Table of contents for Miskolczi
- The Virial Theorem (Miskolczi Part 2)
- Kirchhoff Law (Miskolczi Part 3)
- Radiative Equilibrium (Miskolczi Part 4)
- Models of Greenhouse Effect
- Greenhouse Effect Physics
- Greenhouse Heat Engine
The first post in this series showed a theoretical proof that ‘runaway’ greenhouse effect is not possible, based on Miskolczi’s derivation of a constant (and maximum) greenhouse effect from energy conservation laws in a cloudy atmosphere. The virial theorem solves the semi-transparent (non-cloudy) case, where a fraction of the longwave radiation is transmitted directly from the surface to space, without absorption by the atmosphere.
The strategy we are using in this modeling process is to add an additional constraint (after energy conservation) in order to find the Eu term, the radiation emitted up from Earth’s absorbing atmosphere. Before, Eu was not defined and could have been zero, (in the case of a planet with no greenhouse effect). The virial theorem (and conservation of energy) allows the relationships between all the major radiation terms in a greenhouse system to be derived from first principles.
The virial theorem is a very general theorem used in cosmology (see Wikipedia entry) relating kinetic energy (KE) to potential energy (PE) in bound systems. A simple physical example is a small object orbiting around a larger object, bound by a force (or even an elastic string). The virial theorem states the KE (in the angular velocity) is half the PE (in the distance from the object):
PE = 2KE
Miskolczi relates without derivation the KE with the Eu, the longwave radiation emitted upward from the atmosphere, on the condition of hydrostatic equilibrium. The following was posted at the ClimateAudit forum.
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It’s actually introduced on page 6
Regarding the origin,is more closely related to the total internal kinetic energy of the atmosphere, which – according to the virial theorem – in hydrostatic equilibrium balances the total gravitational potential energy.
Anyone have a problem with this? For the moment I’ll assume not. This balancing act is mediated by the virial theorem which may be generally expressed as where
is the average kinetic energy (relation to temperature is well known) and
is the total potential energy, so 2KE = PE. He takes the internal kinetic energy to be represented by
(Is this valid? It is certainly related) now the potential energy I am thinking derives from the absorbed energy that is converted to potential energy as the air rises until hydrostatic balance is attained. The source of this energy is
(IMO) but he takes it as being
I’m not sure this is a fair thing since I would expect
. Hence taking his representation of the internal kinetic energy and what I think is his original source of the potential energy we get
.
At least we do have an idea where it comes from whether or not it’s right or valid I’m not yet ready to judge.
I hope this helps.
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The following is an example I thought of that has the flavor of the virial theorem in atmospheric absorption processes (but may not be relevant at all). Imagine an old-time dance hall where only couples of opposite sex can dance together (we are not in San Francisco now) and there are an equal number of males and females. There must be an equal number so that there is the ‘potential’ for all couples to be dancing simultaneously. Every few bars of the music, couples separate, turn to the nearest person, and if they are of the opposite sex, they dance. How many couples are dancing at any time?
Clearly, in a well mixed room (at hydrostatic equilibrium) as there is a 0.5 chance of a person encountering another of the opposite sex, half of the ‘potential’ couples will be dancing at any time. The ‘potential’ couples represent the PE, the actual couples dancing represents the KE. In the atmospheric case, photon-molecule interactions are the KE, and PE=2KE.
Back to the atmosphere, the potential energy is the longwave radiation up from the surface (Su) and the kinetic energy is the longwave radiation emitted from the atmosphere (Eu) (see figure). By virality, Su=2Eu. But from the previous post Su=2OLR/3. In the cloudy atmosphere, the outgoing longwave radiation is entirely due to the atmosphere Eu, i.e. OLR=Eu. But Su=2Eu and Su=2OLR/3 cannot be simultaneously equal if OLR=Eu.
A term is needed to allow
both the Su=2Eu and the Su=(3/2)OLR equations to be valid.
