1) It seems to me that if cycles greater than 100 years cannot be recovered, the thing to do would be filter it with a 100 year bandpass filter, and then subtract the filtered data from the original data to eliminate the long-cycle swings. Is this correct?

As richardT pointed out, there is no need to remove the low frequencies because they are already gone from the processing.

That said, normally, a filter operation does not subtract the output from the input in such a manner, i.e. a highpass filter would be used to remove the low frequencies, and a separate lowpass filter would be used to remove the high frequencies .

Mann does the subtraction method in his RegEM application, subtracting the lowpass from the composite to generate the highpass (It’s been a while since I read the code, so it could have been somewhere else). I’d have to look at tractability a little closer before making definitive conclusions, but this is generally not done in signal processing apps. The primary problem is that you need to account for filter delay. Mann solved this by using a zero-phase filter, which is non-causal for anyone that wants to investigate.

Mark

1) Observe the raw ring widths
2) Cross-date
3) Scale individual series to unity variance (?)
4) Age-align (innermost rings to t=1)
5) Compute the mean value over age-aligned series (+smoothing ?) = RC
6) Compute departures from RC
7) re-align these departures, back to correct age
8) Compute the mean
9) Apply the Osborn variance adjustment

Mann must have used different detrending method in MBH99:

The substantial secular spectral peak is highly significant relative to red noise, associated with a long-term cooling trend in the NH series prior to industrialization ( /century). This cooling is possibly related to astronomical forcing, which is thought to have driven long-term temperatures downward since the mid-Holocene at a rate within the range of -0.01 to -0.04 C / century [see Berger, 1988].

Berger, A., Milankovitch theory and climate, Rev. of Geophys., 26,624-657, 1988.

9) Scale. They say “Cook et al. (1995) state that using traditional’ individual series detrending methods, as done in this study, the lowest frequency of climate information that can be realistically recovered is 3/n cycles per year (where n = the mean sample length). Therefore, with a mean (sites equally weighted) sample length of 260 years (Table 1), such individual series detrending will result in chronologies that can only represent variability at centennial or higher-frequency time scales.” If so, it seems that the thing to do with your results is filter them with a 100 year bandpass filter, since the smaller scale information is not reliable. But from an initial look at the data, that’s going to to give something not far from a straight line …

Also, while the equally weighted average sample length is 260 years, that’s not meaningful. What is the weighted average sample length?

A couple of people pointed out correctly that I was interpreting it backwards, that it is the cycles greater than 100 years which are not significant. In that case, two questions:

1) It seems to me that if cycles greater than 100 years cannot be recovered, the thing to do would be filter it with a 100 year bandpass filter, and then subtract the filtered data from the original data to eliminate the long-cycle swings. Is this correct? I haven’t found any reference to doing this in Rob’s paper, but I could have missed it.

2) If cycles over 100 years are not recovered, how can we do millennial reconstructions using tree rings?

All answers welcome …

w.

Dear Sir,

The manuscript “Cycles and shifts: 1,300 years of multi-decadal temperature variability in the Gulf of Alaska”, by Rob Wilson, Greg Wiles, Rosanne D’Arrigo, Chris Zweck contains a table providing the location of the dendrochronological series, so that any laboratory can go to the place and duplicate the work.

Archiving raw data is a normal process and should follow accepted practices, but this is not the responsibility of journal editors.

Sincerely

Jean-Claude Duplessy

Gotta love the journal folks, they have requirements for archiving as a precondition for publication, but when they don’t enforce the requirements, somehow it’s up to the authors and the journal has no responsibility … does this all sound strangely familiar?

I do note that the editor at least acknowledges that archiving is normal and should be done … I guess that’s progress.

w.