Comments on Untitled Post : Rabett Run

Re Kramm:

I know more than the average Joe about some of what he rants about. He is at my alma mater - the U of Ak Fairbanks, up on the West Ridge. He was a colleague of ex-professor, ex-researcher, and in many ways ex-scientist Syun-Ichi Sakasofu and sort of uses that as a bizarre club against other scientists and lay supporters of AGW (Obviously that's only one of his large array of tactics).

Akasofu's expertise is in high-energy atmospheric physics, and in particular the auroras. If the global warming debate was about HAARP, he'd be a world-class expert. He deservedly has a monument on campus. But he disgraced himself completely on the Great Global Warming Swindle, expounding on things that had nothing to do with AGW and attempting to conflate them with things that did, and chose to leave his career as a right-wing crank instead of a distinguished scientist.

I bring this up because the most glaring hole in Kramm's head is his repetition of the fact that Akasofu was a protege of Sidney Chapman, a very good space scientist, after whom our space science building is named. How dare you, he thunders, question a protege of Sidney Chapman on, well, anything??

Meanwhile, he is unceasing in his personal and professional attacks on James Hansen, who was a protege of James Van Allen!

Kramm is an educated fool for many reasons, but maybe the top one is, he doesn't even do ad authoritem arguments well.

From the discussion on PrimaKlima, Kramm doesn't seem to understand the math in my arXiv paper either, at least from his comments there (though my German is too poor to clearly follow what he's up to). He claims he found something wrong with one of the equations there? I'm pretty sure there were no typos or errors of that sort in any of the version I posted, but if there's a need for correction I'd love to hear it. His argument in the comments didn't make sense to me though - maybe somebody here can interpret?

Arthur, I presume, you mean this part. I hope, my English doesn't fail:

"The manuscript of Smith contains a few errors concerning the averaging. If you want to find the global average of a parameter, he following definition equation has to be used:
y^M = INT_A_s(y dA_s)/INT_A_s dA_s
Here A_s is the spheric angle (4 pi in case of a globe) and dA_s the differential spheric angle . y^M is the average over the globe for y. INT means integral. Contrary to eq. 6 by Smith the radius of the earth doesn't appear. When will you debunk the work by Smith?
There is to mention, that the globally average temperature of the air near the surface (y=T) of about 288 K was calculated using the definition of a global average, too. This globally averaged temperature of the air near the surface has no connection with the temperature of 255 K, which is assumed to be homogeneous. "

Jörg Zimmermann

Well, that's silly - obviously the 'dx' I used there is whatever suitable physical surface coordinates you like, not angular coordinates, hence the r^2 ratio.

But I thought Kramm had some follow-up later on with some kind of actual calculation he thought I'd done wrong?

Arthur,

the steps from your Eq. (7) to Eq. (9) are simply not correct.

One can define effective values as you did in the case of T^4. That leads to

[T^4] = 1/(4 pi) Int_A_s (T^4 dA_s)

In this equation A_s is the solid angle (for a sphere A_s = 4 pi), and dA_s is the differential solid angle.

However, if we consider eps T^4 we will obtain

[eps T^4] = 1/(4 pi) Int_A_s (eps T^4 dA_s)

The quantity [eps T^4], however, is not equal to [eps] x [T^4] because it would mean that

Int_A_s (eps T^4 dA_s) = Int_A_s (eps dA_s) x Int_A_s (T^4 dA_s)

And this is sheer mathematical nonsense.

Best regards

Gerhard Kramm

Hmm, this is hardly an important point, since later on (like G&T) I assumed epsilon = 1 everywhere for the surface.

But Dr. Kramm, I have no idea what you mean by [eps]. I defined a quantity, eps_eff, in equation 8. Equation 9 is then a simple substitution using eq's 6 and 8, as can be easily seen by replacing the integral term in eq. 8 with E_emitted(t) divided by sigma (from eq. 6), and rearranging the terms.

I am german and I can promise you that Georg Hoffmann has nothing to say to the Gerlich @ Tscheuschner paper. He doesn't talk to Mr Kramm at all and is insulting everybody who doesn't believe in realclimatism.

Who are you to criticise Mr Kramm?

What is this joke all about? If there were a scientific debate, why is Mr Hoffmann so silent?

@Delgado

You are a hero, a great scientist!

Über mich
Did a cult show - situationist - in Alaska for years - Experiment Alpha - the BBC ran some of our shows, and Alaskan Public Radio did a show on us.

Interessen
Emo punk Open Source Situationism Buffy the vampire slayer


WOW

Sorry Arthur,

it is an important point. Not only is that a violation of basic rules of calculus, but it leads also to different results. However, this is not the real problem. We all make mistakes. This can only be avoided by doing nothing, and this is the biggest mistake.

The real problem is the style of scientific debates. To disagree with statements of the G & T paper is one thing, to initiate a cultural war is another one.

I took a look on various weblogs. It seems to me that a concerted action against the G & T paper has been installed. The publisher was bombarded with tons of e-mails. The journal IJMPB was put in the same corner like companies which make illegal copies of DVDs etc. (Take a look on Georg Hoffmann's weblog.) This is really sad.

I wonder why all these "experts" do not write comments to the G & T paper and submit it to the editor of the IJMPB. I promise you many of these "experts" will not do that because it is indispensable to use the correct name and affiliation. A comment, for instance, authored by the pseudonym "Eli Rabett" will not be accepted.

Commonly, comments to a paper submitted to the editor are given to reviewers and after they accept them to the authors. The authors have then the right to reply.

