Subsequent to MM05 (GRL), the issue of covariance and correlation PCs as applied to the North American tree ring network was considered in Huybers , our Reply to Huybers  and the NAS Panel. It was also discussed in the rejected Ammann and Wahl submission to GRL. Juckes did not even cite the discussion on this topic in Huybers or the NAS Panel, but does cite Wahl and Ammann’s Climatic Change submission.
The story so far
Just to review the bidding, contrary to what one might think in reading Juckes, there are no actual differences between the parties in the values of the different series. There is a difference in terminology – I’ve referred to covariance and correlation PCs; instead of using these terms, Juckes uses the terms "centered " (cen) and "standardized" (std). The term "standardization" is also used in dendroclimatology to describe the process of making tree ring chronologies, so I think that the terms covariance and correlation PCs are more precise.
Here is Figure 3 from our GRL article, which compared the MBH98 PC1 for the NOAMER network with the covariance PC1 (which is what we had used in MM03 as the most plausible interpretation of "conventional" PC methodology in a network denominated in common dimensionaless units.)
MM05 (GRL). Figure 3. PC1 for AD1400 North American Tree Ring Network. Top: Result with MBH98 data transformation; Bottom: recalculated on the same data without MBH98 data transformation. Both standardized to 1902–1980 period.
We’ve provided many supporting references for this interpretation – Overland and Preisendorfer 1982; Rencher 1992, 1995, 2002; North et al 1982. No one has ever provided an external statistical reference supporting the primary use of correlation PCs in this context. It’s not that we advocate covariance PCs as a way of making sense of the dog’s breakfast of tree ring chronologies; it’s just that that’s what an innocent reader of MBH98 would assume that they did based on their description of their methodology – just as an innocent reader would have assumed that when they said that they considered verification r2 values, the innocent reader would have assumed that the verification r2 values were significantly greater than 0. As we said in our Reply to Huybers, we neither endorse or oppose PCs as a sensible way of approaching the problem – the onus was on the original authors to prove the methodology. There’s been endless discussion of covariance versus correlation PCs. For now, I’ve excerpted the figure merely to show what we actually published.
Next here is a figure produced from the PCs archived at the MITRIE SI, plotted in the same way. Obviously the MBH series match, as does the covariance PC1 and the CEN version at MITRIE. I’ve added in the correlation PC1 in the same format.
From Juckes archive. Series 16 mppc01_itrdb_namer_1400_mbh_01, 24 (mppc01_itrdb_namer_1400_cen_01), 22 mppc01_itrdb_namer_1400_std_01. Standardized to 1902-1980 as in MM05a Figure 3
Next, here is an excerpt from Figure 1 in our Reply to Huybers, showing covariance and correlation PC1s. Again, you can see that the series precisely match to Juckes’ versions, although you’d never know it from all the huffing and puffing. " Calculating standard deviations in autocorrelated series has some subtleties and just for fun, we also illustrated a PC1 calculated from chronologies standardized with autocorrelation-consistent standard deviations – which by chance produced something rather like the covariance PC1.
Reply to Huybers Figure 1 Excerpt. MBH98 North American AD1400 network. (c) Covariance PC1; (d) mean of all 212 series. (e) Correlation PC1; (f) mean of 70 full-length series. (g) Autocorrelation-consistent correlation PC1; (h) correlation PC1 with bristlecone pines censored.
In our Reply to Huybers, we discussed the various PC1s and observed:
The differences among these PC series can be traced to differing weights for bristlecones… Bristlecone impact can be seen directly by comparing the MBH98 PC1 (Figure 1a), which is weighted almost entirely from bristlecones, with an unreported PC1 from Mann’s FTP site (Figure 1b), which Mann obtained by applying MBH98 PC methodology while excluding 20 bristlecone sites (ftp://holocene.evsc.virginia.edu/pub/MBH98/TREE/ITRDB/NOAMER/BACKTO_1400-CENSORED/pc01.out). Given the tendency of the MBH98 method to yield hockey stick shaped PC1s (MM05), it is remarkable that this PC1 does not have a hockey stick shape. The correlation PC1 without bristlecones (Figure 1g) is virtually identical, showing that the actual PC method has little impact in this case once the bristlecones are removed.
This is a completely simple point and yet no one on the Team wants to discuss it. If there’s a problem with the bristlecones, then it makes no sense to say that a methodology that increases the weight of the bristlecones is the "right" method.
A Puzzle in the Juckes SI Figure
Now here’s a problem where I’m stumped and which illustrates why source code is a good idea. I’ve spent a lot of time trying to figure out this graphic. I know this material inside-out and I can’t figure it out. It’s a total waste of time when I could sort it out in a few minutes with properly annotated code. Here’s the figure:
Juckes SI Fig. 1. Proxy principal components: the rst principal component of the North American ITRDB network of Mann et al., 1998. (1) Using the normalisation as in Mann et al. 1998, (2) as (1), but using full variance for normalisation rather than detrended variance, (3) normalised and centred on the whole series, (4) centred only (5) as archived by MBH1998. 21-year running means.
Here’s my attempt to replicate the Figure using archived Mitrie PCs (mbh, mbhx, std, cen and the archived MBH98 PC1). The smoothing is a 21-year running average with end-point extrapolation (this is not disclosed but is used in the code in their MM05b Figure 2 Comment). Although the legend says that the PC1s have been "normalised", the series are obviously not centered on 0. I guess they are scaled on some subperiod, but I haven’t been able to figure it out. The worst thing is that I don’t see anything that corresponds to the covariance PC1. Juckes "cen" series ends higher than the covariance PC1.
Emulation of Juckes SI Figure 1. All PC1s scaled on 1400-1980 period.
The odd thing is that Figure 3 in the Juckes Comment on MM05b Figure 2 seems to match my emulation. Here it is with its legend:
Comment Figure 3: As figure 2, but using a 21 year block average instead of Gaussian smoothing. Figure 2: As figure 1, but using the grey curve is generated using the “princomp” function instead of the “svd” function, so that the data is automatically centred. Also shown is the PC generated when the data is also standardised (grey dashed curve). As in figure 1, the PCs have been smoothed with a Gaussian weighting. Here the curves have also been normalised to unit variance. All these curves have, by construction, zero mean (prior to smoothing).
If anyone can figure it out, I’d appreciate it. I’ve tried 1856-1980 scaling and 1902-1980 scaling and neither seemed to work. I’ve archived the 6 relevant PC1 s here http://data.climateaudit.org/data/mitrie/mitrie.pcs.txt and a short script to produce my emulation figure at http://data.climateaudit.org/scripts/mitrie/si.figure1.rtf