and the absorbed sunlight should equal the atmospheric longwave emitted upward. For K&T97, we have 102 + 67 = 195, or 169 = 195, which is an equation that will get you a big red X from the teacher.
There is no reason K + F should equal EU, therefore Miskolczi’s equation (4) is wrong. Q.E.D.

BPL:
Are you getting all that from his equations BEFORE (4) or his equations AFTER (4)?

Just in case anyone thinks Zagoni is making this up:
KT1997, p. 4:

The ERBE data imply a global mean clear sky outgoing longwave flux of nearly 265 W m-2. This observation can be used to check the consistency of the assumed profile and the radiation model. Using the U.S. Standard Atmosphere, 1976 profile in the narrowband model yields a flux of 262 W m-2, surprisingly close to the observed flux. We reduce the standard atmosphere tropospheric specific humidity profile by 12% to ensure agreement between the model and observed global mean clear sky flux. The need to adjust the water vapor profile may be due in part to a bias in the longwave clear sky ERBE data (see Hartmann and Doelling 1991; Kiehl and Briegleb 1992).

Sounds like a bit of a strange thing to do…?

I note, with interest, that Zagoni defines a 12% reduction in water vapor as cutting the amount of water vapor in half. The court finds itself unable to follow the alleged reasoning.

BPL:
Alright, I am rather frustrated. You wrote:

The passage … on [G&Y] page 3 runs “Since clouds, ground and atmosphere do not differ greatly in temperature, it follows from Kirchhoff’s laws that emission and absorption are approximately equal.” You are mistaking a special case for a general law. Yes, if two bodies are at about the same temperature and have the same composition, emission and absorption will be about the same. But this is NOT Kirchhoff’s Law…

Later you said very definitely that the textbook is not wrong. It’s all very difficult to understand what you’re saying here. Textbook says, “it follows from Kirchhoff’s laws that emission & absorption are about the same.” You say “this is NOT Kirchhoff’s Law.” Then I asked, is the textbook wrong? You said, “No!” Further requests for clarification have all been met with silence or insults. Yet these are your own words: “Yes, if two bodies are at about the same temperature and have the same composition, emission and absorption will be about the same.” Miskolczi is assuming nothing other than what I have quoted you as saying yourself right here.

Alex Harvey & BPL:
OK, I’ve thought about it: I don’t believe eqn.(4).
If you go back to the continuum radiation-transport model, it is equivalent to saying that:
B(0)*(1 – exp(X_o) = Integral(0, X_o) (B(x)*exp(-x) dx
where B(x) is the blackbody radiation for the specific wavelength at the temperature that obtains at the particular optical depth x.
x = 0 implies ground level
x = X_o means “top of the atmosphere”
The left-hand side is the difference between the radiation that left the Earth’s surface and what made it through the atmosphere; not including what was added in by E_u. (E_u = Integral(0,X_o)(B(X_o – x)*exp(-(X_o -x)). So this should be S_u*(1 – T)
The right-hand side is the intensity of the downward radiation that comes from emission by the atmosphere, so it should be E_d.
If B(x) = B(0) for all x, the equation is true. But in general, it’s not.
That explains why what Miskolczi said about eqn.(4) sounded reasonable to me when it’s expressed in terms of three big bulk items: the Earth, the atmosphere, and outer space. But when you take into consideration that the atmosphere does not have one overall temperature, you have to apply local thermal equilibrium (meaning that you can apply the concept of temperature locally), but you cannot apply results for a real thermal equilibrium to this.
So, sorry Alex, I don’t back eqn.(4) either.

Neal:
You write:

If B(x) = B(0) for all x, the equation is true. But in general, it’s not.

I think you are saying that the equation would be true for the case x=0 but not for all x; is that correct?
If so, let’s suppose for the sake of argument that for an arbitrary 0 < x < 60km (i.e. wherever the LTE approximation is valid), the portion of S_G that is absorbed locally at altitude x, call it AA_x, is re-emitted downward in the amount ED_x? Let’s also suppose for the sake of argument that AA_x = ED_x. Would you agree that if AA_x = ED_x is true for any altitude 0 < x < 60km, and if AA = ED is true at the surface (for x=0), it follows that AA = ED would be true for all 0 < x < 60km?

Alex Harvey, BPL, Nick Stokes:
I have been trying to explain to Jan Pompe (on the ClimateAudit discussion thread, at http://www.climateaudit.org/phpBB3/viewtopic.php?f=4&t=161&p=9509#p9509 ) how to derive the result of the Virial Theorem in the case of a solid planet, but it hasn’t worked.
So tomorrow I will post a completely independent proof that is based on the equations of hydrostatic equilibrium.
I believe both proofs are perfectly valid, but the one based on hydrostatic equilibrium is harder to get confused about.

Alex Harvey:
The question is a little tricky, because even if each “clump of gas” along the way were reflecting downward an equal flux as it was absorbing from the upward S_g, it doesn’t just bop on back down to the surface: that flux has to propagate its way past all the other clumps of gas, so by the time it gets down to ground-zero, it will be an attenuated version of what was emitted downward.
Now, actually the only way for your FtSoA assumption to hold, however, is if the temperature were the same for all values of x. In that case, even though the downward flux due specifically to the clump at a specific value of x has been attenuated, the total flux will have been augmented by the downward radiation from the intervening clumps to make up for it.
Essentially, this is because when all the LTE situations are at the same temperature, this is a case of real thermal equilibrium. And in real TE, colloquially speaking, everything can fill in for everything else: you can be guaranteed that what you lost on the way down will be made up for by the stuff in-between, because the properties of the radiation field will depend only on the temperature (there being no temperature gradient) and the temperature is the same. In other words, real TE is really simple, because there are no options or free variation. And in that case, A_a = E_d.
But none of this works out when the temperature is decreasing as you go up in altitude. Even though you have LTE at every point, you do not have TE for the atmosphere overall. So you can’t get the equation above from an overall perspective (which is what M is trying to do), and from a detailed view (all along the range of x), it fails because of the radiative-transfer equations I was citing in the earlier posts.
I hope this clarifies the matter. What I am trying to do is to interpret the radiative-transfer equations. It’s a bit funny, because the equations don’t “care” about exactly what fraction of the radiation flux came from where; but one can do an attribution anyway, because the equations are linear in the fluxes.

Alex Harvey:
Yes, it applies in the direction of propagation. But when you said that some portion of S_g is absorbed locally (by the clump), you have to assume that it is from the part that has propagated to that point already.
The whole process of absorption and emission is intermingled. Another way of visualizing it is to see that some radiation gets absorbed, and then re-emitted equally upwards and downwards. But it’s very complicated to try to follow things in this way. It’s much easier to view it through the radiative-transfer equation itself (although I’m using a simplified version that is 1-dimensional, it doesn’t change the essential nature of what’s going on). Based on this equation, you can figure out what happens from ground-to-sky based on the temperature profile, and you can sort out how much of it is “left over” from an original input (ground radiation) and how much has been added along the way.

Neal:
Thanks for your time & patience.
I remain somewhat persuaded by the apparent empirical support & feel that at the very least the mystery needs to be explained. Miskolczi’s various plots showing the computed relationship of AA & ED at various altitudes, in various atmospheric profiles, derived by various methods, cry out to me for an explanation.
However, I agree that your questions deserve a response & I can’t answer them. So I’m going to sit back & patiently wait to see if Dr. Miskolczi responds.

Neal,
I take it Miskolczi never responded?

Interestingly, I tried to leave a comment on that thread, and it disappeared into moderator-land.

Eli Rabbet 29/06/08 (20:31:29) :
What do you think how much your own comments worth? All over the web you contributed with quite a number…
You say the Kirchoff’s law and the Virial concept is not applicable for the
atmosphere. Why do not you try to prove it? Just because you say something it is not necessarily true. This thing is bi-directional, you also has to prove what you say. Think of Neal King’s effort regarding the Virial concept.
I showed that the atmospheres of the Earth and Mars obeys the Su=Ed/A relationship. You may call it whatever you like. Long time ago, back in Hungary I was taught that it is the Kirchhoff’s law. But simply take an atmosphere compute Ed and A and show that the Su=Ed/A relationship is not true…and then it will be fair to increase the number of your comments on the web.

Alex Harvey:
At http://landshape.org/enm/greenhouse-heat-engine/#comment-170534, I am having a discussion with Ferenc on the paper. You may find this interesting.

At http://landshape.org/stats/greenhouse-effect-in-semi-planetary-atmospheres/ is posted another note, adiabatic_VT, describing a numerical verification that the adiabatic atmosphere on a spherical Earth does indeed satisfy the equation derived from the Virial Theorem,
KE = (-PE – 4(pi)R^3 * P(r=R))/2
Since that note was posted, I remembered how to accelerate convergence of a numerical integral and obtained the results:
directly calculated KE = 5.08134E+23
directly calculated PE = -3.29664E+26
and hence:
KE_vt = 5.07923E+23 calculated from the equation; and
KE_vt/ KE = 0.99958 shows that agreement between the two is excellent.

I began this discussion to discuss public available web proxies:
Which are really anonymous?
Which can unblock facebook, myspace etc, in other words: are fresh ?
Which can you recommend?
Thanks for your help,
Dschibut
P.S.: In my land, the freedom of speech is somehow limited, please give me a hint, if you are not sure about your recommendation.