Principal components do not necessarily have an orientation. However, when you are making principal components from networks of tree ring widths, it’s a good idea to try to think about physical interpretations. Here’s a funny example where the Euro Hockey Team has lost its way. They observe the following:
for the proxy principal components in the MBH collection the sign is arbitrary: these series have, where necessary, had the sign reversed so that they have a positive correlation with the northern hemisphere temperature record).
Now there’s an interesting way to illustrate the potential pitfalls of this assumption in the Stahle/Southwestern US-Mexico network where the Euro Hockey Team has unwisely waded in. The EHT has made duplicate calculations in most AD1400 situations of PCs without using series extended to 1980. (As I noted in a post, in MM03, we noted that many of the series had been extended to 1980, but it’s not a point that we dwelled on and I’m pretty sure that we subsequently said that this was not an issue that we were particularly fussed about.) Nonetheless, the EHT have re-done all these calculations. Maybe they were checking to see, if by reducing the number of series being used, they could enhance the “desired signal” – this is perhaps the case in the NOAMER network. Trying to enhance the “desired signal” is an established dendrochronological procedure as stated by elsewhere by coauthor Esper as follows:
this does not mean that one could not improve a chronology by reducing the number of series used if the purpose of removing samples is to enhance a desired signal. The ability to pick and choose which samples to use is an advantage unique to dendroclimatology.
In doing so, they might not have noticed that the SWM network declines to only 2 series in the AD1400 network in their 00 network option. While they don’t say that they only used 2 series in this network, I’ve been able to replicate series #11 in archived mitrie_new_proxy_pcs_1400_v01.nc using two series obtained through this culling and am confident that this is what they did. Now the PC1 of two series is the average – which has a fairly obvious interpretation. In this particular case, I’m satisfied that the two series in the Euro Team “network” are the earlywood and latewood widths of Cerro Durango and Los Angeles Sawmill, WDCP/ITRDB codes mexi023e and mexi023l (which I’ve specifically compared and matched to Mann series swmxdfew09.dat and swmxdflw09.dat.
Figure 1 below shows the plot of the Euro SWM PC1 and the two contributing series. As you see, the underlying series have greater ring widths in the 15th century than in the 20th century. The site in question is at 3170 meters. We’re told that ring widths of these high-altitude sites are supposed to be linearly correlated to temperature so the ring widths themselves are supposed to have some physical meaning. However, in establishing an orientiation for the SWM PC1, the EHT have flipped them over “so that they have a positive correlation with the northern hemisphere temperature record”, disregarding the presumed physical interpretation of the ring widths. While this, in some small way, aids the project of enhancing 20th century values relative to 15th century values, the flipping of the PC1, in this particular case, seems a little, shall we say, opportunistic on the part of the Team.
Figure 1. PC1 is downloaded from mitrie_new_proxy_pcs_1400_v01.nc. The EW and LW series are Mann’s versions, which can be traced to mexi023e and mexi023l, Cerro Durango and Los Angeles Sawmill, PSME, 3170 m.
Does it “matter”? I don’t think that it “matters” very much to the final reconstruction. But, at this point, people should be trying for a little craftsmanship.
This little fiasco also nicely points out one of the problems with using PCs at all. PCs discard information on the orientation of a series – whether it points up or down, requiring later potentially ad hoc interpretations of the results using expedients like correlation with NH temperature to determine whether the PC series is pointing up or down. It would be better not to discard the information on the orientation. If the Euro Team were actually trying to advance the state of the art, that’s what they’d be thinking about. As it is, I think that someone on the Euro Team deserves a few minutes in the penalty box, don’t you?