Scientific debates are very important. One of the finest hours of scientific debates can be related to the 5th Solvay Conference held in Brussels in 1927, when the giants of theoretical physics Albert Einstein, Niels Bohr and their pupils disputed quantum mechanics. When Einstein remarked "God does not play dice." Bohr replied, "Einstein, stop telling God what to do." This debate was a milestone in quantum mechanics. However, all participants did it under their own names, but not under pseudonyms. After this Solvey Conference quantum mechanics was more accepted as before. Even though Einstein was not entirely convinced he eventually recommended Werner Heisenberg for the Nobel-Prize in physics. That is greatness.

Best regards

Gerhard Kramm

Dr Kramm is incorrect. The equations (7) to (9) in Dr Smith's paper (Proof of the Greenhouse Effect) are perfectly sensible and correct.

Equation (6) is important here, and Dr Kramm appears to follow that ok. It is an ordinary surface integral of the energy emitted from each point of the surface, using Stefan-Boltzmann law, to obtain the total energy emitted from the surface.

Equation (7) is a definition, for effective temperature T_eff. It uses another conventional surface integral to define a temperature value. Basically, it integrates fourth power of temperature over the surface, and then divides by total surface area.

Equation (8) is a definition also, for an effective emissitivity ε_eff. It uses same integral used in equation (6), and in order to relate the effective temperature to the total emitted energy..

Equation (9) is obtained by simple high school algebra. Just substitute in the definitions for T_eff and ε_eff, and you get equation 6 right back at you.

-----

So what's the problem? It's certainly not technical errors in Arthur's paper. Dr Kramm's comments on "solid angle" suggest he might merely be getting confused over co-ordinate systems. The equations (6) through (9) could be made more concrete in any co-ordinate system you like, such as latitude and longitude, in which case you could give the dx as a 4πr^2.dA, where dA is a small solid angle. But changing co-ordinate systems or variables is not a change to the equations, and Arthur properly uses the most general abstraction dx for a patch of area in a surface integral.

The equations given use local functions for temperature and emissivity, and they have two arguments: t, and x. These are not explicitly defined, but clearly t is time and x is location on the surface. Precisely what kind of co-ordinates are used for location is not important, any more than what units are used for the time.

Equation 6 is the total emitted radiant energy from a planet's surface. It's a really simple and basic formulation, and should be more than sufficient for someone to sort out the nature of variables used. Equation 6 simply adds up all the local bits of energy from each patch of surface area. It uses local emissivity and local temperature, for local energy, and integrates this over the planet's surface. The integral in equation 6 uses dx, which is clearly an area here, because x is a location on a surface. The units of the integration are therefore correct, because the Stefan Boltzmann law gives power per unit area.

Now; if you can figure that out, you just do precisely the same things with the definitions in Equations (7) and (8). They are just as mathematically meaningful. They are also physical sensible quantities. But to say the mathematics therein is nonsense is, well, nonsense!

----

I totally reject the idea that anyone is immune from criticism by virtue of qualifications or standing. As it happens, I have a PhD in maths myself – although it is in discrete maths and graph theory rather than calculus. I've been involved in formal scientific/mathematical publishing, as author and as reviewer; although I have no particular prominence. I'm a very minor player. My own name is Chris Ho-Stuart, and am retired from academia and am no longer publishing.

The point is: it doesn’t matter. I don't care if you have the Field's medal or a Nobel prize; every statement or theorem or claim stands or falls on its own merits. Perhaps there's a language issue here with reading English, or perhaps it is a minor slip up; but Arthur's equations are good mathematical expressions of a basic surface integral.

Stick to the technical stuff. You've claimed a mathematical nonsense. I claim you're wrong, and the maths is trivially correct. I dismiss with contempt any attempt to bypass the specifics with grandstanding about standing.

If my explanation is any help and Dr Kramm retracts, then no harm done. It might just be a difficulty with language. Resolving such things is a win/win situation.

But if you still think the equations (7) to (9) are actually wrong or nonsensical, at least answer this: is equation (6) mathematically meaningful to you?

Sorry,

obviously, you are believing that

INT (f(x) g(x) dx) = INT (f(x)dx) times INT (g(x)dx)

is correct. Please take a sharp look into textbooks on calculus.

Best regards

Gerhard Kramm

That is a total non-sequitur, of no relevance whatsoever to the point. Nothing in my comments, or in Arthur's equations, has anything involving equating a product of two integrals to a single integral. It's not just not there.

If you do this again, I'll get angry.

Answer the question, please. Does equation (6) make sense to you?

How would you calculate the total energy emitted from a surface, given functions for local temperature and emissivity?

Arthur's equations involve simple surface integrals, which are correct not only for a sphere but any radiating object.

Here is an example

f(x)= x^2, g(x)= x^2

INT (f(x) g(x) dx) = INT (x^4 dx)

INT (f(x) dx) times

INT (g(x) dx) = INT (x^2 dx) times INT (x^2 dx) = {INT (x^2 dx)}^2

To state that

INT (f(x) g(x) dx) = INT (f(x) dx) times INT (g(x) dx)

is correct, has nothing to do with the basic rules of calculus.

Best regards

Gerhard Kramm

of course, it is. Consider Eq. (8) of Smith (2008). It can simply be rearranged to yield


eps_eff T^4_eff = C INT (eps T^4) dx

C = 1/(4 pi r^2)

This is mathematical nonsense.

Best regards

Gerhard Kramm

Eq. (6) of Smith is inappropriate because averaging over the surface of a sphere leads to

[y] = 1/(4 pi) INT_A_s y dA_s

A_s is the solid angle (= 4 pi) and dA_s is the differential solid angle. The radius of the sphere plays no role.

Best regards

Gerhard Kramm

Dr. Kramm, you have not shown anywhere that the equations in question logically lead to an equation where the product of two integrals is equal to the integral of the product. It is just not in there.

