We’ve spent a lot of time arguing about RE statistics versus r2 statistics. Now think about this dispute in the context of Figure 7. Mann "verifies" his reconstruction by claiming that it has a high RE statistic. In his case, this is calculated based on a 1902-1980 calibration period and a 1854-1901 verification period. The solar coefficients in Figure 7 were an implicit further vindication in the sense that the correlations of the Mann index to solar were shown to be positive with a particularly high correlation in the 19th century, so that this knit tightly to the verification periods.
But when you re-examine Mann’s solar coefficients, shown again below, in a 100-year window, which is a period that is sized more closely to the size of the calibration and verification periods, the 19th century solar coefficient collapses and we have a negative correlation between solar and the Mann index. If there’s a strong negative correlation between solar and the Mann index in the verification period, then maybe there’s something wrong with the Mann index in the verification period. I don’t view this as an incidental problem. A process of statistical “verification” is at the heart of Mann’s methodology and a figure showing negative correlations would have called that verification process into question.
There’s another interesting point when one re-examines the solar forcing graphic on the right. I’ve marked the average post-1950 solar level and the average pre-1900 solar level. Levitus and Hansen have been getting excited about a build-up of 0.2 wm-2 in the oceans going on for many years and attributed this to CO2. Multiply this by 4 to deal with sphere factors and you need 0.8 wm-2 radiance equivalent. Looks to me like 0.8 wm-2 is there with plenty to spare.
I know that there are lots of issues and much else. Here I’m really just reacting to information published by Mann in Nature and used to draw conclusions about forcing. I haven’t re-read Levitus or Hansen to see how they attribute the 0.2 wm-2 build-up to CO2 rather than solar, but simply looking at the forcing data used by Mann, I would have thought that it would be extremely difficult to exclude high late 20th century solar leading to a build-up in the oceans as a driving mechanism in late 20th century warmth. In a sense, the build-up in the ocean is more favorable to this view as opposed to less favorable.
None of this "matters" to Figure 7. It’s toast regardless. I’m just musing about solar because it’s a blog and the solar correlations are on the table.
With window length of 201 I got bit-true emulation of Fig 7 correlations. Code in here. Seems to be OLS with everything standardized (is there a name for this?), not partial correlations. These can quite easily be larger than one.
The code includes non-Monte Carlo way to compute the ‘90%, 95%, 99%
significance levels’. The scaling part still needs help from CA statisticians, but I
suspect that the MBH98 statement ‘The associated confidence limits are approximately constant between sliding 200-year windows’ is there to add some HS-ness to the CO2 in the bottom panel:
(larger image )
This might be outdated topic (nostalgia isn’t what it used to be!). But in this kind of statistical attribution exercises I see a large gap between the attributions (natural factors cannot explain the recent warming!) and the ability to predict the future: