## The absence of mathematics

Marotzke and Forster have published a response to Nic Lewis's critique of their paper. It can be seen here, at Ed Hawkins' Climate Lab book site. Here's the start.

No circularityIt has been alleged that in Marotzke & Forster (2015) we applied circular logic. This allegation is incorrect. The important point is to recognise that, physically, radiative forcing is the root cause of changes in the climate system, and our approach takes that into account. Because radiative forcing over the historical period cannot be directly diagnosed from the model simulations, it had to be reconstructed from the available top-of-atmosphere radiative imbalance in Forster et al. (2013) by applying a correction term that involves the change in surface temperature. This correction removed, rather than introduced, from the top-of-atmosphere imbalance the very contribution that would cause circularity. We stand by the main conclusions of our paper: Differences between simulations and observations are dominated by internal variability for 15-year trends and by spread in radiative forcing for 62-year trends.

Unfortunately, when they continue to the section called "Specifics" I can't actually see any mathematics that purports to show that their original regression model was *not *circular. My impression is of handwaving. Steve McIntyre, in the comments at CA seems to have reached similar conclusions:

I’ve done a quick read of the post at Climate Lab Book. I don’t get how their article is supposed to rebut Nic’s article. They do not appear to contest Nic’s equation linking F and N – an equation that I did not notice in the original article. Their only defence seems to be that the N series needs to be “corrected” but they do not face up to the statistical consequences of having T series on both sides.

Based on my re-reading of the two articles, Nic’s equation (6) seems to me to be the only logical exit and Nic’s comments on the implications of (6) the only conclusions that have a chance of meaning anything. (But this is based on cursory reading only.)

I guess we will have to wait and see what Nic Lewis makes of it before reaching firm conclusions.

Piers Forster comments at Climate Lab Book.

Nic is right that deltaT does appear on both sides, we are not arguing about this we are arguing about the implications.

We see the method as a necessary correction to N, to estimate the forcing, F. This is what we are looking for in the model spread, not the role of N – it would be more circular to use N as this contains a large component of surface T response.

We know this method of diagnosing F work very well – e.g. see Fig 5 of Forster et al. 2013

http://onlinelibrary.wiley.com/store/10.1002/jgrd.50174/asset/image_n/jgrd50174-fig-0005.png?v=1&t=i5xs0usz&s=4575b4038f30bacc5c54f4474456faf952af926dWe only see it as a problem as it affects the partitioning of the spread between alpha and F. We find that this creates some ambiguity over the 62 year trends but not the 15 year trends.

Uncertainty in the partitioning is different than creating a circular argument. We simply don’t do this.

I'm not sure I'm any the wiser.

## Reader Comments (37)

Well, they acknowledge the criticism.

It can't be ignored as irrelevant from now on.

A start.

Their basic claim seems to be that they used 'models' because there is lack of real data and therefore given they are 'better than nothing ' we should just accept they are right and never mind reality .

In the end the lack of good data should have lead them to consider if it was at all possible to make the type of claims they wanted to in any meaningful way. Instead knowing that a friendly press would jump on the claims , and never mind the details and that such an approach is not only normal for climate 'science' but often rewarded they went ahead anyway.

The saddest part is they are right , no matter how much BS is found in this paper interest has moved on , the quality of this paper means nothing for has we have seen in their area time and again , its 'value ' is not in its honest or accuracy. And I would bet its a shoe in for the next IPCC report and will be used in Paris has 'proof '

They are not only handwaving, they are ignoring the bigger critique that their conclusion is logically absurd. (Well, given a possibility that only the CMIP5 models are absurd, and not them.)

Surely what you mean is absence of explicit equations, although it seems strange that anyone would confuse that with an absence of mathematics?

I need to read both sides of the exchange more carefully. But on first reading it seems to me that the claim that their arithmetic "removed, rather than introduced, from the top-of-atmosphere imbalance the very contribution that would cause circularity" is straightforward.

If dF really is physically independent of dT, while dN is physically dependent on dT, then it is quite possible that regression on dN would contain the circularity that Nic Lewis worries about, while regression on alpha dT + dN does not.

If this is the crux of the argument then it seems we need to think about interpretation of what the equations mean to determine if adding the dT term is introducing or removing circularity.

91% say GW exaggerated : Survey result on the Telegraph page on Arctic Temperature adjustments

91% AGREE of 60862 voters.

- Probably cos the Drudge Report now links to that page and the Guardian doesn't.

- If the count started at zero 60,000 votes is significant

The halt leading the blind, but it's the halt that's blinding.

================

Check out Briggs comments. He says the whole proposition of declaring the models are right except for natural variability is a confession of the failure of the models.