In one comment here you rearrange equation 8 as:

eps_eff T^4_eff = C INT (eps T^4) dx

C = 1/(4 pi r^2)

However, this is still not the product of two integrals, because the definition of eps_eff includes T_eff^4 (defined by an integral) in the denominator and you are left with a tautology. As is obvious given that (7) and (8) are merely definitions of T_eff and eps_eff, respectively.

Physically, equation 8 defines an "effective" emissivity by weighting the local emissivity by the fourth power of local temperature. A perfectly natural thing to do.

I see Arthur has made a short comment going to the heart of Dr Kramm's errors. But as I had prepared this longer reply, I'll post also. Dr Kramm has a succession of comments here.

(A) Integral of a product

Dr Kramm has made some remarks about integrals of a product (in a comment at 9:03pm), but they are irrelevant. Neither Arthur nor I have ever equated the integral of a product with a product of the integrals. Continued invocation of this point is an irrelevant distraction. It indicates that Dr Kramm is very sloppy in looking the equations he presumed to criticize.

I can only guess that Dr Kramm noticed two integrals that do appear within these equations: In equation (6) and (8), there is a reference to INT ( ε(t,x) T(t,x)^4 dx). In equation (7) there is a reference to INT ( T(x,t)^4 dx ). But nowhere is there an integral of ε(t,x) by itself.

It appears that Dr Kramm has merely jumped to the conclusion, on the basis of nothing at all, that there must be a distribution of an integral across a product somewhere. But there isn't. Dr Kramm frankly ought to apologise for this distraction and for the dig about reading text books.

(B) Re-arranging equation (8)

In a comment at 9:08pm, Dr Kramm speaks of a rearrangement of equation 8.

Here's the equation as it appears in Smith (2008).

(8) εeff(t) = { 1/ ( 4πr^2 Teff(t)^4 ) } { INT ( ε(t,x) T(t,x)^4 dx) }

In his comment, Dr Kramm states that this equation 8 can be simply rearrange to give this:
eps_eff T^4_eff = C INT (eps T^4) dx
where C is 1/(4πr^2)

Then Dr Kramm states that this is a nonsense. But it isn't a nonsense at all. The claim that this simple rearrangement is "nonsense" drops out of thin air with no basis at all.

This equation is being used to define the quantity eps_eff, and this rearranged formulae is a perfectly proper way to express the definition. The eps inside the integral is the given local eps, which is defined over different locations. Equation 8 proposes a definition for a global effective emissivity. It's a perfectly good mathematical definition, with no mathematical errors. The number obtained is a sensible way of representing a kind of effective global emissivity. It's not an "average", but an "effective" emissivity.

(C) Integrating over a sphere

Dr Kramm states that equation 6 is nonsense because

[y] = 1/(4 pi) INT_A_s y dA_s

is the proper way to integrate over a sphere. But this is just a co-ordinate issue. It's a particular case of the more general surface integral, where you integrate over areas.

The equation Arthur has used is the more general surface integral, which applies to any surface. The Earth, in fact, is NOT a sphere. You can handle that in polar co-ordinates, or in any co-ordinates you like, but ultimately the check for whether you are integrating correctly is whether or not you are doing INT(y dx) where dx is a small surface area.

Dr Kramm states that the radius of a sphere plays no role in this integral. That should make him think twice! Recall, we want to calculate the total energy being emitted from the Earth. Stephan Boltzmann gives you energy per unit area. So you have to multiply it by an area to get an energy.

In a conventional surface integral, as used by Arthur, the dx is an area; we integrate over many small patches of area. If there is a co-ordinate transform of some kind so that you can integrate over the solid angle in a sphere, then you'll find the radius of the sphere has to go into the function y, as part of the change of variable operation… and you are no longer integrating simply a Stephan-Boltzmann term for power per unit area!

If Dr Kramm would just think for a minute, he'd surely recognize that ANY calculation of the total energy emitted by a sphere at a certain temperature is going to use the radius of the sphere somewhere! If he thinks about where it goes, he'll get precisely what I explained in the first place. It's just a basic co-ordinate transform, and the "dx" area has to be replaced by 4πr^2.dA where dA now has units of solid angle.

To say that one of these alternatives is "wrong" while the other is "right" is… well, words fail me.

----

The major point that strikes me is that this is all so very elementary. If Dr Kramm applied a bit of simple algebra to the equations he presumes to criticize, then he'd see that the remarks about product of integrals were irrelevant.

If Dr Kramm actually carried through a calculation of total energy with his preferred solid angle method, he would see the radius of a sphere appearing inside the integral, in precisely the form needed to make dA into a small patch of area as used in the more conventional surface integrals by Dr Smith, using dx.

And finally, the bland claim, based on nothing at all that I can see, of equation 8 being "mathematical nonsense", is surreal. This is a definition, which should be considered on its physical merits -- which are pretty obvious. Its mathematical standing is fine. Dr Kramm has no meaningful mathematical objections at all.

I'm not satisfied with my remarks on surface integrals, and I'll try to say it again more clearly. Sorry for the extra space...

If you want to integrate some quantity over the surface of a sphere, you do a surface integral. Suppose, for example, we want to know how much water there is in the ocean. We can integrate the depth of the ocean over the surface area. So let D(x) be the depth in a given area x.

In full generality, the surface integral is INT( D(x) dx ) where dx represents a small patch of area.

You can convert units, by expressing a small area dx = 4πr^2 dA, where dA is a small solid angle, and r is the radius of the earth. The integral becomes INT (D(A) 4πr^2 dA). For a sphere, r is constant, and you can bring it out of the integral to get 4πr^2 INT (D(A) dA).

For an ellipsoid planet, however, that would be an error. In general, r may be a function of the part of the surface being considered. On Earth, for example, the equatorial radius is about a third of a percent larger than the polar radius. In general, r is a function of A, and you can't just bring it out of the integral as you can for a sphere.

