Here’s another interesting mystery in Mann et al 2008. Their SI table rtable1209 reports correlations to 1850-1995 instrumental temperature. The correlations reported in their PNAS SI Table SD1 sets all but 484 “significant” values to NA, so the r1209 table is more comprehensive. The instrumental version supposedly used in their calculations is now archived at WDCP (hooray), though it wasn’t archived in their Penn State SI, and this can be used to test reported correlations. In their SI, they report lat-longs of all 1209 series.
I calculated 1850-1995 correlations between proxies and corresponding gridcell values and compared to reported values, yielding the graphic below (color coded by proxy “type”). As you can see, many correlations match exactly up to rounding) – showing that the calculation is grabbing the “right” things for many of the series, but many don’t. There is also a remarkable pattern in the differences, which is evident as soon as you look at the graphic and which I’ll discuss below.
The pattern is this: if the Mann correlation is positive, then the reported value is equal to or greater than the value that I calculated; while if the Mann correlation is negative, the reported value is less than or equal to the value that I calculated. So if you multiple the difference by the sign of the Mann correlation, you get the following highly non-random pattern:
If one now looks at histograms of the correlation, one gets the following. The reported correlations are “hollowed out” around 0, yielding a somewhat trimodal distribution. The bump out on the high end of the correlations comes from the Luterbacher series, which use instrumental data. These are claimed in the 484 “significant” correlations, though they are unrepresentative of proxy series used in the MWP. There are also a lot of Briffa MXD gridded series in the 484.
There’s a tricky little comment in the SI which I’m going to investigate in this connection:
To pass screening, a series was required to exhibit a statistically significant (P > 0.10) correlation with either one of the two closest instrumental surface temperature grid points
This would tend to hollow out the distribution as there are two chances at a “significant” correlation. So far, I haven’t figured out how (or whether) Mann adjusted his significance benchmark for this double dip and would be interested in any reader thoughts on this (see the SI.)