Telling people how MBH99 confidence intervals were calculated? I think that is a trade secret.

Using well-known methods (CCE) to calibration and error analysis would not fit the agenda

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]]>“I floated the idea of bringing Anders Moberg and Jan Esper in on the proposal (offering them both travel money), because one of the things I would want to do would be to get a better grasp of their error analysis, and it’s

always a lot easier to do this by talking friendlily to people than by reverse-engineering their papers. I tried and failed to understand Mann’s error analysis using both approaches about 5 years ago, so I don’t think it is worth trying again, particularly given his current level of sensitivity….”

The consequences of scientific fraud vary based on the severity of the fraud, the level of notice it receives, and how long it goes undetected.

The Team should very very fast inform us, where do we go wrong?

]]>In contrast to MBH98 where uncertainties were self-consistently estimated based on the observation of Gaussian residuals, we here take account of the spectrum of unresolved variance, separately treating unresolved components of variance in the secular (longer than the 79 year calibration interval in this case) and higher-frequency bands.

and from that submission version

In contrast to MBH98 where uncertainties were estimated from the unresolved calibration variance based on the assumption of Gaussian statistics, we estimate uncertainties in the reconstructions here taking separate account of the unresolved calibration variance in the secular (longer than 79 year timescale) and higher-frequency bands, the former inflated relative to the white noise levels by the factors noted above.

Maybe reviewer found something wrong with term *Gaussian statistics* , and they corrected it to *Gaussian residuals* (not much better, autocorrelation is the key issue actually).. In addition, the reviewer thought that this is so simple and we have limited space, so cut down it a bit.

Anyway, secular band is inflated, maybe they expand 79-bin FFT’s first bin to equal 1000-bin FFT frequency band, and assume that noise power is flat in that frequency band. Simply take the variance of residuals (sparse) and multiply it by 5*1000/(83*79), and you’ll get (almost) IGNORE1. Remaining part is the non-inflated variance, but there’s now overlap in the first frequency bin (after DC). Thus, you need to multiply the non-inflated variance by 2/3, because someone assumed that 1/3 of it was in the first band originally. I’m not sure if I should put a smiley here or not.

]]>1) MBH98 CI sigma (s98) is simply RMSE between the reconstruction and the instrumental temperature in the **calibration period**. This can be verified from the supplementary information table to MBH98 which reports Mann’s “betas”, i.e. RE-statistics. As always with MBH, nothing is perfect: you get perfectly the values for all other steps except for 1750/1760/1780, which all have reported betas of 0.74. I think in this case it is simply a mistake in the table. Notice also that the instrumental series used is the **dense** (see below).

2) Now, MBH99 CIs are different from MBH98. The key here is to notice that the file contains two columns labeled “Ignore these”. The relation between MBH99 sigma (s99) and the ignore columns (I1, I2) is simply s99^2=I1^2+I2^2. IMO, understanding what are these ignore columns is the key to understanding the whole mystery. The relations to s98: I2^2/s98^2=0.66 (perfectly), but I1^2/s98^2 is bi-level with the cut off time 1600. Before 1600 the ralation is about 2.04 and after about 0.7480.

3) There exists a submission version of MBH99 still available in the WayBack machine. This paper has some additional figures. It has a plot of the residuals (figure 2a) for AD1000 and AD1820 steps. I scanned those (available here). It was noticed earlier that AD1820 step residuals are with respect to the “sparse” version of the instrumental series. Now we have been able to reverse engineer (perfectly) the MBH99 AD1000 step, so it is possible to confirm that also those AD1000 residuals are with respect to the **sparse** intrumental series. Futhermore, we have been able to reproduce the calibration spectrum figure (figure 2 in MBH99, figure 2b in the submission version), see discussion in this thread/the script in the above link. This shows that CIs of MBH99 might have something to with sparse residuals as the discussion of CIs in MBH99 refers to the figure 2.

mean(nhde(1:79,3)) % nhem-dense.dat

ans =

-1.26582278449519e-009

I guess Mann’s Beta assumes that calibration reference is always centered. And I can’t figure out what WA Appendix 4 actually says..

So, is it true that MBH99 CIs (and Figure 2) are computed using sparse temperature as reference, and reported REs are computed using full temperature as reference?

]]>Here’s what I think:

-I suppose 0.6886 in 2) (#184) is not actually verification RE reported… For calculating that verification RE you should really use *mean of sparse Temp 1902-1980*. I know… now the value drops to 0.6838 which is not the reported (0.69).

-However, check the definition of in MBH98, there is no centering! How about if we do not center our instrumental values… I get 0.7551 for caliberation and 0.6886 for verification, which round nicely to the reported values. This would give much simpler explenation for the rather big “reduction” in (verification) RE values repoted in Wahl&Ammann (see Table 1) for which they offer an ad-hoc explenation (Appendix 4).

Summary: I think Mann did not actually calculate RE-values but his own (“resolved variance”), which is not always the same thing!

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