In either case, however, the integral must still be equivalent to INT ( D(x) dx ). It's just a transformation of variables, and to single out solid angle as the only way to write a surface integral over a sphere is just ignorant.

In a general discussion of temperature and emissivity, the best method is the most general method, where you keep explicit that it is a surface integral over small patches of surface area. It's completely accurate, it is simpler to express, and it is fully general.

Gerhard Kramm writes:

It seems to me that a concerted action against the G & T paper has been installed. The publisher was bombarded with tons of e-mails.

That's because all those people were amazed and upset that a blatant work of pseudoscientific idiocy got published in a real journal, even if a minor one. It's rather as if a paper by creationists had been published in a biology journal.

Duae - thanks - so does anybody want to translate this explanation of Kramm's errors into German to respond on the PrimaKlima thread? Or maybe somebody already pointed out his nonsense there? The discussion there has overwhelmed my limited German, I'm afraid!

Interesting that the publishers were overwhelmed with emails about this paper. I'm glad people actually care, that's encouraging.

Duae Quartunciae

I wrote: Eq. (6) of Smith is inappropriate because averaging over the surface of a sphere leads to

[y] = 1/(4 pi) INT_A_s y dA_s



Equation (8) of Smith (2008) reads:

eps_eff(t) = 1/(4 pi r^2 T_eff(t)^4) INT (eps(x, t) T^4(x,t) dx)

Small rearranging leads to

eps_eff(t) T_eff(t)^4 = 1/(4 pi r^2) INT (eps(x, t) T^4(x,t) dx)

Effective quatities were defined by Smith according to Eq. (6), i.e.,

T_eff(t)^4 = 1/(4 pi r^2) INT (T^4(x,t) dx)

This means that eps_eff(t) is defind by

eps_eff(t) = 1/(4 pi r^2) INT (eps(x, t) dx)

Thus, according to this logic we would have

eps_eff(t) T_eff(t)^4 = 1/(4 pi r^2) INT (eps(x, t) dx) . 1/(4 pi r^2) INT (T^4(x,t) dx) = 1/(4 pi r^2) INT (eps(x, t) T^4(x,t) dx)

This is sheer mathematical nonsense.

If this would be correct, one could simply show that variances and covariances or terms higher order must not be occurred in the governing equations of turbulent systems.

Best regards

Gerhard Kramm

Dr. Kramm - um, no. Your logic bears no relation to the discussion in my article. My equation 7 defines only T_eff. eps_eff is defined by equation 8.

By your logic, the definition of eps_eff would require substitution of eps for T everywhere in equation 7, which would NOT lead to:

eps_eff(t) = 1/(4 pi r^2) INT (eps(x, t) dx)

but rather would lead to:

eps_eff(t)^4 = 1/(4 pi r^2) INT (eps(x, t)^4 dx)

which is a completely different equation anyway.

But I meant, and wrote, neither of those things to define eps_eff. I wrote equation 8 to define eps_eff. That is the definition. I'm sorry that this has confused you, but it seems not to have confused any of the dozens of others who have read the paper.

I think this all boils down to Dr. Kramm reading "an effective emissivity [...] can be defined as an average over the planetary surface" as "an effective emissivity [...] can be defined as unweighted average of the emissivity over the planetary surface".
Dr. Kramm, please correct me, if I should be wrong with the above.

I do not agree with the above reading, because:
A) The sentence in question starts out with "Similar to the effective albedo", which is not a simple average either.
B) The sentence leads up to equations (7) and (8), where T_eff and eps_eff are explicitly defined.

I do not see, how one can construe that Arthur Smith intended to use or actually did use the unweighted average of the emissivity in equation (9), when he clearly took care to define an effective emissivity, which clearly is the correct choice in equation (9).

This is ridiculous. Let me single out one absolutely trivial point.

In the 11th comment at 8:42 pm, Dr Kramm responds to my detailed explanations by saying that I must believe integration distributes over multiplication, and makes a rather belittling remark about needing to look at textbooks on calculus. He's repeated the insinuation several times subsequently.

Now in fact, there is absolutely nowhere in any of my work or Arthur's paper where an integration is distributed over a product as he implies. It is simply not there. A high school student could see this.

I can accept a slip up. With a decent and honest person, when this is pointed out they will apologize, and acknowledge that they were wrong to make the accusation, and progress is made. That I even need to ask this is telling. My normal expectation with anyone having a bare minimum of competence and decency is that they would recognize they had slipped up, acknowledge it, and we could move on.

I will, sometime soon, be addressing the various other claims by Dr Kramm, but I am choosing to single out this one issue as a point where I want to see if progress is possible. Whatever else we address, please take up this one.

You explicitly accused me of thinking integration distributes over a product. I don't mind in the least if someone points out when I make a stupid error in calculations – but if the mistake isn't there, I expect them to recognize the error and retract the insinuation. If you can't even do that, how can we hope to progress on anything?

The only mistake I made is that I wrote in some of my remarks Eq. (6) of Smith. It must read Eq. (7).

Arthur,

with your Eq. (7) you defined what an effective quantity does mean. It is an average over the surface of the entire globe.

Consequently, the quantity eps T^4 under the integral of the right-hand side of Eq. (8) has to be treated in the same manner. This means that your Eq. (8) has to be written

{eps T^4}_eff = C INT (eps T^4) dx

with

C = 1/(4 pi r^2). The left-hand side of this equation is the effective emitted energy normalized by the Stefan constant.

If you consider your Eq. (8) as the definition of eps_eff, then your eps_eff diagrees with the definition of an effective quantity as the average over a sphere. It is an attempt to compare apples with pears.

In turbulence there is a similar problem: Let the braces [ ] define the averaging integral. The average of a product a b is then given by

[a b] = [a] [b] + [a' b']

In accord with your Eq. (8) It would mean that

[a] = [a b]/[b]

However, the correct one is

[a] = ([a b] - [a' b'])/[b]

Since the covariance term [a' b'] is not generally equal to zero, your mathematical treatment is not self-consistent.

