Over the past year or so, Mann’s “ClimateBall” defenders have taken an increasing interest in trying to vindicate Mannian principal components, the flaws of which Mann himself has never admitted. Indeed, in Mann’s self-serving Hockey Stick Wars, Mann once again claimed that the defective method was simply an “alternative centering convention”. So far, I’ve taken little interest in such efforts because, as far as I’m concerned, the defectiveness of Mannian principal components is established beyond any reasonable cavil. My attitude towards such efforts is probably not unlike Andrew Lacis’ attitude towards skydragons and their supposed slayers.

But the rhetoric of such efforts has increased in both volume and intensity. In recent comments at at Judy Curry’s (here), Kevin O’Neill accused the Wegman Report of “real fraud”, citing, as one of his major counts, its supposedly “deceptive display of only upward-pointing ‘hockey sticks’ – though half of them would have had to be downward pointing” . O’Neill challenged Curry for her supposed failure to recognize “real fraud”. O’Neill’s explanation for the supposed “fraud” was that it was “pretty obvious that a downward sloping hockey stick wouldn’t look like MBH. The Wegman Report was a political hatchett job.”

However, the 2006 NAS Panel also showed only upside-up simulated PC1s in their figure 9-2 illustrating the bias in Mannian principal components, explaining that the sign of a principal component series is arbitrary (a point previously made in MM05) and therefore selecting the arbitrary sign to align the PC1s to be upward-pointing. In addition, the coauthors of Juckes et al 2007 (including Briffa, Osborn, Myles Allen) similarly observed that the sign of PC series is arbitrary and re-oriented them to match the 20th century trend. So, if the technique is “real fraud”, as O’Neill alleges, the supposed “fraud” reaches far beyond the walls of the Wegman report, including both the NAS panel and the coauthors of Juckes et al 2007, a conspiracy of Lewandowskian proportions.

Further, Mann himself flipped over the downward-pointing MBH99 PC1 not just in the regression, but for the calculation of the Mannkovitch bodge illustrated in MBH99 Figure 2. Jean S has ably exposed the Mannkovitch bodge, but even Jean S did not take exception to Mann re-orienting the MBH99 PC1 to be upward pointing. But if O’Neill is correct in characterizing such re-orientation as “deceptive” and as “fraud” (on which I firmly disagree), he would, ironically, be providing an additional reason for Steyn to have used the term “fraudulent” to describe the MBH99 hockey stick.

But, in fact, far from being “deceptive”, the technique used by the NAS Panel (and Wegman) is not only legitimate, but more appropriate than displays that fail to allow for the fact that the sign of a PC series is arbitrary.



MM05

In my opinion, MM05 (GRL) stated that simulated PC1s occurred in both upside-up and upside-down orientations about as clearly as one could possibly wish for.

The hockey sticks were upside-up about half the time and upside-down half the time, but the 1902-1980 mean is almost never within one sigma of the 1400-1980 mean under the MBH98 method.

We also showed a histogram showing a bifurcated distribution of the difference between 1902-1980 means and 1400-1980 means divided by standard deviation (a simple measure of what we termed “Hockey Stick Index” (HSI) ): about half the values were positive (upside-up) and half were negative (upside-down.) We observed that PCs had “no inherent orientation”and that any apparent orientation of a PC1 was washed out in the regression step anyway, also pointing out that the archived MBH99 PC1 pointed down and was inverted in the regression step:

PC series have no inherent orientation and, since the MBH98 methodology uses proxies (including the NOAMER PC1) in a regression calculation, the fit of the regression is indifferent to whether the hockey stick is upside-up or upside-down. In the latter case, the slope coefficient is negative.

Because of this property, we considered the absolute value of the HSI in observing that Mannian PCs “nearly always” produced a HS-shaped PC1: we reported that the HSI was greater than 1 more than 99% of the time using Mannian PCs.

This property also entailed that graphical representation of the hockeystick-ness of PC1 series was most appropriately demonstrated by choosing the arbitrary sign of an individual PC series so that the hockeysticks pointed up.

While we did not show a 12-panel figure corresponding to Wegman Figure 4.4 in our two contemporary articles (MM05-GRL or MM05 -EE) or (to my recollection in any contemporary presentations), we did show a four-panel figure of this type in contemporary presentations, e.g. in one of the earliest CA posts here. In addition, MM05 Figure 1 is a two-panel figure showing one simulated PC1 upside-up, with the following covering text:

The simulations nearly always yielded PC1s with a hockey stick shape, some of which bore a quite remarkable similarity to the actual MBH98 temperature reconstruction – as shown by the example in Figure 1.

Because Wegman’s Figure 4.4 has also attracted controversy, I will discuss it separately in a follow-up post.

