# Debate Thread: Miskolczi semi-transparent atmosphere model

This thread debates the Miskolczi semi-transparent atmosphere model.

The link with the easiest introduction to the subject is http://hps.elte.hu/zagoni/Proofs_of_the_Miskolczi_theory.htm

## 214 thoughts on “Debate Thread: Miskolczi semi-transparent atmosphere model”

1. BillSheldon says:

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…

2. Mark Nodine says:

Let me prime the discussion a little with a comment I posted on an earlier thread that received no responses.

———————–

Does anybody know how to pronounce “Miskolczi”? His work (http://hps.elte.hu/zagoni/Proofs_of_the_Miskolczi_theory.htm) seems to me to be more robust than that of Gerlich and Tscheuschner (http://arxiv.org/abs/0707.1161).

Although the latter has the best description I’ve seen of why the greenhouse effect works and how it differs from the atmosphere, they seem to go too far in several arguments: denying the existence of an average surface temperature of a body (because it cannot be calculated from first principles), the proposition that because the atmospheric greenhouse effect as commonly described constitutes a perpetuum mobile of the second kind the atmosphere does not provide overall warming, and their questioning of the meaning of the arrows in the radiative heating diagrams (the obvious answer being “energy”, which is conserved). On they other hand, their description of the folly of trusting GCMs, especially those that would purport to give accurate solutions to the Navier-Stokes equation from uncertain initial conditions over dozens of years, is exactly right. Their analysis left me puzzled by certain observations, such as why it becomes much colder at nights where there is no cloud cover than on nights where there is.

The analysis by Miskolczi has much more explanatory power, in my opinion, taking into account convection and the optical depth; it also makes predictions that are upheld by current measurements, such as the drop in water vapor as CO2 increases.

3. crosspatch says:

I find this one statement somewhat of an over-reach:

“The observed global warming on the Earth has nothing to do with the changes of atmospheric LW absorber concentrations; it must be related to changes in the total available incoming energy (solar, geothermal, ocean-atmosphere heat exchange, etc.)”

It doesn’t take into account changes in surface land use. For example, if I paved the entire North American continent, I would expect there to be a significant change in the climate of Kansas with no change in solar input. Ripping out millions of acres of native grasses or forests and replacing them with various crops, housing developments, and asphalt roofs might result in some changes as would dams and large scale irrigation. To say that ALL observed warming MUST be caused by only solar changes is, in my opinion, a bit of a reach. BUT I will add the caveat that land use changes would tend to be step changes and their impact on a global scale would probably be minimal at this time. By that I mean that the building of Chicago probably hasn’t melted any Antarctic ice.

4. Bill Marsh says:

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.

5. Ron McCarley says:

Many kudos on the 6/25 and 6/26 posts. No offense to others, but to me you have the best GW website on the web. The format changes that you made recently were very good, and you should be proud. It’s the first site that I go to each morning. BTW, I haven’t heard anything lately about earthshine. The last that I saw, it seemed as if they were trying to get a few other measurement locations on-line, to go along with a new scope. Are they coming back with more data? What’s there is several years old.

REPLY: Thanks for the kind words. As for earthshine they are still working on getting the worldwide robotic telescope network up and running.

6. Robert Wood says:

Crosspatch, his terms Sg, K and P are the “landuse” variables.

I’ve been reading the PDF of the published paper, where he takes more care in defining the terms. This, remember, is taken from a presentation so some of the verbal information is missing. The PDF is pointed to at the beginning I believe.

7. BUCKO36 says:

I’m an AGW Skeptic, however I am not a climate scientist. That said, I am really interested in the assessment of Dr. Miskolczi article, by those of you who are.

8. crosspatch says:

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.

9. David Segesta says:

That paper is well beyond my knowlege of the subject. But I hope other skeptics, who are ture climate scientists such as Lindzen and Spencer, will review it.

10. David Segesta says:

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

11. Jim Arndt says:

OUCH my brain hurts I think I need a brain surgeon. Man the equations made my brain go numb about page 19. Very well articulated paper. Clearly spells out the problem the current AGW theory has. That is why they can’t explain past CO2 to temperature issues. The number are just wrong. This is a book mark page for me.

12. swampie says:

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.

Like many other who are skeptical, my own expertise is in a field other than climate physics. I too will be lurking back here to see what folks with a better uderstanding of the physics think on Miskolczi’s (Miss Coal Ski?) alternative to modeling CO2 in infinitely thick atmospeheres.

14. stas peterson says:

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.

15. Dishman says:

Mark Nodine wrote:
denying the existence of an average surface temperature of a body (because it cannot be calculated from first principles),

If that’s a fair description of what they’ve done, as Miskolczi also seems to indicate…
then it sounds to me like they’ve failed their basic thermodynamics.

If their atmosphere model does not match the actual surface temperatures, then it’s not because the surface temperature doesn’t exist, it’s because the model is wrong.

16. crosspatch says:

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.

17. D Buller says:

BillSheldon,
If you put a lid on your pot, would not the water temperature increase even though you do not increase the heat applied to the heat? If you prevent some heat from escaping, would not the water temperature increase?

18. leebert says:

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://i27.tinypic.com/25fuk8w.jpg

19. Philip_B says:

This goes to the heart of the Forcings Model of the Earth’s climate.

Simply put, the Forcings Model says any change to energy inputs results in climate warming or cooling (using some multiple that includes feedbacks).

If the Earth’s climate is in dynamic equilibrium, then forcings have no (significant) effect. And everything the IPCC and most climate scientists say is irrelevant. Put another way, feedbacks swamp forcings.

Which leads to the interesting question – If feedbacks swamp forcings why does the climate change at all? And we know that it does – glacial and interglacial phases of the current ice age.

The answer is that things that affect feedbacks drive the Earth’s climate (as well as oscillations such as PDO and AMO). So the primary determinants of climate change are galactic cosmic rays, dust and particulates, and irrigation.

These are things that affect phase changes of water and the net amount of water vapour in the atmosphere.

IMHO, as always.

20. 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).

21. James Van Winkle says:

I am happy to see this thread as I was hoping for more eyes looking at this theory. I found this web site that has picked the theory apart, and might be of interest. http://landshape.org/enm/category/science/climate/page/2/

A couple of things to note, previous papers by Miskolczi laid the ground work for this paper, and Miskolczi views the atmosphere as a heat engine with corrected boundary conditions (one of which is no energy is coming from volcanism).

I check this web site daily as a sure bet to see new insights of the follies of GW.

22. “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.

23. Robert Wood says:

I recommend the link pointed to by JSH, or go directly to http://www.friendsofscience .org for a good explanation.

I like the agreement with empirical data.

24. Evan Jones says:

No offense to others, but to me you have the best GW website on the web.

Nobody beats the Rev!

If you put a lid on your pot, would not the water temperature increase even though you do not increase the heat applied to the heat? If you prevent some heat from escaping, would not the water temperature increase?

That makes sense to me. Also, if you added salt and the boiling point went up, so would the that of both the water and the “atmosphere”, assuming the lid was loose (like the “lid” on the atmosphere) allowing steam to escape?

The tightness of the lid would affect the equation.

25. Thanks very much for the inlinks, and I am glad to see M’s work profiled. I hope that the posts and discussions on the landshape.org/enm site give people enough background to the issues that potential future responses to the paper from RealClimate and the literature can be reasonably assessed.

I would also like to bring your attention to the post http://landshape.org/enm/another-theory-of-global-warming/ announcing a publication in AIG where I have explored possible mechanisms for explaining surface temperature changes despite constant troposphere temperatures. This is to address one objection to M’s theory that it cannot account for surface temperature variations.

26. Bob Cormack says:

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.

27. Rico says:

While reasonably proficient with numbers, I have no ability to evaluate the underlying physics. One thing does bother me though… clearly there were epochs in earth’s history where global temperature was much warmer than it is now. And they appear to be much more easily explained on the basis of gas concentrations in the atmosphere than any other variable. And yet Miskolczi’s model suggests that gas concentrations aren’t important. No discussion of Miskolczi’s model I’ve ever come across discusses that apparenty discrepancy. I think that’s kind of important. Does anyone know where I can find such a discussion?

28. DAV says:

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.

29. crosspatch says:

“One thing does bother me though… clearly there were epochs in earth’s history where global temperature was much warmer than it is now”

The last interglacial period was warmer than this one has been. Sea levels were some 40 to 60 feet higher than today. Trees grew farther North. The Arctic was probably ice-free in summer.

And the polar bear survived.

30. Robert Wood says:

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.

The theorem here that the earth’s atmosphere maintains a maximal “greenhouse” effect assumes a constant external input of energy.

31. Robert Wood says:

Sorry tyupo correction for clarity

Rico, The gross (large) variations in the Earth’s climate are due to externalities, such as passing through cosmic dust clouds, precession of the equinoxes, variations in the Sun etc.

The theorem here that the earth’s atmosphere maintains a maximal “greenhouse” effect assumes a constant external input of energy. In fact, the whole end point of the theory is that gloabl warming or cooling can only be produced by external variations.

32. DAV says:

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.”

33. Michael Hauber says:

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?

Apparently K, P0 and P are listed as a ‘radiative flux’ of ‘non radiative origin’.

