Table of contents for Miskolczi
Next is this series is Kirchhoff law. Kirchhoff is the third principle in Miskolczi’s atmospheric greenhouse theory, after energy conservation (part one) and the virial theorem (part two).
Miskolczi attributes Kirchhoff’s law (KL) to the significant findings of the paper. On page 6, two equations that are the direct consequence of KL and “may fundamentally change the general concept of greenhouse theories”. Elsewhere M states the validity of KL “is not trivial” and “we give a simple theoretical proof of the KL for atmospheres in radiative equilibrium”. So KL is important, and I wanted to understand that and flesh out the proof he refers to.
Firsly, KL is a law concerning thermal equilibrium, not to be confused with radiative equilibrium. Here, it concerns not only temperature but also black body radiation due to the temperature of bodies. Wikipedia states in Kirchhoff law the emissivity of a body (or surface) equals its absorptivity as at thermal equilibrium. A poor reflector is a good emitter, and a good reflector is a poor emitter. KL is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings: they lose little heat by radiation.
Miskolczi relates Kirchhoff law to the equality of IR absorbance of the atmosphere Aa (from the surface IR up Su) and the IR emission from the atmosphere down Ed. So the side of the atmosphere facing the earth acts like a body with equal absorptivity and emissivity of IR radiation. This formulation excludes the absorptions of SW by the atmosphere. Miskolczi also treats As=Ed as equivalent to surface/atmosphere thermal equilibrium.
Now the absorbed atmospheric flux Aa is equal to the surface IR Su minus the transmitted part Ta or Su(1-Ta), so I would assume that surface/atmosphere thermal equilibrium follows from Aa=Ed, though I am not going to pursue that. As evidence of Kirchhoff law Miskolczi presents the following linear regression that is the absorbed part of IR in the atmosphere Su(1-Ta) equals the IR down to the surface Ed.
Fig. Empirical evidence of the Kirchhoff law relationship in atmospheres provided by Miskolczi.
The first figure shows the relevant quantities at each point in the atmospheric profile: B the blackbody source function, Ed the IR down, Ta the flux transmittance (surface up Su transmission not absorbed in the atmosphere), and red dots are B(1-Ta). Evidence Kirchhoff law holds is shown by the correspondence of Ed with B(1-Ta). The second image is the linear regression of Su against Ed/(1-Ta) for selected radiosonde measurements.
Because the IRs are related, the temperatures of the atmosphere at the surface and the temperature of the ground must be closely related. Keep in mind that reasonable as this sounds it is not the basis of the current radiative models. Elsewhere pliny objects there is no reason to expect Aa=Ed. Nevertheless, this is the result that obtains from the proof I show later, which is why I suppose Miskolczi flags it as “non-trivial”.
Perhaps a flow-on effect of Aa!=Ed in current radiative models is a very large temperature discontinuity at the ground. Below is Fig 5 from Miskolczi’s paper.
His Fig 5 with original caption compares the new semi-transparent model, with a widely used reference atmosphere USST-76. Notice first the semi-transparent model almost fits exactly the observed lapse rate in the atmosphere. The USST-76 reference is a straight line approximation only. Note however the black dots on the USST-76 reference showing the temperature discontinuity at the ground. It is a whopping 125W/m2 between the air and ground emission! I find this incredible! How it is derived and gets to be so large is subject of another post.
Elsewhere M explains how the discontinuity comes about through the semi-infinite atmosphere assumption. Calculations of the temperature profile as a linear function of the absorption path length, without reference to the surface temperature are referred to as the Schwarzschild-Milne approximation (M’s eqn 5). Warming of the atmosphere occurs in this model via path length increases due to increased GHG. Where the atmosphere is optically thin, Miskolczi claims the equation is invalid as it does not contain a lower boundary condition (the surface). He cites a number of papers to 2003 using results from the Schwartzchild-Milne approximation to derive surface and air temperatures with two (disconnected) equations.
t4A=t4E(1+τA)/2
t4G=t4E(2+τA)/2
At optical depth τ of 1.84, then tA/tG is 0.93 which is a temperature discontinuity at the surface of about 25 degrees C. A paper by Weaver and Ramanathan in 1995 suggest the Schwarzchild model was discarded 3 decades ago due to deficiencies, and replaced with “more sophisticated computer models”. It also suggests that addition of a spectral window, and unlinking optical depth and atmospheric pressure improves the Schwartzchild model. These are both features inherent in the Miskolczi model.
