### GIGO

Eli has learned over the years that all sorts of strange people write the same paper, very long, very hard to follow and very wrong. These papers and their defenders play the Gallileo card early and often. No one can follow the algebra (these things always hide under a blizzard of algebraic incantation), but you can look at the assumptions, and when you do this carefully you find some amazing stuff, not believable, not correct, but amazin. The bunnies have been through this with Gerlich and Tscheuschner, had a neat recent dissection of the Robinson, Robinson and Soon OISM paper, and yr. humble hare dabbles in classical quantum numerology including this classic of the genre. A recent paper by Ferenc Miskolczi falls neatly into this category and has been adopted enthusiastically by the usual suspects. If you have trouble with the paper, Miklos Zagoni's web site might make it easier for you, but the rubber really meets the road in a number of web sites including a 309 and counting thread at the climate audit bulletin board and a four part analysis at Niche Modeling. There is also something worth looking at on 2nd Sex and Arthur Smith took a brief run at it in the comments at Rabett Run.

Before looking at the science, a reply by Nick Stokes (who carried much of the argument at CA) is worth quoting

## Re: What do people think of this new paper?

Have you found anyone who thinks it is right, and can explain why?alexharv074 wrote:Having searched the web far & wide I am unable to find that anyone has actually contradicted M on this point.

I think Miskolczi's paper could have been written in two sentences:

Seriously, if you are making a claim like this, you need a good argument, put with some clarity. You would usually write down a model with some unknowns, state some physical principles with their resulting equations, and derive relations which characterise the unknowns. M does this, but at least three of his basic equations appear to be totally wrong. They actually look like elementary errors. Or if they are right, it seems no-one can explain them."The greenhouse gas theory that has been used for the last century is TOTALLY WRONG! The proof is left as an exercise for the reader."

So this is Black Knight stuff. OK the use of Kirchhoff may be wrong, not sure about virial or that pesky Eq 7, but can anyone prove this is wrong, or that? People just lose patience.

Especially as these questions also come with no referencing or explanation. Who exactly is using Eddington's equation wrongly, and how? And re Qn 2, what on earth is that graph? It just says that he computed two sets of points which seem to align. He didn't say anything about how they were computed. What comment could be made?

Nick Stokes

Well you ask, where is the beef (which shows how old Eli is)?

A number of beefs there are with this paper which make it unnecessary to read through the whole thing, although some brave souls have done so multiple times. This includes Arthur Smith, Nick Stokes and David Stockwell, the proprietor of Niche Modeling. You can catch up with them at Niche Modeling or at the CA thread, links above.

It boils down to the following:

A. Miskolczi does not understand Kirchoff's Law. As Stokes puts it

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.”There is a rather longer version of this at CA

B. Miskolczi claims a virial relationship between the IR emission from the surface, Su and the IR emission from the top of the atmosphere Eu. At best this is roughly true for the Earth's atmosphere as an experimental fact, but it is not a mathematical relationship. In essence, as Arthur Smith points out, this is a constraint that Miskolczi arbitrarily imposes on the Earth system## Re: What do people think of this new paper?

I think Miskolczi's paper goes wrong in its treatment of Kirchhoff's Law. But firstly, I'd like to note some of the cogent objections made earlier in this thread. Hans Erren queries the grey-body assumption, which lead to some discussion. stevo and apsmith queried the virial theorem statement; apsmith followed it up with the author, without apparently a convincing reply. That looks odd to me too.

But my main sticking point was the use of Kirchhoff's law. Steve Milesworthy raised it here. He hoped it wouldn't affect the paper's conclusions, but I think it does. There was some discussion on equilibrium discussions later in the thread. I'll summarise the problem.

Miskolczi says, in Sec 3:

That isn't the definition I know. Thermal equilibrium, at least as often interpreted, is very restrictive, and suggests no nett flux at all. The more usual criterion is Local Thermodynamic Equilibrium (LTE), which is generally thought to be true in the atmosphere, except at rarefied levels. And then, in Pierrehumbert's bookAccording to the Kirchhoff law, two systems in thermal equilibrium exchange energy by absorption and emission in equal amounts, therefore, the thermal energy of either system can not be changed.