34. Nick Stokes says:

As Carl W says, the most extensive debate has been at CA. I’ve been a detractor of the paper there, under my blogname of pliny. The main items of the case against are:

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). No GCM or practical climate study would use such an assumption, or use any gray-body theory due to Milne. A gray-body model is sometimes used for teaching purposes to convey concepts.

2. The paper is presented as a physics-based theoretical analysis. It is based on three fundamental errors:
a. Kirchhoff’s Law, which is completely mis-stated. KL says that emissivity equals absorptivity. These are coefficients, which are used with other environment variables (temperature, incident radiation) to determine actual emittances and absorbances (total energy amounts). Dr Miskolczi simply assumes the emittances and absorbances can be equated.
b. The Virial Theorem. People who know about this scratch their heads here, because it is a principle which can be important in stars, but applied to Earth just describes the hydrostatic balance of the atmosphere. Dr Miskolczi’s statement is totally mystifying – he says that because of some relation between energies, two fluxes must have a certain relation. No-one can work that out.
c. A third equation, (7) in the paper and on this site. Dr Miskolczi has two equations which describe the result of applying conservation of energy to the Earth and the atmosphere, the two entities in his simple model. In the paper he introduced (7) as a third, but never said over what entity or region energy balance was being assessed. In an earlier version of this on-line “proof”, he sought to invoke conservation of momentum instead – a different principle, and very strange in the context. In this latest version, it sounds like it’s back to energy conservation, but eq (7) still makes no sense.

So with the physics not really working so well, he (or Zagoni) says now on this site
“Regardsless of the names and laws referred to in their derivation, the equations of Dr Miskolczi given in the points 3.-9. above are original and proved to be valid.”

3. So the proof is now, presumably, held to be empirical. But what does empirical mean here? In the paper, Dr M makes frequent reference to plots of 228 points, which seem to have reasonable regression fits. But what are the points? He sometimes talks of (“selected”) radiosonde readings, but there isn’t much detail offerred. And sometimes of simulations, using his code “HartCode”. In this site he assembles the results to prove the main principles, but the claim to their observational nature is somewhat undermined by the fact that he has similar graphs for Mars. It seems clear the results are simulations – how real-world observations fit in is quite unclear.

The key finding, often quoted, is that the greenhouse effect is limited. This result follows from his claim that the optical depth has a theoretical value (about 1.84), so if more CO2 is put into the atmosphere, somehow water is squeezed out. But that theoretical depth is based on a claim that the atmosphere must somehow optimise cooling, which he never justifies. Towards the end of this “proof” site, he lists comments from some of the referees of journals that rejected his paper. I don’t know why; the referees seem to make very strong points. On this particular point, one said: ”The overall concluding statement that ‘the existence of a stable climate requires a unique surface upward flux density and a unique optical depth of 1.841’ makes absolutely no sense at all. An atmosphere can be in stable radiative equilibrium for any LW optical depth, but the equilibrium surface temperature will monotonically depend on the value of the optical depth….” Quite right – the radiative balance can’t remove or add gases to the atmosphere.

35. Michael H.: see comment at 11:22:24 above

36. Alan D. McIntire says:

In response to RICO: Temperatures in the past were also strongly
influenced by the location of continents and seas.

– A. McIntire

37. Bruce Cobb says:

clearly there were epochs in earth’s history where global temperature was much warmer than it is now. And they appear to be much more easily explained on the basis of gas concentrations in the atmosphere than any other variable. It’s the sun that drives climate, not atmospheric gasses. Yes, of course there’s a “greenhouse effect” – no one has ever said otherwise. It’s overall role in climate, although important is rather limited, though. You might try this paper by David Archibald: The Past and Future of Climate .

38. Robert Wood says:

Michael Huaber,

You are looking at a presentation, without the words. If you follow a couple of the links suggested here, by me among others, you will come to the original paper, wherein the Ps and Qs are defined.

But remember, this analysis and theory is not about a “radiative budget” but an “energy budget”. This takes into account thermal expansion of the atmosphere (gravitational energy) as well. The specific details are not required top sketch teh theory. But look at the match of theory and reality.

The variable “K” basically stand for the non-radiative processes (Konvection, get it?). The radiative part is Sg, or as he unfortunatley decides to rename it Su, which confusing. P0 stands for all those things, inclduign human heating and tidal heating and volcanoes, that are not included in other theories. They all inject energy into the atmosphere.

39. Robert Wood says:

OK I don’t know much about the virial theorem, but I understand its application in this situation is to account for the effect of heat expansion and gravitation on the energy content of the atmosphere. I mean, ultimately, if the atmosphere got warmer, wouldn’t it also expand? I would have expected something more complex, but it is a first approximation, which no other theory contains.

40. Rico says:

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?

41. DAV says:

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.

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”

42. Robert Wood says:

Ah, Rico, what do I do with you?

What would the internal causes be for the known and accepted gross climatic variations in the Earth’s history? There are facts, and there are explanations. What are your explanations? Mine are externallities. Your’s?

43. Nick Stokes says:

Robert W,
Yes, for the atmosphere, the virial theorem just amounts to the ideal gas law plus gravity. So it expands when warmer.

44. MrMGA says:

Have any of you read the posts about Miskolczi on the Real Climate message boards? Go to the search engine on their web site and enter “Miskolczi” to retrieve all relevant posts. They trash Miskolczi’s paper pretty good. Then Miskolczi himself posts a few messages in his defense and he is insulted by Gavin and ‘raypierre.’

Gavin and ‘raypierre’ claim that Mikolczi makes several blatant algebraic errors in the first 9 pages of his report that invalidate his entire thesis. They don’t say what those errors are; they are apparently saving them for a paper written by a sophomore physics class as a class project. In other words, Miklosci’s math errors are so obvious that sophomore physics majors can point them out.

Maybe they are right, but that was in March and, as far as I can tell, the “class paper” has not been posted yet.

45. Steve in SC says:

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.

46. retired engineer says:

“If you put a lid on your pot, would not the water temperature increase even though you do not increase the heat applied to the heat? If you prevent some heat from escaping, would not the water temperature increase?”

Certainly. Without a lid, you reach a point of equilibrium, heat in=heat out. Add the lid, the point shifts. Heat in will eventually equal heat out, but requires a higher temperature to achieve it.

As one who has boiled over many a pot of pasta…)

47. Rico says:

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!

48. Alan D. McIntire says:

Nir Shaviv, the Israeli astrophysicist, has some articles on his website regarding the effect of the galaxy’s spiral arms and cosmic rays on ice ages:

http://www.sciencebits.com/myresearch

Also, you must consider the location of continents and oceans in affecting climate. During the Mesozoic Era, most continents were closer to the equator, also the Arctic wasn’t closed off as it is now, and there was no continent covering the Antarctic. Warm equatorial water could more easily flow to the Arctic and Antarctic regions, moderating climate throughout the earth.

With an ice covered Antarctic, we get lower ocean levels. Also, the Arctic is relatively closed off from the rest of the world’s oceans, limiting the moderating effects of equatorial current flow. This would have a much more significant effect on climate than CO2 levels- A. McIntire

49. Aviator says:

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

50. anna v says:

I have not delved in this paper. But I do like the concentration on energy conservation and not this funny “radiative budget”.

Radiative budget reminds me of house budget where the incoming outgoing cash is counted and cards ignored. ( in an mostly cash economy ?)

51. Gary Gulrud says:

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.

52. old construcion worker says:

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.

53. Robert Wood says:

Michael H, this isn’t just a radiative analysis, it is an enrgy analsyis.

54. Robert Wood says:

By externallities, I mean external to the radiative budget. This is an energy budget, not a tradiative budget.

55. MarkW says:

The pot on the stove model is flawed because all it is measuring is how easily does heat move from the pot to the surrounding air.

That would be the same as measuring how well heat moves from the upper levels of the atmosphere into space.

Quite obviously, changes in CO2 would have no impact on this transfer.

Assuming that there is no heat loss from the sides of the pot. Which would make it analogous to a column of air, running from the surface to space.

The question we are asking is not, does the average temperature of the pot change, but rather, does the bottom layer of water in the pot get warmer.

If the salt that you are adding to the pot makes it harder for heat to flow from the point of heating, to the point of escape, then the heat gradient will change.

56. Bruce Cobb says:

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”.

57. MarkW says:

If the atmosphere were warming, it would expand.

If it expands, the average space between molecules gets greater.

If the average space between molecules gets greater, then the distance an IR photon travels before being absorbed increases.

If the distance a photon travels before being absorbed increases, then the effective transparency of the atmosphere to IR also increases. In other words, at any altitude, if the atmosphere is less dense, the chances of a particular photon escaping to space without being absorbed increase.

58. leebert says:

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).

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.

59. John Nicklin says:

Alan D. McIntire (16:53:17) :

In response to RICO: Temperatures in the past were also strongly
influenced by the location of continents and seas.

True enough, however, temperatures during the last interglacial appear to be higher even though the continents were, more or less, where they are today. Assuming a drift of 8 cm/year for 100,000 years, most places on the globe are within 800 Km of where they were back then.

Or am I missing something?

60. George Tobin says:

I read Nick Stokes’ thoughtful analysis at CA and at Niche Modeling. It was not only substantive but entirely free of the snarkiness that infects a lot of climate blog commentary. A very professional job and a valuable contribution.

