A Different Yamal – Corrections and Signals
Posted by Jeff Id on October 8, 2009
This post investigates the effects of RCS on the Yamal proxy data. It started out with a thought that it might be possible to create a simple method for creating series from tree ring widths that would act as a sanity check for the other methods. However, it turned into a learning experience with the tree ring data. Here’s what I found.
Figure 1 is an average of the entire Yamal dataset. The change in variance from the zero age to the 400 age is due entirely to the number of trees available in the series. The far left is from 252 trees while the far right is from one. This data is fit to a function of Corrected= a + b * e^-(c*age). However, all the individual trees are fit which of course weights the fit very heavily toward the younger trees. So the question becomes what do the 252 Yamal trees look like when plotted. The red curve is the mean overlaid.
The next plot depicts the RCS correction factors fit to the orignal Yamal in Blue on top of the mean data.
The blue line is an excellent fit up to about 200 years and then it diverges from the data. This occurs because the series is very heavily weighted to younger trees in this form of RCS. My next thought was to try and fit the curve to the mean of the data. This weights all years equally even if less data is available in older trees – Green line. Consider that in collecting tree chronologies it would be much easier to find older trees which are still alive. The fossilized or sub fossil trees are more rare and far more difficult to come by. This would create a problem where the most recent data in typical RCS reconstructions is the least corrected for.
The next plot is the 12 trees which make up the most recent years of the Yamal hockey stick. The red lines are the corrected data while the black are the original ring widths divided by 50 (mean of the correction factor).
This plot was interesting to me because the red lines in the longer series are almost universally amplified at their endpoints in relation to the original black lines, while shorter series are a decent match. Yad 06 starts out with the historic black ring widths being higher than the recent ones and the opposite in the most recent portion of the curve.
Basically everything makes sense that the living trees are under corrected for in relation to the rest of the series resulting in some bias in the final trend. So the next plan was to do the reconstructions using the two different corrections calculated above.
The black curve is the emulated original per modified code from Steve McIntyre and the red line is the version which uses RCS calculated from the mean of the annual data allowing each year to have equal weight in the RCS curve fit. The end of the graph has dropped by about 0.5 C while the historic portion remains nearly unchanged. Not terribly unexpected considering the fact that the beginnings and ends of fossilized trees overlap prior to 1800 allowing for an averaging of defects in the RCS method. However, the endpoints are strongly affected by different fits simply due to the inhomogeneity of tree age in the record.
While this method makes more sense to me, the net result of this curve is still dependent on very few series.
UPDATE: RomanM’s plot of tree age and specemin count clarifies the point some.