Mission Impossible Team, here’s your assignment today. Unfortunately you failed your last assignment: replicating Mann’s claimed correlations. But that probably was impossible. Today your assignment is probably possible, but is a dangerous expedition into the dark underground – into the terrifying world of Mannian RegEM. Courage and perseverance will be required. You may not return alive.
Let’s start with something simple and seemingly innocent – a location map of Loehle’s proxy selections. This shows the locations of 18 proxies in various locations around the world. Three “regional” proxies – two in China and one in North America – are shown at their approximate centroid.
Next here is a location map for the 22 proxies in the Mann et al 2007 network (the network formerly known as MBH98). As with the Loehle network, the two North American PCs are shown in locations near their approximate centers of gravity.) It’s more land-oriented than the Loehle network, perhaps a little more North American-oriented, but it looks innocent enough.
Although Mann et al said (and Zorita et al 2003 unfortunately adopted this point) that it was impossible to allocate weights to the individual proxies, this is untrue. Vast quantities of linear algebra cancel out enabling the NH reconstruction to be expressed as a linear weighting of the individual proxies (some with negative weights.) In the graphic below, I’ve made the area of each dot proportional to the MBH98 weight of the Mann et al 2007 proxy. The visual impression is obviously entirely different. The point here is one that’s been very clear to me for a long time and I’ve tried various ways to convey this message, but I think that this image may finally enable a wider audience to fully understand what the “more sophisticated” (using JEG’s words) algorithm does.
The MBH98 network is essentially a combination of only 4 series: the North American PC1 (which is 95% Graybill bristlecone chronologies), Gasp” – a questionable series, which had an unreported extrapolation to get it into the AD1400 network (this is the sort of unreported accounting adjustment that sets off alarm bells in the real world although not in real climate; Briffa’s Tornetrask series (which was manually altered by Briffa in Briffa et al 1992 – an alteration reported but nonetheless unjustified; and Cook’s Tasmania ring width series. The other series are just nothings under MBH98 weighting. Some negative weighted proxies (e.g. ice core accumulation) have a plausible physical interpretation as inverted. In my opinion, these can be counted as positive correlations and arguably the negative of the proxy should be collated. One should not otherwise invert things like tree ring proxies after the fact.
Now you’ve all heard that Mann can “get” a HS without using PCs. Again I’ve observed in the past that this is really just a trick for using the bristlecones, but this point can be illustrated rather neatly using the graphic technique of the above maps. First here is a map of the locations of all 95 series in the Rutherford et al 2005-Wahl and Ammann 2007-Mann et al 2007 AD1400 network, with the size of the dots set so that the total dot area is equal to the other two cases. You don’t have to be Ethan Hawkes to notice that the no-PC network is predominantly in the U.S.
Now in the world of temperature histories that we’ve been exploring from time to time, we know that the U.S. temperature history in the 20th century has a different course than the ROW; indeed, in the US, according to NASA, 1934 was the warmest year of the century (inquiring minds want to know whether it was the warmest in a millennium or even in a millllll-yun years). But Gavin Schmidt, functioning both as NASA spokesman and as an able real climate spokesman, has told us, as has Hansen, that the US constitutes only 6% of the global land surface and 2% of the surface and is thus unrepresentative. One would presume that the weightings in the no-PC network would downweight the over-populated U.S. proxy network to reflect the lack of geographic balance introduced by abandoning PC networks – even if it meant downweighting the bristlecones.
OK, I was just teasing. I didn’t really expect you to think that they’d downweight the bristlecones. Here’s what the weights work out to in the no-PC network. They are – if anything – even more concentrated in the U.S. southwest (bristlecones) than the unweighted distribution, which was already heavily weighted to the U.S. The main HS-shaped Graybill bristlecone chronologies each strongly impact the final results, so that the early portion of the MBH reconstruction – whether modulated through Mannian PCs or in the no-PC situation – still is essentially the sum of the Graybill bristlecone chronologies. Mann’s incorrect PC method is not the only method of overweighting the bristlecones.
What caused the MM reconstruction to differ was that different weights were assigned to the proxies – with less weight to the bristlecones, other series, especially Tornetrask, Quelccaya and (oddly) Tasmania gained weight. It wasn’t that we believed tha a weighting of these series was specially wonderful as a reconstruction, but that the recon was unstable to bristlecone weighting.
You can immediately see the problems that the Ababneh update of the Sheep Mountain chronology pose for these weightings. The image below (previously posted) compares the Graybill Sheep Mountain chronology (the most heavily weighted series in the MBH98 network) to the Ababneh version. Merely substituting this version for Sheep Mountain in other networks already accounts for change. In this case, there are a few other highly weighted bristlecone chronologies, but all are by Graybill in the 1980s and the replication problems at Sheep Mountain should be setting off alarm bells for the other chronologies. (Of course, there is heavy security on the updated Sheep Mountain measurement data, security which will be too hard for even a Mission Impossible Team.)
Although this network was first used in MBH98, it has been applied subsequently in Rutherford et al 2005, Wahl and Ammann 2007 and most recently Mann et al 2007.
In each new guise, it has become harder and harder to determine what the weights of the individual series are in the final reconstruction. Mann et al 2007 says that it is impossible to know, but Tapio Schneider has observed that, while the algorithm is nonlinear, the regression coefficients can be extracted from the RegEM algorithm.
So, Mission Impossible Team, your task is to determine the weights of the individual proxies in the Mann et al 2007 RegEM version and to plot them on a map such as the above. Your instructor, the brave and resourceful JEG, has unfortunately gone missing, perhaps swallowed up in the swamp of Mannian pseudo-covariances. But before going missing, he left us with the message that the failure to show location maps was pseudo-science. (Yes, he didn’t say that the failure to show a weighted location map was pseudo-science, but he’d probably have agreed that it was a good idea.) So, Team, in memory of JEG, return with the weighted location map for the AD1400 Mann et al 2007 RegEM proxy network. The fate of the planet depends on you.