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.