Surely what you mean is absence of explicit equations, although it seems strange that anyone would confuse that with an absence of mathematics?Mathematics without equations is Philosophy.

If they had good explicit equations, they should use them. If they don't, why don't they?

Handwaving "a correction term" of unstated magnitude inspires little confidence.

I have been discussing this a bit at Judith Curry's and putting aside the wrongs and the rights of it all the thing I find depressing there and in this response is the difficulty in having a dialog in the methodological domain. Lewis' fundamental issue is with the methodological but the response all seem to revolve around repeating what was done, with no engagement on the question whether doing it made sense.

Is this willful, or do people just not understand this stuff?

Andrew, there must be a punctuation error. It should read:

"

This allegation is incorrect: the important point is to recognise that, physically, radiative forcing is the root cause of changes in the climate system, and our approach takes that into accountThe problem with their approach is that these two statements are contradictory:

"physically, radiative forcing is the root cause of changes in the climate system"

"Differences between simulations and observations are dominated by internal variability"

Natural variation is an internal change (unless you can show a natural change in radiation). So by saying radiative forcing is causing all the change they cannot then come to the conclusion that natural variation is causing the change making their (supposedly correct) models wrong. Because if natural variation is causing the change physically radiative forcing is

notthe dominant root cause of changes.They cannot have their cake and eat it. They cannot say that climate changes are not affected by internal variability and then claim internal variability is the reason for the lack of climate change.

In the end, the main contention by us sceptics is that the null hypothesis of natural variation cannot be refuted. Their critique is to say "because variation is driven externally there must be natural variation - therefore sceptics are wrong". Clearly their logic is completely nuts, but because the null hypothesis wins in such a situation, the conclusion is still right: the null hypothesis still wins .... so we sceptics are still right.

from Climate Audit Blog:

http://climateaudit.org/2015/02/05/marotzke-and-forsters-circular-attribution-of-cmip5-intermodel-warming-differences/

'[Professor] Gordon Hughes had some pithy comments about the Marotzke and Forster paper:

"The statistical methods used in the paper are so bad as to merit use in a class on how not to do applied statistics.

All this paper demonstrates is that climate scientists should take some basic courses in statistics and Nature should get some competent referees."'

It appears that Marotzke is engaged in the current rather odd behaviour of the Clan Catastrophe in that they seem to be trying to trump their own king.

We first had a period of denial that there has been a cessation of atmospheric warming, when that was no longer tenable they arrived at about 53 different causes for the cessation, all of them natural. Now we are being told that they have shown that the models are not wrong, just unable to predict natural variations. So they are admitting that the climate has been subject to natural variation but that the man made forcings that they have deliberately based their models on do not occur hence their models are not agreeing with the real data, even to the point where they do not agree with Gavin's fiddled data either. My immediate thought for them would be that as they are banging their heads against the brick wall of natural climate variability now is the time to stop. To continue on their path is rather like the 100 hundred monkeys with 100 typewriters trying to write Shakespeare. They are creating an awful lot of contradictory drivel which does not help their case with us plebeians.

It is irrelevant whether the paper is correct or not.

The fact of the matter it has done its job- that is to provide a "fig-leaf" to cover-up the continued failure of climate models to match reality.

I'm sure that Richard Betts would wish to comment on the relevative merits of Marotzke and Forster's paper and Lewis's critique.

"Differences between simulations and observations are dominated by internal variability"

Roughly translated "the models cannot deal with reality".

It is handwaving, and their argument can be summarized as follows:

We calculated the forcing from the immaculately conceived models, so immediately it's a magical unicorn and we don't have to show the mathematical derivation of the regression because UNICORNS!

@MCourtney

...Well, they acknowledge the criticism.It can't be ignored as irrelevant from now on....

Not only have they acknowledged the criticism, they have issued a rebuttal.

According to the rules of Climate Science, Nick Stokes' comments ARE now irrelevant, because they have been rebutted...

JK wrote:

If I'm reading this right, this is a crux of the issue. M&F state that there are no accurate historical values available for dF, so they use dT to derive it (plus some adjustments) - in which case all they can show is that dF depends on dF.

@ Radical Rodent …radiative forcing is the root cause of changes in the climate system… But is it?

Absolutely not. 'Radiative forcing' is pure and utter nonsense. It is not physics.

So they acknowledge the circularity issue and just assert that it has to be accepted/corrected when in fact all they had to do was re-arrange the equation (as Nic & Ross show) to get rid of it. Neither Betts nor Hawkins comment on this brain fart by Marotzke & Forster. Well of course because basic numeracy isn't required in climate science. This will be just one more circular argument among several others already in the IPCC report.

Meanwhile I agree with their tacit conclusion that the models are inadequate for policy.

