Climate Audit

Continued from previous post link.

The data associated with the Climategate “dirty laundry” email had other interesting information on Mann’s calculation of confidence intervals and the related calculation of RE statistic.  This post draws heavily on offline comments by Jean S and UC, both long before and after Climategate.

The left panel below is Tim Osborn’s summer 2003 plot of the AD1000 residuals in one of the “dirty laundry” datasets sent to him by Mann. It matches the AD1000 data in the right panel – Figure 1a in the submission version of Mann et al 1999.  UC had noticed this figure in submission version in 2006 or so.

While the plot of calibration residuals was not carried forward into the published version of Mann et al 1999, an identical figure showing the spectrum of calibration residuals appears in both versions (see below). This almost certainly precludes an unreported switch of the calculation of calibration residuals between submission version and publication (though, with Mann et al, nothing can be excluded.)

Here’s the rub: the standard errors (RE_calibration) values reported in MBH98 and MBH99 are lower (much higher) than values calculated using the Dirty Laundry data.

The RE_NH_cal(ibration) values for MBH98 were reported in its original statistical SI (link) and, for MBH99, in its running text. The MBH98 sigmas (standard error of residuals) for each step can be extracted from the archived stepwise reconstruction mannnhem.dat (NOAA link).  The standard error of residuals in the Climategate “dirty laundry” datasets (AD1000, AD1400, AD1600) can be trivially calculated. Osborn did so in his August 2003 Climategate I document entitled Mann uncertainty.docx.  I verified the calculation – values are shown below.  The calibration RE (RE_cal) is trivially calculated as 1- (se_residuals/sd_obs)^2. (The standard deviation of the target observation data used in the above Dirty Laundry datasets is 0.2511.)

Conclusions:

The Dirty Laundry residual datasets do NOT match the reported RE calibration or sigmas (standard error of residuals) reported for MBH98 (AD1400, AD1600) or the RE calibration reported for MBH99, even though the Dirty Laundry residuals for AD1000 match Figure 1 in the MBH99 submission.  The calculation of MBH confidence intervals was a standing puzzle in pre-Climategate discussion – see review here – and never fully resolved. While the reported numbers do not match the data in the Dirty Laundry residual datasets, the glimpses of the underlying reconstructions in the Dirty Laundry datasets provides data that can be used to finally resolve the calculation of MBH98 confidence intervals.  More on this in next post. See here

Footnotes:

(1)  Here is a screengrab of relevant statistics in the original SI for MBH98 (link):

(2) Here is 2005 figure showing MBH98 confidence intervals for each step as extracted from the reconstruction archive:

Figure S1. Standard error (“sigma”) of MBH98 Reconstruction Steps. Calculated from confidence intervals for MBH98 reconstruction at NOAA archive here.