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
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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.
Neal writes:
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.
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.
And for “Kitchhoff” read “Kirchhoff.” Never post early in the morning…
BPL:
But is there anything you see wrong in eqn(4) itself? Putting aside the mis-attributed justification for it?
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.
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.
BPL:
Are you getting all that from his equations BEFORE (4) or his equations AFTER (4)?
BPL:
I’m glad you’ve clarified your view; I’d like to know if Neal agrees. Meanwhile I have a question. You write:
But on M2007, p. 3:
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:
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:
Just in case anyone thinks Zagoni is making this up:
KT1997, p. 4:
Sounds like a bit of a strange thing to do…?
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.
I note, with interest, that Zagoni defines a 12% reduction in water vapor as cutting the amount of water vapor in half. The court finds itself unable to follow the alleged reasoning.
BPL:
Let me help you out here.
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?
BPL:
Alright, I am rather frustrated. You wrote:
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.
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.
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.
Correction: The equation should be:
B(0)*(1 – exp(–X_o) = Integral(0, X_o) (B(x)*exp(-x) dx
Neal:
You write:
I think you are saying that the equation would be true for the case x=0 but not for all x; is that correct?
If so, let’s suppose for the sake of argument that for an arbitrary 0 < x < 60km (i.e. wherever the LTE approximation is valid), the portion of S_G that is absorbed locally at altitude x, call it AA_x, is re-emitted downward in the amount ED_x? Let’s also suppose for the sake of argument that AA_x = ED_x. Would you agree that if AA_x = ED_x is true for any altitude 0 < x < 60km, and if AA = ED is true at the surface (for x=0), it follows that AA = ED would be true for all 0 < x < 60km?
Alex Harvey:
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.
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.
Neal wrote:
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?
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.
Neal writes:
But surely this “attenuation” would apply equally in both directions?
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.
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.