## Monday, February 11, 2008

Kramm steps on another rake

Just when you think that Michael Fumento has retired the Golden Rake Award, Gerlich and Tscheuschner (also here) send Gehard Kramm up to the plate again (#999)

The sole question is: Is the criticism of Gerlich & Tscheuschner on the explanation of the greenhouse effect justified or not?

The basis for this explanation is the equation of the planetary radiation balance given in my comment #770. When we recognize that, in contrast to the common assumption, the Earth not a blackbody radiator is, then this radiation balance must read

(1 – a) S/4 = eps sigma T_e^4 .

The symbols are explained in my comment #770, with exception of eps, a planetary emissivity. If we use a value for eps less than unity, we will obtain an equilibrium temperature T_e higher than 255 K. For eps = 0.61 the temperature T_e amounts to 288 K. In such a case there would be no greenhouse effect. This means that this simple instance of a planetary radiation balance is inappropriate to explain the greenhouse effect, as correctly stated by Gerlich & Tscheuschner.

UPDATE: One of the anonymice has found where 0.61 comes from, the Wikipedia, go RTFR

Now, true this is an advance over G&T (light on the G please, Eli has work to do) who manage to completely bollix the thing by using the solar intensity in orbit in the plane perpendicular to the sun rather than the average intensity on a m^2 of the earth. This means that G&T take the average intensity of the sun on the ground to be four times higher than it is even without correction for the aldebo. In Kramm's equation G&T are taking S to be ~1368 W/m^2 as can be seen in the section of page 61 of their Arxiv manuscript

If one accounts for both the geometric correction and the earths average albedo using a reasonable estimate of a~.3 then eps = (1-.3)*1/4 = . and T for the ground is ~255 K. This is a major error by Gerlich and Tscheuschner. After that you can basically say never mind and walk away with your ears covering your mouth to avoid laughing. It won't work.

However, Kramm goes this one better by taking eps, the emissivity of the earth to be what G&T should have taken the aldebo, a, to be.

But what is the emissivity of the earth. Good of you to ask little mice. In the visible 0.61 ain't bad, but the infrared, that is a very different story. Try between 0.95 and 1.00. If you don't trust Eli look at the MODIS emissivity data base
and for those who like to plot here are values btw .97 and .98 for a wind roughened sea.

It's not as if Kramm hasn't been told about all this by Arthur Smith who went over the whole, according to Kramm, vitally important section 3.7, with an even finer comb at dot earth #776.

In section 3.7.1, Introduction, they set the agenda: “Though there exists a huge family of generalizations, one common aspect is the assumption of a radiative balance, which plays a central role in the publications of the IPCC and, hence, in the public propaganda. In the following it is proved that this assumption is physically wrong.”

So they are setting out to demolish the idea of radiative balance. Let’s see how they do.

Section 3.7.2 - A note on “radiation balance” diagrams. They claim “the popular climatologic radiation balance diagrams describing quasi-one-dimensional situations (cf. Figure 23) are scientific misconduct since they do not properly represent the mathematical and physical fundamentals.”

In fact, the radiation balance diagrams are completely physically well defined as an integral of radiative (or convective/evaporative) energy flux over the globe, averaged over time, at the various physically relevant altitudes. The fluxes are usually expressed in the diagrams in watts per square meter; that should make pretty clear what these diagrams refer to.

Nevertheless, they insist the diagrams are nonsense since the authors claim they don’t fit into one of the categories they believe they should fit into. In particular, they claim the diagrams “cannot represent radiation intensities” and refer back to two earlier sections (2.1.2 and 2.1.5) that talk about the details of radiation fields. They don’t even seem to consider the integration across Earth’s surface that makes a one-dimensional analysis as shown in the radiative diagrams perfectly well-defined.

One value of radiation balance diagrams is in forcing conservation of energy on the system - what goes in has to come out or, in the case of imbalance, has to warm or cool the planet beneath.

So the authors somehow are unable to understand a well-defined basic concept. Moving on…

Section 3.7.3: the case of purely radiative balance. Here they start off with an elementary error: equation 73 is valid only for a flat planet always facing the sun. Their numbers in table 10 are ridiculously wrong as a result. And why do they call epslion “phenomenological”? It’s a measurable albedo factor for sunlight, not some parameter somebody would adjust to fit some other agenda.

They correct themselves reluctantly in equation 76 (and 80) and table 11, but hit themselves with another elementary error in the claim that setting the albedo to 0.7 means you are saying “a grey body absorber is a black body radiator, contrary to the laws of physics.”

In fact, the low temperature of Earth’s surface relative to the sun means the spectrum radiated is at much longer wavelengths than the incoming radiation. And at those long wavelengths Earth is in fact essentially a full absorbing black body, while it is partially reflective for the incoming short-wave radiation. Those conditions are perfectly consistent with the laws of physics - and are exactly what happens here on this planet.

So error upon error upon error here. Well, what comes next?

Section 3.7.4 - “The average temperature of a radiation-exposed globe”. Here they put up a straw-man atmosphere-free planet and look at how averaging works for temperature, and for temperature to the fourth power. Obviously, you get different numbers. But that has little relevance to any argument any climatologist ever makes. When the temperatures are relatively close, as they are on our actual planet, the two averages come much closer. But in their straw man planet where the sun is always in the same position overhead on one side and never seen on the other, they get a much lower average temperature. Fine as a calculation - relevant? Even the Moon has an average temperature of some -23 degrees C, because it doesn’t lose all its heat on the dark side during the two-week night-time. The climatologist’s effective temperature is much closer to the real number for an actual rotating planet with a nonzero heat capacity.

Section 3.7.5 - “Non-existence of the natural greenhouse effect”. Here they take their -129 C average temperature on their straw-man planet and the fact that actual temperatures are about +15 C, and claim that the resulting 144 C “physical” greenhouse effect is evidence that “something must be fundamentally wrong here”. The only thing wrong is their idea that their straw-man is what anybody else is talking about.

The rest of this section comes from their confusion about the radiation balance arguments and what climate scientists mean when talking about cause and effect. They claim that “the radiation is locally determined by the local temperature.” Cause and effect here are simple: incoming solar energy and energy coming from the atmosphere heats the surface. Outgoing radiation (and other energy) from the surface is determined by whatever temperature the surface has gotten to. The radiation balance diagrams explain what happens when everything is back in a steady-state situation, but the instantaneous cause and effect is clear. The authors are making extraordinary claims here.

The next section rehashes the fourth-power vs first-power averaging problem. This only proves that a 30-degree temperature range across a new-straw-man planet makes less than half a degree difference to the average with the two methods. So a realistic planetary model, rather than their original straw man, might need a greenhouse effect of 33.5 degrees rather than 33. The authors ironically claim at this point they have proved there is “no longer any room for a natural greenhouse effect”. They have of course proved no such thing.

Section 3.7.7 is just incoherent. There is no global mean temperature? They’ve just calculated one, twice! Maybe a global mean fourth-power-of-temperature would be more physically relevant - but that’s exactly what the radiation diagrams look at (energy fluxes, which vary as fourth power of temperature).

3.7.8 and 3.7.9 finally look at a rotating globe with a (unexplained?) heat capacity lambda. They seem to believe no computer could solve their equations - well, no, they can’t be solved in analytic closed form. But they provide a very simple model that in fact is almost trivially integrable - engineers tackle differential equations ten times as hard before breakfast every morning. Really, “Rough estimates indicate that even these oversimplified problems cannot be tackled with any computer”!!! And when you solve it, you’ll get numbers very much like what you see on the Moon.

Section 3.7.10 seems to be an attempt to add an atmosphere to their straw-man models, but I doubt it would add much enlightenment. The more heat capacity you add to the system, the closer you get to the “effective” temperature that climatologists talk about, rather than their straw-man “physical” temperature.

Section 3.7.11 finally discusses CO2, based on some ancient papers from a fellow named Schack. I don’t think we need to delve into this too much, but their one statement that “He did not get the absurd idea to heat the radiating warmer ground with the radiation absorbed and re-radiated by the gas.” indicates pretty clearly that the authors of this paper are still very confused about radiation balance diagrams and the way the real greenhouse effect works.

And that’s it for the tremendously important section 3.7. Did we learn anything? The authors made many errors, displayed ignorance of several critical topics they claimed to be conversant with. They set up several straw-man models to attack them because of their unphysical nature, then set up a slightly more realistic straw-man and claimed it was too hard to solve. Nowhere did they prove anything about CO2 not causing greenhouse warming - they didn’t even get into discussing the meaning of the radiation balance diagrams that proves this, because they dismiss them out of hand.

Not a promising start. Is there another section of this paper you somehow feel is more representative? I’d be happy to demolish that too.

Anonymous said...

>> And why do they call epslion “phenomenological”?