One has to say "not surprised".

The wider context of the paper is arguing in the abstract that the models are still correct, despite increasing divergence from reality. And the consequences of publishing mistakes in high-profile journals is high-profile mistakes which are more painful to back away from. Once again Cli-Sci expects to have to meet a lower set of standards than are held to be the norm in other disciplines.

To the physics-challenged (me), the only obvious way out of this statistical mess seems to be if the dN term is appreciably larger than the dT term when calculating dF. As I read it, M&F suggest this to be the case for 15-year intervals. In which case, the circular nature of the regression (4) in their paper becomes less fatal for this time period, since dF is approx. dN.

Richard Betts did comment over at CA, but made no attempt to grapple with the fundamental mathematical problem of regressing a function upon itself.

"So they are aware that they rely on some assumptions, but have already checked these out in previous work.

This can of course can be tested here in future work – if the CMIP6 models allow F to be obtained more directly, the M&F procedure can be re-done with that."

"If you can't explain it simply, you don't understand it well enough."

Albert Einstein

Sums up 97% of climate "scientists"

Oh, I get it: It is not circular because the authors say it is not circular.

Makes perfect sense now.

Or not.

Bitter&Twisted | Feb 9, 2015 at 10:00 AM

McIntyre responded to Richard Betts:

I don't think we'll hear from Betts on this again.

On latest estimate (I should do a "mean" one day) I have 5300 books on statistics..

Yet I am miffed by this discussion

it is getting colder btw?

we shall ask Maroke to do a calculation again

The heart of the debate seems to be summed up by Ed Hawkins comment:

The modelers seem to think that the "way the equations are written" doesn't matter. And it is your fault for not grasping that.

Let me get this straight, ↑CO2 causes ↑T, which ↑ water vapor, which ↑↑F which ↑↑T ... looks circular to me.

I have asked this in a couple of places; just what the hell are the units of these things they are trying to define/

Temperature and 'forcing' are easy, K and W, but they seem to add or multiply N, a and z without respect for the damned units. Just what the hell are these units in any of these equations; you can add mpg to tire pressure or multiply battery voltage by the retail price index. What are the 'physical' things they are trying to define?

Fifty three hundred books on statistics?

Now that's a serious collecting

~~affliction~~, er strike that, collecting addiction. Unless of course you run a bookstore or library for statistics.Well the equation is simple: F = N + α.T

And here is the cluster-bluster of climateers:

E. Hawkins: We have to use the correction to get a best estimate of F – which doesn’t depend on T, even though it looks like it from the way the equations are written

E. Hawkins (contradicting himself later): But note that N also depends on T.

T. Osborne: It might appear from F = N + αT that F and T will be correlated, but this isn’t necessarily the case if N and T are themselves (anti)correlated

P. Foster (correcting Osborne): Through the energy budget all these terms are related, so you expect correlations

I'm just waiting someone to suggest F = N + α T + something-pulled-out-of-my-backside. Anything to avoid admitting they were wrong, the paper is rubbish and the models are inadequate in any event.

JamesG

"We have to use the correction to get a best estimate of F – which doesn’t depend on T."

Yes, F does not depend on T. However, the *estimate* of F, derived this way, *does* depend on T. N's negative dependence on T -- not a contradiction, by the way -- doesn't change this.

α was derived from regressing F-N vs. ΔT in a previous GCM run. So to get an estimate of F, computing N+αΔT, makes sense. But that is not F, it's an estimate of F. The residuals of regressing this F_est will not be the same as the residuals of F.

HaroldW

I read it as "best estimate of F – which doesn’t depend on T" rather than "F – which doesn’t depend on T".

But anyway if α.T (obviously) and N both depend on T then so does N + α.T, hence F, regardless of how α was derived and Hawkins is talking the purest babblegaff. That's what I meant. This circular argumentation seems infectious.

I would say Temp anomaly is independent of Temp anomaly

This because Temperature is a LOCAL measure, and to get at Temp anomaly one does a thorough homogenisation whereby any Temp anomaly taken is entirely independent of the previous one in the Time series. It is in other

disciplines called "white noise".

Nobody seems to have yet noticed that linear regression is not a valid assumption in a system that is so obviously nonlinear, nor can we actually glean anything at all from applying stats to the temperature series because we already know the underlying statistical model is just guesswork unless you know how to predict natural variation in the first place - the very reason why only physically based models can ever be useful. And those models must be corrected/tested with reference to the real world, not blindly believed despite their disagreement with nature. Plus they have initially assumed natural variation can be neglected only to conclude, yet again, that natural variation can't be neglected. This isn't science at all; it's like regarding abstract art. People see just what they want to see, not what is actually there!