The temperature discontinuity at the surface are huge differences, and if due to a misspecified model, I can see the source of Miskolczi’s concerns. GCMs containing these models would need to be tuned to even approximate the correct radiation budget, and would demonstrate quite different behavior than the real atmosphere with even small deltas. If there is a basis for auditing the assumptions of the models, it is here. It is hard to believe they have been operating with such a large misspecification. However, it may explain the large systematic warming bias reported in almost all GCMs examined in Douglass et al. 2008.
Proof of Kirchhoff holding for atmosphere
We need to get to Aa=Ed to obtain Kirchhoff law in the atmosphere.
In section 4.2 M derives (21) a general solution temperature profiles for both the semi-infinite and semi-transparent case assuming radiative balance in a bounded atmosphere. When the optical path length is infinite (21) reduces to the semi-infinite case.
His eqn (28) Su=OLR/f derived from (21) for high emissivity and opaque areas is superficially similar to Su=2OLR/3 (8) derived earlier assuming energy balance and Kirchhoff. But Su=2OLR/3 is an overall energy balance requirement (not IR). In (28) f is a function of the optical path length τ:
f(τ)=2/(1 + τ + exp(-τ))
This function partitions the surface upward radiation into OLR by optical depth. For example, at the top of atmosphere, τ=0 and f(τ)=1. These two are not necessarily equal.
Miskolczi splits up outgoing LW radiation OLR to get an expression for Eu using two processes:
- Su * f which is the part of surface radiation Su converted from solar SW radiation Fo to OLR
- Su * Ta which is the transmitted part of the surface radiation
Then:
Su * f=Su * Ta+Eu as (OLR=Su* Ta + Eu)
Eu=Su * f - Su * Ta
Miskolczi argues that the difference above is the contribution to the OLR from energy processes not related to LW absorption, ie. from absorption of SW in the atmosphere F and from convection and other non-radiatiative surface processes K.
Therefore Eu = F + K.
He then substitutes the above into the surface balance equation.
Fo + Ed - F - K - Aa - St = 0 OK
St + Eu + Ed - F - K - Aa - St = 0 (as Fo = St + Eu)
St + F + K + Ed - F - K - Aa - St = 0 (as Eu = F + K)
and obtains Ed=Aa by cancellation.
The IR emitted down by the atmosphere equals the IR absorbed and Kirchoff law is obtained from radiative balance and energy balance at the surface. In real surfaces due to emissivity ε
t4
and given ε=0.95 and Ta=0.17 there will be a temperature discontinuity of 0.9% or 2.5deg.
This is much less than 25C obtained in the Schwartzchild equations and can be balanced by energy transport of non-radiative origin.
There is a view that uncertainty of future climate is either inherent in the system or or can be eliminated with more petaflops in computers. Miskolczi’s results argue that problems have been introduced due to an incorrent model of climate. Based on the types of errors reported by GCMS, especially those shown in Douglass et al 2008, I still find this to be a plausible explanation. In fact, the main alarmist claims:
- increasing greenhouse effect with larger τ,
- runaway greenhouse effects t unbounded with increasing τ, and
- positive feedback
have been shown by Miskolczi to result from misspecification of the atmospheric model. It is not the first time that errors propagated through the literature by mindless repetition of past claims. I will go into this further in the next post on radiative equilibrium.
20 responses so far ↓
David, I’m afraid this leaves me none the wiser:
“Miskolczi claims the condition for the Kirchhoff law to be true is that the IR absorbance of the atmosphere Aa (from the surface IR up Su) equals the IR emission from the atmosphere down Ed.”. No, he claims this as a consequence, not a condition. And apparently I didn’t manage to communicate the complete wrongness of it. You’ve correctly stated that Kirchhoff’s Law links emissivity to absorptivity. These are coefficients, material properties. It doesn’t, and can’t link an absorbance to an emittance. M’s statement is like saying that because silicon and boron have the same density, so any two lumps of Si and B will have the same mass. They may, but not for this reason.