To obtain this Miskolczi uses St, the IR radiation from the ground transmitted
directly through the atmosphere. The outgoing
radiation is equal to the sum of the transmitted IR radiation
and the radiation up from the atmosphere OLR = St+Eu
(rather than just Eu as in the cloudy case). Then given
the equations:
Su = 3OLR/2 (energy conservation)
Su = 2Eu (Virial theorem)
The derivation of St/Su is easy, just basic algebraic substitution.
Su = 3(St+Eu)/2 as OLR = St+Eu
Su = 3(St+Su/2)/2 as Su=2Eu
Su = 3St/2 + 3Su/4
Su/4 = 3St/2
Su = 6St
As evidence Miskolczi presents the following figure relating Eu to Su from radiosonde observations.
The global average cloud cover of an Earth-like planet will organize itself so that one-sixth of the IR radiation is transmitted from the surface to space. Miskolczi states (but does not derive) an expected global average cloud cover of 0.6. He derives these relationships without any reference to the optical absorption of greenhouse gasses. Therefore they are not as important to temperatures as fundamental energy constraints on the system as a whole.
Miskolczi’s theory develops two types of stable atmosphere as possible solutions of the first principles analysis, Mars and Earth, and a third (Venus) is in development. These types are:
- Planets with atmospheres largely transparent to IR, and very low greenhouse effect, that will not satisfy the virial theorem (hydrostatic equilibrium). Planets like Mars are of this type.
- Planets with semi-transparent atmospheres, and transmittance from the surface around 1/6 of total IR emission, saturated greenhouse effect, with mixed cloud cover. Earth is a planet of this type.
- Planets with semi-infinite atmospheres (no effective surface), permanently cloudy, with no appreciable transmittance.
So far this is a considerable achievement. There are a number of results that, if correct, render the some main themes of 10 years of climate modeling irrelevant: constant greenhouse effect, constant fractional cloud cover, to name only two. No wonder this paper sticks in their craw. The busywork of modelers is confirmed by the independent evaluation of models such as Douglass et al. 2007 and Koutsoyiannis et al. 2008, who conclude in an Assessment of the reliability of climate predictions based on comparisons with historical time series.
(M)odel outputs at annual and climatic (30‐year) scales are irrelevant with reality; also, they do not reproduce the natural overyear fluctuation and, generally, underestimate the variance and the Hurst coefficient of the observed series; none of the models proves to be systematically better than the others.
The huge negative values of coefficients of efficiency at those scales show that model predictions are much poorer that an elementary prediction based on the time average.
This makes future climate projections not credible.
Next I think I will tackle the existing models; what are the incorrect assumptions Miskolczi was referring to when he said that the “equations were totally wrong”, and exactly how does Miskolczi’s theory correct them. You will be surprised how simple they are, and learn more about the importance of assumptions in developing a model.
35 responses so far ↓
David,
Your last post said that you were going to deal with the Kirchhoff’s Law issues in an upcoming post, but I don’t think it’s here. I think this is one place where Miskolczi goes wrong, and it matters. I’ve just written a post explaining this at Climate Audit, in a thread there on this paper.
Nick Stokes
David,
A curiosity - I couldn’t find that figure (your second) which is supposed to validate the virial theorem application, in either of Miskolczi’s papers. Do you have a figure number?
Where does this virial result stand? It seems you couldn’t work out how it related to the equation he quotes. At CA, apsmith had the same problem. He tried emailing the author, but said he couldn’t get a clear answer. I couldn’t figure it out either.
Nick Stokes
Hi Nick,
First, I want to be sure I understand what he is saying correctly, and have been in contact with the author on the previous post, but not this one yet. He provided the linear regression figures. I will probably tweak it over the next week as I catch up with him.
