Ryan O has observed a remarkable property of the Mannian algorithm used in Steig et al’s Antarctic temperature reconstruction described in a lengthy post at Jeff Id’s here and cross-posted at Anthony’s. Source code here (the source code style BTW evidencing engineering tidiness from which we should all take heed). I’m reporting here on one aspect of the post; readers are urged to consult either of the original postings.
As I understand his exposition, he took a hypothetical Antarctic temperature history (his “model_frame”) in which the overall Antarctic trend was 0.060 deg C/decade, with cooling on the Ross and Weddel ice shelves and near the South Pole and with a maximum trend in the Peninsula, as illustrated below (showing 1957-2002 trends):
Ryan extracted from this:
1) the post-1982 gridcells in lieu of AVHRR data;
2) for stations, the same pattern of missing data as in the actual Steig reconstruction;
He then did a Mannian reconstruction in which he:
1) used 3 PCs for the “AVHRR” data;
2) set the PTTLS regpar parameter equal to 3.
In this case, we know the “correct” answer (0.06 deg C per decade.) Instead of getting the correct answer of 0.060 deg/C , the Mannian algorithm yielded a trend that was 70% higher (0.102 deg C/decade).
In climate science terminology, this trend is “remarkably similar” to the trend reported in the original article. Ryan dryly observed:
If “robust” means the same answer pops out of a fancy computer algorithm regardless of what the input data is, then I guess Antarctic warming is, indeed, “robust”.
Ryan’s example is pretty convincing evidence that this particular Mannian algorithm is biased towards yielding higher trends. However, I think that it’s important to understand the mechanism of the bias a little more clearly.
For example, in our analysis of Mannian PCA, it was important that we were able to demonstrate the mechanism of the bias – short-segment centering led to the algorithm in effect “mining” for HS-shaped series, which, in that case, were the bristlecones. In the present case, our collective understanding of the problem is still a little empirical – though obviously even that seems to be a considerable advance, to say the least, on the level of analysis achieved by the Nature referees. IMO it should be possible to provide a more analytic explanation. With this end in mind, some time in the next few days, I’ll post some notes that will attempt to connect RegEM with known statistical methods i.e. methods used by someone other than a Team member.