Anthony Watts draws attention to a new Nature article (LI et al 2011) purporting to reconstruct El Nino activity. The Supplementary Information shows a very obvious Chladni pattern, that went unnoticed by the Nature reviewers. The eigenvector shown here is what one would expect from principal components carried out on spatially autocorrelated data on a […]

Some of the CA posts that I’ve found most interesting to write have been about identifying Chladni patterns in supposedly “significant” reconstructions when principal component methods have been applied to spatially autocorrelated red noise. (This is by no means a new observation, as warnings about the risks of building “castles in the air” using principal […]

In his RC post yesterday – also see here – Steig used North et al (1982) as supposed authority for retaining three PCs, a reference unfortunately omitted from the original article. Steig also linked to an earlier RC post on principal components retention, which advocated a completely different “standard approach” to determining which PCs to […]

Ryan O has produced a very interesting series of Antarctic tiles by calculating Steigian trends under various settings of retained AVHRR principal components and retained Truncated Total Least Squares eigenvectors (Schneider’s “regpar”). The figure below re-arranges various trend tiles provided by Ryan in a previous comment, arranging them more or less in increasing retained AVHRR […]

In recent discussions of Steig’s Antarctic reconstruction, one of the interesting statistical issues is how many principal components to retain. As so often with Team studies, Steig provided no principled reasoning for his selection of 3 PCs, statements about their supposed physical interpretation were untrue and, from some perspectives, the choice of 3 seems opportunistic. […]

CA reader hfl, who cited Buell’s documentation of the dependence of principal component patterns on shapes, has sent me a scanned pdf version now available here. It concludes by observing that analyses that fail to consider this phenomenon (and there is ample evidence that Steig et al falls into this category) “may well be scientific […]

Yesterday, I showed an interesting comparison between the 3 Steig eigenvectors and “Chladni patterns” generated by performing principal components on a grid of spatially autocorrelated sites on a disk. Today I’ll show a similar analysis, but this time using a random sample of points from actual Antarctica. The results are pretty interesting, to say the […]

Last year, I did a few posts connecting spatial autocorrelation to something as mundane as the Stahle/SWM tree ring network. In the process, I observed something that I found quite interesting – that principal components applied to geometric shapes with spatially autocorrelated series generated Chladni patterns, familiar from violins and sounds. The Antarctica vortex represents […]

A few days ago, I showed some plots showing distribution of weights arising from principal components carried out on data from a region arranged as a line segment (think Chile). Today I’ve done a similar analysis for a square shaped region again assuming spatial autocorrelation governed by distance. In this case, I made a regular […]

As I observed a couple of posts ago, the Stahle SWM network can be arranged so that its correlation matrix is closely approximated by a Toeplitz matrix i.e. there is a “natural” linear order. I also noted that results from matrix algebra proving that, under relevant conditions, all the coefficients in the PC1 were of […]