Second, Kirchoff is the main difference in assumptions between his and GCM (based on Eddington) solutions, so I will have to be a component of the next. He goes to a lot of trouble to ‘prove’ the validity of Kirchoff in the paper, and claims to derive it independently. This is as it should be, if it is the main controversial assumption. So I am not prepared to say much about it until I understand his proof throughly. I didn’t see anywhere in the many of the blog comments concerned with Kirchoff that addressed all the work that is put into his proof of Kirchoff. They just disagreed and stopped there, which is not what I am about here.
As a mechanism, I think he claims that emissivity of the surface leads to heat loss despite Kirchoff equilibrium, as the nonequivalent temperature from e<1 must be balanced also, and convection etc does this.
As to the virial, I hope to talk more about that with the author this week. It doesn’t worry me so much that there are a few leaps like this as it sounds plausible and is the sort of thing that could be cleared up by someone else later.
It seems first you dispute in your post that up and down radiation can be equal. But his is an equilibrium model. Then you think what he applies is not Kirchoff, is that right? Where Kirchoff is applied, which is only TOA and surface, the balance will be the summed across all frequencies. Line matched balance seems a much stronger condition.
Hello David,
Thanks for clearing up where the diagram comes from. It doesn’t help, though, with the query I had when I went looking for it - where does this radiosonde data come from? Su is surface emission, Eu presumably TOA. Were they measured by the same radiosonde? If so, how?
Good luck with following his ‘proof’ of Kirchhoff’s Law. It isn’t set out as a proof at all; at some late stage he juggles a few of his equations, and the equality of A and E_D pops out. He says that none of the equations use Kirchhoff’s Law, but it’s hard to check. In any case, there’s a logical conundrum. If he can deduce this relation, then why does he need to invoke Kirchhoff’s Law at all?
His invocation of K’s Law isn’t saying that up and down radiation is equal. The balance at the surface is expressed in his Eq 2. What he is equating is down radiation E_D and an absorbance A. Why I say that this isn’t Kirchhoff is that, in any statement of K that I have seen, emissivity is equal to absorptivity. These are coefficients, properties of objects. A body has much the same emissivity regardless of how much it IR is emitting. But no, M equates an actual emittance E_D with an actual absorption A, which I think is quite wrong. He then says “The physical interpretations of these two equations may fundamentally change the general concept of greenhouse theories.”
Hi Nick,
I understand your concern with application of KL now. Thanks for the best wishes. I will try to fill in the gaps where M seems to follow the maths style of ‘leaving the derivation as an exercise’. It seems like his radiative equation 28 (that generalizes over the semi-transparent and semi-infinite cases) does not use KL, and this leads to the proof. KL is used earlier in the overview conservation equations. I hope to find the minimal algebra there and fill in the details so anyone can understand it.
One needs to go to the earlier paper for the radiosonde work, and yes there is modeling involved as many of these components are unmeasurable (how to distinguish St from Eu?). Unfortunately I know nothing at the moment how these measuremens are done.
So, as to your concerns. You think KL is a=e say (coefficients), but M claims that A_A=E_D (fluxes) is based in KL. Are you taking exception to incorrectly stating KL? If so, that would not materially affect A_A=E_D though would it? Or do you think A_A!=E_D? Cheers
Well, David, yes, the mis-statement of KL does affect A_A=E_D; it takes away that basis for believing that it is true. But it is also a worry; if you mis-state a law, that might be a slip, but if you go on to use the mis-stated version to make a sweeping claim, I find that alarming.
A_A and E_D are determined thus: A_A=a*Su and E_D=e*sigma*T_E^4. While a=e, there is no reason to expect A_A=E_D. T_E, the effective temperature, makes a fleeting appearance in M’s eq 17, and never again. It’s a kind of average lower atmosphere temperature at which the emission creating E_D occurs.
Hi Nick,
Thanks. That gives me something to work with. I am the kind of nerd where things don’t make sense until they are equations, so I should be able to work that into the next post. Even if there is no reason to expect it, does it mean it is wrong? The temperature discontinuity thing from the classical solution at the surface is the main thing and it needs to be tied into that. Hard to explain simply, but I think the paper is fascinating nonetheless. I read your post on the BB about Greenhouse BTW. Very helpful. Cheers.
