Most CA readers are aware that proxy reconstructions use linear methods and that, accordingly, all the huffing and puffing of complicated multivariate methodologies simply end up assigning a vector of weights. Surprisingly this obvious point was not understood by paleos when I started in this field.

Because one can assign a vector of weights, it’s possible to make highly informative maps showing the weights of proxies by the size of the disk at the proxy location, designating the sign by a different color. Unfortunately, this sensible practice of examining proxy weights has not been adopted by paleos. Their failure to show proxy weights inevitably leads to quite a bit of (in my opinion) aimless thrashing, with the Smith paper being a recent example.

Smith was perplexed by the difference between McShane-Wyner reconstruction. The figure below shows what bothered him. In this case, retaining one PC led to an MBH-style Stick, while retaining 10 PCs had a pronounced MWP.



Figure 1. Mc-W Figure 14. Red – with one PC; green – with 10 PCs.

Last fall, I tweaked the McShane Wyner code so that weights of the various proxies was extracted in the process. I prepared the graphics below last October but didn’t post them up at the time – I guess that I must have gotten distracted by something else.

The figure below shows the weights for the “red” reconstruction (made from one retained PC.) The overwhelming weighting of US southwestern tree ring chronologies is evident. The largest weights are in gridcells with bristlecones. Nothing else really contributes. This is a classic distribution of weights in a Mann network. MBH reconstructions in its various guises also weight the bristlecones. The reason why supposedly “independent” reconstructions look so similar is that the proxies are commonly not independent. The Mann et al 2008 network of 1209 proxies contains the same Graybill bristlecone as MBH98.

Notice that the Central American lake sediment series (which have a prominent MWP) are flipped over. This is a result of the PC algorithm. Flipping them over makes them line up better with the bristlecones.



Figure 2. Weights for Red Reconstruction. Orange dot is only because red dot was too big. Red – positive weight; blue negative weight.

Update – For amusement, here are the weights for Gavin Schmidt’s selection of 55 of 93 proxies using the McShane Wyner Figure 14 method. Needless to say, Gavin’s reconstruction is fully addicted to bristlecones. For greater certainty, Gavin flipped over the Central American lake sediment series that offended Smith.

The green reconstruction is not dominated by bristlecones. More prominent are sediment series in Central America, a speleothem in Yemen and some Chinese speleothem series. This time, there are a number of negatively oriented series – some tree ring series in the southeast US that were originally reported as precipitation proxies, a speleothem in Scotland. The Tiljander series are flipped over to cohere better with lake sediments in Central America.



Figure 3. Weights for Green Reconstruction.

Obviously lots of readers will “like” the green series, but it’s not clear to me that it makes any more sense than red reconstruction.

In my opinion, the problem is that you can’t simply throw a bunch of inconsistent time series into a multivariate mannomatic and expect to get a statistically significant response. If a scientist cannot specify the sign of a proxy in advance, then the proxy shouldn’t be used.



