This is a continuation of a TRF analysis calledSteve McIntyre.
Click to zoom in. See it in different colors.
The picture shows the distribution both of different correlation coefficients, a priori between -1 and +1, for pairs of 5,509 Antarctic stations, as well as the distances in the pair. It shows how the correlation tends to disappear as the distances increase.
The chart has been calculated from the temperature anomalies during a period of 300 months: by the temperature anomaly, I mean the temperature for a given month minus the average temperature for the same station and the same month calculated from those 25 years.
The raw data were taken from the last, cloud* file on Steig's website. I didn't use any code of Steve which increases the independence of the calculation. The colors that have only made the picture slightly more attractive and more informative than Steve's graphs are pretty much the only visible contribution from your humble correspondent. ;-)
Download the Steig2 notebook for Mathematica 7.0.1Interpretation
Download its zipped PDF preview
This observation extracted from the reality heavily disagrees with Steig's assumptions/claims/approximations. The latter imply that for distances below 1,500 km or so, a vast majority of Steig's correlation coefficients are almost exactly equal to +1.0. Also, his reconstructed temperatures at distant places of Antarctica seem to be almost always correlated.
Click to zoom in. White background.
This effect occurs because the continental temperature is universally assumed to be a time-dependent linear combination of three or four spatial patterns. Amusingly enough, many pairs of stations have a huge negative correlation of Steig's temperatures (that's because the spatial patterns are often combined with negative coefficients - a type of anticorrelation between two places that rarely takes place in reality). While the real-world correlation never drops below -0.4, Steig offers many distant pairs whose correlation is below -0.6 or more.
However, the internal structure of a CDF file seems nontrivial, and if R is not equipped with gadgets to decode CDF files, it may be pretty hard to do it manually. For example, the climate files under consideration contain 25 pieces of data (25 matrices, if you wish), each of which comes with a different length of vectors, different formats for numbers, and different annotations: see PDF printout of a Mathematica notebook clarifying the structure of the CDF file.
Wolfram's software seems to be very convenient for such things - but yes, R is free.