He deduces two equations from these wrong statements and says (sec 3) “The physical interpretations of these two equations may fundamentally change the general concept of greenhouse theories.” As you said earlier, people often stop reading at that stage, and I think that is a reasonable response.
“Miskolczi also treats As=Ed as equivalent to surface/atmosphere thermal equilibrium.” I see no basis for this. He has a separate thermal balance equation (2), which is different and correct. He isn’t that clear on what he means by thermal equilibrium, but at least sometimes it is just continuity of temperature, which is a separate (and reasonable) assumption ( (h) in his list).
The temperature discontinuity stuff puzzled me. Fig 5 is a mess, with four axis labels, and I can’t make any sense of it, and your description doesn’t help. USST-76 isn’t a computer model, it is the US Standard Atmosphere, first defined to summarise experimental observations in 1958. It isn’t meant as a predictor of anything.
I couldn’t make sense of M’s proof, and I can’t of your version either. Let’s start at the opening equation Su * f=Su * Ta+Eu. As far as I can see, Su * Ta+Eu is the IR from the top of the atmosphere, and I guess Su * f is the IR source from sunlight. Why are they equal?
No, he claims this as a consequence, not a condition.
Yes, at the beginning claims Aa=Ed is a consequence, but then at the end claims via Aa=Ed that Kirchhoff law holds in this case (I shouldn’t say shows KL to be true).
Now you seem to be saying that even if Aa!=Ed (which you questioned in your previous comment and is what I was responding to) it is not because of Kirchhoff law. Due to KL in an object at thermal equilibrium, a=e and also absorbance equals emittance does it not, or it would not be at thermal equilibrium? Perhaps Kirchhoff law is not required at all. But that doesn’t affect Aa=Ed which is deduced from radiative equilibrium.
I don’t see the problem with Fig 5. Its just the atmospheric temperature profile and the axes show the linear relationship of the quantities. OK, its not a computer model, it is a model though, but I will clarify the wording, thanks.
The equation Su * f=Su * Ta+Eu is based on Su=OLR/f as noted, and this eqn (28) Su=OLR/f is derived from (21) for high emissivity and opaque areas from the generalization of the classical radiative equations in the atmosphere. Not being cute, but they are equal because they follow from the assumption via the equations, 18-27 and further details in Appendix B. Not helpful I know, but handwaving only goes so far. I will probably summarize this part next.
It seems to me that the partion into Eu and Ed is too neat, that Ed is the atmospheric LW absorption, and Eu is atmospheric SW and other sources (convection etc). But that is what falls out.
Thanks pliny for your comments. It is great that someone wants to sink their teeth into it.
Well, David, we really need the algebra leading to the “proof” of KL set out clearly, and we don’t have that yet. It’s surprising, because it is linear, not many variables, and only a few physical principles to invoke. But anyway, counting those principles would help.
He has 3 entities - Earth, Atmosphere and space. You can write energy conservation equations for two of them - his eqs 1 and 2. What else? There is no separate radiative equilibrium, unless you use Kirchhoff properly, which he doesn’t do (no mention of gas emissivity). There’s the viirial theorem, which noone can figure out. But that’s about it. So where does this deductuion (A=Ed) come from?
My suspicion is that eq 28 is a reduced version of the atmosphere balance equation, and he has added it into the set of equations, but kept the original one as well. And the difference between the two is, surprise, A-Ed. But of course you can’t do that. Because of the murkiness of the description, I can’t be sure of this.
Nick Stokes
we really need the algebra leading to the “proof” of KL set out clearly
The post above has fSu=OLR to Eu=Aa. The algebra up to fSu=OLR is going to be my next assingment. Its getting harder to explain this in a simple way, so its going to take longer. But it is the core of it, and also where the difference between the infinite and semi-transparent cases are most clear, so important from the AGW audit POV.
I am hoping M can send me something on the virial application, and I can put it in the previous post, and people can understand it so we can get it off the table.
Greetings Niche Modelers. I dropped by here because I noticed that you were examining Miskolczi’s paper. I too was intrigued by it upon a first superficial reading, enough to look into it further. For what they’re worth, here are my comments.
1. Miskolczi’s eqn 7 (your eqn 2) is not a correct energy conservation equation for this model. His eqns 1 and 2 are the proper energy conservation eqns. (One should be suspicious of 3 independent energy eqns for a two-component model, if no further constraints or assumptions have been introduced.)
2. Kirchhoff law is incorrectly applied, as described by pliny and Nick Stokes on these threads.
3. I cannot make heads or tails of his application of the virial theorem, which, in any case, should not be required to solve the system.
4. His assertion that feedbacks drive the atmosphere to an optical depth that represents the most efficient cooling is flawed in multiple ways. First, note that substitution of his solution for Bg (from eqn. B-11) into the expression for Bo (eqn. 20), results in a simple monotonic function of TauA: Bo = [1+ exp(-TauA) ]. So why is there a maximum in the plot of Bo in figure 3? One can get a clue from the derivative in eqns B-9 and B-10 where he holds Bg constant (independent of TauA), in clear contradiction to the result in B-11. [And why the hocus-pocus of seeking an extreme in Bo, when simple substitution of B(TauA) = Bg would give the same result?] Anyway, the only way I can get something like Fig 3 is to hold Bg constant, despite B-11. This is all nonesense.
Does his solution mean anything? I would have to go dig out a textbook, but I suspect that the solution eqn 13 has already incorporated the Eddington closure assumption in the constant (3/4*pi), and that it is contradictory to find Bo to be anything but the standard value set by the outer boundary condition. His assertion that “..solving Eq. (14) at H = H(TauA) will be equivalent to solving the same equation at H = H(0)” is true only in a general formal way, but not for determining the real atmospheric parameters.
I should say that I did contact Dr. Miskolczi on point 4 above, and he graciously replied, but not with a satisfactory answer to my questions.
I suspect that Goody and Yung, greenhouse gas theory, etc. will survive Miskolczi 1997.
Hi Pat,
It is great to have informed readers to bounce this paper against. I will look into your comment 4 this week when I do the next post. For the moment:
1. I scratched my head alot about this equation. You say it is not a correct energy balance equation. My understanding is that it represents the equality of energy flow in three ‘boxes’, the solar box, the greenhouse box, and the IR out box. Can you please give an example of how this equation is not correct?
2. Miskolczi has provided a new figure of the relevant quantities throughout the profile to help explain the Kirchhoff relationship. Does this help?
3. I’m not telling you anything but the virial theorem is well established for gaseous bodies under gravity. I just hadn’t heard of it, but that’s because I hadn’t studied that area. You claim it is not necessary. Miskolczi is not necessarily demonstrating the minimal constraints to solve the system, but using the constraints that he thinks actually apply to planetary atmospheres. One way the virial theorem is necessary is the generalization of the whole theory to Mars, where he claims he uses that the virial doesn’t hold. Isn’t that necessary?
I should say that I did contact Dr. Miskolczi on point 4 above, and he graciously replied, but not with a satisfactory answer to my questions.
Perhaps you would like to post the reply so we can review it too. You might have guessed we try to deal in evidence not innuendo around here.
Regards and thanks for visiting. Appreciate you making time to respond.
7 Niche Modeling » Greenhouse Effect Physics // May 15, 2008 at 12:19 pm
[...] admin @ Kirchhoff Law (Miskolczi Part 3) [...]
David,
I couldn’t make sense of M’s eq (7) either. And I can’t make sense of your response to Pat Cassen. What are these boxes? There are only two closed systems to which you can apply energy conservation - the Earth and the atmosphere. He’s done them in (1) and (2). You can’t get another conservation of energy equation. And it seems to me he’s not even adding the energy gains; he’s subtracting them.
I have to say I find your response to some of these issues a bit odd. It isn’t a situation where M can write down an equation, and then you can ask the world to show why it’s wrong, even if we don’t understand it. Someone has to show the equation is right. It should have been M.
Hi Nick,
Its really a matter of the blog moderation policy I choose. There are plenty of forums where people can express their opinion, but I try to encourage people here to evidence why they think what they do. Pat’s point 4 was just fine I think, and I tried to point out the blog policy about the others. I try to make every post contain evidence too, not be another opinion piece.
You say, Someone has to show the equation is right. It should have been M. This is not a journal, and I am not reviewing a paper for publication. So far, I have been working on the basis that there is a derivation, as so far there has been. Granted the derivations I have looked at have suited my meager maths ability.
