Saturday, March 17, 2007

Eli writes a letter (cont.)

The following argument in Essex, McKitrick and Andresen proceeds from their flawed (FUBAR occurs as a kind description, FUMTU could suffice, although MOAFU might be better were it not needed for other parts of this paper ) discussion of the cup of coffee and the cold water. Clearly the linear average is preferred on physical grounds. A mass weighted linear average :

  • reproduces the cooling curve one would obtain if the two liquids were first mixed.
  • is independent of the zero of the temperature scale, and depends only on the magnitude of the degree as a multiplicative constant.
  • is proportional to total energy for homogeneous systems using the Kelvin scale.
None of the other proposed averaging methods have these qualities. The only other proposed averaging method which had any physical justification was T^4, but in that case, instead of using the mandatory Kelvin scale, Celsius was used. Having misinterpreted the implications of their own example, the authors use their error to motivate (either that or they really want an IgNoble and the cash prize that goes with it) a detailed discussion of averaging, defining two types of averages:
r-mean Average = [1/N (x1^r + x2^r+ ....... +xN^r)]^(1/r)

s-mean Average =(1/s) [ln{ 1/N (exp[sx1] + exp[sx2]+ ....... +exp[sxN])}]
The r-mean for r=0 is unity. The s-mean is undefined. (Wait young bunnies.) While for other r and s these are mathematically well defined their utility varies. For example, for even powers of r, negative and positive temperatures will contribute equally and the average will always be positive. If r=2 and T=-2, -2, -2, the average would be +2. Applying the same principal to a balance sheet would make three years of losses an average gain (reality is a harsh Ms. Rabett). For negative values of r, if there were a zero in the data, the average would blow up. In those cases one might try a temperature scale where the zero was always lower than the lowest data value. (Kelvin anyone?)

For r>1 the averaging overweights large values, the same is true for the s averages which are used in economics. For the series 3, 4, 2, 5, 3, 5, 345 the average for r=1 is 52, r=3 is 180, r=5 is 234 and for s=1 the average is 343. While there may be reasons why one wants to do this, measuring the average temperature of a system is not as was shown in the first part of this letter.

In Section 4 Essex, et al. describe methods used to calculate global temperature anomalies. While the description is correct, Essex, et al., make a series of ex cathedra claims about these methods which are not justified in the text other than as tenets of belief, and for which there is a considerable refereed literature justifying the methods and discussing the magnitude of uncertainty or error that would be introduced. Essex, et al. draw broad and confident conclusions without justification or reference to other studies, refereed or not, and base further arguments on their assertions. One wonders why the referees did not object to this bootstrapping. Certainly a more sophisticated (adult, grown up.....) discussion of these issues is needed in this article. Essex, McKitrick and Anresen use this to claim that
So far we have shown that different averages exist (true), they are used (sometimes appropriately and sometimes not) and that contradictory trends can emerge between them (if you use them inappropriately). We have shown that the conditions exist in the atmosphere where such paradoxical behavior can be expected to be found. (not done, asserted, but probably true if you use an inappropriate average)
More tomorrow......

10 comments:

Anonymous said...

"One wonders why the referees did not object to this bootstrapping."

Based on the failure of the referees to catch the misuse of Celsius in the Stefan-Boltzmann radiation equation, what's to wonder about?

All the wonder and mystery (about the referees and the authors) was removed in one fell swoop.

I taught high school physics and many of my students knew far more physics than these guys (the authors or the referees).

In fact, I'd have to say that my average student had a better physical sense than the Three Blind Mice & Three Blind Referees (if you will humor me for a moment and allow me to average students.)

TBM & TBR may have some knowledge of mathematical equations, but they clearly have no idea how to apply them to the real world -- or how to interpret the answers they get when they do.

McKitrick and friends get an "F" for physics in my book. It's really absurd that a scientific journal that purports to be about thermodynamics (has it in its name, for God's sake) would accept such sheer physical nonsense for publication (except perhaps in the April Fools day spoof edition).

I intend to write to this journal. You bet I do.

John A said...

McKitrick and friends get an "F" for physics in my book. It's really absurd that a scientific journal that purports to be about thermodynamics (has it in its name, for God's sake) would accept such sheer physical nonsense for publication (except perhaps in the April Fools day spoof edition).

Actually you've missed the crucial part where you, Rabett, Lambert and the other ignoramuses all fall down.

It's about NON-EQUILIBRIUM thermdynamics. The stuff you've been teaching is all about gases in local thermodynamic equilibrium.

Which is why you'd get a "U" (unclassified) because you failed to understand the question.

I intend to write to this journal. You bet I do.

I look forward to it. Can you include Rabett and Lambert so you can spread the blame?

All of this entertainment for free. I can hardly believe it.

John A said...

Clearly the linear average is preferred on physical grounds. A mass weighted linear average :

* reproduces the cooling curve one would obtain if the two liquids were first mixed.
* is independent of the zero of the temperature scale, and depends only on the magnitude of the degree as a multiplicative constant.
* is proportional to total energy for homogeneous systems using the Kelvin scale.


Oh dear. Do you want to think about this?

Anonymous said...

"Actually you've missed the crucial part where you, Rabett, Lambert and the other ignoramuses all fall down."

The crucial part?

The authors of the paper in question are using Celsius temperatures in the Stefan-Boltzmann equation, for goodness sake.

That's rubbish -- and if you don't know that, I would suggest that you take a (very) basic physics class at the local community college (or high school, for that matter).


"Can you include Rabett and Lambert so you can spread the blame?"

Spread the blame? What in the world has that got to do with whether the physics in the paper in question is wrong?

(and I don't know about "Lambert", but "Rabett" is a fictitious name, by the way)

Steve Bloom said...

As is "A." Well, actually, apparently it stands for Andrews, but we're not supposed to know about that little slip.

Anonymous said...

John Andrews (Thanks Steve) said: "It's about NON-EQUILIBRIUM thermdynamics. The stuff you've been teaching is all about gases in local thermodynamic equilibrium."

John, before you make a bigger fool of yourself than you already have, you may want to read what I wrote about local thermodynamic equilibrium in the comments here

Though I must admit, I have serious doubts that you will be able to understand the physics, basic as it is.

EliRabett said...

Steve, mice,

We want to be kind to guests before Ethon has them for lunch. Please refer to John as John A. In accord with our policy we respect anonymity and privacy at Rabett Run. Besides which, Eli finds rather prefers a different completion for A.

Steve Bloom said...

John A. for lunch? Eli, you might want to first establish whether it's possible for Ethon to OD on bile.

Anonymous said...

We -- the undersigned anonymice -- also have the utmost respect for anonymity (Edimome too)

Respectfully yours,

Anon Y. Mouse, III
(aka A. Nony Mouse)

Joel Shore said...

Eli:

Minor nitpick: Both the r-mean and s-mean are undefined when r=0 or s=0. However, both are well-defined in the limit that r -> 0 and s -> 0 so, for example, if you are doing it computationally, you can compute the value at, e.g., r=0.001 instead of r=0.