## Away with the fairies

Journalist David Appell appears a couple of times in *The Hockey Stick Illusion*, firstly in Chapter 4, in the section entitled "Mann's mouthpiece", where he is the source (if perhaps not the ultimate source) of the (false) claim that Mann sent McIntyre an Excel spreadsheet. It's worth reading again if you have a moment.

Anyway, in the wake of Mark Steyn's book on Michael Mann, Appell has written to Jonathan Jones enquiring about the latter's comments on the Hockey Stick and the results have been written up in a blog post here. It's hilarious.

For example, Jones observes that bristlecones are not reliable temperature proxies and that principal components analysis requires data to be centred, before following up with similar scientific objections to a couple of other papers that Appell has cited in support of Mann. Appell's response to all of these objections is, in total:

This is clearly just a lot of hand-waving.

Read the rest of it too. The guy is away with the fairies.

## Reader Comments (231)

Latimer Alder wrote:

"No doubt he can prove it by showing us the superexponential equation that describes the data."

I've already done that, at

http://davidappell.blogspot.com/2015/08/more-about-generating-hockey-sticks.html

and with the fits as given by Hüsler and Sornette, linked to in that post.

WFC wrote: "If this is the definition you rely on, can you please explain:

(a) what is X? And

(b) why did X stop changing in the 1960s?"

1) X is the growth rate of some quantity Y:

dY/dt = XY

where t is time.

2) I don't know. Various reasons, I'm sure, but it doens't matter for my argument.

lapogus wrote:

"25% ? That's funny...."

Funny how?

Jim R wrote:

"Appell seems to feel that because of increasing CO2 the Hockey Stick is an obvious result."

False. It's because of the superexponentially increasing CO2.

"But that would indicate a belief that there had been no natural variability in Earth's climate... despite all the evidence that climate have varied in the past."

Of course there's natural variabity, but that isn't forced. Climate varies when it's forced to vary. Now the forcing is anthropogenic GHGs.

Wrong. You have seriously misunderstood the math I've presented.You haven't presented any math. I presented a clear solution to a differential equation. I explained why, for any bounded value of r, the result is still exponential. From first principles.

You need to read harder -- I clearly explained here what I meant by superexponential: a growth rate X%/yr where X is an increasing function of time.And as I explained, and provided a formalisation to demonstrate, where X is bounded that is still exponential. And in both carbon emissions and population, X is bounded. The growth is then never greater than the ordinary exponential term max(X%/Yr). Your term "superexponential" is redundant.

The low-level of mathematics displayed here is disappointing.Laughable. Given I have presented a complete formalisation of the problems you are describing, and the reasons why they cannot be anything other than exponential from first principles, and you respond by assertion without any formalisation of the problem that I'm wrong.

Your response is utterly pathetic. You have presented no actual mathematics, just hand-waving nonsense. You are an embarrassment to science journalism.

JimR wrote:

"Few if any show the flat, unchanging climate as MBH."

MBH doesn't show that.

Have you even read the papers?

What forcing do you think should be causing nonflatness?

Oh and Appell, when you quoted my example, you missed an important bit off. I'll add it back on for you:

His claim amounts to observing that the sequence 6^X rises faster than 5^X, therefore 6^X is "superexponential". This is complete nonsense. The sequence 6^X, orany composite sequence involving 5^X and 6^Xnever rises faster than 6^X, which is itself exponential, and not super-exponential.Please note the bolded bit, which explains why your claim of a varying rate makes it something other than exponential is utterly wrong.

SpenceUK wrote:

"Yep, they create a "superexponential" population rate by assuming r is unbounded. In other words, at some point in the future, they assume every woman in the human population will be giving birth to literally thousands of babies every year."

False. We've already had superexponential growth in population (growth of growth rate > 0), without every women having a thousand babies.

But the growth of the growth rate is now < 0, meaning the increase is no longer superexponential.

David Appell

You have accepted that Mann's proxies stopped recording temperature growth during the 1960s - which is why temperature readings were spliced on at the end.

You have suggested that this was because something experienced "superexponental" growth until the 1960s, but stopped thereafter. My question is simple - what?

I cannot believe that you don't realise how and why this matters for your argument.

If there is no good reason why the reconstructions would have been inaccurate during a period when they could be measured against actual temperatures, there can be no confidence in their being accurate for periods when they couldn't be so measured.