Best regards

Gerhard Kramm

Dr Kramm. You explicitly accused me of thinking integration distributes over multiplication! Here is what you said previously.

Quoting Dr Kramm: "obviously, you are believing that

INT (f(x) g(x) dx) = INT (f(x)dx) times INT (g(x)dx)

is correct. Please take a sharp look into textbooks on calculus."

That is a specific claim of a specific and very silly error in my calculations. If I do ever make such a silly mistake, I'll have no problem with you pointing it out and I'll thank you for the correction sincerely. Anyone can make silly mistakes.

But if YOU are incorrect to claim I have been distributing integration over a product, then elementary decency means you acknowledge it and retract your claim about my making this mistake.

Is this hard to understand? Deal with the question. I insist that you either retract this claim, or else repeat it.

We'll get onto the other stuff, but your integrity is on the line here. Anyone can make a dumb mistake from time to time. All it takes is simple high school algebra to see that there's no distribution of integration over a product here. And you should own up to that, and admit you were wrong to suggest I've done any such thing.

This is an error, by you, and you should admit it.

If you have the elementary decency and competence to manage that, then there may be some hope for progress as I move on to the other points.

Gerhard Kramm said: "It seems to me that a concerted action against the G & T paper has been installed. The publisher was bombarded with tons of e-mails. The journal IJMPB was put in the same corner like companies which make illegal copies of DVDs etc."

As one of the people who wrote an e-mail to the editors, I would like to say that I have absolutely no regrets about such action. It is simply inexcusable that the editors of a serious scientific journal publish a piece of polemical nonsense that launches utterly fallacious attacks on a whole field of science and is called a "review article". If they can't find a competent reviewer then they shouldn't publish it...In fact, it should have been clear simply from the tone of the article that it was unpublishable as is, let alone the mistakes one finds once one subjects it to any real scientific review.

Gerhard Kramm says: "I wonder why all these 'experts' do not write comments to the G & T paper and submit it to the editor of the IJMPB. I promise you many of these 'experts' will not do that because it is indispensable to use the correct name and affiliation. A comment, for instance, authored by the pseudonym 'Eli Rabett' will not be accepted."

Many of us here, including myself and Arthur Smith, are using our names and I am sure others would be willing to in appropriate circumstances. As for submitting a comment or a paper in response, that is something that we have been working on collaboratively here. However, since it is very time-consuming to do this, since the nature of G&T writing is so obtuse that it is difficult to pin them down exactly on what they are saying (for example, please give me a clear statement of EXACTLY why the believe the atmospheric greenhouse effect violates the 2nd Law of Thermodynamics), and since there is little reward to be earned by rebutting something that almost all serious scientists know is just garbage, this is a pretty thankless task.

For the record, I also sent a brief and polite email to the journal, in my own name, suggesting that their normal processes for quality control and review are broken. I was advised to submit any corrections as a paper to the journal.

I have subsequently made some contributions to the response being worked on here, which might or might not go to IJMP(B); in which case I again use my own name.

However, in my opinion, it is simply not appropriate to carry on a debate over undergraduate level physics and high school level maths in a professional journal. If there is a need to do that, then the journal has failed its proper role.

The fact is, in this instance the editors failed the journal, and published a blatant bit of outright crackpottery, riddled with trivial errors. This happens occasionally, and in an ideal world the journal itself takes note of how it occurred and cleans up their procedures.

If there are editors who actually need to have formal submissions to see such fundamental problems, then they are completely useless as editors of a professional journal. Hopefully someone at IJMP is doing something about this and cleaning house a bit. But that's up to them.

In the meantime, I don't mind trying to explain matter in a forum like these comments, but there's no way this kind of discussion should appear in a professional journal. We have some people claiming that there are trivial errors in calculus, and others claiming that the calculus is 100% correct. Some people are claiming that a certain physical model violates fundamental laws of thermodynamics, while others say that the model is perfectly consistent with thermodynamics and indeed a consequence of thermodynamics.

This is not a debate appropriate to a credible journal! It might be needed, but if so that is a damning indictment on the journal.

If I may make a meta-comment here, it seems to me that Dr. Kramm is using a rhetorical technique rather similar to that of G&T themselves. What it seems to amount to is this: One takes something and then finds an interpretation of it (sometimes quite convoluted) and then says that because one has come up with an interpretation of it where it does not make sense, therefore it is nonsense.

Of course, the correct way to read a scientific paper is to understand what the author actually meant by what he said and to see if it makes sense under that interpretation. Admittedly, if you think that what the author meant from what he said is sufficiently unclear, one would note that the paper has a pedagogical issue but one would not conclude that it is nonsense. (The fact that most of us reading Arthur's paper didn't seem to have any significant trouble interpreting what he said makes it unclear whether there is even any potential pedagogical issue here.)

In relating this to G&T, I think it is instructive to compare, say, their section where they complain about various statements of the greenhouse effect with this website: http://www.ems.psu.edu/~fraser/BadMeteorology.html Fraser is quite a stickler for pedagogy and, in fact, he is a bit too militant about pedagogy for my tastes. However, the important thing is that when he comes across a statement about the greenhouse effect that he objects to, he makes a complaint about the pedagogy and does not jump to the conclusion that the whole of the science is nonsense. Apparently, there are people in this world who are missing the ability to make this distinction (or, if one wants to be more cynical about motives, which I would like to avoid but find hard to sometimes, who are purposely confusing the issues to obfuscate rather than illuminate).