Or in these online lecture notesKirchoff’s Law states that the emissivity of a substance at any given frequency equals the absorptivity measured at the same frequency....

We will content ourselves here with the statement that all known liquid and solid planetary materials, as well as the gases making up atmospheres, conform very well to Kirchoff’s Law, except perhaps in the most tenuous outer reaches of atmospheres where the gas itself is not in thermodynamic equilibrium.

Note that absorptivity and emissivity are properties of objects - they do not imply any particular absorption or emission. The absorption will depend on the incident radiation, and the emission will depend on the temperature.Kirchhoff’s law states that absorptivity and emissivity are always equal....

Kirchhoff’s law may be considered valid for all processes of relevance to the atmosphere.

But Miskolczi's Eq (4) is absolute. It says that the upward LW radiation absorbed is equal to the downward LW radiation, as a result of Kirchhoff's Law. This means that the downward radiation is independent of air temperature, and hence also, I think, of GHG content beyond a limit. This is why he gets the limit on the greenhouse effect. This statement is different from his conservation of energy statement there.

But you can see this is wrong by applying the same logic to other levels of the atmosphere - there is nothing special about the surface. At TOA, there is upward emitted LW radiation, clearly measurable; it is Eu in M's model. But there is no absorption of downward LW to balance it - because there is no downward LW at all (or only a tiny amount from the Sun).

and## Re: What do people think of this new paper?

## by

Steveo, I think you've hit the nail on the head there.apsmithon Wed Mar 12, 2008 7:22 am

I actually sent the author an email the other day asking that very question - how does he go from KE = PE/2 to Eu = Su/2? His response so far was not very clear, and included the word "guess" which left me a little concerned.

By adding in this relationship, Eu = Su/2, he overconstrains the problem, and that means you can get out of it just about any result you could wish, at least if you did a full analysis.

Eu is a flux of energy from the atmosphere into space - but he claims it "represents" the total kinetic energy of the atmosphere. Su is the flux of energy from the ground (at least, if going through his rather odd list of assumptions we take the point Su = Sg in his diagram figure 1), but he claims it "represents" the total gravitational potential energy, because the surface temperature is related to the total gravitational potential through the surface pressure and density.

He does not explicitly state any linear relationship or other analysis that justifies the Eu = Su/2 claim. Eu depends on the absorptive properties of the atmosphere and the vertical temperature profile, which doesn't seem to be derived or discussed here at all.

It does happen that for Earth, Eu is roughly half of the surface radiative flux, so Miskolczi's relationship roughly holds for our planet. But it sounds like he "guessed" that it was some sort of universal law based on looking at the parameters for Earth, rather than actually deriving it from the physics of the situation. At least I don't see any physical basis for the claim in this paper, and it's certainly not obvious from the meanings given to the terms here.

C. Pat Cassen has some additional problems with the mathematical analysis## Re: What do people think of this new paper?

You can compute total internal kinetic energy from the molecular formula for a gas - the average of 1/2 mv^2 = 3/2 kT. That means total kinetic energy = 3/2 n R T (n = number of moles of gas), or total kinetic energy = 3/2 P V (for a small region at constant pressure and temperature - you would need to integrate over the range of temperatures in the real atmosphere to get the proper number).

But what bearing does this have on outgoing thermal radiation (E_U) from the atmosphere? If the atmosphere absorbs most infrared radiation then there's going to be some rough top-level layer of the atmosphere (the photosphere) from which most of the outgoing thermal energy is coming; if temperature in this region is T_A then E_U would be given by the Stefan-Boltzmann relation, i.e. proportional to T_A^4. If the atmospheric temperature was roughly constant, that would give you an E_U value varying as (total kinetic energy)^4, rather than linearly, but then it also depends on the total mass of the atmosphere (the 'n' value above). In any case, the author's claim that E_U literally "represents" the total kinetic energy seems very far from reality.

I've exchanged some email with the author now, and it seems pretty clear he does not have an actual derivation of this relationship from physical principles. Rather he seems to have done some simulations relevant for Earth's atmosphere, noticed that this relationship roughly held, and then claimed this analogy to the virial relationship that has no actual basis in physics. As far as I can tell, anyway....