It is noteworthy that each of the defects he finds in the paper seem to boil down to Miskolczi making broad assumptions about equilibrium, conservation and/or the triumph of (unspecified) negative feedbacks. I say it is noteworthy because even if Miskolczi has completely failed to do any of the heavy lifting required to specify and identify these elements of negative feedback and ultimate balance, merely assuming they exist produces a model whose predictions are probably currently closer to observed reality than the orthodox AGW GCMs: CO2 is up but temperature is not up at the surface nor in the troposphere and humidity is down. Even without the hum od a mainframe in the background, merely assuming Gaia is more accurate than merely assuming Gore.

Miskolczi’s alleged breezy assumptions about Kirchoff’s law and the virial theorem are well matched by AGW orthodoxy’s functional dismissal of negative feedback modeling. If nothing else Dr. M has provided some perspective on the gross incompleteness of climate science models. After Raypierre and Gavin unveil their long-anticipated snarkfest regarding Miskolczi’s math skills, perhaps they can include a sidebar about the increasingly apparent limitations of their own working assumptions and models.

61. George, That’s one of the best statements I have seen about the issues. It should be remembered that theories (aka models) are just theories, that observations trump theories, and that well structured statistical tests trump observations. All necessary, but the quality of evidence contributed very different.

62. Mark Nodine says:

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.

63. Gary Gulrud says:

Like annav (I have only skimmed through a few times) I find the “radiative budget” obtuse, but balanced equations- analogous to chemical reactions-which he retains, are silly too.
The paper does not appear to advance the discussion other than to point out one significant flaw: waving our hands over the H20 feed-back.
In his defence, his use of Kirchoff’s law, though cursory, has nothing to gain from AGW orthodoxy as the standard Beers-Lambert solution is trivially inadequate. Both preceded modern physics and I’ve never seen an attempt to transform absorptivity/emissivity of one to the other. They are simply assumed to be equivalent.

64. Nick Stokes says:

Mark N,
Thanks for the kind words. Yes, you’re right that a lot of the paper does not use (or need) a gray-body simplification. But the result that has attracted a lot of attention, that the mean optical depth of the atmosphere is constrained to be about 1.84, is necessarily gray-body, as is the reasoning leading to it. It is this result which is claimed to put a strong limit on the greenhouse effect.

65. Eli Rabbet says:

FWIW way back at the beginning crosspatch asked about land use changes. While the earth was not paved over, the 19th century saw a huge amount of surface turned into farms in North America, Australia and Russia. You can see the effect in various climate records including global temperature. It is sometimes called the pioneer effect.

Nick Stokes pretty much has it. The assumption of a virial theorem is particularly weak IEHO. Also take a look at this.

66. kim says:

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

67. Mark Nodine writes:

The analysis by Miskolczi has much more explanatory power, in my opinion, taking into account convection and the optical depth…

Mark, atmosphere models have taken convection and optical depth into account at least since Manabe and Strickler’s classic paper of 1964. Miskolczi’s paper is impressive only to someone who has never studied atmospheric radiation.

68. 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?

69. Stas Peterson writes:

There is not some “discontinuity”, some piece of vacuum between the atmosphere and the Earth’s surface, as the “simplification” postulates.

The E.A. Milne infinite-atmosphere approximation says nothing at all about the surface temperature discontinuity, which, BTW, is a discontinuity in temperature, not a layer of vacuum between the atmosphere and the surface. The discontinuity is seen in any radiative equilibrium model which uses any version of the equation of radiative transfer. Try reading chapter 2 of Houghton’s The Physics of Atmospheres for a simple example. The discontinuity doesn’t exist in practice because the real atmosphere convects. In a temperature inversion you can indeed measure a temperature difference even between very low levels of air and the surface material. Try it some time, or talk to a meteorologist who has.

Also, no real atmosphere model for the past 50 years or so has assumed an infinite atmosphere, other than as a theoretical exercise. When such a thing is assumed (never in a model, but always as a theoretical exercise), it’s to provide a simplified starting point, as when we assume the sun is infinitely far away for purposes of explaining why rays of sunlight are roughly parallel at the Earth’s surface.

70. 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.

71. George Tobin writes:

CO2 is up but temperature is not up at the surface nor in the troposphere and humidity is down.

Which planet are you talking about? On Earth, temperatures have risen over the past 150 years, and humidity is up at a rate of about 0.9 millimeters of precipitable water per decade — consistent with the Clausius-Clapeyron law, and thus with a positive water-vapor feedback.

Dr. Miskolczi’s theory does NOT explain the evidence better than conventional climate models. It fails egregiously any test I can think of — current Earth, Venus, ice ages. In fact, it’s a bit of pseudoscience. For details try here:

Miskolczi

72. kim says:

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

73. statePoet1775 says:

BPL,

Since you are a Christian, do you find it plausible that God would allow a runaway greenhouse effect on earth? Is God more concerned about CO2 than the way we treat each other?

The evidence to me is that the climate on earth is extremely finely balanced, which begs the question what or whom keeps it that way.

My concern is a hasty political solution which is likely to do far more harm than good.

74. Bruce Cobb says:

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.

75. Peter says:

BPL, perhaps you can explain how ‘conventional climate models’ explain Venus, with its opaque, extremely high-density atmosphere and high albedo – especially as you seem to indicate that the ‘runaway greenhouse effect’ cannot happen.

76. Gary Gulrud says:

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.

77. George Tobin says:

“Which planet are you talking about? On Earth, temperatures have risen over the past 150 years, and humidity is up at a rate of about 0.9 millimeters of precipitable water per decade — consistent with the Clausius-Clapeyron law, and thus with a positive water-vapor feedback.” –Barton Paul Levenson

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.

My point was that even if Miskolzi’s approach is completely bogus, his contention that (a) CO2 sensitivity is lower than currently accepted because (b) negative feedbacks (however badly described) will make net AGW far less than generally expected is a better fit for current reality than the big temp upswing we were told to expect in IPCC AR4.

I was duly impressed with your gratuitous reference to Clausius-Clapeyron. It reminds us how elements of truly settled science (e.g., ideal gas, change of state) are insufficient to explain things like cloud formation and thus leave us with big gaps in the descriptive and predictive power of climate science. Models filled to the brim with such settled science goodies are destined to fail if it is known at the outset that the tool set is incomplete with respect to the task at hand.

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.

79. Gary Gulrud says:

AGW also gets Kirchoff’s law flat wrong. The Atmosphere is not in thermal equilibrium therefore Kirchoff does not apply.
Even if CO2 weakly absorbs it must more weakly emit. Arrhenius was a loon.

80. 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.

81. Gary Gulrud says:

Eli or whomever, go take Thermodynamics, e.g., with “Thermal Physics”, Kittel & Kroemer, or more feasibly, read “QED” by Richard Feynman. The latter is short and accessible.
It is AGW modellers who mistake absorptance for absorptivity (not absorbtivity as you have it) conflating Beers’ signal attenuation with an electromagnetic propagation.
The Beers result grossly understates absorption and therefore overstates emission. At no time is the instantaneous ‘optical depth’ derived which would make clear the impossibility of the AGW result of variously 0.6 to 0.9.
Your definition of equilibrium is gibberish.

82. 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.

83. Gary Gulrud says:

In the sense that my daughter’s eyes are blue are a property of hers.

84. JAE says:

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?

85. stas peterson says:

Wow Hansen’s’ minions have emerged from the monastery at Real Climate dsipatched by Herr Gavin, to argue, demean, disdain , dismiss and destroy Dr, Miskolczi work.

Nick Stokes could conduct a civil discourse and disagree with some theoretical posits, of Dr. M. as not proved. There is nothing wrong with that.

The er “gentlemen from RC, like Barton Paul Levenson, Eli Rabett, et cetera have deigned to honor this conversation with their Revealations and bon mots scoring what they consider points, before ascending back to the hallowed Sanctuary of RC, happily having shed heat but no light. Never actually revealing or discussing the Emperors’s non existent Clothes.

86. 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.

87. Gary Gulrud says:

“about Miskolczi’s paper. He has at least two basic assumptions which are a) unjustified and b) wrong.”

If the incremental improvement has so many issues version 0.1 must be unusable.

88. JAE says:

“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?

89. Neal J. King says:

I have also been studying Miskolczi’s paper, and have gotten through about to page 10 before being stopped by a series of problems and apparent non sequitors, some of which have been mentioned by Nick Stokes and BPL above.

I have written this up and sent my comments to Dr. Miskolczi, who said he would be traveling until August and might be able to respond at that time. The main points can be summarized as follows:

– The validity of the “classical” statement of the Virial Theorem (specifically, the ratio [total KE]/[total PE] = ½) seems very doubtful in this application. (There is a lot of calculation behind this simple statement.)

– The relationships between the bulk quantities and the fluxes ([total KE] and EU, and [total PE] and the radiation flux) are not clear. What are the equations relating them?

– It is not clear how to interpret Eq. (7) in terms of the total energy flux into a specific system. It seems to me that any argument based on conservation of energy must have such an interpretation.

– It is not clear how the factor of (3/2) between SU and OLR jumps discontinuously to (1) as the strength of the radiation-molecule interaction vanishes.

– I do not understand the derivation of Eq. (9) from Eq. (8).

I hope he gets back to me.

