NSIDC Sat Data PCA
Posted by Jeff Id on March 26, 2009
I thought about titling it NSIDC AVHRR PCA just for fun. I ‘ve done a short PC analysis of the antarctic data to see if I could replicate Steig’s 3 pc’s. It didn’t work out very well but it returned some interesting results. I had to post this now because we just got the real data from Eric Steig and will be using that next and will have something to compare it to.
Before I get started, credit for the code goes to about a dozen people, Jeff C, SteveM, Roman, Ryan and myself. I may have added someone or left someone off inadvertently but it has a pile of people involved.
First here is a plot of the first 100 eigenvalues.
Compare this to SteveM’s plot on CA of the processed data from Steig.
Remeber this is the statement in Steig’s paper.
Principal component analysis of the weather station data produces results
similar to those of the satellite data analysis, yielding three separable principal
components. We therefore used the RegEM algorithm with a cut-off parameter
k53. A disadvantage of excluding higher-order terms (k.3) is that this fails to
fully capture the variance in the Antarctic Peninsula region.Weaccept this tradeoff
because the Peninsula is already the best-observed region of the Antarctic.
It’s clear from my plot above that the data has strong eigenvalues at levels much greater than K = 3. The NSIDC data used to create the plots is processed differently than Steig but it is from the same instruments. I fully expected this to look different because there simply isn’t enough covariance information to get proper spatial weighting. It just means they left too much information out
Here is a plot of the first 10 pc’s.
I then decided to plot the eigenvectors.
This is the same as the patterns SteveM produced but if you’ve read the posts you see the pattern is different. I expected the secondary oscillation to be top left to bottom right but the ocean cell contamination of the data overpowered the spatial covariance of the matrix. The fact that ocean pixels are more stable created a non-spatially or less spatially autocorrelated pixels in the data so the pattern is between the ocean pixels positive and center land positive and a ring in between negative. A link to a movie which plays the data and shows the ocean pixel contamination clearly is here.
I will need to rerun the analysis masking the ocean contaminated parts which should result in the autocorrelation patterns we would expect.