By contrast, in our discussions of the G&T paper, we have labored quite hard to understand what they are saying...but can't find any way to make what they say make sense. Hence, there are some of us who think that G&T are wrong because they didn't realize that the fact that the atmosphere can warm the earth's surface more than its absence does not imply that the NET flow of heat is still from earth to atmosphere. There are others of us who believe they just didn't understand that one can only apply the Clausius statement to the NET heat flow. However, regardless of how we interpret what G&T are saying, we cannot come up with a interpretation in which their claim that the greenhouse effect violates the 2nd Law is correct.

Hmmm...my phrase "does not imply that the NET flow of heat is still from earth to atmosphere" in the previous post seems to have either too few or too many not's in it, depending on your point of view.

Perhaps the best fix is to replace "imply" with "contradict the fact".

You know, sometimes there is just no there there. Gerlich, Tscheuschner and Kramm are simply clueless. Undergraduates who never came to a lecture, never cracked a book and sailed through on aggression and attitude because it was easier to walk away from them then deal with the nonsense.

So Dr. Kramm, please tell us how all those radiometers that have measured emission from the atmosphere to the ground are doing criminal physics, or is there some majic shield on the surface that prevents the radiated energy from being absorbed.

Undergraduates who never came to a lecture, never cracked a book and sailed through on aggression and attitude because it was easier to walk away from them then deal with the nonsense."

Reminds me of some other nonsense in the news these days: the economic nonsense of Alan Greenspan, Larry Summers, Robert Rubin, Tim Geithner, et al.

The above description fits these folks to a T. For example, Greenspan, Summers and Rubin were quite insistent (to the point of bullying) that a woman named Brooksley Born was wrong when she warned that unregulated derivatives could bring our banking system and economy crashing down. Born persisted in her warnings to no effect -- because pretty much everyone else backed off and she was cut off at the pass by the bullies.

Of course, Born was right and the Bullies were dead wrong.

But the Bullies nonetheless won the day and the American people lost (big time) because, as we all know, bullies have big egos, big mouths and even bigger sticks (metaphorically speaking, of course).

http://www.thenation.com/blogs/edcut/370925/the_woman_greenspan_rubin_summers_silenced

The Bullies NEVER back off themselves but have to be forced out -- as Summers was finally forced out of the Harvard Presidency by the words and actions of folks who are MUCH smarter an much more cunning than he is.

The Bullies are attracted to bureaucratic positions like a moth toward the flame, since that's the one place where they can get away with their badgering.

Unfortunately, the Bullies (Summers, Geithner and others) are back in the saddle in the Obama administration.

And the results are entirely predictable.

Dr Kram (your 3:06 pm comment)

My equation 7 defines, as the text explicitly states, a quantity T_eff. This is *not* the average value of the temperature T - that is why I called it an "effective radiative temperature", and not the "average temperature". Similarly, equation 8 *defines* an "effective emissivity". The very brief sentence before 7 and 8 explains that these quantities *can be defined* by the following equations. Now I did use the word "averages over the planetary surface", but these obviously weighted averages - the effective temperature is weighted by the fourth power of itself, and the effective emissivity is weighted by the forth power of local temperature.

The paper later goes on to discuss actual averages, as in equation 11, which defines T_ave.

The primary object of this entire first section of the paper is the inequality of equation 12, which relates that actual average temperature T_ave, to the weighted averages T_eff, eps_eff and a_eff, in the case of a planet with no atmosphere.

Why do you insist that eps_eff is an unweighted average of the emissivity, when I make no such claim? It is, as you point out, mathematically incorrect to use the unweighted average. *That is why I did not use it!*

Arthur:

It SHOULD be pretty clear to anyone who reads further than number 8 -- and especially to those of us who get as far as number 12 -- that you are drawing a distinction between "effective" and (simple) "average".

How someone who has a PhD in meteorology and teaches atmospheric science at the university level (even as an associate faculty member) could fail to grasp that is really hard to fathom.

in fact, i don't buy that kramm does not understand.

I have to agree with Joel's assessment above. it's the only possibility that makes any logical sense.

..which means that trying to further clarify it to Kramm is a waste of time (yours).

My last word on the subject.

Is it a language issue? How do you manage to be a professor in Alaska without a good comprehension of English? Or mathematical notation, for that matter? Oh well.

Arthur:

I think you are assuming that Kramm honestly believes you are mistaken.

Given that Kramm is actually "arguing" about are essentially definitions (eg, of effective emissivity), that assumption is really hard to swallow.

He understands all right. That's almost certainly not the issue here.

Not sure whether that's the issue with T&G. They may actually believe that there is no atmospheric greenhouse effect, kind of like the guy who sits pertrified wondering when he will fall through the spaces between the atoms in his chair. I suspect that he's not subject to logic either.

Dear all,

I wonder whether you have read the manuscript of Smith (2008, see http://aps.arxiv.org/abs/0802.4324v1). Directly after his equation (6) Smith stated:

"Similar to the effective albedo, an effective emissivity and effective radiative temperature can be defined as averages over the planetary surface."

The planetary average of any arbitrary variable Y is defined by

[Y] = 1/A INT_A (Y dA) = 1/(r^2 A_s) INT_A_s (Y r^2 dA_s) = 1/(4 pi) INT_A_s (Y dA_s)

Here, A is the surface of the sphere, A_s is the solid angle (A_s = 4 pi in the case of a sphere), dA_s is the differential solid angle, and r is the radius of the sphere. There is no other way to define a reasonable surface average. Obviously, the radius plays no role.

If we set Y = T^4, then the planetary average is given by

[T^4] = 1/(4 pi) INT_A_s (T^4 dA_s)

It is clear that [T^4] is not equal to (T_eff)^4.

In the case of Y = eps, the planetary average reads

[eps] = 1/(4 pi) INT_A_s (eps dA_s)

This means that Smith's eps_eff given by his Eq. (8) is not a planetary average as he stated before.

