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 level with the observations of children who see castles in the clouds”. [Update: Here is a rendering by a CA reader (now using Lucy Skywalker hockeystick version)]
Here is hfl’s summary:
Forgive me if this has been discussed in past threads on PCA (although I couldn’t find it in a quick search of the site), but it’s worth noting that the issue of principal component pattern dependence on domain shape is (or was) well known within the atmospheric sciences community. It was first documented by C. Eugene Buell in a 1975 paper published in the Proceedings of the Fourth Conference on Probability and Statistics in Atmospheric Sciences. Buell’s work focused on square/rectangular domains, particularly because the latter approximated the shape of the conterminous U.S. This was followed by a second paper at the Sixth P&S Conference in 1979 which states: “When a region with well defined boundaries is concerned, the EOF’s computed over this region are expected to be very strongly influenced by the geometrical shape of the region and to a large extent independent of where the region is located. As a consequence, the interpretation of the topography of the EOF’s in terms of geographical area and associated meteorological phenomena should be looked on with suspicion unless the influence of the effect of the shape of the region has been completely accounted for. Otherwise, such interpretations may well be on a scientific level with the observations of children who see castles in the clouds.”
Buell’s work generated considerable discussion within the atmospheric sciences literature because PCA (or, as they referred to it, EOF [empirical orthogonal function]) analysis was in widespread use. Mike Richman, in a paper published in the Journal of Climatology (1986) entitled “Rotation of Principal Components” made the case that component rotation appears to eliminate the problem of domain shape dependence. Richman’s paper is worth reading in that it reviews and considers nearly all of the important work that had been done using PCA on meteorological and climatological data up to that time, including work by Gerry North and others familiar to CA readers. So these problems have been well documented and understood for a long time. Like so many other elements of meteorology and climatology, though, modern climate science appears to have forgotten some important statistical insights produced by it’s own practitioners . . . indeed, some of the practitioners themselves appear to have forgotten what they wrote.