8 Niche Modeling » Kirchhoff Law (Miskolczi Part 3) // May 13, 2008 at 8:20 pm
[...] admin @ The Virial Theorem (Miskolczi Part 2) [...]
9 Niche Modeling » Greenhouse Effect Physics // May 15, 2008 at 12:18 pm
[...] Niche Modeling » Kirchhoff Law (Miskolczi Part 3) @ The Virial Theorem (Miskolczi Part 2) [...]
Hi David, I now you’ve moved on some from here but while it caused me a moment or two of disorientation is was pleasantly surprised to see my post from ClimateAudit posted here. Thank you.
Regarding ” The source of this energy is A_A (IMO) but he takes it as being S_U I’m not sure this is a fair thing since I would expect A_A
something went wrong with this part of the comment is missing.
Anyway I satisfied myself taking a somewhat different approach that Surface and skin layer are in long term balance or equilibrium and Kichoff’s holds.
Hi Jan,
Ferenc pointed out your post to me because he thought you explained it well.
I know that your group has been discussing this for some time over at CA_BBs. I am still working on resolving outstanding objections, and think I have made some progress in my latest post called Greenhouse Heat Engine. I think the necessity of gravity in the system comes from the workings of natural convection (unlike a Stirling engine say that could operate weightlessly), and so the virial theorem is relevant. The Su ‘drives’ the heat engine. It seems like a connection Su=PE.
What was your approach that led to Ed=Su via Kirchhoff’s (link)? Thanks
Hi Dave,
I approached it from a spectrographic angle as it’s somewhat familiar territory for me especially relevant is the atomic absorption spectrometer. When the flame is at the same temperature, that is at thermal equilibrium, as a light source behind it one sees only a black body emission, i.e. no emission or absorption lines for any absorbing species excited in the flame which was essentially the means of atomising the sample. We would operate the system with the lamp much hotter than the flame so we would see absorption, according to Beer-Lambert law and there by measure concentration - great for trace quantities. It’s the no emission lines in the case of lamp temperature = flame temperature that is analogous to earth surface as source an the atmosphere as the flame for IR radiation if one turns an FTIR downwards at say 100 m you’ll see a Stefan/Boltzmann black (grey) body spectrum indicating thermal equilibrium with the surface and that Kirchoff’s law holds. You can check it with the MODTRAN simulation program by setting height to something like .1 KM.
14 Niche Modeling » Radiative Equilibrium (Miskolczi Part 4) // May 24, 2008 at 11:03 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). [...]
Su=2Eu
If you adjust Su to get Aa with an absorption coefficient
Then Eu also needs to be coefficient adjusted ?
IsoVirial Atmosphere concept
Earth Particle excludes, reflects back, other particles.
Orbit below the surface of Particle Earth, not allowed.
Subtracting the not allowed time and kinetic,
KE becomes less and PE more.
The reflected back would increase near surface density. 0K temperature of surface molecule would have PE, but 0 KE etc.
I can find numerous Isothermal, Isobaric, ideal gas,
Looking for links developing this idea.
Astronomy link somewhere ?
#16
I’m not exactly sure what you are after but these are some I like.
One
Two
Three
Fun with Entropy
Thanks !
What I want is a virial which includes the radius of particles. — Gasses are compared to the ideal, zero radius, gas law. — But atmospheres, every bouncing thing, should be compared to another ideal - a Virial, which assigns particle radius.
Slowly figuring out that isothermal is not a virial system.
Franko #18
Indeed isothermal -> no convection -> not virial. YOu might have to go to the literature that will be behind a money wall to get what you are looking for but I will see what I can find but I think there you will be getting into quantum mechanical applications of VT.
