The calculation of the PAGES2K regional average contains a very odd procedure that thus far has escaped commentary. The centerpiece of the PAGES2K program was the calculation of regional reconstructions in deg C anomalies. Having done these calculations, most readers would presume that their area weighted average (deg C) would be the weighted average of these regional reconstructions already expressed in deg C.
But this isn’t what they did. Instead, they first smoothed by taking 30-year averages, then converted the smoothed deg C regional reconstructions to SD units (basis 1200-1965) and took an average in SD units, converting the result back to deg C by “visual scaling”.
This procedure had a dramatic impact on the Gergis reconstruction. Expressed in deg C and as illustrated in the SI, it has a very mild blade. But, the peculiar PAGES2K procedure amplified the relatively small amplitude reconstruction into a monster blade with a 4 sigma closing value. Following the Arctic2K non-corrigendum correction, it is the largest blade in the reconstruction (and has the greatest area weight.)
I’ll show this procedure in today’s post.
PAGES2K Figure S2
First, here is PAGES2K Figure S2, showing the seven regional reconstructions (the Arctic obviously pre-corrections), The amplitude of the Australasian temperature change estimates (for whatever they are worth) are the smallest.
Figure 1. Excerpted from PAGES2K Figure S2. Original caption: Proxy temperature reconstructions for the seven regions of the PAGES 2k Network. Temperature anomalies are relative to the 1961-1990 CE reference period. Grey lines around expected-value estimates indicate uncertainty ranges as defined by each regional group (Supplemental Information Part II), namely: Antarctica, Australasia, North America pollen, and South America = ± 2SE; Asia = ± 2 RMSE; Europe = 95% confidence bands; Arctic = 90% confidence; North American trees = upper/lower 5% bootstrap bounds (these are inherently narrower than those of many other regions because they are reported at decadal and multi-decadal, rather than annual resolution). Instrumental temperatures are area-weighted mean annual temperatures over the reconstruction domains shown in Figure 1 from HadCRUT4 (ref. 9) land and ocean, rather than the target temperature series used in the regional reconstructions. This facilitates a uniform comparison among regions using a data series that extends to 2010. The actual reconstruction targets for each region are specified in Table 1. Reconstruction time series are listed in Supplementary Database S2.
Re-converting to SD Units
It’s hard to understand why the PAGES2K authors would convert series expressed in deg C back to SD units in order to calculate an area average, but that’s what they did. The calculation is not described in detail, but is illustrated in their Figure 4b (and the nearly identical top panel of SI Figure 5.) As I understand their procedure, they first calculated 30-year averages for each reconstruction (ending in 2000) ; then they converted the 30-year average series to SD units (basis 1200-1965) and then calculated an area average – shown in their Figure 4b (and SI Figure 5) as blue dots – see below. This was then converted to temperature (see scale on right axis) by a super-sophisticated statistical methodology described in the caption as “scaled visually to match the standardized values over the instrumental period.”
Figure 2. Excerpt from PAGES2K Figure 4b (period 0-2000). Similar figure in PAGES2K SI Figure 5 top panel. Original caption: Composite temperature reconstructions with climate forcings and previous hemisphere-scale reconstructions. … . b, Standardized 30-year-mean temperatures averaged across all seven continental-scale regions. Blue symbols are area-weighted averages using domain areas listed in Table 1, and bars show twenty-fifth and seventy-fifth unweighted percentiles to illustrate the variability among regions; open black boxes are unweighted medians. The red line is the 30-year-average annual global temperature from the HadCRUT4 (ref. 29) instrumental time series relative to 1961–1990, and scaled visually to match the standardized values over the instrumental period
Regional Panel in SD Units,
PAGES2K did not show the regional reconstructions in SD units – the form in which they contributed to the area-weighted average – an oversight which is remedied below. I’ve also used the PAGES2K-2014 Arctic version and added the average of 2014 versions. PAGES2K emphasized the long-term cooling trend up to the 20th century. Squinting at these reconstructions, I’d be inclined to say that reversal of long-term cooling occurred somewhat earlier in their European and Asian reconstructions than their Arctic reconstruction and that no reversal is yet discernible in Antarctica, much the coldest area. Curiously, the Gergis’ Australia reconstruction has, by a considerable margin, the largest blade, closing at over 4 sigma. Thus, although it has a deceptively mild appearance when expressed in deg C (as in the main SI illustration excerpted above), it has a monster blade as used in the regional averaging. This contribution is further exacerbated by the assignment of weights, as the Gergis’ Australasian reconstruction is assigned the largest area of any of the regions.
Figure 3. Seven regional reconstructions expressed in SD Units, together with area-weighted average (red). The Gergis reconstruction (left column, bottom row) closes at over 4 sigma, The uncorrected Arctic reconstruction had a similarly large blade, but is more muted incorporating corrections to date.
This very large contribution from the Gergis reconstruction invites further examination, which I plan in a subsequent post. The original Gergis reconstruction was discussed at length when it was released in 2012. Their screening procedure was examined closely at CA, with Jean S demonstrating that, despite claims in their article that they had used detrended correlation to guard again spurious correlation, they had actually used non-detrended correlation. This led to a non-retraction retraction: the article was disappeared without an obituary or retraction notice. The authors did not acknowledge CA, instead they claimed that they had “independently” discovered the problem at exactly the same time as the CA discussion. Mann and Schmidt both wrote to Gergis supporting ex post screening. Gergis and coauthors (including Karoly) tried to persuade Journal of Climate that they should be allowed to change their description of methodology, but the journal asked them to show results using the described methodology as well and the article disappeared.
The Gergis reconstruction in PAGES2K uses an almost identical network to the retracted article: of the 27 proxies in the original network, 20 are used in the P2K network: out are 1 tree ring, 2 ice core and 4 coral. The new network has 28 proxies: in are 2 tree ring, 1 speleo and 5 coral records. As discussed in my original commentary, there are only two records in this network going back to the MWP – both tree ring records considered in Mann and Jones 2003 without much centennial variability. As in the original reconstruction, the Gergis blade does not arise from multiple long records exhibiting modern values elevated relative to medieval values, but is more like a moustache stapled onto a shaft. I’ll revisit the revised Gergis reconstruction in a separate post.