And when the unmeasurable period includes a period (the MWP) for which there is ample historical evidence of an unusually warm climate - yet which disappears from the "hockey stick" - the need for such confidence is greater still.

(And, before you voice the objection that the historical evidence relates almost wholly to the NH - for obvious reasons - I would remind you that the "hockey stick" was likewise limited to the NH.)

So ... what changed in the 1960s?

Spenceuk wrote:

"You haven't presented any math."

Funny....

http://davidappell.blogspot.com/2015/08/more-about-generating-hockey-sticks.html

"And as I explained, and provided a formalisation to demonstrate, where X is bounded that is still exponential."

Of course X is bounded. What matters is whether dX/dt = 0. For human population, and for CO2, there was a substantial period of time where it wasn't. That's the superexponential growth.

WFC:

My argument has nothing to do with MBH's proxies. Or anyone's proxies. Nothing.

"You have suggested that this was because something experienced "superexponental" growth until the 1960s, but stopped thereafter. My question is simple - what?"

I'm not a demographer.

But I would guess that as the world's population became more affluent and more educated, having lots of children became less important.

But my argument doesn't depend on that, only on the observation that the growth rate X peaked at some point and then started to decline, meaning the end of superexponential growth.

WFC wrote:

"And when the unmeasurable period includes a period (the MWP) for which there is ample historical evidence of an unusually warm climate - yet which disappears from the "hockey stick" - the need for such confidence is greater still."

What "ample evidence?"

Analyzing the evidence is exactly what MBH did, as have all reconstructions since.

They do not find a global, or NH, MWP.

So what evidence are you citing to say there WAS a global MWP? Some hand-drawn graph from Lamb for Northern Europe?

"(And, before you voice the objection that the historical evidence relates almost wholly to the NH - for obvious reasons - I would remind you that the "hockey stick" was likewise limited to the NH.)"

And it did not find a global MWP. Nor have followup reconstructions, the most comprehensive of which is PAGES 2k.

SpenceUK wrote:

"You have presented no actual mathematics, just hand-waving nonsense."

False. I have, in fact, presented a very clearly defined mathematical system. Once again:

1) Suppose atmospheric_CO2(t) increases superexponentially -- that is, that its growth rate X(t) satisfies dX/dt >0

2) Suppose temperature change T(t) is proportional to forcing change F(t).

3) Suppose F(t) = constant*log(atmospheric_CO2(t)) + constant

Then the temperature change T(t) will follow a hockey stick curve.

David Appell, you refute my statement that it has stopped getting warmer, and refer me to articles written by David Appell.

Based on track records, why should I trust any climate scientist trying to hype global warming? I did once, but in the absence of any predicted consequences, I cannot see the point in taking it seriously anymore, apart from the lives ruined, money wasted etc.

It would be better for the world if climate scientists were paid for forecasting correctly, rather than predicting wildly. No other taxpayer funded 'profession' would get away with this level of perpetual inaccuracy, especially as all the inaccuracies point in the same, wrong direction.

golf charlie:'

"Based on track records, why should I trust any climate scientist trying to hype global warming?"

shorter golf charlie:

"I make up my mind without looking at the data, thank you very much."

David Appell

"growth rate X"

What, I ask again, is X?

David Appell

Perhaps you can explain to me exactly how MBH "analysed the evidence" for the MWP. (Not a link, please. A man with your understanding should be able to explain it succinctly.)

Since you mention him, you could start by explaining how MBH analysed it better than Lamb did, before them, and then go on to explain how all the previous historians and geologists got it wrong also.

Then, perhaps, you can go on to explain how MBH "analysed the evidence" showing that there wasn't a LIA, either.

WFC wrote:

""growth rate X"

What, I ask again, is X?"

I'm not explaining it a third time -- it's clearly beyond you.

WFC wrote:

"Since you mention him, you could start by explaining how MBH analysed it better than Lamb did"

Link to Lamb's papers?

Try

You mean, you don't already know? How can that be?

Not like you to be dismissive of something you know nothing about.

Well, perhaps, instead, you can start by answering my first question : namely, how did MBH analyse the evidence for a MWP?

David Appell,

I made up my mind based on the Hockey Stick and data presented by Michael Mann. I have the honesty to admit I made a mistake.

You don't.

WFC:

You can't list Lamb's evidence. Clearly.

Yet more of a waste of time here.