If they're using it the right way, they just mean that epsilon isn't derived exactly from some microscopic principle. Which is probably right, seeings as you just measure it. Not that there's anything wrong with that - thermodynamics is a phenomenological theory, and it's solid as.

The term is used a lot in the literature of non-equilibrium statistical mechanics (and almost nowhere else), usually to make distinctions between microscopic and macroscopic regimes.

I'm not sure their use of the word adds much meaning, but it's not a term of abuse - doesn't imply that there is dodgyness going on with epsilon.

-Griffin

EliRabett said...

True Griffin, but they have bundles several different things together in that eps (emissivity of the earth and oceans, albedo, etc), and their calculation makes it clear that they either don't know or are resisting using a realistic value. Instead they are playing the game, oh this could be anything, what if were something it could not be.

Their entire argument rests on picking a value of eps which is

a. Not within the bounds of possibility and
b. Supports the idea that there is no greenhouse effect.

So color my fur dubious. This is another one of those implausible but technically possible arguments.

William M. Connolley said...

Errm yes. Haven't they simply calculated the value of eps which gives you 288K given all the other parameters? Of course, in the real world, if you suddenly changed eps from 1 to 0.61 then the T would change too.

Anonymous said...

yes, it's no accident that the value kramm uses for emissivity is 0.61

That is the value that makes the earth's surface temp work out to about 288K (288.6, actually) using his equation:(1 – a) S/4 = eps sigma T_e^4 .

where "eps" is emissivity

But if you look at RealClimate's derivation for the simple model with an IR absorbing atmosphere, you will note that their equation

G= S/ (1 - (.5)lamda )

where lamda is emissivity

has a [ 1 - .5(emissivity) ] factor instead of the "bare" "emissivity" factor that kramm has in his equation (since real climate considers the fact that there is emission and absorption in the IR by the atmosphere -- ie, greenhouse effect).

(Note that Kramm's "S" is actually equivalent to real Climates "TSI", so real Climate's "S" is equivalent to everything on the left hand side of kramm's equation: (1 – a) S/4 )

The value real climate gives for emissivity is 0.769, so

real climates factor

1 - 0.5*emissivity = 1 - 0.5 (0.769) = .616 (essentially, the value Kramm uses for his emissivity)

In other words, Kramm's emissivity value was CHOSEN to give the right answer for the earth's temp (assuming as he did that there was no greenhouse effect)

How convenient.

--T

Anonymous said...

Then again, one could probably say the same thing about the emissivity value given by real climate for that simple model: that is was chosen to make the temp come out right :)

I honestly don't know whether that was the case or whether the 0.769 was determined independently.

--T

guthrie said...

The G&T failed my sniff test because they spent too much time ranting, and never actually put anything up evidence wise. There was plenty of symbol manipulation, but no real connection to the actual world. It is too long since I last did thermodynamics, and it wasn;t that kind anyway, so I do not know enough to critique it properly.

Anonymous said...

Looks like kramm may have copied right off the wikipedia page for Climate Model

The problem is, he apparently does not understand what "effective emissivity" is -- ie, that it already includes the influence of the greenhouse effect due to atmosphere.

From wikipedia

* ε is the effective emissivity of earth, about 0.612

The constant πr2 can be factored out, giving

(1 − a)S = 4εσT4

This yields an average earth temperature of 288 K [3]. This is because the above equation represents the effective radiative temperature of the Earth (including the clouds and atmosphere). The use of effective emissivity already accounts for the greenhouse effect. (along with clouds and other stuff)

So, in effect, kramm is trying to "prove" that with no greenhouse effect, the earth would have the same temperature that it actually does by using an effective emissivity that already takes into account the greenhouse effect!

Also from wikipedia:

The average emissivity of the earth is readily estimated from available data. The emissivities of terrestrial surfaces are all in the range of 0.96 to 0.99 [4] [5] (except for some small desert areas which may be as low as 0.7). Clouds, however, which cover about half of the earth’s surface, have an average emissivity of about 0.5 [6] (which must be reduced by the fourth power of the ratio of cloud absolute temperature to average earth absolute temperature) and an average cloud temperature of about 258 K [7]. Taking all this properly into account results in an effective earth emissivity of about 0.64 (earth average temperature 285 K).

Anonymous said...

Hello,
the angle very important! Taking an angle of 90° the emissivity of water is about 0,65. The earth radiates at right angle, thus I estimate that the earth has an emissivity of about 0,7 (the seas are covering about 70% of earths surface). Thus the greenhouse effect is much weaker than often thougt.