Just when you thought that there was nothing left to say about MBH98, look at this MBH98 "flavor" that the cat dragged in today. This is a MBH-flavor reconstruction using MBH methodology and MBH proxies, following one of the NAS panel suggestions!! What did I do?
Figure 1. A New MBH98 Flavor
Before I say what I did, let me explain why I’m doing another MBH flavor at all. Surprisingly, it seems that the Wegman Report and NAS Panel have not driven a silver spike through MBH and devout climate scientists still believe in it. Here’s where the wiggle room is left.
The Wegman Report did not discuss Wahl and Ammann; Jay Gulledge of the Pew Center, who was one of the panelists with me at the second House E&C hearing, strongly criticized them for that, believing that Wahl and Ammann had somehow bailed out MBH – by arguing that the PC error didn’t "matter". Of course, he didn’t criticize the NAS panel for not trying to replicate Wahl and Ammann.
The NAS panel was simply schizophrenic. As we noted before, they condemned the use of substandard materials in bridge construction, but then cited designs using substandard materials. They cited Wahl and Ammann as somehow showing that Mann’s PC errors did not "matter" without reflecting that the entire rationale of Wahl and Ammann was how to include substandard materials in a reconstruction (bristlecones).
One of the Wahl and Ammann arguments which has got a lot of traction in the climate science community is that they can "get" a HS without using PC methods by using all the proxies. We had previously discussed this result in MM05 (E&E 2005b) – it was already in the air at realclimate. We pointed out that all this means is that the reconstruction has abandoned any pretence to geographic balance and that the Mannian regression phase picks up bristlecones. Of course, Wahl and Ammann did not cite this prior discussion nor did the NAS Panel (which did not even include MM05 (EE) in its bibliography. It really pisses me off that the NAS panel could, on the one hand, cite this particular Wahl and Ammann finding approvingly although it relies on bristlecones, while on the other hand condemning the use of bristlecones. So I guess that we’ll have to reply to Wahl and Ammann after all.
The NAS panel mentioned in passing that the average of tree ring networks might be more sensible than PC methods – a possibility mentioned in Huybers 2005. Here’s what they said:
Huybers (2005) and Bürger and Cubasch (2005) raise an additional concern that must be considered carefully in future research: There are many choices to be made in the statistical analysis of proxy data, and these choices influence the conclusions. Huybers (2005) recommends that to avoid ambiguity, simple averages should be used rather than principal components when estimating spatial means.
While I doubt that there’s any sensible way of extracting useful information from the bilge of MBH tree ring networks, I thought that it would be an interesting exercise to do what they recommend here – calculate the average of the 6 tree ring networks, both with and without dividing by standard deviations, and then include these 6 proxies in the MBH reconstruction. Here are the averages of the 6 networks (the versions with division by standard deviation.) Obviously no big Hockey Sticks here.
Figure 2. Averages of Six MBH98 Tree Ring Networks
But when you insert these 6 series into the MBH network leaving the 81 non-PC proxies unchanged, you get the result shown above, which I’ve shown below with the averages over each calculation step in red. There are dramatic downward steps occurring in the 1750 and 1760 steps and back up in the 17780 step.
Figure 3. MBH98 Reconstruction using tree ring network averages. Step average in red.
What happens in these steps? Two things – the number of temperature eigenvectors used in the reconstruction changes. If you recall my posts on the linear algebra of MBH, I pointed out that the NH reconstruction was a linear combination of the RPCs (and these coefficients remain unchanged in the steps regardless of the number of RPCs used.) The figure below shows the weights of each RPC in the NH average. An amusing result of this linear algebra is that you can calculate theNH average from the RPCs without having to do the matrix expansion to individual gridcells, since the algebra cancels. (I’ve quadruple-checked this both in the algebra and reconciling against Wahl-Ammann results.) The most important weight comes from the RPC1, which is hardly a surprise. In the 1750 step, RPC7 and 9 are added in; 1750 and then RPC9 in 1760 and then RPC14 and 16 in 1780. (Actually MBH substitutes RPC6 and RPC8 in the 1750 step – the only step in which these two RPCs are used. I’ve used RPC7 and 9 which are used in all later steps. ) No one has any idea how the selection of RPCs was made; MBH failed to archive this code in response to the House Energy and Commerce Committee request.)