Dave Appell wrote:

"Have you even read the papers?"

After reading your many postings over the past several days I would have to ask you the same thing.

Do you realize the subject of MBH was proxy reconstructions? I ask because you keep focusing on the blade and better metrics of 20th century temperature rise already existed prior to MBH. You said today in comments to another post "My argument does not depend on proxies in any way whatsoever." which is odd when you seem to be defending Mann and his multiproxy reconstructions.

Do you realize that the issue with decentered PCA is about proxies and the shaft of the hockey stick? Bristlecones are a proxy and are a major influence he shaft of the stick? You basically want to call people stupid for not understanding physics when you are completely talking past actual the issues with Mann's hockey stick and simply want to focus on the blade.

I realize you have written extensively on the subject and yet here you are simply talking past the many issues with Mann because you want to focus on the physics of CO2 climate forcing.

JimR wrote:

"My argument does not depend on proxies in any way whatsoever." which is odd when you seem to be defending Mann and his multiproxy reconstructions."

I haven't defended Mann et al (everyone forgets the et al) about anything.

I've said general physics says there should be a hockey stick curve.

JimR wrote:

"Do you realize that the issue with decentered PCA is about proxies and the shaft of the hockey stick?"

My argument does not depend on any proxies or any centering or any methodological choices of that sort. It's a very general argument, which is its strength.

However:

"Figure 1 (top) shows the result of these pseudoreconstructions for one realization of the white noise (with noise variance 50%) and (bottom) one realization of the red noise (high-frequency noise variance 50% and with 1-year lag autocorrelation of a = 0.8):

in both cases PCA-centerings has a small relevance for the final result and the differences are within the uncertainty range(Figure 1). The conclusion is essentially the same for all realizations and other constructions of noise. For instance, white noise with r = 0.7 yields a standard deviation of the differences of 0.006K; r = 0.4 yields 0.007K; red noise with a = 0.5 and r = 0.7 (r = 0.4) yields 0.01K (0.02K); red noise with a = 0.8 and r = 0.7 (r = 0.4) yields 0.02K(0.03K). Therefore, the differences increase slightly with the amount and redness of the noise, but they remain small, even in the case of high and red noise with a steep red spectrum."-- "Comment on ‘‘Hockey sticks, principal components, and spurious significance by S. McIntyre and R. McKitrick," Hans von Storch and Eduardo Zorita, Geophysical Research Letters, v32 L20701, doi:10.1029/2005GL022753, 2005.

Dave Appell wrote:

"I haven't defended Mann et al (everyone forgets the et al) about anything."

Wow, you have fooled me. I did notice that when you reached out to Jonathan Jones of Oxford instead of giving him your 'no proxy necessary physics proves it all' theme your questions to Jones were on his criticisms of MBH.

So do you realize that many other reconstructions do not show a hockey stick shape due to higher past variability?

Or did you just join the comments to Bishop's posts and talk on a completely different subject? Because it gave all appearances of you engaging in the discussion to defend Mann's shoddy work.

Hey, I'm OK with you not defending Mann's work as it is a bit of a carnival side show and not a reflection on currently climate conditions. It has always been confusing that so many do defend his work.

Ian Joliffee upon finding out his name was being used in support of MBH decentered PCA made clear he did not support the use of decentered PCA and said "It therefore seems crazy that the MBH hockey stick has been given such prominence and that a group of influential climate scientists have doggedly defended a piece of dubious statistics."

So I'm happy to hear you are following this path and no longer doggedly defending Mann's "dubious statistics" as IIan Jolliffe described Mann's work.

JimR wrote:

"So do you realize that many other reconstructions do not show a hockey stick shape due to higher past variability?"

Which?

Jim R wrote:

"Or did you just join the comments to Bishop's posts and talk on a completely different subject? Because it gave all appearances of you engaging in the discussion to defend Mann's shoddy work."

I haven't said a thing about Mann et al's work.

In what way is MBH's work "shoddy?"

JimR:

I haven't said a thing about Mann et al's work.

Except that simple physics shows it is not a surprising result.

Do you understand basic physics, Jim?

David Appell, you could find links to numerous non-hockey-stick studies through this secondary source.

http://hockeyschtick.blogspot.fi/#uds-search-results

and by using "non-hockey-stick" as your search key.

However, based on previous exchange with you, I would be surprised if you find the courage to question your faith.