90. Alex Harvey says:

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.

91. Alex Harvey says:

Neal, I’ll also be interested to know the outcome of your queries to Dr. Miskolczi. It should be noted, though, that the Virial section is referred to by M. Zagoni as a “fine-tuning” of the theory. See the “historical reconstruction” slide. http://hps.elte.hu/zagoni/Proofs_of_the_Miskolczi_theory_elemei/image060.jpg It only enters in point 8 of the 12 points. Once the atmospheric Kirchhoff law is accepted, and the derivation of the general greenhouse equation (eq 21) is agreed to be valid (Nick Stokes, at least, already agreed), we are most of the way there. It would no longer be possible to pretend that this theory isn’t important, whatever the outcome on the Virial theorem.

92. Neal J. King says:

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…

93. Alex Harvey says:

Neal,

– Regarding the Zagoni slides, you missed the point. I simply wanted an online high-level summary that shows the virial work in context.

– Regarding “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.”

This is just misinformation that originates on someone or other’s blog. It’s true that on Zagoni’s website is a statement to the effect, “look, even if you reject the theoretical arguments, the empirical support is so strong that you would still have to accept the laws as empirical facts.” However, nothing on Zagoni’s site or in Miskolczi’s New York slides contradicts Miskolczi’s actual papers in any way. I believe Zagoni’s remark is a concession arising from his frustration that climate scientists don’t seem to know even basic physics (i.e. where Kirchhoff’s Law can be applied).

– Regarding “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).”

You are quite wrong here. Miskolczi doesn’t apply the Kirchhoff Law in the upper atmosphere any more than Goody & Yung do (see his assumption (c) on p. 3 or have a look at his Y-axes and note that they never extend beyond 60km). Again, Miskolczi is simply following a standard textbook on atmospheric radiation at this point.

As for the “other sources” you must be talking about the “experts” at RealClimate:

Gavin Schmidt: He appears to have made at least two fundamental mistakes. First he assumes that Kirchoff’s Law implies that absorbed radiation is equal to emitted radiation in the atmosphere (it is not – absorptivity and emittance are the same, but not the fluxes). …

That’s fine, but he’s clearly wrong. And all the others who have, yes, said exactly the same as Gavin? Well, who are we going to believe here: the standard textbook or the people who have copied Gavin Schmidt & Nick Stokes?

The standard textbook is using Kirchhoff’s Law to equate the fluxes — in the quote above and in several other sections. I think this echoes what Gary Gulrud has been saying all along in this thread.

If you’d like full references, have a look at the ClimateAudit BB discussion.

94. Alex Harvey says:

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?

95. Neal J. King says:

Alex Harvey:

– wrt Kirchoff’s law: As I already said, I don’t have much insight into the application here of Kirchoff’s laws. Therefore, nothing among my originally expressed concerns depends on it, one way or the other. My argument is focused solely on what I do understand; and based upon what I do understand, I see some problems in Miskolczi’s full original paper, as stated above (16-07-2008).

– wrt the ladder: If even one step in the ladder is missing, you can’t use the ladder, because it’s not valid. (Think of a real ladder, for instance: If a step in the ladder is missing, even if it’s the stairway to heaven, it’s not going to do you any good.) If you can fix the step, then you’ve got something – but if you can’t, you don’t. Sorry.

And don’t blame it on “[my] virial objection”: I did not choose to structure the argument this way, the whole ladder is due to Miskolczi. I did not remove the step, I’ve just been pointing out that Miskolczi didn’t put one in (or put in a cardboard piece).

If you want a good theory, you can start by fixing (or getting Miskolczi to fix) this step, as well as the other problems I’ve pointed out. Otherwise, it’s the same situation as applied for so many years: “I’ve got this great proof of Fermat’s Last Theorem, surely you can’t disqualify it because of one tiny little mistake at the beginning…” Yes, we can and we must. In the end, Wiles provided a proof that the experts accept, based upon new insights into number theory – So isn’t it a good thing that we didn’t accept all the thousands of would-be proofs that had “minor” flaws in them? In mathematical and theoretical proofs, a proof is right – or it’s nothing.

But cheer up: If the result is really true, there should be a way to prove it. In reading some of Einstein’s early relativity papers, I myself even found a couple of mistakes. That was a thrill! Unfortunately for my Nobel-Prize shelf, I also immediately thought of a way to side-step those mistakes. So, no cigar.

96. Alex Harvey says:

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.

97. Neal J. King says:

Alex Harvey:

– I understand through Eq.(3) quite clearly.

– Eq.(4) is under debate by many people on this blog. But I’m not even worrying about it.

– Based on Eq.(4), I will allow through to Eq.(6). But, to follow M’s text, I will not interpret it here, since he does not. I will remark, however, that one of the reviewers wrote: “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.

– Then comes the Virial Theorem. Aside from the fact that I don’t agree with his factor of ½, I wish he would just say what equations he is using to relate total potential energy to temperature, and total kinetic energy to Eu.

– Eqs.(7) doesn’t make any sense to me at all: It cannot, as far as I can tell, be interpreted as equating the input and output of any system, so I don’t see how it can be interpreted as conservation of energy. Others (see above) have had the same problem.

– Eq.(7) leads to Eq.(8) gives a factor of (3/2) without any conditions. Yet this factor must be (1) if the interaction between the gas and the radiation vanish. However, I do not see how the logic would be disrupted by the vanishing of this interaction. (But then I don’t follow the logic to Eq.(7) at all.) So the question is, If conservation of energy implies Eq.(7), how does Eq.(7) fail when the interaction vanishes?

– Eq.(8) is one of the equations Miskolczi keeps coming back to in deriving his claims to new results. I can’t get there from here, so I don’t see any point in walking on air until it becomes clearer.

– I’ve looked at Miskolczi & Mlynczak: I don’t see that it helps at all with what I’m trying to do, which is to get straight the logic of the first few pages.

– It really doesn’t matter to me about the history of Miskolczi’s ideas: I’m trying to understand his paper, as written. As written, it depends on the Virial Theorem; in a way that I find unclear – nor am I the only person in this position.

– If Eq.(4) and (21) don’t depend on anything coming along before, why not put them upfront?

– If you think you understand M’s paper so well, I’d be pleased to send you my questions directly, and you can answer them in his place. It’s only eight pages.

In the meantime: Extraordinary claims require extraordinary evidence. So far, I’m not seeing the evidence…

98. Alex Harvey says:

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.

99. Neal J. King says:

Alex Harvey,

I’ll wait to draw any conclusions on the significance of this paper until I understand whether it makes any sense. To me, it does not make sense to try to evaluate bits and pieces of it separately: a scientific paper is a communication, that must hang together.

Miskolczi has responded on weblogs before, so I assume that he would be willing to have his answers shared. On another blog, someone reported an email correspondence with him, but did not obtain enough clarification that he felt it worthwhile to present it. In my case, I’ve actually drafted up a document in great detail (lots of equations and explanations of what’s bothering me), so if his response is more than “telegraphic”, something should be revealed.

100. Alex Harvey says:

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?

101. Neal J. King says:

I would love to look into the question, but my copy of Goody & Yung is thousands of miles away, and I’ve actually never had a chance to look at it so far: I bought it used by mail and had it sent to the U.S.

However, my last brush with a full textbook on radiative transfer left me with a distinct memory that this is not a subject upon which I would want to rely upon a fragment of text. It reminded me of hydrodynamics: The boundary conditions are really important in ways that are not quite intuitive.

102. Alex Harvey says:

Well a lot of the textbook is available in preview online:

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.

103. Neal J. King says:

Ironically, when I looked at your link, pp. 27-29 were not part of the preview! Possibly they don’t show all the same pages all the time…

104. Neal J. King says:

Alex Harvey:

– I’ve looked at what Zagoni scanned in. That fills in the picture a bit. My conclusion is that I don’t have any particular beef with Eq.(4). But then again, I didn’t before, either.

– However, you claim that the “revolutionary” Eq.(21) is independent of preceding equations. This is not correct: The top of page 14 clearly shows that M derives Eq.(21) from the equation:

OLR = S_G – E_D + E_U

I am not exactly sure where he gets this, but it looks to be coming from the “family” of equations in the neighborhood of Eq.(7) & Eq.(8) – none of which make any sense to me (as I laid out earlier). So, as a starting point, I will challenge Eq.(21).

– MM2004 may be easier to follow than the current paper, but recall that the results of scientific papers are accepted not on the basis that someone has stated something, but that he has proven it, by logic, by evidence or both. “Following the concept” cannot replace “understanding the cogency of the logic”.

– Going back to your earlier issue, “none of the LW energy that escapes to space represents emission directly from the surface”, whether this is true or not does not affect the explication of the enhanced greenhouse effect according to standard atmospheric physics. In fact, the way the theory works is that the outgoing LW radiation intensity reflects the gas and temperature one optical depth into the atmosphere: If it only depended on emission intensity from the surface, there would BE no enhanced greenhouse effect. So I’m not sure what it is you are suggesting NASA check?

105. Alex Harvey says:

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…

106. Alex Harvey says:

On why Pierrehumbert owes an apology:

# Miskolczi Says:
22 May 2008 at 9:21 PM

To response of raypierre:

If you are so sensitive to the elementary errors did you comment the Kiehl-Trenberth IR planetary radiation budget?