And no-one has shown them to be wrong. If Fermat writes “The equation xn+yn = zn has no solution for non-zero integers x, y, and z if n is an integer greater than 2.” in the margin of a book, does that mean he is wrong, or he has to show it is right?
Well, David, Pat and I have said why we think eq (7) is wrong. There are only two closed systems, and you can’t get three energy conservation equations out of them. You’ve said there are three “boxes”, but could you please explain what they are?
Pat, This is the best picture I have worked out for what I think he means.
Three boxes: Fo = G = OLR. Energy in, greenhouse, energy out.
G can be seen as a two layered box, perspex on metal if you like,
but it supposed to represent the atmosphere and the surface.
Each layer is being heated by the respective net fluxes viz,
Su-Fo
Fo = —– = OLR
Ed-Eu
Therefore
Fo = Su-Fo+Ed-Eu = OLR
Do you think this makes any sense?
David –
1. Equation 1 expresses the balance of energy in the atmosphere. Equation 2 expresses the balance of energy at the surface. Equation 7 expresses the balance of energy of…what? I don’t know. (Just saw your latest post; I’m afraid it doesn’t help.)
Note that the relation Su = (3/2)*OLR = (3/2)*Fo is a direct consequence of eqns 1, 2 and 7. [Miskolczi’s (incorrect) Kirchoff’s Law is not required]. Miskolczi says of this relation “This equation might make the impression that G does not depend on the atmospheric absorption, which is generally not true.” Well yes indeed, that’s exactly what this equation says, so does Miskolczi believe it or not? If he does, bingo, problem solved: tell me Fo and I have the ground temperature, independent of atmospheric composition and everything else. If he doesn’t believe it, why write it down?
2. I am not knowledgable about the sources of this data, and so have no basis for making a judgement about the figure.
3. The atmospheric structure problem is usually solved by direct application of the energy equations (radiative, etc.), equation of state, the hydrostatic equation, and supplementary relations like the lapse rates. (I’m sure the Goody and Yung textbook gives full details.) I cannot figure out how Miskolczi is applying the virial theorem, or why it is necessary for any planetary atmosphere.
I would request permission of Miskolczi to post our correspondence had it been enlightening, but it wasn’t. No innuendo here, just a statement of fact. Let it suffice that my last email to him, which remains unanswered, stated:
“But I am still at a loss to understand how tauA is constrained by a local maximum in Bo, when substitution of eqn. (B-11) into (B-20) yields a monotonic function for Bo(tauA):
pi*Bo = (H/2)*[ (2/A*f) - tauA - (2*Ta/A*f) ] = (H/2)*[1+ exp(-tauA) ],
using the definitions of f, A and Ta.”
I think that Nick Stokes and others have given you good feedback on this paper, and I hope my comments have also been useful. At this point, I’ve pretty much lost interest in it. I’m afraid that you will not find anything that disturbs established atmospheric science here.
Thanks for your courteous reception.
Pat, Thanks for elaborating, and thanks for visiting.
Ferenc provided the following exchange between Pat Cassen and himself referred to by Pat above. This a good and civil academic discussion and is a good example of the need to be patient, as it can take a long time and a lot of interaction to properly resolve these issues.
Pat:
Dear Dr. Miscolczi: I have been reading your very interesting
paper entitled “Greenhouse effect in semi-transparent planetary
atmospheres”, which I downloaded from the web. I hope that you
can clarify a couple of points for me. If your solution for
B_G (from eqn. B-11) is substituted into the expression for
B_o (eqn. 20), one obtains a simple monotonic function of
Tau_A: [1+ exp(-Tau_A) ]. So precisely what function is being
plotted in Figure 3? Also, in taking the derivative of B_o
(in eqn. B-9), it appears that you have regarded
B_G as constant, independent of Tau_A. But clearly
this condition is contradicted by the solution for B_G
given by B-11. Perhaps I am misinterpreting something basic.
I would greatly appreciate your clarification of these points.