Petfin: I'm not going on a wild goose chase for you. Either you can cite science, or you can't.

David Appell, why would I waste any more time with you when we both know that you would not read any blasphemy against your CO2-religion. You would easily find the citations under each of the search results if you had the slightest amount of scientific mind in you. Heck you would even find the abstracts and links to the publications. Too much for you to handle though.

Appell, you continue to be absolutely clueless about simple mathematics

Of course X is bounded. What matters is whether dX/dt = 0.No, it doesn't matter one tiny bit. To avoid confusion, I will refer to the growth rate as r instead of X since I have used X for other things earlier. Consider the condition where r is DISCONTINUOUS. That is, r is undifferentiatable and dr/dt is undefined at that location. What impact does this have on the population curve?

As I noted above, the population curve follows e^(rt), so let us consider the case where r undergoes a step change (that's a discontinuity to you and me) from r=0.01 to r=0.02. The resulting population curve remains continuous, before the step it follows the curve e^(0.01t) and after the curve it follows e^(0.02t). Neither of these portions of the curve increase at a rate faster than the simple exponential e^(0.02t), so the resulting curve is not, and is never anything other than a simple exponential. Note the discontinuity in r (with associated undefined dr/dt) does not invalidate the population curve which remains continuous with a join of two different exponentials.

Your simple mathematical error is to note that the curve is increasing faster than e^(0.01t), and therefore declare it to be greater than one specific exponential. That does not mean it is increasing faster than an exponential generally, because I can choose a different simple exponential which is increasing faster.

The example with discontinuous r is the most extreme case of a change in r. Any more gradual change in r, including one that is continuous and differentiable, simply results in a composite curve which transitions from e^(0.01t) to e^(0.02t), which once again, never increases any faster than the simple exponential e^(0.02t) for any arbitrarily large value of t.

More amusingly, you could try the condition r=ln(5) transitioning to r=ln(6). Guess what that gives you? It gives you a portion of the line being 5^t, followed by a portion of the line being 6^t. A line which does not increase faster than 6^t, a simple exponential.

Your very strange belief that a positive dr/dt gives anything other than exponential growth for bounded (but variable) r is "not even wrong". It is simply the ramblings of an activist with a very poor grasp of mathematics.

Now I don't rate the arXiv preprint linked by Halpern very highly at all, but at least they don't make the same mathematical error that you do. In order to create their "super-exponential" population growth, they make r an unbounded function of population size. Why do you think they do that, David? Could it be because they want to avoid making the same simple error you do? At least they genuinely do create a curve which will exceed any finite exponential at some point, so their concept of "super-exponential" is at least mathematically meaningful, unlike yours. Of course, their model is then physically meaningless, but that's another story.

SpenceUK: r will not be discontinuous in any physical system.

Petfin: I simply asked who funds CO2science. Why is that such a problem to answer?

SpencerUK wrote:

"Your simple mathematical error is to note that the curve is increasing faster than e^(0.01t), and therefore declare it to be greater than one specific exponential."

You are as dense as WFC.

Can't you read?? I said exponential growth of the quantity Y is when

dY/dt = X(t)Y(t)

where dX/dt >0.

This leads to solutions that increase superexponentially.

I can't make it any simplier than this.

Oh, and as an aside, your "proof" of a hockey stick falls over from this assumption:

2) Suppose temperature change T(t) is proportional to forcing change F(t).Temperature change T(t) includes a stochastic element (unforced natural variability) which trashes this assumption. That's the failure of your reasoning right there. The purpose of the hockey stick was to undermine the idea that unforced variability was large enough to explain the 20th century climate change. However, other temperature reconstructions show much larger unforced variability than Mann's hockey stick - in fact, most recent reconstructions have estimates of standard deviation which directly contradict (i.e., have non-overlapping confidence intervals) Mann's hockey stick in the pre-industrial period.

The failure to properly characterise unforced natural variability is the single biggest failure of climate science as an enterprise. That activists like you want to pretend it doesn't exist is no surprise, since it busts your narrative. The only word to describe this is "delusional".

"Temperature change T(t) includes a stochastic element (unforced natural variability) which trashes this assumption."

Natural variability averages to zero over sufficient time. It cannot create a permanent change in T(t).

"The purpose of the hockey stick was to undermine the idea that unforced variability was large enough to explain the 20th century climate change."

A lie. The purpose was to reconstruct 20th century temperatures.