Kirchhoff law: I stated that Ed=Su(1-Ta) and I proved this relationship theoretically for a bounded semi-transparent radiative equilibrium atmosphere. I put a figure at the

http://www.globalwarmingskeptics.info/modules.php?name=Forums&file=viewtopic&t=331

link. You probably would like to explain the shown relationship between the flux density terms to those who mistakenly attribute it to the Kirchhoff law.

In case you manage to explain this figure or (Fig. 2 in the paper), we may go on to discuss dimensional analaysis and virial theorem. I am very much impressed with your students. My students have no problem to read this paper and understand what it wants to say.

[Response: Your poor students. I won’t spoil the surprise by stealing the thunder of the Bowdoin class. I’m going to give them the first shot at writing this up, even if it takes them a while since they have other class work to attend to as well. –raypierre]

107. Alex Harvey says:

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. :)

108. Alex Harvey says:

Neal,

Continuing with the question of the significance of eq (4), what about the following quotations that Zagoni has on his website:

V. Ramanathan: Trace-Gas Greenhouse Effect and Global Warming. Underlying Principles and Outstanding Issues. Volvo Environmental Prize Lecture. 1997:

Global warming: How will the planet restore global energy balance? The surface-troposhere system should warm (in response to the excess energy) and radiate more longwave radiation to space until the OLR emission to space balances the absorbed solar radiation, i.e., the increase in OLR from warming compensates for the reduction in OLR due to trace-gas increase. This is the underlying theory of global warming. It relies on the fundamental Planck’s law that the electromagnetic energy emitted by any body in local thermodynamic equilibrium increases with its temperature; the functional form of this increase is given by the so-called Planck function.

Spencer Weart, Discovery of Global Warming, 2008:

Consider a layer of the atmosphere so high and thin that heat radiation from lower down would slip through. Add more gas, and the layer would absorb some of the rays. Therefore the place from which heat energy finally left the Earth would shift to a higher layer. That would be a colder layer, unable to radiate heat so efficiently. The imbalance would cause all the lower levels to get warmer, until the high levels became hot enough to radiate as much energy back out as the planet received.

M2007, p. 6:

Eq. (5) shows that the source of the upward atmospheric radiation is not related to LW absorption processes. The F+K+P flux term is always dissipated within the atmosphere increasing (or decreasing) its total thermal energy. The Ed=Su-St functional relationship implies that G-Ed=-Eu, therefore, the interpretation of G-Ed as the LW radiative heating (or cooling) of the atmosphere in Inamdar and Ramanathan (1997) could be misleading.

Now are you really saying that a discovery that Eu = F + K + P (eq 5) and OLR = Sg – Ed + Eu (eq 6) will not see the received view revised in some way? That it’s just irrelevant, “who cares what OLR is really equal to … “?

109. Alex Harvey says:

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.

110. Alex Harvey says:

Neal,

More on eq (21). In case you’re planning to follow it through yourself, you may like to read what Nick has written here:

http://www.climateaudit.org/phpBB3/viewtopic.php?f=4&t=161&st=0&sk=t&sd=a&start=340#p7721

I have to say that I think you are right about M21 [eq (21)]. I’ve followed it through carefully, and though he uses his physical arguments later with M25 and when he requires f to be 2/3, he hasn’t used it with M21. I now see that what he has done in Appendix B is to take the first order solution and substitute it back into the full radiance formulae to get what may be an upgrade, at a cost of violating the top condition. That may improve accuracy; I’ll have to check further. If it is an improvement, it would only be the first step in an iterative process. The argument beyond B8 relies on his optimal cooling argument, which he hasn’t justified.

Mathematically, I think eq 21 can be regarded as a first step in a Picard iteration, which may or may not produce improvement.

The dispute about the fit at the TOA was discussed at length in the CA BB; I’m inclined to find Jan Pompe’s response more persuasive: a discontinuity at the TOA makes a lot of sense as a finite source (the atmosphere) tries to warm an infinite sink (space).

111. Neal J. King says:

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.

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?

112. Alex Harvey says:

Neal,

– The energy minimum principle is merely a restatement of the second law of thermodynamics. “[F]or a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium.”

http://en.wikipedia.org/wiki/Principle_of_minimum_energy

Having demonstrated in MM2004 that the earth-atmosphere is in radiative equilibrium, it follows that the principle of minimum energy applies.

– Optical depth of Mars, read the paper (see Fig. 13 for instance).

113. Alex Harvey says:

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

114. Neal J. King says:

Alex Harvey:

– Of course, I agree with the applicability of thermodynamics in general. However, what you are describing as “the energy minimum principle” is not what Miskolczi is stating on page 16, Section 5.1: “The principle of minimum energy requires the most efficient disposal of the thermal energy of the atmosphere. Since in radiative equilibrium the quantity (pi)B_0 is an additive constant to the source function, for a given OLR and S_G we may assume that in the atmosphere the total absorber amount (water vapor) will maximize B_0.” There is a very far stretch from saying that the second-law of thermodynamics is applicable to saying that the water-vapor concentration will adjust itself so that the planet will cool most quickly! This is another example of Miskolczi’s drawing conclusions for which I would like to see some justification. I don’t buy it.

– Thanks for referring me to Figure 13, according to which the optical depth of Mars seems to be 0.175. Why isn’t it 1.87, in accordance with the very “energy minimum principle” that we discussed before?

115. Alex Harvey says:

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.

116. Neal J. King says:

Alex Harvey:

– Even if the local subsystem attains a minimal-energy state, that does not imply that it must take the fastest way to get there. But that’s what Miskolczi claims.

Here’s an analogous non sequitur: Take a sealed aquarium divided into two sections by a glass wall, that goes nearly, but not all the way, to the top. Put a lot of water on the left half, a little water in the right half. This represents an unstable situation, because the water level is higher on the left than on the right. A lower-energy configuration would have them at equal levels. So, it is true that in thermal equilibrium, the water levels will be equal. That fact does not enable one to conclude that the water on the left will bust through the glass to the other side, simply because that is the fastest way to get there. What I would expect would happen over time will be the gradual evaporation and condensation of water on both sides of the partition, leading to a gradual build-up of water on the RHS and a gradual decrease of water on the LHS. Eventually, the water levels will be equal. This is not going to be a flowing process: this will be due to the fact that the humidity of the air at the lower water-level will be higher than at the higher water level, so the condensation rate will be higher on the RHS; whereas the evaporation rates on each side will be the same (because the temperature is the same). Now, the “fastest” way for this to happen would be for all the evaporation from the LHS to promptly condense on the RHS: poof! But in fact, it’s not going to be that fast.

– Page 23: Yes, and what I see is: “It follows from Eqs. (8) and (28) that 3*OLR/2 = OLR/f and f = 2/3 = f+, giving an equilibrium optical depth of tau_+A = 1.841. Using Eq. (9) and (28) the equilibrium optical depth beomes tau_oA = 1.867.”

Now, I don’t see anything here that applies to the Earth but not to Mars. (Granted, I don’t see how he gets to (8) and (9) anyway, as stated earlier; but I don’t see any reason why, if you believe them as applied to the Earth, that you should not believe them as applied to Mars.) But in that case, why is the tau for Earth so close to this result, but for Mars it’s a factor of 10 smaller? If you believe his proof, he’s proved too much. And if you don’t believe his proof (which is where I am right now), he’s proven nothing.

Now there is a section 9.2 on Mars, but I find it more confusing than helpful:
– p.31: “With P0 ~ 0 assumption, Mars does not satisfy the IR radiative equilibrium and the overall energy balance criteria at the surface.” But the Earth is also assumed to have P0 ~ 0; and anyway, what is Mars supposed to do, violate conservation of energy?
– p.32: “, and apparently, the Martian atmosphere accommodates the radiative transfer scheme of Eq.(10).” But Eq.(10) was originally (p.8) described as just a simplified version of Eq.(9), so I don’t see how that gets Mars off the hook.

117. Alex Harvey says:

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.

118. Neal J. King says:

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.

119. Neal J. King says:

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…

120. Neal J. King says:

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…

121. Alex Harvey says:

Neal,

– You now seem to be saying that it’s the radiative equilibrium assumption that is at fault. However, you haven’t provided any reasons for rejecting it; you’re just asserting that it’s false.

– In the following: “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.” I’m not sure where you’re coming from or where you’re going for a few reasons:

i) Miskolczi doesn’t talk about “fastness” anywhere in the paper. My feeling is that you’re just changing his words to set up a bit of straw man here. The word he uses is “efficient,” which, if nothing else, sounds less ridiculous than “fast.” If I hold up a pen (=increase this pen’s potential energy) and then let I let it go, gravity will see to it that the potential energy is disposed as efficiently as possible. Is there a problem with this statement? Or I could say, “the pen will move as fast as possible towards the ground.” Alright, same meaning, but it sounds a little ridiculous. The wording suggests intentionality within the pen, rather than the deterministic workings of the laws of physics. So… are you just playing with words here?

ii) Do you agree or do you disagree that the earth-atmosphere system takes H2O from the oceans in the process of cloud formation?

– Mars, as stated, it would be more interesting to wait for Dr. Miskolczi’s response to your detailed questions.

– Ken Gregory’s response, perhaps if he’s still out there he might respond himself to this one.