The 2006 NAS Panel

The 2006 NAS Panel likewise observed that principal components have an “arbitrary sign” (a statement that is equivalent to our prior statement that they had no “inherent orientation”) and, for their Figure 9-2 illustrating the bias from Mannian principal components, they selected the sign so that “the last 100 values [was] higher on average than the remainder” (a positive HSI):

The figure [Figure 9-2] shows the first components from five such simulations overlaid. Principal components have an arbitrary sign, which was chosen here to make the last 100 values higher on average than the remainder.

This procedure ensured that all hockey sticks pointed up in their Figure 9-2 as shown below. If O’Neill’s accusation against Wegman is valid (which it isn’t), then the NAS panel was guilty of the same offence, a conspiracy of Lewandowsky-size immensity.

Figure 1. NAS Panel 2006 figure 9-2, demonstrating bias in Mannian “principal components”. Recognizing the “arbitrary sign” of PC series (but they could also have invoked the subsequent regression), the NAS panel oriented all five PC series upside-up to demonstrate the bias.

Juckes et al 2007

Juckes et al 2007 likewise observed that the sign of principal components is “arbitrary” and reversed the sign to yield a positive correlation:

for the proxy principal components in the MBH collection the sign is arbitrary: these series have, where necessary, had the sign reversed so that they have a positive correlation with the Northern Hemisphere temperature record).

If O’Neill is correct and this practice is “real fraud”, offending coauthors of Juckes et al included prominent IPCC scientists Myles Allen, Briffa, Esper, Hegerl, Moberg, Osborn, Nanne Weber (now deceased) and Juckes himself.

MBH99 and the Mannkovitch Bodge

As noted above, in MM05, we observed that the archived MBH99 PC1 was an upside-down hockeystick. (The post-1400 archive is plotted in the left panel below).

the North American PC1 of Mann et al. [1999] is an upside-down hockey stick, as shown at ftp://ftp. ngdc. noaa. gov/ paleo/contributions_by_author/mann1999/proxies/itrdbnamer- pc1. dat.

In Mann’s calculation of the Mannkovitch bodge, ably exposed by Jean S several years ago here, Mann inverted the orientation of the MBH99 PC1 so that it pointed up, as shown in MBH99 Figure 1a (right panel below.) Mann also rescaled the PC1 from the PC scale (sum of squares equals 1) to “relative amplitude”. While I regard the Mannkovitch bodge as a prime example of “data torture”, I do not take exception to Mann’s selection of a sign for the PC series so that it points upward, a protocol that, as noted above, was also adopted by the NAS panel. If, 0n the other hand, selecting the arbitrary sign to orient a PC upside-up constitutes “real fraud” – as O’Neill alleged – then its original perpetrator was Mann himself, adding more ammunition to Steyn’s case.

Figure 2. left – plot of archived MBH99 PC1 in downward orientation from NOAA archive; right – MBH99 Figure 1a, showing MBH99 AD1000 PC1 from 1400-1980 in upward orientation; .

Conclusion

Over the past year or so, Mann’s “ClimateBall” defenders have taken an increasing interest in trying to vindicate Mannian principal components, the flaws of which Mann himself has never admitted. Indeed, in Mann’s self-serving Hockey Stick Wars, Mann once again claimed that the defective method was simply an “alternative centering convention”. So far, I’ve taken little interest in such efforts because, as far as I’m concerned, the defectiveness of Mannian principal components is established beyond any reasonable cavil. I’m not talking here about efforts to demonstrate that the modern warm period is warmer than the medieval warm period – which I regard as an entirely legitimate enterprise – but on efforts to vindicate Mann on the narrowest issue of his erroneous principal components method. . It is with more than a little reluctance that I’m pushing back on a topic on which there ought to be no dispute.

Brandon Shollenberger previously discussed some of these issues in his sensible comments to O’Neill in the original thread at Judy Curry’s and in a followup post at his own blog, but overlooked the NAS panel diagram, which ought to clinch the issue even for O’Neill and Nick Stokes (a protagonist in the ClimateBaller counterattack and active participant in the thread).

On O’Neill’s specific allegation that the display of simulated PCs only in an upward orientation is “deceptive” and “real fraud”, O’Neill’s allegation, if true, would condemn not only Wegman, but the NAS panel, the coauthors of Juckes et al 2007 and even Mann himself. In fact, the technique used by the NAS Panel (and Wegman) is not only a legitimate method of illustrating the hockeystick-ness of Mannian principal components, but more appropriate than failing to recognize that the sign of a PC series is arbitrary – an error made in a figure by Nick Stokes that is heavily relied upon by ClimateBallers and which I will discuss in a forthcoming post.

While I’ve started with O’Neill’s allegation of deception and “real fraud” related to sign selection, I intend to cover several other ClimateBaller disputes, including allegations that our MM05 simulations were defective because they failed to first remove the “climate signal” (and that the simulated networks were therefore not “trendless”) and the false claim that HS-shaped Mannian PC1s are not “typical”, but actually “rare” and merely the result of “100:1” cherrypicking.