"The failure to properly characterise unforced natural variability is the single biggest failure of climate science as an enterprise."

Ridiculous. An unforced factor cannot force climate to change. It shifts heat around -- it does not add heat to the system.

SpenceUK: r will not be discontinuous in any physical system.Wow, you are completely inept. The point I made was that even if it were discontinuous, the population curve is still exponential. For anything less than discontinuous, guess what: it is still exponential.

Can't you read?? I said exponential growth of the quantity Y is whendY/dt = X(t)Y(t)where dX/dt >0.This leads to solutions that increase superexponentially.You can make stuff up all you like and declare redundant, mathematically meaningless expressions until you are blue in the face. As I've shown, for population growth, the relationship is always exponential, i.e. there is always a defined, finite, simple exponential that exceeds the rate of population growth, and the term "superexponential" is redundant and daft. The relationship is "exponential", your arbitrary and mathematically meaningless "superexponential" is pointless, redundant hyperbole.

David, who care who funds co2science if what they do is listing references to scientific MWP-publications by independent research groups? By declining to read through the science publications that they are referring to, you try to deny the existence of those numerous scientific publications, like this one:

Goni, M.A., Woodworth, M.P., Aceves, H.L., Thunell, R.C., Tappa, E., Black, D., Muller-Karger, F., Astor, Y. and Varela, R. 2004. Generation, transport, and preservation of the alkenone-based U37K' sea surface temperature index in the water column and sediments of the Cariaco Basin (Venezuela). Global Biogeochemical Cycles 18: 10.1029/2003GB002132

Since you never answer any of my questions above, lack basic understanding of the distinction between primary and secondary sources, and continue unscientific hand-waving, we are through wasting my time.

Population growth rates are never discontinuous.

Nor are growth rates for any real physical system.

"As I've shown, for population growth, the relationship is always exponential"

Baloney. Solve the equation

dY/dt = X(t)Y(t)

where X(t) = exp(at^2) where a is a constant.

Natural variability averages to zero over sufficient time.That assumption is almost certainly wrong, due to long-term persistence in the climate system. You don't know what "sufficient time" is, and could well be far longer than the hockey stick period.

But this is priceless:

A lie. The purpose was to reconstruct 20th century temperatures.The purpose of the hockey stick was now to reconstruct 20th century temperatures?

Oh please stop, my sides are aching from laughing too much.

Petfin: I care who funds CO2science. WHo is it?

I care because they are clearly propagandists who avoid the peer reviewed scientific literature and conferences where their ideas would be challenged by knowledgable.

They don't even give their phone number, last time I looked.

They're afraid, because they realize their work doest not meet professional standards.

But they don't care. They get paid well, and all they want to do is fool people just like you, who don't know enough to ask hard question, and who will repeat their crap without thinking much about it.

Sorry -- the purpose of the hockey stick was to reconstruct temperature for the period covered by the proxies, whatever that was.

Petfin: Which of the authors of your paper come from CO2 science?

None, that's who.

Population growth rates are never discontinuous.Well done *golf clap*, I didn't say they were. I used the discontinuity to illustrate the most extreme change in r, and noted that even under that extreme change, the result remained a simple exponential. I then went on to explain that anything less than a discontinuity would also remain a simple exponential. Why can't you follow simple reasoning?

"As I've shown, for population growth, the relationship is always exponential"Baloney. Solve the equationdY/dt = X(t)Y(t)where X(t) = exp(at^2) where a is a constant.Which part of bounded and unbounded are you having difficulty with?

X(t) is ALWAYS bounded for population growth

X(t) = exp(at^2) is unbounded, and therefore unphysical as a representation of population growth

Good grief what a farce

X(t) is not bounded for population growth.

If you think it is, give its bound.

In any case, it doesn't matter if X(t) is bounded.

It matters if dX/dt > 0. When it is, growth is superexponential in Y

David Appell Sep 2, 2015 at 8:41 AM

That was my point precisely! Take a deep breath, you are completely loosing it. Here is a list of people who's scientific publications co2science is referring to:

http://www.co2science.org/data/mwp/scientists.php

and here's a list of institutions those scientist belong to:

http://www.co2science.org/data/mwp/institutions.php

Read through them before making a complete fool of yourself.

petfin: so what?

Science isn't judged based on lists of people, or lists of institutions.

It's judged on evidence and quality.