Thanks very much in advance. With best regards,
Me:
Dear Pat Cassen, In Fig. 3 Eq. (20) is plotted with different H
(OLR) and Bg values as the function of tauA. Eq. (20)
is identical with Eq. (B7) which appears in the outer bracket
of Eq. (B9). We obtained Eq. (28) assuming the thermal equilibrium
at the ground. With Eq. (11) I wanted to show, that the same
equation may be obtained from Eqs. (20) or (B7) by maximizing
them for Bo. Bg is a constant, representing the lower boundary
condition and Eq. (B11) tells that this boundary condition should
satisfy the same equation, which was obtained by assuming the
thermal equilibrium at the ground, Eq. (28).
Is this OK?
best regards, Ferenc
Pat:
Dear Dr. Miskolczi: Thanks very much for your prompt and
considerate response. I understand your intent to show
that eqns. (20) and (21) may be found in two different ways.
However I am still having a problem with Fig. 3,
and the idea that maximizing Bo is a proper procedure.
Let me explain further. Since you are interested in the
situation in which the ground temperature and air temperature
are equal, one might simply set B(tauA) = Bg in eqn. (21).
(Assuming epsilonG = 1, of course.) This substitution yields
your eqn. (B-11) for Bg directly. Fine. But putting this
result for Bg into eqn. (20) for Bo
yields Bo = (constant)*[1 + exp(-tuaA)],
a monotonic function of tauA, in contrast to the
function shown in Fig. 3. Now I can reproduce your Fig. 3
only by holding Bg constant, independent of tauA
(while varying f, Ta, and A). Furthermore, in seeking
a maximum of Bo (eqn. B-9), it appears that you have also
held Bg constant. It seems to me that this cannot be
justified, in view of (B-11), which shows Bg = Bg(tauA).
Thanks once again for your attention and patience.
Best regards, Pat Cassen
Me:
Dear Patrick, Here is again my concept: Eq. (28) was obtained
by assuming that ta=tg. In this case (ignoring the emissivity
dependence) Su=olr/f. Now, if you put the question in a way
that: what is the optimum Bo for a given OLR and Bg, you will
end up with the Sg=OLR/f relationship, and this gives you the
Su=Sg equation. In Fig 3. for real (average) atmospheres
apparently the tauA will pick the maximum Bo. Eq. B11 is only
showing that Sg=pi*Bg depends on the transfer function and
olr the same way as Su does (in Eq. 28). Keep also in mind,
that Bg and tauA are a boundary condition parameters…
You may not interpret Eq. B11 as a Bg(tauA) function…..
The important relationship here is between the Bg and olr….?
Best regards, Ferenc
Pat:
Dear Dr. Miskolczi: This seems to be the crux of my problem:
‘ Bg and tauA are a boundary condition parameters…
You may not interpret Eq. B11 as a Bg(tauA) function…..
The important relationship here is between the Bg and olr….?’
Overall conservation of energy demands that OLR = Fo, a
known quantity (if the atmosphere is in equilibrium). So
it would seem that I am not free to specify tauA and Bg
independently, as boundary condition parameters. That is,
it seems that I must interpret Eq. B11 as a Bg(tauA) function…?
Best regards, and thanks once again for your attention and patience!
Me:
Dear Patrick, Yes, if you put it this way, that is right. The OLR=Fo
condition and the Su=Sa condition constrains the tauA.
The whole paper is about this… There is only one global
average tauA ( ~1.87) which can satisfy both constraints.
And according to the observations, Earth has this tauA.
Ferenc
—-
15 Niche Modeling » Greenhouse Heat Engine // May 20, 2008 at 9:25 pm
[...] admin @ Kirchhoff Law (Miskolczi Part 3) [...]
16 Niche Modeling » Radiative Equilibrium (Miskolczi Part 4) // May 24, 2008 at 11:11 pm
[...] The last installment of my review of Miskolczi’s theory of (almost) constant greenhouse effect examines his claim that attribution of global warming to greenhouse gases is due to an error in the equations. This part deals exclusively with equations of radiative equilibrium in the atmosphere. The other three parts dealt with various aspects of the overall energetic constraints on the atmospheric system: energy conservation (part one), the virial theorem (part two), and Kirchhoff’s law (part three). [...]
