On Yet Another False Claim by McIntyre and McKitrick

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.

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