122. Alex Harvey says:

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.

123. Neal J. King says:

Alex Harvey:

– “Radiative equilibrium at fault”: No, I’m just pointing out that it’s not correct for you to state that the Earth’s atmosphere is in equilibrium. Steady-state is not the same as thermal equilibrium.

– “Efficient vs fast”: You’re picking on words. The point is that the fact that the final state for a system (or more accurately, subsystem) in thermal equilibrium has the minimum energy does not dictate any specific path towards getting there: most efficient, least efficient, fastest, slowest, greenest, cutest – there’s no implication. Miskolczi attempts to draw one, hence he maximizes the radiative transport rate to get his tau = 1.87 result. I don’t see any reason to follow him there.

The most popular minimal principle associated with dropping a pen is the principle of least action, where the action is the integral of (KE – PE) over time. There is no reason to consider that particularly “efficient” however.

– “H2O taken up from the ocean in the process of cloud formation”: Yes, so? The point is that M is looking for a mechanism that will make his tau = 1.87 true. So he’s picking on cloud formation at altitude 2 km (p.35) or look at other possibilities at the bottom of p.23. From my point of view, there is just no reason that the atmosphere should be obligated to accommodate him. Actually, it’s very similar to the game several people have already mentioned about his use of the virial theorem: Even if the VT applies (and I’ve argued that it doesn’t give what he wants), there seems to be no sensible way to turn a relationship concerning bulk energies into a relationship on fluxes (rates of energy transfer). Analogously, here he is trying to turn a principle regarding the existence of a minimum-energy configuration into a condition on rate of energy loss. In my view, that dog won’t hunt.

– I have dropped Miskolczi a line reminding him that I am still interested in clarification of my questions: According to what he said earlier, he should be back in town by now. Until I hear from him, I will frankly not be too interested in trying to salvage sections of the argument: It is the author’s responsibility to make sure a paper hangs together, not the reader’s responsibility to find parts that work. I am willing to be convinced that it makes sense; but only if I get answers that make sense to me.

124. Neal J. King says:

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.

125. Alex Harvey says:

Neal,

– fast / efficient:

fast: as mentioned above, this concept does not appear in the paper at all.

efficient: although the word appears in the text, the assumption that the critical optical depth will be found at the maxima for B0 does not derive from any actual assumption of “efficiency.” The word you’re making so much about is just a word in the text. Delete the word and we can still follow the paper. Perhaps it is awkward? Who cares?

– In the following link: http://asd-www.larc.nasa.gov/~yhu/paper/thesisall/node54.html it appears to my layperson’s eyes that a similar procedure is being applied. By the looks of these are Miskolczi’s colleagues at Langley, no less.

– radiative equilibrium / thermal equilibrium / steady-state: is that a yes, no, or a maybe? Miskolczi’s assumption is not steady-state, and it’s not thermal equilibrium. The assumption again is radiative equilibrium — “long-term radiative equilibrium between the solar and terrestrial radiation…” MM2004, p. 210. It is this assumption and this assumption only we are talking about. It appears that you reject the assumption. If so, why? What are your reasons / evidence for rejecting the radiative equilibrium assumption?

– If I drop my pen, do the laws of physics specify a particular path by which the pen will come to rest or not? I think they do.

– Your thought experiment: crucial in Miskolczi’s model is the existence of a near-infinite supply of H2O on the earth in the oceans. I fail to see where you’re going with this.

126. Alex Harvey says:

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?

127. 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.

128. kim writes:

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

Wrong on both counts. For water vapor, see:

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.

For temperature:

Tim Ball’s errors

Tilo Reber’s errors

129. Alex Harvey says:

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.

130. Alex Harvey says:

BPL: Another question: your website previously stated that you were writing up your objections to Miskolczi’s theory as a journal article that would be submitted to peer review. If accepted, you would provide a link to your published article. There is no mention of this any longer, and a revised version of your original page seems to have reappeared. Since a lot has been made of the fact that Miskolczi’s paper was rejected by the peer reviewers from some major journals, it seems only fair to ask what happened during the peer review of your own paper?

131. Neal J. King says:

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.”

132. statePoet writes:

Since you are a Christian, do you find it plausible that God would allow a runaway greenhouse effect on earth? Is God more concerned about CO2 than the way we treat each other?

No one is saying there’s going to be a “runaway greenhouse effect.” On the present Earth you can’t have one. What climatologists are saying is that the greenhouse effect is being enhanced by human production of greenhouse gases, and that the effects on our agriculture and economy will be severe.

The evidence to me is that the climate on earth is extremely finely balanced, which begs the question what or whom keeps it that way.

It is finely balanced, but it has gotten out of balance many times, e.g. during the “snowball Earth” episodes 2.3 billion, 800 million and 600 million years ago. What keeps it approximately balanced are feedback mechanisms such as the carbonate-silicate cycle. But we are pouring carbon dioxide and other greenhouse gases into the air much faster than natural cycles can easily handle.

133. 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.

134. Peter writes:

BPL, perhaps you can explain how ‘conventional climate models’ explain Venus, with its opaque, extremely high-density atmosphere and high albedo – especially as you seem to indicate that the ‘runaway greenhouse effect’ cannot happen.

I didn’t say the runaway greenhouse effect couldn’t happen. It can’t happen on present-day Earth, but it certainly did happen on Venus. I think you mistook me critiquing Miskolczi for what I believed. If Miskolczi’s theory is correct, Venus shouldn’t be anywhere near as hot as it it.

135. 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

136. Alex Harvey writes:

BPL: Another question: your website previously stated that you were writing up your objections to Miskolczi’s theory as a journal article that would be submitted to peer review. If accepted, you would provide a link to your published article. There is no mention of this any longer, and a revised version of your original page seems to have reappeared. Since a lot has been made of the fact that Miskolczi’s paper was rejected by the peer reviewers from some major journals, it seems only fair to ask what happened during the peer review of your own paper?

Surely. I submitted it to JGR, but they told me that since Miskolczi’s article hadn’t appeared there, I couldn’t reply to it there. So I decided to just put the article up on my web site.

137. Neal J. King says:

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.

138. Alex Harvey says:

BPL:

…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…

I am mistaking a special case for a general law am I. That’s funny, though. Since the specific bodies in this “special case” appear to be those “layers of the atmosphere” we care about. The text continues, “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.”

But then you continue, this is NOT “Kirchhoff’s Law.” Followed by lots of lovely examples of statements of Kirchhoff’s Law in italic font that aren’t relevant to Miskolczi’s paper.

So who really cares whether it’s Kirchhoff’s Law or a special case of Kirchhoff’s Law or a consequence of Kirchhoff’s laws plural?

Where is the contradiction here? Perhaps what you really want to say is that the textbook is wrong? If so, say it. Also, can you explain to me how a textbook called “Atmospheric Radiation” can not be relevant to atmospheric modeling?

139. Alex Harvey says:

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.

140. Neal J. King says:

Alex Harvey:

I guess it just shows you can find junk on the internet anywhere.

But this document may not be that recent: It is dated 21 December 1996.

It might be an early draft of something that never got very far. If anyone reviewed it and didn’t catch problems…

141. Alex Harvey says:

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.

142. Alex Harvey says:

Actually, I shouldn’t say “contradiction.” Clearly, a law known commonly just as “Kirchhoff’s Law” is used to equate absorptivity & emissivity in LTE as you say. Perhaps this is the one familiar to climatologists? I note that your quotes all came from climatology textbooks rather than physics textbooks. At any rate, equally clearly, Kirchhoff’s laws are also used to equate absorption & emission. 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.”

143. Alex Harvey says:

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

144. Alex Harvey writes:

Where is the contradiction here? Perhaps what you really want to say is that the textbook is wrong? If so, say it.

The textbook is not wrong. You didn’t understand it.

Also, can you explain to me how a textbook called “Atmospheric Radiation” can not be relevant to atmospheric modeling?

Because it’s a book about radiation theory, not about how to write atmosphere models. The former long predates the latter. There is some discussion of atmosphere modeling in Goody and Yung, but that’s not the primary focus of the book.

145. 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.

146. Alex Harvey says:

BPL:

That’s right, I didn’t understand. I’m a computer programmer. You’re a science fiction writer; Miskolczi is a specialist in radiative transfer with 30 years experience, many of those as a research scientist with Langley. He has a long publishing history of at least 15 peer-reviewed papers since the late 1980s; his specialisation is in radiative transfer. You want me to believe that a man hired & retained for many years by NASA as a research scientist doesn’t understand the ABC’s of theoretical physics. Indeed, you want me to believe that his NASA colleague, Martin G. Mlynczak, likewise makes these sorts of “freshman” errors.

http://www.nasa.gov/centers/langley/news/researchernews/rn_mylnczak.html

And it’s not just these two. There are plenty of posts out there on the blogosphere from people saying, “er, actually, I don’t see a problem with this part of Miskolczi’s paper actually.”

Now apologies for the polemics but I would prefer a response that goes a little deeper than, “I could tell you, but you wouldn’t understand.”

Eq (2.76) is an equation relating absorptivity & emissivity, is it BPL. Look on p. 28 & read the words, “Kirchhoff’s deductions were as follows [some conditions and then] … (b) the source function is equal to the intensity.”

That is, absorption=emission.

