Hans Erren has digitized the Ababneh Sheep Mountain version and I’m going to show some extremely interesting knock-on results both on MBH98-99 and Mann and Jones 2003. I started in on Mann and Jones 2003, partly for a little variety and partly because the Sheep Mountain impact was particularly strong on this network.
Before I get to analyzing the impact of the Ababneh version on this network, there are some baffling adjustments to the Mannian PC1 that I’ve been unable to figure out and maybe readers can help. I’ve posted up all the relevant materials and some analysis script.
Mann archived the Mann and Jones PC1 in the Jones and Mann 2004 archive here. They state that they used 6 chronologies, but do not state which ones. Within the MBH99 network, there are exactly 6 series that start in AD200 or earlier. I then calculated the (erroneous) Mannomatic PC1 and compared it to the archived PC1 – it was a pretty close match, but not exact. By experimenting with it – and I hate to say how much time these experiments take – I deduced that there was a correlation of more than 0.9999 between values up to 1700 and a much lower correlation after that. This confirmed that I’d spotted the correct 6 chronologies and that the JM04 PC1 was a re-scaled re-centered version of the Mannomatic PC1 up to 1700 and was a splice of some other series after 1700.
Needless to say, there’s no account of the splicing in Mann and Jones 2003, but by now I can sometimes anticipate Mannian ad hockeries. I tried the MBH99 “fixed” PC1 in the AD1000 network (“fixed” implies a rational process; let’s use the term “adjusted” instead) since there is no evidence that the PC1 is in any sense “fixed”. The “adjusted” and raw AD1000 PC1 were formerly available at Virginia Mann’s FTP site, but with the evolution of PennState Mann, this archive is no longer available. I saved it in Nov 2003 when it was first made public and I’ve posted up the PC1s from that network here. Experimenting some more, I determined that the correlation of the AD1000 PC1
fixed adjusted had a correlation of more than 0.999 with the JM04 archived PC1 for the period after 1700, showing that it had been re-scaled and re-centered somehow to yield the JM04 version.
There was some evidence on the re-scaling and re-centering of the AD1000
fixed adjusted PC1. Jones and Mann 2004 (though not Mann and Jones 2003) Figure 4 caption said that the series had been standardized on 1750-1950. This yielded an emulation of the archived PC1 that was pretty close – it was a bit more than rounding but not a lot more. See the top panel of Figure 1 below showing the discrepancies between the trial rescaling of the AD1000 fixed adjusted PC1 and the JM04 archived version – there is a relatively good match after 1700 and poor match prior to 1700.. So far so good.
Now another problem arose – and this is one that I’ve not been able to figure out at all. One’s first assumption is that the AD200 PC1 would be rescaled and recentered in the same way (on 1750-1950). This proved not to be the case as shown in the graphic below -see the middle panel. The second panel shows the discrepancies between the AD200 PC1 re-scaled in the same way and the archived PC1. Neither the centering nor the scaling match.
The third panel shows my best attempt to re-scale using actual periods. While the match is pretty good, the scaling and centering rationale that I’ve found necessary to achieve this make no sense at all.
In order to get the right centering, I found that it was necessary to re-center on a subperiod of 1000-1700. Re-centering with later values was substantially off in the same way as the middle panel (subperiod 1600-1950). Experimenting, I found that the mean discrepancy in 1000-1700 was reduced to much smaller positive value using 1000-1700 as a base period; with 1000-1600 as a base period, the mean discrepancy was negative. So interpolating, I tried a base period of 1000-1650 and got a mean discrepancy close to zero. So for now I’m guessing that the AD200 PC1 was re-centered on 1000-1650 – 1650 is a date that emerges inexplicably in the MBH98 archive – although it is date not mentioned in any MBH98 periodization. Why this period (if indeed this guess is correct)? I have no idea.
However scaling on 1000-1650 didn’t work. It didn’t reduce the amplitude quite enough. Again through much experimentation, I concluded that the re-scaling period had to include values from the 20th century in order to get enough amplitude reduction. If the period ended in 1980, the length required to get the right amplitude was implausibly short. 1950 is a date used elsewhere and only a few periods ending 1950 yield an appropriate amplitude reduction – most of which were not round periods. One such round period started in 1600. Using 1600-1950 to re-scale, I got a pretty decent re-scaling. The bottom panel shows the match scaling on 1600-1950 and centering on 1000-1650. Does this make any sense? Of course not.
Perhaps there’s a simpler and more plausible system for rescaling and recentering, but there’s no hint in Mann and Jones 2003 that anything of this sort is even going on, much less any hints on how he did it. I’ve posted up a script showing some of my experiments and downloaded the various relevant time series.