McIntyre and McKitrick (MM), in one of their many false claims regarding the Mann et al (MBH98) temperature reconstruction, assert that the “Hockey Stick” shape of the reconstruction is an artifact of the “non-centered” Principal Components Analysis (PCA) convention used by MBH98 in representing the North American International Tree Ring Data Bank (ITRDB) data series. We already demonstrated the falsehood of this assertion here by showing (a) that the hockey stick pattern emerges using either the MM (centered) or MBH98 (non-centered) PCA conventions, but was censored by MM through an inappropriate application of selection rules for determining the number of Principal Component (PC) to retain, (b) that use of the correct number of PC series (5) to be kept with the MM (centered) convention retains the characteristic “Hockey Stick” pattern as an important predictor, and yields essentially the same temperature reconstruction as MBH98, and finally (c) the MBH98 reconstruction is recovered even if PCA is not used at all to represent the North American ITRDB Data (i.e., each individual tree-ring series is used as a predictor with equal weight in the analysis). The claim by MM that the hockey stick pattern arises as an artifact of the PCA centering convention used by MBH98 is seen to be false on multiple levels.
Here, however, we choose to focus on some curious additional related assertions made by MM holding that (1) use of non-centered PCA (as by MBH98) is somehow not statistically valid, and (2) that “Hockey Stick” patterns arise naturally from application of non-centered PCA to purely random “red noise”. Both claims, which are of course false, were made in a comment on MBH98 by MM that was rejected by Nature , and subsequently parroted by astronomer Richard Muller in a non peer-reviewed setting–see e.g. this nice discussion by science journalist David Appell of Muller’s uncritical repetition of these false claims. These claims were discredited in the response provided by Mann and coworkers to the Nature editor and reviewers, which presumably formed the primary basis for the rejection of the MM comment.
Contrary to MM’s assertions, the use of non-centered PCA is well-established in the statistical literature, and in some cases is shown to give superior results to standard, centered PCA. See for example page 3 (middle paragraph) of this review. For specific applications of non-centered PCA to climate data, consider this presentation provided by statistical climatologist Ian Jolliffe who specializes in applications of PCA in the atmospheric sciences, having written a widely used text book on PCA. In his presentation, Jollife explains that non-centered PCA is appropriate when the reference means are chosen to have some a priori meaningful interpretation for the problem at hand. In the case of the North American ITRDB data used by MBH98, the reference means were chosen to be the 20th century calibration period climatological means. Use of non-centered PCA thus emphasized, as was desired, changes in past centuries relative to the 20th century calibration period.
Lets turn, now, to MM’s claim that the “Hockey Stick” arises simply from the application of non-centered PCA to red noise. Given a large enough “fishing expedition” analysis, it is of course possible to find “Hockey-Stick like” PC series out of red noise. But this is a meaningless exercise. Given a large enough number of analyses, one can of course produce a series that is arbitrarily close to just about any chosen reference series via application of PCA to random red noise. The more meaningful statistical question, however is this one: Given the “null hypothesis” of red noise with the same statistical attributes (i.e., variance and lag-one autocorrelation coefficients) as the actual North American ITRDB series, and applying the MBH98 (non-centered) PCA convention, how likely is one to produce the “Hockey Stick” pattern from chance alone. Precisely that question was addressed by Mann and coworkers in their response to the rejected MM comment through the use of so-called “Monte Carlo” simulations that generate an ensemble of realizations of the random process in question (see here) to determine the “null” eigenvalue spectrum that would be expected from simple red noise with the statistical attributes of the North American ITRDB data. The Monte Carlo experiments were performed for both the MBH98 (non-centered) and MM (centered) PCA conventions. This analysis showed that the “Hockey Stick” pattern is highly significant in comparison with the expectations from random (red) noise for both the MBH98 and MM conventions. In the MBH98 convention, the “Hockey Stick” pattern corresponds to PC#1 , and the variance carried by that pattern (blue circle at x=1: y=0.38) is more than 5 times what would be expected from chance alone under the null hypothesis of red noise (blue curve at x=1: y = 0.07), significant well above the 99% confidence level (the first 2 PCs are statistically significant at the 95% level in this case). For comparison, in the MM convention, the “Hockey Stick” pattern corresponds to PC#4, and the variance carried by that pattern (red ‘+” at x=4: y=0.07) is about 2 times what would be expected from chance alone (red curve at x=4: y=0.035), and still clearly significant (the first 5 PCs are statistically significant at the 95% level in this case).