Arthur,

please, do not try to correct Gerlich and Tscheuschner with wrong or inappropriate equations.

Gerhard Kramm

P.S.: In my manuscript on Smith's averaging procedures (see http://www.gi.alaska.edu/~kramm/climate/Arthur%20Smith%20and%20the%20basic%20rules%20of%20calculus.pdf ), one can find a more detailed explanation.

Dr. Kramm,

If you find Arthur's terminology confusing, I suggest that you replace the word "averages" with "appropriately-weighted averages". However, I have to admit that I am puzzled as to why a little ambiguity in terminology has thrown you off so much. Clearly there are different sorts of averages and Arthur's equations define the sort of averages that he has found it useful to define. You seem to be the only one who was so hopelessly confused by this point.

And, Gerlich and Tscheuschner seem to be the only ones who were so hopelessly confused by the different statements in the literature regarding the atmospheric greenhouse effect that they came to the ridiculous conclusion that it violates the Second Law of Thermodynamics.

And, frankly, I find myself confused about whether it is really possible for PhD physicists and meteorologists to get so easily confused by minor issues of terminology and definitions or whether there is actually a purposeful attempt at obfuscation going on. Or, maybe it is just a shining example of people not understanding what they do not want to understand. I don't know.

Joel Shore

Kramm:

Smith's equations speak for themselves. The way he has DEFINED effective emissivity is perfectly reasonable and in line with how it is normally defined in the literature.

If you can't see this, it's not Smith's fault -- and certainly not something he should even concern himself about.

For such a trivial case, words are only necessary for the non-mathematically inclined.

If you indeed don't understand this (and are among the non-mathematically inclined), the ones who should really be concerned are your colleagues at the U of Alaska. (Just my opinion, of course)

But I think that you do understand it and quite frankly find it absolutely pathetic that you would resort to a petty rhetorical "argument" over terminology rather than admit you are wrong in this case.

Dear Joel Shore,

Since I am well familiar with density-weighted averages (see, e.g., Kramm and Meixner, 2000, Tellus 52A, 500-522), I immediately checked, whether Smith's "average" is in substantial agreement with a weighted average. It is not.

Dear Anonymous (7:26)

please list textbooks or papers in which Smith's averaging procedure used in his Eqs. (7) and (8) is defined. I would like to laugh.

Gerhard Kramm

Averages get calculated with all kinds of weights.

For convenience we can use square brackets to represent a simple surface average. If V(x) is some variable that has different values in different regions, then the average may be denoted [V], which is a single value for the whole surface.

This is defined by a surface integral. [V] = INT(V(x) dx) / Area.

In the special case of a sphere you can do a substitution of variables, so as to integrate over solid angles, rather than over small areas directly, if you really want. The substitution is dx = r^2 dA, where dA is a small solid angle and r is the sphere's radius. For a sphere, you get
INT(V(x) dx) / Area = INT(V(A) r^2 dA) / 4.pi.r^2 = INT(V(A) dA) / 4.pi
[V] = INT(V(A) dA) / 4.pi

The two formulations are exactly the same, as long as you have a sphere. Arthur's paper uses the more general formulation, which is better because the Earth is not quite a perfect sphere.

Every time you see Dr Kramm insisting that the only way to handle this integration is with solid angles rather than with areas, or every time you see him say that the "radius" should or shouldn't appear in some formulae, you are seeing him make this mistake in elementary calculus – an inability to do a simple change of variable.

A weighted average is simply [V.w]/[w], or [V.w/[w]], since [w] is a constant value that does not depend on the part of the surface. The expression w is the weight. What you use for a weight depends on the application.

Using this notation, the equations in Arthur's paper could be given as follows.
(7) Τ_eff ^4 = [T^4] -- defines T_eff using an unweighted average of T^4
(8) e_eff = [ε.T^4] / T_eff^4 -- defines e_eff as a ratio of unweighted averages.
That is, the effective emissivity is simply defined to be that which gives you the average energy when applied to the average temperature^4 using Stefan-Boltzmann.

You can also think of e_eff as a weighted average. It's not "density" weighted, of course, unless you use density as a synonym for weight; it's weighted by T^4.
e_eff = [ε.T^4] / T_eff^4 = [ε.Τ^4]/[Τ^4]
... and that is what a weighted average means.

Nothing shows up better how completely confused Dr Kramm is that he actually wants a text book for this. Whether this is deliberate malice in attempt to confuse readers, or whether Dr Kramm is actually this incompetent, I cannot judge. Which ever it is, it won't help to hold his hand through simple text book definitions and try to teaching him how to apply them in reading a real paper. The explanations given here will be enough for anyone with minimal ability. If these explanations are not enough, a text book won't help either.

Like I said before, what both Dr. Kramm and G&T are doing is nitpicking pedagogy but pretending that this then leads to something that is incorrect by deliberately refusing to understand what the author meant. I.e., they work their hardest to come up with convoluted interpretations different from what they authors meant under which they can argue that what is written does not make sense. This is completely against the spirit of scientific inquiry. It is perhaps what a lawyer would do if he had to defend a client who was so obviously guilty that he didn't have any serious arguments that he could make.

The only people who don't see through this sort of deceitfulness (or extreme self-delusion) are those who want to be fooled, but I suppose that is the whole point: Now, those on the internet who want to believe that Arthur's critique of G&T is wrong will be able to point to Dr. Kramm's nonsense to convince themselves and their compatriots to continue to believe real scientific nonsense.

My Dear Kramm:

You have convinced me (again).

You actually don't know what "effective emissivity" means.

You had actually convinced me of that some time ago when I posted this comment on an earlier thread, but your clueless-ness had slipped my mind in the interim.

