The PAGES2K (2013) Arctic reconstruction of Kaufman et al has attracted considerable attention as a non-Mannian hockey stick. However, it’s been fraught with problems since day one, including a major re-statement of results in August 2014 (McKay and Kaufman, 2014 pdf), in which Kaufman conceded (without direct acknowledgement) Climate Audit criticism that their results had been impacted by the use of contaminated data and upside-down data. But there’s a lot more.

In March 2013, almost exactly contemporaneous with PAGES2K, Hanhijarvi et al, pdf here, the originators of the paico method, published their own Arctic reconstruction, which has undeservedly received almost no publicity. (In this post, I will use “PAGES2K” to refer to the PAGES2K Arctic reconstruction; the full PAGES2K study includes other areas, including Gergis’ Australian reconstruction.) But unlike PAGES2K, its medieval reconstruction has higher values than its modern reconstruction – a finding that has received negligible coverage. Because its methodology matches the PAGES2K methodology, the difference necessarily arises from proxies, not from method.

Nor is the issue merely “regional” coverage though Hanhijarvi et al’s Arctic reconstruction is based on North Atlantic proxies though it would be puzzling even as a “regional” result. These proxies from a very large subset of the PAGES2K Arctic data (27 of 59 series, using no other data). With such a large subset, one can only obtain the PAGES2K Arctic results if there is a superstick for the rest of the data (non-H13 proxies). As a regional result, specialists would have to explain the physics of a medieval warm period in the North Atlantic concurrent with extreme cold in the rest of the Arctic, if one were to take these results at face value.

But before attempting such a complicated solution, it is important to note that Kaufman’s proxies are fraught with defects. Kaufman has already acknowledged that one of his supersticks (Igaliku) was contaminated by modern agriculture; and that another non-H13 series (Hvitarvatn) was used upside down. Several series, thought to be temperature proxies as recently as 2013, were removed in August as no longer “temperature proxies”. For inexplicable reasons, Kaufman failed to remove all the contamination from the Igaliku series and his inversion of the Hvitarvatn points to major inconsistencies with other series. Further, although Kaufman has acknowledged multiple errors in the PAGES2K Arctic reconstruction, he has not issued a corrigendum, thereby permitting the erroneous series to continue in circulation, while, oddly, thus far not providing a digital version of the amended reconstruction.

Figure 1.Histograms of t-statistic for difference of 1902-1980 mean and 1400-1901 means showing centered PC1s (light grey) and Mannian PC1s (medium grey). The curve is a t-distribution (df=180). The red lines at +- 1.65 and +-1.96 correspond to 90% and 95% two-sided t-tests.The distribution of the simulated t-statistic for centered PC1s is similar to a high-df t-distribution, though it appears to be somewhat overweighted to values near zero and underweighted on the tails: there are approximately half the values in the 5% and 10% tails that one would expect from the t-distribution. At present, I haven’t thought through potential implications.

The distribution of the simulated t-statistic for Mannian PC1s bears no relationship to the expected t-distribution. Values are concentrated in the tails: 85% of t-statistics for Mannian PC1s are in the 5% tails ( nearly 97% in the 10% tails.) This is what was shown in MM05 and it’s hard to understand why ClimateBallers contest this.

What This MeansThe result is that Mannian PC1s “nearly always” (97% in 10% tails and 85% in 5% tails) produce series which have a “statistically significant” difference between the blade (1902-1980) and the shaft (1400-1901). If you are trying to do a meaningful analysis of whether there actually is a statistically meaningful difference between the 20th century and prior periods,

it is impossible to contemplate a worse methodand you have to go about it a different way. Fabrications by ClimateBallers, such as false claims that MM05 Figure 2 histograms were calculated from only 100 cherrypicked series, do not change this fact.The comparison of the Mannian PC histogram to a conventional t-distribution curve also reinforces the degree to which the Mannian PCs are in the extreme tails of the t-dstribution. As noted above (and see Appendix), the t-stat is monotonically related to the HSI: rather than discussing the median HSI of 1.62, we can observe that the median t-stat for Mannian PC1s is 2.44, a value which is at the 99.2 percentile of the t-distribution. Even median Mannian PC1s are far into the right tail. The top-percentile Mannian PC1s illustrated in Wegman’s Figure 4.4 correspond to a t-statistic of approximately 3.49, which is at the 99.97 percentile of the t-distribution. While there is some difference in visual HS-ness, contrary to Stokes, both median and top-percentile Mannian PC1s have very strong HS appearance.

Stokes is presently attempting to argue that representation of a network through a biased Mannian PC1 is mitigated in the representation of the network, by accommodation in lower order PCs. However, Stokes has a poor grasp on the method as a whole and almost zero grasp of the properties of the proxies. When the biased PC method is combined with regression against 20th century trends, the spurious Mannian PC1s will be highly weighted. In our 2005 simulations of RE statistics (MM05-GRL, amended in MM05 (Reply to Huybers – the Reply containing new material), we showed that Mannian PC1s combined with networks of white noise yielded RE distributions that were completely different than those used in MBH98 and WA benchmarking. (WA acknowledged the problem, but shut their eyes.)

Nor, as I’ve repeatedly stated, did we argue that the MBH hockeystick arose from red noise: we observed that the powerful HS-data mining algorithm (Mannian principal components) placed the Graybill stripbark chronologies into the PC1 and misled Mann into thinking that they were the “dominant pattern of variance”. If they are not the “dominant pattern of variance” and merely a problematic lower order PC, then the premise of MBH98 no longer holds.

Appendix