So the facts deal a death blow to yet another false claim by McIntyre and McKitrick. Despite the plain facts, as laid out here, however, their false claims have nonetheless been parroted in op-ed pieces of dubious origin and other non-peer-reviewed venues. One of the primary missions of “RealClimate” is indeed to expose the false, disingenuous, and misleading claims often found in such venues.
Nice piece, Mike. And, it deals a ‘death blow’ only to those who choose to listen or to those who have the time to digest your words. To the ideologues and rubes who believe them, you are [insert pejorative here] and you’ll never change those minds.
I deal with politicians often in my work. What would be helpful in analyses like these is a short wrap-up for decision-makers; they do not have the time to wade thru this analysis – nor do their aides – and I suspect the effectiveness of your message may be lost on some.
For decision-makers to have a chance to make good policy when faced with the emotional agitprop of the indy-fundeds, they need to be able to access the material. Simple, cogent bullets somewhere (best at the beginning) will allow decision-makers to scan your work and get the rational message contained within.
Keep up the good work, sir.
D
All of this technical, statistical jargon is over my head, but I get the impression that the data on which the climate reconstruction is based is so sparse and uncertain that you can’t draw any firm conclusions supporting either MM’s or Mann’s side of the debate.
[Response: Even without technical training or a statistical background, you should have an adequate basis for discerning which of the two parties is likely wrong here. Only one of the parties involved has (1) had their claims fail scientific peer-review, (2) produced a reconstruction that is completely at odds with all other existing estimates (note that there is no sign of the anomalous 15th century warmth claimed by MM in any of the roughly dozen other model and proxy-based estimates shown here), and (3) been established to have made egregious elementary errors in other published work that render the work thoroughly invalid. These observations would seem quite telling. -mike]
The question that I wish someone would address is “What difference does it make?”. CO2 is reaching levels that haven’t existed for hundreds of millennia, and it seems to me that on that time scale the climate a few hundred years ago provides no better basis for extrapolating future climate than does yesterday’s weather. Can any conclusion regarding future climate change be drawn from the “hockey stick” reconstruction, and can any level of statistical confidence be placed on the conclusion?
[Response: Refer to this post (and references therein) for a detailed discussion of how comparisons of proxy-based climate reconstructions with theoretical climate model simulations can inform our assessment of the role of both natural and anthropogenic factors in recent climate change.
It is often more instructive in this regard, however, to compare not just hemispheric mean series, but the actual spatial patterns of estimated and observed climate changes in past centuries. See e.g. the review paper: Schmidt, G.A., D.T. Shindell, R.L. Miller, M.E. Mann, and D. Rind 2004. General circulation modelling of Holocene climate variability. Quaternary Sci. Rev., 23, 2167-2181, doi:10.1016. -mike]
In considering the issue of earth warming, I believe that the question of “Is it or is it not occurring?” is irrelevant. The more important question is, it seems to me, “How should we behave?”
In this, I take my thinking from Pascal: There are two “realities” and two “behaviors”, paired to give us four scenarios:
1) We behave as though earth-warming is not occuring and it isn’t.
2) We behave as though earth-warming is not occuring and it is.
3) We behave as though earth-warming is occuring and it isn’t.
4) We behave as though earth-warming is occuring and it is.
If one thinks through the implications of each of these four scenarios, our course of action seems clear. What’s the problem???
Mike:
According to lay people that I talk to who have been influenced by the op-ed pieces that you mention, “global warming has been disproved”. The MM story is indicative of a pattern in which industry (and now our own government) PR machines latch on to minority scientific articles to claim that an environmental issue has no basis. The journal Science (in the late ’70s or early 80’s) once published an article in which the author claimed that the major components of acid rain were weak acids. The article should have failed peer review and never been published: the scientist conducting the work titrated the samples in open air, effectively measuring not only the weak acids in the samples but also the carbon dioxide from the room. The work was plain wrong. Nevertheless representatives of the power companies parroted the “findings” for several years to claim that acid rain was NOT related to industrial air pollution.