Figure 4. Weights of Reconstructed Temperature PCs to MBH98 NH Reconstruction
While the RPC selections may contribute to the strange effect shown above, I don’t think that this is what’s involved. Here are the RPC1 contributions to the NH reconstruction for the four century steps: 1400, 1750, 1760 and 1780. Obviously, the RPC1 changes dramatically with the roster changes. (The 1730 step is at a similar level to the 1400 step.)
Figure 5. RPC1 Contribution to NH reconstruction for four steps: black – 1780; red – 1760; blue – 1750; green – 1400
What is it that causes these changes? I’ll try to get to that over the week-end. I haven’t got that far right now. It sure is a bizarre result as it stands. It’s possible that there’s some artifact that I inadvertently introduced in modifying code for this case where no tree ring PCs are used. These calculations are very fresh and it’s possible to get blindsided whenever you tweak code. However, I don’t think so and I suspect that there would still be an interesting result regardless. I think that the situation occurs because the proxies are so poor, causing the algorithm to select slightly different noise patterns in different steps, leading to very unstable results.
So there’s still some juice in this particular lemon for statisticians to explain.
One other prediction that may result from this calculation. In statistical literature, you see certain data sets from the distant past used over and over again to illustrate new methods – as benchmarks. I think that there’s a decent chance that the MBH98 data set will become a statistical classic, although perhaps not in the way intended by the authors. I’ve sometimes said that you could do a yearlong seminar on all the statistical problems of MBH98. I think that there’s a decent chance that the MBH98 will come into increasing use as a classic benchmark in multivariate statistical studies as multivariate statisticians come to understand its many and interesting perversions.
UPDATE (a couple of hours later):
Here is a barplot of the weights (implicitly) assigned by the MBH algorithm to the proxies for the 4 steps illustrated above from the MBH data set with 6 tree ring network averages. As you can see, the weights assigned to the individual proxies are very unstable (BTW recall that both Mann and VZ said that you could not allocate the contributions of individual proxies !) Below the figure, I’ll discuss which proxies are contributing heavily to the reconstruction step.
Figure 6. Weights in four MBH steps. The bold number shows the average value in the step (as shown in red in Figure 3).
In the bottom panel (AD1400 step), the positive values are from Stahle’s Georgia precipitation reconstruciton, then Stahle’s South Carolina precipitation reconstruction; the largest negative value is from the Svalbard melt series.
In the second panel from the bottom (AD1750 step), the two large positive weights are from the precipition series from gridcell 42.5N, 2.5E (which, by recollection, is Marseilles instrumenal precipitation) and the Stahle South Carolina precipitation reconstruction; the two negative weights are from Svalbard melt and the Yakutia temperature reconstruction – note the negative weight to the temperature reconstruction.
In the second panel from the top (AD1760 – the most negative step), the largest positive weights are from the two Quelccaya dO18 records; instrumental precipitation from gridcell 42.5N 2.5E, then the CEng and CEur instrumental temperature series. The Quelccaya dO18 go back to AD1400; I odn’t know why the coefficients jump around so much. The negative values are from Svalbard melt, Yakutia T-reconstruction, Galapagos dO18 and instrumental temperature 57.5N, 32.5E (Moscow). Again, note that instrumental temperature has a negative contribution to the MBH-style reconstruction; this also occurs for some gridcell temperature series in the MBH reconstruction itself.
In the top panel (AD1780), the largest positive values are from Dunde dO18, Central Europe instrumental, Quelccaya 1 dO18, Central England instrumental and Leningrad instrumental; the largest negative contributions are frp, Galapagos dO18, the Yakutia T-reconstruction, New Caledonia dO18; the NOAMER tree ring average and the Stahle SWM tree ring average.
What a pile of garbage this stuff is.