I just read some ClimateAudit.ORG articles about
This is the PC1 visualized by my favorite Voronoi diagrams. Finally, you should also see two more diagrams of this kind, namely PC2 and PC3. There are no other PCs! What the hell is your humble correspondent talking about?
Fifty megabytes of junk
A few weeks ago, Nature printed a paper by Steig et al. about the temperatures in Antarctica. Michael "hockey stick" Mann is among the authors. Curiously enough, the data used in the paper are publicly available:
- Tir_lats.txt (latitudes)
- Tir_lons.txt (longitudes)
- ant_recon.txt (temperatures)
A priori, I would be completely overwhelmed by such a huge file with seemingly uncontrollable numbers. Fortunately, some people around ClimateAudit.ORG are more courageous. It turns out that exactly 99.5% of the figures in the file are redundant junk. The file pretends to describe 600 x 5509 independent numbers but it can actually be calculated from 3 x 5509 numbers!
Alternatively, you may try some free Mathematica players that won't work with my notebooks. Or you can download and learn a free programming language called "R" - Steve McIntyre's favorite choice - which is largely impenetrable unless you are a statistical geek. :-)
Download the steig.nb notebookFine. So what I did was to download the three files into my special Antarctica directory. I imported the files as matrices into Mathematica: it was smoother than ever before. No problems with the exponential notation, either. Then I converted the 600 x 5509 matrix into the principal components, using a function that is aptly called PrincipalComponents[...].
... (or PDF preview)
Update: See Spatial correlations in Antarctica for another, "future" TRF article about these topicsI looked at the result. And indeed, only 3 rows out of 600 were nonzero - when you looked at a large number of initial entries (close enough to the beginning of the measurements in 1957). More precisely, lots of the initial entries in the 4th row were about one billion times smaller than those in the 3rd row. Wow. Clearly, it was meant to be zero and the nonzero values came from some rounding errors and other negligible effects. The three principal components were drawn, using Voronoi diagrams and the TemperatureMap color scheme, with positions on Earth projected stereographically on the plane touching the South Pole.
Instead of the file with 600 vectors, each of which has 5509 components, they could offer a file with 3 vectors only, each of which has 5509 components, plus 600 x 3 numbers telling you the weights of PC1, PC2, PC3 for each month. OK, I mean 600 x 4 numbers because I also need an additive shift (another time series) for the linear fit.