In February 2006, Luckman and Wilson archived their STD chronology for the Athabasca Glacier, Alberta site (STD fits each tree individually; RCS fits trees in groups.) Rob Wilson wrote in criticizing an earlier post for, among other things, not showing their STD version and for how I implemented the RCS emulation for Esper et al .
Figure 1 below shows the "archived" Esper RCS ring width version ("archived" meaning the version that Science sent me in February 2006 after months of quasi-litigation) together with the LW05 STD ring width version (archived at WDCP in February 2006) and my emulation of the Esper RCS version using cana170w and cana171w with one regional curve. All curves have been smoothed and then the smoothed versions have been scaled – a common spaghetti graph methodology. There are some differences between the blue (Esper) and black (emulation) versions, but I don’t think that my emulation is "horrendous". (Esper et al 2002 does not contain any information on stratification of the site.) There are obviously significant differences between the Esper RCS version (blue) and the LW05 STD version (red).
Figure 1. Athabaska Glacier, Alberta (smoothed with 40 year gaussian filter, then scaled). Blue – Archived Esper RCS version; red – archived LW05 STD version; black – my emulation of Esper RCS version.
Next is a figure showing a more detailed comparison of my emulation of the Esper RCS series, which was done without dividing trees into "linear" and "nonlinear". Rob has criticized my emulation as being "horrendous", but why is it? I’ve attempted for months to obtain information on how Esper distinguished between linear and nonlinear trees. This should have been in the original SI. But even with an operational defintion, it is surely relevant to examine the effect of distinguishing between "linear" and "nonlinear" trees. The principal effect, regardless of the motivation, is to enhance 20th century levels. Doubtless there is a reason for this, but it’s not been provided so far.
Figure 2. Athabaska Glacier, Alberta RCS RW Versions. Top – Esper contained in Science email; bottom – emulation from cana170w, cana171w using bulk RCS fit. Correlation 0.80.
Rob said that "Significantly more low-frequency information was captured using the MXD data (See Appendix) but no significant gain was observed by using the RCS method on the RW data (analysis not shown)". Figure 3 shows a method that I like for checking the distribution of variance between low- and high-frequency: the distribution of wavelet variance by scale (la8 wavelet used here), in this case for two different "official" chronology versions, Esper RCS and LW05 STD (so that any inadequacies of my emulations are not material.) The graphs show very clearly that the variance share of high-frequency is much larger in the LW05 STD version than in the Esper RCS version. Figure 3 shows an objective method for quantifying statements about "gain in low-frequency information".
Figure 3. Wavelet Variance by Scale for RW Series, Athabasca Glacier, Alberta. Top – Archived LW05 STD chronology. Bottom – Esper RCS chronology.
The only point here, where I’m being critical of LW (as opposed to Esper et al) would be in their conclusion about the "gain" in low-frequency information, where I don’t see that LW05 has provided any support for this claim. I haven’t seen wavelet variance used by dendro people to quantify such statements and I think that it might be a pretty good way. I find these types of barplots to be far more informative than Fourier spectra on noisy series (but they reconcile to Fourier spectra).
The information shown here pertains to ring width site chronologies. The L97 and LW05 temperature reconstructions are primarily based on MXD chronologies; the ring width chronology is negatively weighted in the L97 temperature reconstruction.