Stephen
Great Piece Mike. If you are familiar with Tim Lambert, he has spent much time discussing/discrediting MM.
As an aside, are you familiar with Positive Matrix Factorization (PMF)? We are using it in lieu of PCA for samples we analyzed from a dust storm experiment in Asia. It has several major advantages over PCA including that it doesn’t produce negative (non-real) results and you can incorporate uncertainty into the analysis so you can limit significance of low-level or missing data.
Keep it up, guys. I have a brother-in-law who is a Fox News/Talk Radio junky and he insists global warming is a myth yet has never read or seen a scientific article. Truly unbelievable.
[Response: Thanks very much for your comment Scott. Indeed, there are other statistical approaches, as you note, to the problem of ‘climate field reconstruction’, many of which are somewhat more sophisticated than (and arguably preferable to) PCA-based approaches. In this previous post here, we discuss the results from a recent paper in press in Journal of Climate by Rutherford et al that uses the Regularized Expectation-Maximization (“RegEM”) algorithm to reconstruct past temperature patterns from proxy data–the results are remarkably consistent with past proxy-based reconstructions using other (e.g. PCA-based) methods. Applications to reconstructions of patterns of past continental drought from tree-ring data can be found here. RegEM is an iterative approach for estimating the data covariance of an incomplete data set (and imputing missing values in the process) using what is sometimes referred to as “ridge regression”. In this approach, the main diagonal of the estimated data covariance matrix is inflated using a “smoothing” parameter determined by generalized cross validation (GCV) to insure that the estimated data covariance matrix is not underdetermined in the presence of noise and incomplete information. Estimated missing values are computed based on the smoothed data covariance estimate, and the process is continued until a stable solution is obtained. I believe the method may have some features in common with the alternative approach you describe. A fuller discussion of the methodology in specific, including a discussion of related past work, and of the more general issue of “climate field reconstruction” is provided in the references mentioned above.]
Actually, Mike, I’d be more interested in your views on the criticisms presented by Hans von Storch. I believe he claims that the graph exhibits much less variability than the natural climate.
[Response: We repeat our previous response to a similar previous comment on this site (comment #13 on the “Welcome to RealClimate” post):
von Storch et al purport to test statistical methods used to reconstruct past climate patterns from “noisy” proxy data by constructing false proxy records ( “pseudoproxy” records) based on adding noise to model gridbox temperature series taken from a climate simulation forced with estimated past radiative forcing changes. Several other researchers have published similar studies in the past. One thing that makes the von Storch analysis different is that they use a simulation that exhibits larger forcing, and more variability than most simulations, the very same “GKSS” simulation (Gonzalez-Rouco et al, 2003) discussed here. In their commentary on the paper, Briffa and Osborn note that the results may not generalize to the actual world, where the forced variability may be much smaller than in the GKSS simulation. While von Storch et al focus on the Mann et al (1998) reconstruction method, they argue that their results generalize to other proxy reconstructions methods as well.
The von Storch paper has appeared too recently for responses to have made their way through the appropriate peer-review process. While we are already aware of some recent work arriving at very different conclusions from von Storch et al, it is premature at this time to comment on that work. We hope to be able to comment more fully on the matter when this other work has appeared in the peer-reviewed literature. Respecting the peer-review process, however, we prefer not to post any further comments on this matter until it has played out more fully in the peer-reviewed literature -mike]
McIntyre and McKitrick?
Who are these guys and why are they trying to distort the results of many independent studies?
Maybe I missed this elsewhere on your site. Do they have a political agenda?
Bill (#3) —
I don’t agree with your decision chart for the same reason that I don’t agree with Pascal’s original wager: there are not only two realities and two behaviors. Climate can occur in many degrees, have many causes, and follow many paths. Behavior is ridiculously variable. In this case, I don’t think boiling all the alternatives down to a two-by-two grid will yield anything like a useful approximation of the real world.
Great blog! Keep up the good work! Best wishes, Matt