Virial temperature implies no convection. Just happy stable bouncing orbitals. Departure from the Virial temperature causes bulk, convective effects. How to get convection proportional to T^4 from virial to actual temperature difference ?
Franko #20
I think more precisely it implies stable convection i.e what mass goes up must come down to be replaced by more warm mass but heat keeps going up and out.
As I think David said in one of these threads, the “viral theorem” probably isn’t needed to prove Miskolczi’s ideas, anyway. A simple partitioning of the energy is all that is required.
jae #22
I don’t think so either but it hints of an easier way of doing calculations and getting results so in a sense it’s another hypothesis worthy of exploration. If it is, it will in fact lend support to it.
JanP: Agreed!
Ideal Gas Laws are the conveniently used reference. Extended onto, to model the non-ideal. But the Ideal Gas Laws are, really, just a simplified version of the Virial Theory.
“jae “JanP: Agreed!”"
I agree not !
Convection, in a steady, no input or output, virial temperature system, is just a statistical deviation, (ice cube arising out of your carbonated ethanol spiked drink) — Then, consider T^4 convective adjustment to a forcing.
Miskolczi will turn out to be a special case s the Virial
Perturbed into a near steady state ? Something like a Kirchoff ?
Franko:
“Ideal Gas Laws are the conveniently used reference. Extended onto, to model the non-ideal. But the Ideal Gas Laws are, really, just a simplified version of the Virial Theory. ”
Yes, maybe so. It seems to be completely ignored by modern “science,” eh?
The Astrophysicists are into the Virial — someone send and email to the Astrophysicist who approved Miskilczi’s paper — to lift the curtain for the general public audience.
TomVonk; “The sign of the 2/3 is perturbing and there must be some strange convention regarding PE because PE/KE must be <0″
The clue is the Particle Radii of Exclusion. one particle Radius cannot kinetic below the Radii of others. The particle is surface time forwarded Radii surface bouced
Franko #27
So are quantum physicists it doesn’t matter whether the particles are hydrogen molecules in a gas cloud, suns with planets orbiting around them in a spiral galaxy, a cloud of electrons around a nucleus or a bouncing ball it’s all about particles total kinetic + potential energy as they move through a potential field. If there is a volume of space in the field where they are excluded by a rigid surface or Pauli’s exclusion principle that volume space is just irrelevant regardless of how the particles are excluded.
Take a simple case — little molecule, eliptically orbiting the center of Earth. — Has only little energy, not enough for the Zero Circle of Surface Orbital Eccentricity.
The molecule is excluded from having below Earth surface Kinetic Energies. Subtract the time travelled, napping time — Ellipse area of actual above, and time forwarded (lost), a non-ideal of a Virial ?
“So are quantum physicists it doesn’t matter whether the particles are hydrogen molecules in a gas cloud”
Means that; Quantum Ideal Virial, cannot occupy below Surface of Event Horizon Energies. — Or Protonium molecule is for real ? — Anyway off to looking for the quantum virials.
Franko #30
that’s getting out of my depth now.
BlackLight Power “hydrino” was the intended joke object. — Sub harmonic resonances, — sub orbital quantum states. What kind of non-linear mixer is that ?
IsoVirial — defined by gravity, orbital KE
IsoThermal — defined by radiation equalizing KE
The equilibrium between the two effects via optical depth ?
Franko #33
Interesting thought but don’t think so you have an equation?
The more I Google, the more refinements the simplicity needs.
The IsoVirial is calculated from little, particle radii excluded, bounced, orbitals.
Deep Inside Jupiter, near the center, r^1 dominates , and r^-2 dominates in the upper atmosphere.
For Earth r-2 dominates in the atmosphere; r^1 is ignorably little.
The IsoVirial is calculated from from the tops of elliptical orbits (bouncing).
Looking at Ellipse and Circle intersections, to get the KE PE distribution. This would give clue to Hydrogen, non radiative, IsoVirial version. Adding photons, somehow ?
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