Yesterday, we discussed the remarkable decomposition of the AVHRR reconstruction into 3 PCs, initially observed by Roman and discussed yesterday by Jeff Id. I thought that it would be interesting to see what happened with the PC3 in the AWS reconstruction (and in the process, do some comparisons of the RegEM emulation (file-compatible between Jeff Id and myself) to the archived Steig AWS reconstruction. Again, some interesting results.
First, we again see a loading onto the first three PCs (high values for first three eigenvalues), but the loading is not nearly as concentrated as the AVHRR case. Right now I presume that this is due to the huge number of AVHRR columns (5509 versus 63 AWS) relative to 42 surface columns.
title(“Recon AWS Eigenvalues”)
I then plotted out the first 3 PCs fully expecting to see something like the AVHRR PC3 in which the pre-1980 amplitude was negligible (which I believe to be due to the decision to infill with zeros though I’m not 100% sure of this.) To my surprise, there was no such pattern as shown below.
plot.ts(ts(svd.steig$u[,1:3],start=c(1957,1),freq=12),main=”Recon AWS PC1-3″)
Being cautious about these things, I plotted up the PC4-6 for good measure. (After all, didn’t Mann rely on a PC4 somewhere?) Here they are:
plot.ts(ts(svd.steig$u[,4:6],start=c(1957,1),freq=12),main=”Recon AWS PC1-3″)
As with the AVHRR reconstruction PC3, the AWS PC4-6 – and each has a noticeable eigenvalue – have the same pattern of extreme attenuation in the portion before measurements actually started. In my opinion, these patterns must surely relate to the initial decision to infill missing values with zero.
Schneider said in a comment on another thread that infilling with zero wouldn’t matter, because of the properties of the EM algorithm. Perhaps so, but based on what we’re seeing, it sure doesn’t look like this is necessarily the case for the RegEM PTTLS version used by Steig. So I’d definitely like to understand the basis of Schneider’s assertion better than I do right now and see if there’s something in the Steig PTTLS variation that upsets this property. Now we can’t directly check the Steig variation as he’s refused to disclose his code as used, but I can check with Schneider’s methodology and I’ll try to get to that in a day or two.