In order to illustrate a useful application of principal components, Tamino showed coordinate systems for the motion of a canoe. In the context of MBH, it would have been more instructive to show how principal components apply to tree ring networks than to canoes. In such a context,a non-Mannian centered PC1 will typically show some sort of weighted average and lower PCs will show contrasts, which feature increasingly trivial and local contrasts. I’ll show this in connection with the Stahle SWM network used in MBH98, where there is relatively little difference between Mannian and centered PCs and which will give readers a flavor of exactly how little utility the lower order PCs have.
Readers may also consider the following assumption underlying MBH:
Implicit in our approach are at least three fundamental assumptions. (1) The indicators in our multiproxy trainee network are linearly related to one or more of the instrumental training patterns. In the relatively unlikely event that a proxy indicator represents a truly local climate phenomenon which is uncorrelated with larger scale climate variations, or represents a highly nonlinear response to climate variations, this assumption will not be satisfied.
As you examine the weights of different Stahle/SWM PCs, reflect on whether MBH have successfully excluded the possibility that (say) the Stahle PC8 (or for that matter the PC3, PC2 or PC1) might simply be some local noise.
First here is a location map showing the 10 Stahle SWM sites reported in the original SI. In the Corrigendum, in response to a request for the location of an 11th site used but not listed, Mann said unhelpfully that the site was “Unpublished Southwest US/Mexico Density series (D. W. Stahle, personal communication)” – so we have no information on exactly where it is.
The Stahle SWM network as used in MBH98 consists of 2 series for each site – one said to be earlywood width and one said to be latewood width. The first and 11th sites have identical values for both EW and LW for the first 128 years or so, as shown in the graphic below subtracting the two series from one another. The straight line segments in the early portions denote identical values – are these different versions from the same site? Or is site 11 a different site than site 1 with values from site 1 inadvertently spliced? No one knows. When asked for an explanation, Nature refused to provide one. Obviously there’s some sort of error.
That’s tine. The insulting thing for the climate community is that the data set in Mann et al 2007 is identical to the MBH98 data set, including these obviously incorrect identical values, which remain unchanged, despite the matter being brought to Mann’s attention.
Now for a series of diagrams showing the “eigenvectors” corresponding to each PC. In every case, the eigenvectors are plausibly interpreted as weights, such that the PC1 is a weighted average and the other PCs are contrasts. First are diagrams showing the weights for each series as barplots (update: I’ve added in contour maps showing eigenvector weights separately for Earlywood and Latewood as both are reported for each site.)
First here are the weights for the PC1.
Now here are the weights for PC2-PC9, all said to be “significant”. The PC2 can be interpreted as a contrast between the sites in northern New Mexico and the sites in Texas/Mexico. The PC3 can be interpreted as a contrast between earlywood and latewood. Neither of which seem readily interpretable in terms of the top 16 world climate patterns. But it gets rapidly worse as the later contrasts and contrasts between relatively arbitrary combinations of sites and LW/EW choices. How can the contrast shown in the PC7 be plausibly linked to any world climate pattern? It is total bilge.
Mann et al said that it was “relatively unlikely” that “a proxy indicator represents a truly local climate phenomenon which is uncorrelated with larger scale climate variations”. But surely no one can seriously believe that the Stahle/SWM PC7 is anything other than some local noise. This is an extreme example – but readers should understand that the network is mostly noise. That’s why reconstructions with stocks and white noise do just as well as actual “proxies”.
And the problem is not avoided by not doing PCs. Multiple inverse regression a la MBH and Wahl and Ammann has its own very serious problems, which people have barely scratched the surface of. It’s amazing that this stuff is taken seriously.
These are done using Mannomatic PCs but the effect of the Mannomatic is not large in this network.