Question 1: Do you want to dispute my reading of Goody & Yung pp. 28, 39? If so please don’t return the mantra about LTE, absorptivity & emissivity. Can you explain what it is that I’m missing? In particular, the bit that says the source function is equal to the intensity.

Question 2: Since the textbook is not wrong, can you explain which part of “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” I did not understand?

147. Neal J. King says:

Alex Harvey:

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

148. Alex Harvey says:

Neal, nowhere directly. I doubt that anyone has thought this through, but it is implied: if Miskolczi doesn’t understand Kirchhoff’s Law, then Mlynczak obviously doesn’t either since Miskolczi & Mlynczak (2004) uses Kirchhoff’s law in exactly the same way as Miskolczi (2007):

p. 229:

Rd is computed similarly to Ru, but using the atmospheric
downward emittance : Rd=Ed/Su. According to the Kirchoff’s law, Rd may
be identified as the clear-sky total graybody absorptance: Rd = 1− TrA = A

p. 232:

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. Utilizing the above two facts one may estimate the global (or zonal) average OLR with the simple
expression: OLR=3Eu − Ed.

If Dr. Mlynczak doesn’t agree with what I’ve written here, it’s about time someone from NASA breaks this silence. How is it that no one at NASA ever pointed out to poor Dr. Miskolczi that he misunderstood Kirchhoff’s Law? Most likely, because they knew he didn’t. I’m sorry, this is NASA research. Someone needs to explain this contradiction.

149. Neal J. King says:

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)?

150. Alex, I have tried my damnedest to walk you through this issue. I’ve cited sources and worked examples. You are just completely unwilling to learn. To anyone who knows radiation physics, you come off like the kind of buffoon who thinks he can prove that the Moon landings were faked or that Velikovsky was right about astronomy.

Ignorance can be cured. Stupidity can’t be. Militant ignorance of your sort is a kind of stupidity.

151. Dee Norris says:

Wait a minute here!

Velikovsky was wrong?

Now my entire world is in upheaval.

152. Neal J. King says:

BPL,

You are being rude.

This is not necessary.

Let’s keep things to a higher level.

153. Alex Harvey says:

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.

154. Alex Harvey says:

BPL:

For a body in local thermodynamic equilibrium the amount of thermal energy emitted must be equal to the energy absorbed; otherwise the body would heat up or cool down in time, contrary to the assumption of equilibrium. In an absorbing and emitting medium in which Iλ is the incident spectral radiance, the emitted spectral radiance Rλ is given by
Rλ = ελBλ = aλIλ,
where aλ represents the absorptance at a given wavelength. If the source of radiation is in thermal equilibrium with the absorbing medium, then
Iλ = Bλ,
so that
ελ = aλ.
This is often referred to as Kirchhoff’s Law.

Compare again with Miskolczi’s statement:

According to the Kirchhoff law, two systems in thermal equilibrium exchange energy by absorption and emission in equal amounts, therefore, the thermal energy of either system can not be changed.

155. Neal J. King says:

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.

156. Alex writes:

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.

I have answered your question at great length, and in detail. You simply refused to believe anything I said. There is nothing more I can say to you; you’re immune to evidence. There’s really no point continuing to talk to you at all.

157. Alex Harvey says:

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.

158. Franko says:

“IIgnorance can be cured. Stupidity can’t be. Militant ignorance of your sort is a kind of stupidity.”
Arthur Miller differentiated dumb (lacking ability) and stupid (knowing but choosing otherwise).

My dumb question, regarding radiate and thermal equilibrium. The two are different, averaged concepts, but result in same temperature. If not, perpetual motion, here we come.

Consider the letter C, conductive, but radiate at the gap.
Any way to massage the statistics, (smoke and one way mirrors, prisms, diffraction gratings oscillating, pulsed microwave transmitters with antennas mechanically modulated, magnetically aligned molecules) You can filter in time, frequency, space direction, etc., but to no avail ? How do optical depth and thermal kinetics, freedom degrees, balance it, making perpetual, always ,stupid wrong ?

159. Neal J. King says:

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.

160. Neal J. King says:

Alex Harvey:

Sorry, I don’t get anything out of M&M, pp. 233 onward:

– In eqns (1)-(2), I don’t have a copy of Goody & Yung (as I mentioned earlier), so I don’t know the context of this equation: What is it about, what is the problem being addressed, what kind of tools are they using? In order to understand (not just quote), I have to have that context.

– Confusingly, they say under eqn.(4), “We should note, that the terrestrial graybody optical thickness is not an accurate measure of the atmospheric absorption and cannot be used in Eqs. (1) and (2).” But then, despite some disclaimers, they seem to go on to use it in their further equations.

– I don’t know where eqn.(5) comes from, they just state it. Maybe it’s the output from the “relatively simple computation” that they do not present.

– Under eqn.(6), they say, “The data points in these figures represent only about 10% of the total 230 profiles. Only those cases were selected for these plots, where the simulated and theoretically predicted OLRs agreed within less than 0.5%.” I can’t quite make out what this means: Is this selectivity a valid method of filtering out cases that don’t fit into the scope of investigation, or is it cherry-picking the points you like? I can’t tell.

I could go on, but you see the problem: I don’t really know where they’re coming from or where they’re going. This may not be their fault. But it means I don’t have anything particularly useful to say about M&M.

M (2007) is another matter: He starts out with something well-defined, and at least for the first ten pages I can make sense of what he is trying to do (although, as extensively documented by now, there are several of his steps that I do not agree with).

Sorry, Alex, this is the most I can do.

161. Alex Harvey 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. :)

162. Neal J. King says:

Alex Harvey:

What I can tell you, after trying, is that M&M doesn’t help me.

163. 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.

164. Neal J. King says:

BPL,

I was thinking along similar lines; but my real purpose was to emphasize that M&M don’t provide enough help to put me over any threshold to understanding the intent of M (2007).

Alex, you are grasping at straws. It is not your duty to fight to the last quibble for the sacred honor of Miskolczi’s paper: That is his job, and realistically you cannot do it for him.

I have sent him a list of questions (http://landshape.org/stats/wp-content/uploads/2008/07/m_questions-3.pdf) that are:
– focused & specific
– unanswered (to my satisfaction and to that of at least several participants) in any blog discussion or posting of which I’m aware (and I’ve been watching and participating in 4 of them)
– courteous

I cannot believe that anyone who could write the article M (2007) would have any difficulty understanding these questions, or why they should be answered.

Whether he wants to take the trouble to do so is, of course, his business. Even in this mini-world of Miskolczi analysis, I do not consider myself a very important person. But part of science is explaining things, so most scientists find pleasure in explaining ideas to other people – especially their own ideas.

165. Alex Harvey says:

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.”

166. Neal J. King says:

The system has been blocking the URL to my set of questions.

167. Neal J. King says:

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.

168. Neal J. King says:

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?

P.S. There is something funny happening with the posting times: I keep having my postings come AFTER Alex Harvey’s, even when I post earlier.

169. Alex Harvey says:

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? :)

170. Neal J. King says:

Alex Harvey:

– M&M: Actually, my impression is that M&M is not as controversial, because it DOESN’T propose sweeping new principles. That’s why M (2007) IS controversial, and why some of us are demanding transparent reasoning. As stated before, I have little to say about M&M: To me it seems to require much more in the way of field-specific familiarity than the earlier part of M (2007).

– What you meant: Actually, no, I didn’t catch that. Perhaps if you had been a little fuller in acknowledging BPL’s point, I would have: a “Yes, but” is a little too abrupt.

171. 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.

172. For “depth” read “death” of course, and I really shouldn’t have used the same phrase twice. I wish this blog had a preview function.

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

174. Neal J. King says:

BPL:

But is there anything you see wrong in eqn(4) itself? Putting aside the mis-attributed justification for it?

175. 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.

176. Whoops! Dumb careless mistake on my part! ED in K&T97 is 324 Watts/m^2, not 350 — i.e., AA does not equal ED. But my point stands — Miskolczi’s equation is wrong. He’s declaring that two things have to be equal that don’t really have to be equal. Erase “350” from line 4 of that paragraph and replace it with “324” and the equation balances.

177. Neal J. King says:

BPL:

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

178. Alex Harvey says:

BPL:

I’m glad you’ve clarified your view; I’d like to know if Neal agrees. Meanwhile I have a question. You write:

…[Miskolczi] 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.

But on M2007, p. 3:

(d) — The surface heat capacity is equal to zero, the surface emissivity ε_G is equal to one, and the surface radiates as a perfect blackbody.

So it is as you say; he sets surface emissivity to 1 according to his blackbody assumption.

Anyway, you seem to be saying that this is the reason his results differ from KT1997, i.e. because he sets emissivity to ε_G to 1 instead of 0.95. If that is what you’re saying, it can’t be right because KT1997 also set surface emissivity to 1:

KT1997, p. 5:

Emission from the surface is assumed to follow Planck’s function, assuming a surface emissivity of 1.

On the other hand, if that’s not what you’re saying, then the only other argument I find is that since Kiehl’s & Trenberth’s estimates of the fluxes differ from Miskolczi’s & Mlynczak’s, KT must be right & MM must be wrong.

