Jean S, UC and I spent a considerable amount of time a couple of years ago, trying to figure out how MBH99 confidence intervals were calculated – see here. I asked the NAS panel to investigate the matter, but they failed to do so. After their report, I asked NAS president Cicerone to merely write to Mann asking him to provide an explanation – Cicerone refused. I asked Gerry North to do so; North agreed to do so, but I never heard anything more about it. So either he agreed to ask for an explanation and then didn;t follow through or Mann refused even a request from Gerry North.
North was supposedly one of the reviewers for Mann et al 2008, which also refers to confidence intervals. One would have hoped that North, already on notice about this issue, would have ensured that Mann et al 2008 clearly explained their calculation of confidence intervals. No such luck.
Figures 2, 3 and S5 all illustrate “95% confidence intervals” by “lightly shaded regions of similar color)”. Mann et al observe: “For the CPS (EIV) reconstructions, the instrumental warmth breaches the upper 95% confidence limits of the reconstructions beginning with the decade centered at 1997 (2001)” and in the caption to Figure 3 state “Confidence intervals have been reduced to account for smoothing.”
The “Methods” state:
Uncertainties were estimated from the residual decadal variance during the validation period based (32, 42) on the average validation period r2 (which in this context has the useful property that, unlike RE and CE, it is bounded by 0 and 1 and can therefore be used to define a ‘‘fraction’ of unresolved variance).
That’s it. There is no further explanation. The SI contains a column entitled “uncertainty” which changes in century-steps. I’ve examined the source code and, once again, it appears to be incomplete. I’ve been unable to locate any code evidencing the calculation of the confidence intervals.
Another Caramilk secret. I’ll experiment a bit with some of the endless Butterworth smooths and see if anything turns up.