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
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
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.
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.
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?
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.
Well a lot of the textbook is available in preview online:
http://books.google.com.au/books?id=Ji0vfj4MMH0C&dq=goody+yung+atmospheric+radiation&pg=PP1&ots=7SeRXY4-6l&sig=PQjWjamOhLkjmHhz4wuMfQ_398o&hl=en&sa=X&oi=book_result&resnum=1&ct=result
See esp. p. 3, & pp. 27ff. If you want to look at eq (4) it is necessary to look at MM2004, pp. 209-232 (i.e. to the end of section 3). Miskolczi makes it quite clear that eq (4) was derived in MM2004, yet the people commenting have generally not bothered to read his earlier paper. In fact, it is not necessary to read M2007 at all. Best of all, MM2004 is a lot easier to follow.
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…
Well Zagoni has scanned some of this and added it to his website here: http://hps.elte.hu/zagoni/Kirchhoff.htm
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?
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…
On why Pierrehumbert owes an apology:
In this thread: http://www.realclimate.org/index.php?p=538
# 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]
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. 🙂
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 … “?
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.
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).
Alex Haley,
– I agree that the equation:
OLR = S_G – E_D * E_U
comes from Eq:(3) & Eq.(6), so I don’t have a problem with it (as I don’t see a real issue with the Kirchhof-law question). It must have been too late at night when I checked that question.
– If Nick Stokes wants to buy off on Eq.(21)/(B8), that is his right, but I don’t feel bound by it. I would want to go through more of Goody & Yung to see how these kinds of calculations are usually framed and handled. Unfortunately, probably the most relevant chapter is Chapter 9, which does not seem to be included in anyone’s free preview. (And my copy is thousands of miles away.)
– However, for the sake of discussion, let’s look at the paper from a different angle than the bottom-up approach I’ve taken so far: As Nick pointed out, Eq.(B8) is a stepping stone to Eq.(B11). What I get from this is that he is saying that his Eq.(21)/(B8) formula for radiative loss is maximized when (B11) holds. And then I get the impression that he justifies the actual attainment of the maximum by invocation of some energy-minimum principle. But what is the basis for this principle? As far as I can tell, he says it seems give guidance to calculations that agree with other planetary results, which have reached some sort of steady-state. So on that basis, he wants to conclude that this same principle will apply in the present situation, that it will force the value of the optical depth to be 1.87.
I have doubts about this overall argument:
First, I don’t trust the minimum-energy principle he invokes: I don’t see any reason for it, and I also consider that a minimum is always defined in the context of constraints. One of these constraints is going to be the amount of CO2 in the system. It is not at all clear to me that the climate system can be supposed to be smart enough to generate clouds to make up for the excessive CO2: How does it explore that region of the parameter space in search of a minimum?
Maybe the correct interpretation of the minimum principle is that the CO2 will eventually be flushed out of the system, through ocean absorption and burial.
Maybe the correct interpretation of the minimum principle is that the IPCC is fated to take over the world, and impose a ban on fossil fuels.
I’m being sarcastic, but my point is that there is a gap in logic in saying:
– The fastest way to cool the Earth is to set Optical_Depth = 1.87
=> The minimum principle mandates the fastest cooling
=> OD will find a way to = 1.87, come hell or high water
=> There is no enhanced greenhouse effect.
To me, the gap comes at the point between identifying the possibility of a minimum principle and believing that it will actually be achieved. The Earth is not obligated to support one’s favorite minimum principle.
And by the way, is the optical depth on Mars and Venus equal to 1.87 ? If not, why not?
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).
Oh — and yes the earth is obligated to obey the laws of thermodynamics.
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?
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.
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.
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.
By the way I believe the following post by Ken Gregory at CA BB answered one of your objections: http://www.climateaudit.org/phpBB3/viewtopic.php?f=4&t=161&p=7796#p7796
Alex Harvey:
– First, the Earth-Sun system is not in equilibrium either: It’s in steady-state (or rather, it WAS in steady-state prior to the radiative imbalance caused by the enhanced greenhouse effect).
– Secondly, the point indeed is that one can imagine all sorts of ways in which a process can happen faster or slower: and the system is simply not obligated to take any of them. But it seems to be key to M’s derivation that the Earth’s atmosphere take the fastest one he has in mind, even though doing so involves some kind of alteration of the water-vapor concentration or cloud cover of the atmosphere – elements that heretofore have not entered the discussion. They appear as a deus ex machina to achieve his magical result of 1.87. To get to his result, it is not sufficient that there be a lowest-energy configuration: the system must “rush” to it. So if you take your own objection seriously, your beef is with M, not with me.
– With all of the context about Mars that you added, I still don’t see anything that explains why the equations he uses to “prove” the 1.87 for Earth don’t apply to Mars equally. To me, that suggests either:
a) He’s not mentioning something essential to his derivation for the case of Earth; or else
b) He’s wrong about the Earth as well.
Alex Harvey:
Ken Gregory says:
“I think you have misread the paper. OLR/Su = 2/3 is not the general solution. It is the solution for the Earth type atmosphere.
The general solution is OLR/Su = (3 + 2Ta )/5
In the Earth’s case, Ta = 1/6, so the solution is OLR/Su = (3 + 2/6)/5 = (10/3)/5 = 2/3. ie, Su = 3/2 OLR”
Unfortunately, the bottom of page 7 says:
“For the Earth obviously the T_A ~ 0 condition apply…”
So if you believe Gregory, you disbelieve Miskolczi, and vice versa.
So Ken Gregory has addressed my objection, but hardly answered it. Indeed, with allies like Gregory, Miskolczi does not need enemies…
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…