By the way, do you have any response to this statement from Miklos Zagoni:

Kiehl-Trenberth admit that they manipulated the USST-76 atmosphere and the global average H2O amount in there. Even if the USST-76 atmosphere was in radiative balance, their 12 per cent reduction of the H2O column amount (from 1.43 to 1.26) certainly will destroy it. This is equivalent to reducing the CO2 to one eights of its current value. The global average H2O is around 2.5 and not 1.25. It is not valid to consider a globally balanced radiation budget with only half of the most important GHG in it.

179. Alex Harvey says:

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…?

180. Neal,

I just used equation (4) and looked up what the terms meant, and yes, he didn’t define some of them until after he had used them. All I started with was equation (4) and the definitions, from the paper itself, of the five unique terms in the equation. Miskolczi’s equation (4) implies that the sum of solar and non-radiative input to the atmosphere must always be the same as the upward longwave radiation from the atmosphere. I can’t think of any physical mechanism that could make this work. Does the atmosphere somehow know that the increased warmth is from solar absorption, sensible heat and latent heat, and section that off from increased warmth from longwave input? I don’t know if Miskolczi is promoting animism here or not, but he is surely promoting pseudoscience.

181. 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.

182. Alex Harvey says:

BPL:

Kiehl-Trenberth admit that they manipulated the USST-76 atmosphere and the global average H2O amount in there. Even if the USST-76 atmosphere was in radiative balance, their 12 per cent reduction of the H2O column amount (from 1.43 to 1.26) certainly will destroy it. This is equivalent to reducing the CO2 to one eights of its current value. The global average H2O is around 2.5 and not 1.25. It is not valid to consider a globally balanced radiation budget with only half of the most important GHG in it.

He’s saying that if you reduce 1.43 by 12% you end up with approximately half of 2.5. Confusing isn’t it, but it’s true.

So what about Zagoni’s point, how is it that they KT feel so justified in changing the numbers around willy-nilly to get to the result they want. Is this valid?

183. Alex Harvey says:

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.

184. Neal J. King says:

Going back to eqn.(4): In my understanding, BPL doesn’t believe that it is true.

When I first looked at it, I didn’t worry too much about the detailed meaning of the component fluxes, I just looked at Figure 1 and the arrows to see if they matched up.
a) I tossed out K and P as equaling zero, so forget ’em.
b) I separated the short-wave terms on the right-hand side of the figure from the long-wave terms on the left-hand side of the figure.
c) Then I looked at the arrows on the left-hand side.

Now, eqn.(4) says:
A_a = S_u * A = S_u*(!-T) = E_d

The first few steps are just definitions of A_a, A, and T. But the last step is actually saying something: that the long-wave radiation that was emitted by the ground and subsequently absorbed by the atmosphere is balanced by the long-wave radiation that is “bounced” back downward to Earth by the atmosphere (E_d).

So he seems to be assuming that there is no short-wave to long-wave conversion in the atmosphere (otherwise, you can’t separate the two sets of fluxes by frequency and expect any balance).

But actually, that doesn’t make sense now, because the F term is the short-wave that is absorbed in the atmosphere. If it’s absorbed (not reflected, since this is a clear-sky model), it must be converted into long-wave: What else is it supposed to do? But if you allow for SW/LW conversion in the atmosphere, your LW equation has to be different than eqn.(4):
A_a + F = E_u + E_d
because some of the LW flux is sourced from the SW absorption.

Basically, he seems to be trying to say that in local thermodynamic equilibrium (LTE), the give-and-take in the long-wave is balanced. If this were REAL thermodynamic equilibrium, that would be correct: the principle of detailed balance (more or less equivalent to Kirchhoff’s law in this case) says that in thermal equilibrium, two systems should balance their energy exchanges in each “frequency channel”, without depending upon an excess in one channel to make up for a deficiency in another. (My colloquial expression of it.)

But does LTE imply that? For example, take the case of a copper sphere heated internally by a nuclear reactor, suspended in an atmosphere of gas: Overall, the sphere will be radiating in the LW, so there is a net LW flux outward. Nonetheless, we can assume that the gas right at the surface will have a local temperature close or equal to the temperature of the surface of the sphere. Are we entitled to assume that the LW received by the sphere from the gas (overall) is equal to the LW that is absorbed by the gas from the sphere? Actually, I don’t think so: the LW absorbed by the gas also has to source the LW emitted by the gas into space.

This is all a bit confusing, because Miskolczi is making arguments based on total fluxes (throughput after propagation through the entire atmosphere) but he’s breaking them down by processes ( what gets absorbed here, what gets emitted there). The “right way” to deal with a detailed breakdown is to incorporate it into the partial differential equations of the radiation transfer, so that you can be sure you have properly constrained the behavior of your model. Otherwise, there is the danger of taking something into account with some of your equations, but not with the others.

This is not to say that total-flux arguments are inherently wrong. But to do them and understand them properly, you need to be able to convert back down into the point-by-point radiative transfer argument. I cannot speak for Miskolczi, but I cannot do this without my copy of Goody & Yung, to learn how the radiative-transfer problem is normally done, and how these sub-process exchanges work out. (They may not do them explicitly, but I could see if these throughput arguments actually work out in the end. They may not.)

I should be getting my copy when I visit California in September. Until then, I probably won’t have much to say. Unless meditation on the nuclear-reactor heated sphere gives me any additional insight.

185. Neal J. King says:

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.

186. Neal J. King says:

Correction: The equation should be:

B(0)*(1 – exp(X_o) = Integral(0, X_o) (B(x)*exp(-x) dx

187. Alex Harvey says:

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?

188. Neal J. King says:

Alex Harvey:

Probably better terminology would be:
B(f, T(x)): the blackbody spectral density at frequency f as a function of temperature, where the temperature is that at optical depth x.

So what I’m saying is that if the temperature were constant all the way from
x = 0 to x = X_0, the equation (which is equivalent to eqn.(4)) would be valid. But since the local temperature varies from ground-level temperature up to the top of the atmosphere, decreasing all the way, the equation is not true.

189. Neal J. King says:

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.

190. Alex Harvey says:

Neal wrote:

Probably better terminology would be:
B(f, T(x)): the blackbody spectral density at frequency f as a function of temperature, where the temperature is that at optical depth x.

So what I’m saying is that if the temperature were constant all the way from
x = 0 to x = X_0, the equation (which is equivalent to eqn.(4)) would be valid. But since the local temperature varies from ground-level temperature up to the top of the atmosphere, decreasing all the way, the equation is not true.

I believe I understand what you’re saying.

The question I asked is this: suppose for the sake of argument that at an arbitrary optical depth x, the portion of S_G that is absorbed locally at this optical depth is re-emitted downwards in the same amount such that amount absorbed = amount re-emitted downwards. Suppose that all of this radiation is reflected downwards. I don’t care whether these assumptions are valid, I’m just curious.

Now would you agree that if this rule held for all optical depths wherever the LTE approximation is valid, AND if you agree that there is a thermal equilibrium at the surface such that the rule is true at the surface as well, would it not THEN follow as a general rule that AA = ED wherever the LTE approximation holds?

191. Neal J. King says:

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.

192. Alex Harvey says:

Neal writes:

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.

But surely this “attenuation” would apply equally in both directions?

193. Neal J. King says:

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.

194. Neal J. King says:

By the way, here is my revised & updated letter to Miskolczi: http://landshape.org/stats/wp-content/uploads/2008/08/m_questions-4.pdf

I’m not bringing up the issue with eqn.(4) in this letter: It takes too long to explain the background. Until I get a first real response, I prefer to stick with things that are pretty much cut-and-dried.

195. Alex Harvey says:

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.

196. Neal J. King says:

Alex Harvey:

From what I saw way up above, you might be talking more about self-consistency than actual empirical support. But I admit to not following those issues closely, since I have been more interested in what he was able to show logically & mathematically.

If I get a response, you’ll hear about it here first!

197. Neal J. King says:

BPL,

– He responded initially, and said he would get back to me in August.

– Recently, I revised my original letter and sent it to him; but there was no response.

– He just recently showed up at: http://landshape.org/enm/greenhouse-heat-engine/#comment-168893, where I pointed to the revised letter (now posted). Maybe he will respond to this.

199. Ferenc M. Miskolczi says:

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.

200. Neal J. King says:

Ferenc,

In my letter to you, posted at http://landshape.org/stats/wp-content/uploads/2008/08/m_questions-4.pdf, I pointed out that the proper application of the Virial Theorem leads to different results than you have in your article.

I also ask the question: “Even if we grant [KE]/[PE] = 1/2, what are the equations that specifically relate Eu and [KE], [PE] and temperature?”

I also have other questions in that note, but I would like to focus first on these.

(Sorry I’ve been on travel the last few weeks, so I wasn’t able to participate in the discussion above.)

201. Alex Harvey says:

Neal:

Thanks, yes, I have been following the discussion at landshape.org, and I am indeed finding it very interesting.

202. Neal J. King says:

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.

203. Franko says:

Miskolczi to Eli Rabbet: “and then it will be fair to increase the number of your comments on the web”

Inscribed on his internet grave stone, “Rabbit Goulash Stew” ? or ? – Come on Eli, prove some complex virial atmospheric unknown. Become a leader, by example, inspiration, not only for Wabbit ice cube counters.

Magic of the virial can inter-relate, other atmospheric variables, more directly than Miskolczi ?

204. dschibut says:

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?