Here is a little present for Jean S and UC. Something new from the gift that keeps on giving. Something that even I never noticed before.
What we’re going to see is that in Mann-world, U.S. tree ring series are capable not merely of reconstructing world temperature, but 9 different “climate fields”. In effect, using Mann’s algorithm, one doesn’t need to leave the U.S. to reconstruct world climate in as much detail as one could ever want. It’s funny that actual U.S. temperature readings in the 20th century are held to be unrepresentative of world climate, but U.S. tree rings have such remarkable properties.
Mann, followed by Wahl and Ammann, say that they can “get” a HS without using PCs, by using all proxies. I’ve previously commented on the overfitting problems inherent in this approach, but there’s more when this web begins to get tangled.
Today’s post is about a puzzling corner of MBH98 that even Wahl and Ammann 2007 made no attempt to replicate – the determination of how many “climate fields” could be reconstructed. Wahl and Ammann despaired of even beginning the ascent of this particular mountain and simply adopted the schedule published in the MBH98 SI. Neither Jean S, UC nor myself have made any headway either.
In all our discussions of Mannian principal components until a couple of days ago, we’d only discussed two forms of PC calculation: temperature PCs (which Mann reifies as “climate fields”) and tree ring PCs. When I re-parsed the source code again a couple of days ago, I noticed a third PC calculation (also Mannian short-centered) which we hadn’t discussed before.
In order to determine how many climate fields could be reconstructed, Mann did a Mannian short-centered PC calculation on the proxy network for each step, calculating the number of normalized eigenvalues that exceeded the square root of 2/M, where M is the number of proxies. As noted in my post, although Mann described this as an implementation of Preisendorfer’s Rule N, the rule is not set out in this form in Preisendorfer. Nonetheless, I’ve done some experiments with networks with low-order AR1 coefficients, of the type that Mann uses. It is a more restrictive rule than say the Guttman Rule which would effectively use the square root of 1/M, so it’s not something that I take particular issue with (other than the general point that “significance” under Rule N is nothing more than notice that the PC should be investigated and is not itself a test of scientific significance, contrary to anything that Mann or Ti-mann might say.
The graphic below show an emulation of this test using the MBH AD1400 set of proxies (short-centered tree ring PCs) in a short-centered PC test. As you can see, this calculation shows a calculation which in Mann-world is used as a rationale for only reconstructing one “climate field” in the AD1400 step. According to this test, the network contains only one significant pattern and therefore only one “climate field” is reconstructed. So the calculation here yields the reported result – something that should not pass without a small celebration for Mann crossword puzzle solvers.
Mann, followed by Wahl and Ammann and Tamino, says that they get the same results without using PCs, by using the 19 non-PC proxies in the AD1400 network together with the 76 tree ring proxies in the NOAMER and Stahle SWM networks – added to a few North American tree ring sites in the AD1400 network used directly.
The above calculation was done with 22 series- 19 proxies and 3 PC series. So let’s do the same calculation using the no PC network – using 95 proxies individually, first with Mannian short-centering and then in a centered calculation. In the short-centered calculation, the test states that there are seven “significant” climate fields that the proxy network can reconstruct. Using a centered test, it’s even better: now there are nine “significant” climate fields that can be reconstructed.
Mann said that his erroneous PC method didn’t “matter” because he got the “same” answer without using PCs. Well, did he get the same results? Taking his absurd methodology at face value, had he followed the “no PC” alternative and without short-centering, he would have had to continue through the calculation with nine climate fields. I haven’t followed through this leg of the calculation to its end. There is a process for selecting which “fields” to reconstruct which is still a mountain to climb. But with this new foothold, we may be able to advance on it.
But Mann’s claim that the error had no impact is clearly falsified here. Because of this error, Mann failed to reconstruct nine climate fields in the no PC case that were “permitted” under his methodology. Think of all the lost “information”.
The problem is far more than bristlecones merely being antennae for world temperature. U.S. trees, analysed according to Mannian methods, are supposedly capable of reconstructing ENSO, the Chinese monsoon, the East Asian monsoon, the PDO, the North Atlantic Oscillation, the Indian Ocean Dipole – did I leave anything out?
Think of the time and effort that can be saved for paleoclimate research. Using Mann’s methodology, there’s no need to collect data from remote corners of the world. You can just keep adding to the U.S. tree ring network. More Starbucks for everyone.
A few readers may argue: maybe so, but this is a “10 year old” paper and doesn’t apply to Mann et al 2007. Well, the same issues apply to it, perhaps even more so. Mann et al 2007 uses exactly the same network as MBH98 – right through to the erroneous PCs. Mann has cheekily not changed a comma in his data base in 10 years. The approach in Mann et al 2007 is to calculate an enormous correlation (covariance) matrix between all the proxies in the entire world and use that for reconstruction. In the early stages where the network is dominated by U.S. tree rings, you end up with exactly the same sort of problem as the MBH “all proxy” network – the absurd conceit that patterns in a matrix of U.S. tree rings can be used to reconstruct climate details all over the world.