17 Niche Modeling » Models of Greenhouse Effect // May 26, 2008 at 7:03 am
[...] F — Solar flux in Su — Surface flux up Eu — Atmospheric flux up Ed — Atmospheric flux down They can be represented as equations of linear algebra: 1.1 F = Su - F + Ed - Eu — overall energy balance equation 1.2 0 = F - Eu — energy balance at top of atmosphere The following are different three constraints: 2.1 0 = Ed - Eu — the steel greenhouse, top of atmosphere constraint. 2.2 0 = Su - Ed — the Kirchhoff’s law, IR radiative equilibrium between surface and atmosphere 2.3 0 = Su - F — the third option, for completeness. By substituting each of 2.1, 2.2 and 2.3 into 1.1 and 1.2 we get three different solutions for surface temperature with three decreasing levels of greenhouse effects. 3.1 Su=2F 3.2 Su=3F/2 3.3 Su=F The three models of greenhouse effect are shown in the figure below, ordered by increasing surface temperature. Below the diagrams are representation of the modeled and equilibrium lapse rates, the increase in air temperature with altitude for each of the models. Here are a few points of interest that argue that the middle semi-transparent model is the correct model: [...]
I have recently been looking at Miskolczi’s paper, and the same points that bothered Pat Cassen bothered me. Specifically:
a) One of the essential new insights that Miskolczi wants to bring into the discussion is the application of the virial theorem. However, his actual discussion of it is very short and cryptic. In particular, he relates the upward flux from the atmosphere to the atmospheric kinetic energy, and the surface upward flux to the atmospheric potential energy. What does a flux have to do with an energy?
b) I am not even sure that it makes sense to apply the virial theorem: This is not a body of gas held together by gravitation, but a gas of molecules bound to a huge solid body by gravitation, essentially ignoring each other for gravitational purposes. If the temperature were to drop to near-zero Kelvin, the kinetic energy of the atmosphere would drop to near-zero, but the gravitational potential energy would not change much: the molecules would be sitting on the ground, a few kilometers lower than before, but still thousands of kilometers from the center of the Earth; so if the virial theorem were true earlier, it could not be true now (at near-zero). So what has changed to make it inapplicable? My answer is that it applied neither before nor afterwards.
c) Equation (7): You have provided an attempt to explain this, and Cassen and others have found it unconvincing. So do I, and for the following reason: Looking at M’s original figure 1, all of the fluxes are defined and located. On this basis, you can use conservation of energy to look at what is crossing a border, or what is happening (net) with respect to a box. Based on this, the equations (1), (2) and (3) can easily be derived and understood. Equation (7) cannot be. M’s explanation above (7) is simply an assertion, without any clear basis in either figure 1 or in equations (5) and (6). I don’t think this is legitimate: If it were really based on CoE, it should be evident from figure 1.
d) Equation (8): As a consequence of (7), M derives the relation S_u = (3/2)OLR. However, as a universal relationship, this seems highly suspicious. Let’s take the special case that the atmosphere is totally transparent to all radiation. Then, if we look at figure 1, we would set all the arrows that terminate in/from the atmosphere to zero. When we do that, we find that OLR = S_u = F_0: the radiation comes in, is absorbed only by the ground, and is emitted only to space. So S_u = (1)OLR, not (3/2)OLR. So how did the firm factor of (3/2) disappear? Why doesn’t this general result apply in the trivial case?
For these reasons, I find Miskolczi’s paper cryptic at best; and I’m inclined not to give it the benefit of the doubt. Probably point d) is the most critical, because I believe it is from this point that M is deriving a constraint on the greenhouse effect. I find the derivation of this point unconvincing at best, and the result itself untrue.
Hi. I am not unsympathetic with your view. Kept in perspective, it is a theoretical paper with some basic validation. Level 3-4 in terms of evidence, with some interesting ideas. As such, that puts it on the same level of evidence as GCMs. More testing is needed to improve the quality of evidence.
On point d, the example you give is when no greenhouse warming is in effect. The relation is supposed to cover the greenhouse warming configuration of atmospheres.
Yes, that is what it is supposed to cover. But where does the attenuation of the IR-atmosphere interaction lead to a breakdown of the fundamental reasoning? My argument is that, if the claim is correct, it should also apply to the trivial case, because a continuous modification of the parameters of the model should not lead to a discontinuous jump (from 3/2 to 1) without some rupture in reasoning.
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