But thanks for reminding me (ie, thanks for nothing)

Dear Duae,

You stated:

"The two formulations are exactly the same, as long as you have a sphere. Arthur's paper uses the more general formulation, which is better because the Earth is not quite a perfect sphere."


Smith only considered a sphere because its surface is 4 pi r^2. If one considers the true shape of the earth because the radius of the equator, 6378.14 km, is larger than the radius to the poles, 6356.75 km, owing to centrifugal forces, one has to write for the average over the earth's surface (using your notation):

[V] = INT(V r^ dA_s)/INT(r^ dA_s)

Only in the case of a sphere

INT(r^ dA_s) = 4 pi r^2

Best regards

yours

Gerhard Kramm

Ah, but in the case where the planet is not a sphere, one simply has to take 'r' as the "effective" radius of the planet, and the formula works just fine :-)

Duae, your explanation of why I used the word "average" in the text above and what I meant by equations 7 and 8 is spot on. I might even update the arXiv paper to clarify this a bit better (but then, what would the Kramm's of the world find to complain about? Ah, of course, he still has his solid angle argument to go on).

I did have a few other typos and corrections I've been collecting so now might be a good time to send in an update. Probably not this week though.

What's the difference between "cramming" and "Kramming" for a test?

In the former case ("cramming"), you may start out knowing little to nothing but (usually) end up knowing enough to pass. In other words: it helps.

In the latter case, you may start out knowing enough to pass, but inevitably end up utterly (and hopelessly) confused. In other words: it hurts (usually a lot).

Dr Kramm's formula

[V] = INT(V r^2 dA_s)/INT(r^2 dA_s)

is correct. It's what you have to do when "r" is a function of "A", rather than constant everywhere. The best method, however, is to keep it as simple as possible and use dx = r^2 dA with a simple change of variable to integrate over area directly. That gives:

[V] = INT(V dx) / Area

which is the more fundamental definition of an average over any surface. It avoids an completely irrelevant distraction about "r".

But look! Kramm has just implicitly acknowledged he's been wrong to insist the radius plays no role. For example, see his comment above at 9:17 PM a few days back. Back then he gives an expression than is only strictly correct when "r" is a constant.

[V] = INT(V dA) / 4pi

Kramm has been saying that the more general surface integral dx is "wrong". He's got enough knowledge to understand that he should retract that objection. The reason he's not given the retraction yet is apparently not simply incompetance, but a lack of integrity.

This argument about how to do an average over a surface is really a side (freak?) show to the main event.

Lots of scientists (eg, at NASA and elsewhere) have done that and the answer always comes out close to 288K. This is not rocket science. It's a very simple surface integral that pretty much anyone who has had basic calculus can do, at least to get a ballpark figure, which indeed DOES come out close to 288K.

The fact is, Kramm can't argue against the greenhouse effect -- because that requires a denial of reality.

So he argues about whether an average taken over a surface has to have an "r-squared" appearing explicitly in the formula (or not).

it's absurd.

Apparently no one ever informed Kramm that spherical coordinates are not the only (and not even the most general) coordinate system you can use for the earth.

------- Quote -------
"[Yet, be that what it may, Gerlich and Tscheuschner have found a physics journal to house their contribution. It is the International Journal of Modern Physics, B, not a journal of geophysics, climatology or meteorology but a journal that publishes articles about condensed matter, high temperature superconductors, and statistical and applied physics. To attentive observers this immediately raises red flags that something is seriously wrong. You would not expect editors of such a journal to have much expertise about climate. According to the published rules of the journal all review articles, such as that of Gerlich and Tscheuschner must be invited which is still more concerning]"
------- End Quote -------

You're obviously a fish in a small pond. You think that all you need is to be an expert in climatology in order to understand climate science.

There are lots of climate data analysis tasks that obviously you don't need to be an expert in climatology in order to conduct an analysis.

First, in science (whatever disciplines), you can analysis the data via using axiomatic-driven models (ie, physical processes as in physics/climate models are fully/partially known in advance as apriori) where expertise in this area are definitely needed. Second case, if one doesn't know the underlying processes in advance (apriori), then one has to revert to data-driven models in order to estimate or make rough guesses about those unknown underlying processes. This means that you don't need to be an expert at all in climate science, the only requirement is that one needs to understand the particular data-driven methods being used and that's fact.

I can quote you some examples of climate science data analytics that were published in non-related climate journals, such as computing, data-mining, etc,... If those papers were to submit to a climate related journal, I bet that reviewers from those journals (would have no clue to the methods/algorithms being used in those papers because those methods/algorithms are still unknown to climate scientists). Here are some examples:

#1) "A Parallel Nonnegative Tensor Factorization Algorithm for Mining Global Climate Data"
http://www.springerlink.com/content/u4x12132j06r40h3/ (from LNCS - Lecture Notes in Computer Science)

#2) "Dowinscaling of precipitation for climate change scenarios: A support vector machine approach"
http://eprints.iisc.ernet.in/18799/ (Journal Of Hydrology)

#3) "Semi-supervised learning with data calibration for long-term time series forecasting"
http://portal.acm.org/citation.cfm?id=1401911 (Knowledge Discovery and Data Mining Journal)

There are tons that I can quoted, but the 3 references that I have linked to above clarifies my point. Your criticism of the reviewers for International Journal of Modern Physics is at best unscientific.

Eli thinks it good that anyone writing on climate understand basic thermo. Other than that a passing acquaintance with the data and the basics helps a heap.

Unfortunately G&T have none of the above

With regard to your three papers it would be a good thing if at least one of the authors understood how the data series they are cranking on was constructed.

Eli just picked the second one at random on downscaling, and the authors include people who work on hydrology, so yeah, since they work on hydrology, publish in the Journal of Hydrology, it is dollars to donuts that the editor can find referees, especially since journals always ask you to propose a couple of referees.

You gotta problem with that?