Lightsum and Darksum are Calculated, not Measured

In last year's post The Tiljander Data Series: Data and Graphs, I explained that the four Tiljander data series were actually three: Darksum is calculated as (Thickness minus Lightsum).

I've since discovered that there are actually two Tiljander data series rather than four.

Thickness and XRD are measured values.

Lightsum and Darksum are values that Tiljander et al. calculated by multiplying Thickness and XRD.

Here are the formulas. Varve thicknesses are measured in microns (thousandths of a millimeter, um).

Lightsum = Thickness * XRD * 0.003937

Darksum = Thickness * ( 1 - ( XRD * 0.003937 ))

Solving these two equations for Thickness yields

Thickness = Lightsum + Darksum

The calculated values of Lightsum are within 0.01% of the values archived at NCDC. For Darksum, the calculated values are consistently 0.5% to 0.8% too low. Presumably, this is a rounding error.

[UPDATE Aug 15, 2011 -- Commenter HaroldW figured out the exact formulas by which Lightsum and Darksum are calculated. It strongly suggests that Tiljander et al. made a minor arithmetic error in their formulae, such that

Thickness = Lightsum + (( 255/254 ) * Darksum )

"Exact" means that the calculated values of LS and DS agree with the archived values to within 0.001%. I've updated the Excel file at BitBucket to reflect HaroldW's insight.]

"Discovered" as used above is tongue-in-cheek. Obviously, the authors of Tiljander03 have known from the outset that this was their procedure. However, this finding is new to me. Presumably, it is also news to the authors of Mann08, Mann09, Kaufman09, and to other people who take an interest in paleoclimate reconstructions.

"Does it matter?" From a statistical point of view, yes, it does.

Pattern Recognition

Scientists pride themselves in the ability to tease informative patterns out of masses of data. And with good reason -- that skill (or aptitude) is one of the traits that leads to insight, and thus publications and professional success.
I don't believe that gazing at "spaghetti graph" reconstructions is the best way to evaluate whether or not the Tiljander data series were used correctly in Mann08 (for links to referred-to papers and posts, see here). That's a question that's better answered by reading her paper (Tiljander03), getting a feel of what her data looks like (graphs here), and thinking about the physical meaning of the varve characteristics that go into "XRD," "lightsum," "darksum," and "thickness."

By weaving these threads together, we can figure out the solution to this puzzle:

Can the Tiljander data series be meaningfully calibrated to the instrumental temperature record, 1850-1995?

The answer is No.

There might be a way to indirectly achieve such a calibration, which was the approach that authors of Kaufman09 took with XRD after belatedly coming to grips with this problem. But there's no feasible direct approach, of the type used in Mann08 and Mann09.

This has proven to be a very contentious point. But there's no good reason it should be seen as such. Truly contentious questions have strong arguments on each side of the issue. The defenders of Mann08 don't even argue for "Yes," but rather for a stance akin to "I don't know, and it doesn't matter."

That's silly.

Knowing that the Tiljander data series were massively contaminated by non-climate signals in the 19th and 20th centuries, we can look for patterns in the reconstructions presented in Mann08 and Mann09.

Let's consider a few cartoons.

Voldemort's Question

Updated June 25 & 26, 2011 -- see end of post

Are the Tiljander proxies calibratable to the instrumental temperature record, 1850-1995?

Reader Alex Harvey copied his submission to RealClimate.org as a comment to the just-prior post at this blog, "The Tiljander Data Series Appear Again, This Time in a Sea-Level Study." Some time later, it was allowed into RealClimate's "2000 Years of Sea Level" at position 22. The second of Harvey's two points concerned the use of Tiljander:

The study has also been criticised on various blogs for using “one of the multiproxy reconstructions that employed the four (actually three) uncalibratable [edit] Tiljander lakebed sediment data series” e.g. http://amac1.blogspot.com/2011/06/tiljander-data-series-appear-again-this.html.[edit].

RealClimate's moderators snipped the comment as shown.

Prof. Mann offered this inline commentary --

[Response: No. Just more of the usual deception from dishonest mud-slingers. More on that in short order. -Mike]

The Tiljander Data Series Appear Again, This Time in a Sea-Level Study

At RealClimate.org, Stefan Rahmstorf has written "2000 Years of Sea Level" about a study published on June 20, 2011 in PNAS. Andrew Kemp and co-authors BP Horton, JP Donnelly, ME Mann, M Vermeer, and S Rahmstorf reconstruct sea levels from 500 AD to the present, and relate these levels to the temperatures of the past, using a multi-proxy reconstruction that was first presented in Mann et al. (PNAS, 2008). (The Kemp11 PDF can be downloaded at the RC post.)

It turns out that the chosen temperature recon is heavily dependent on the four three uncalibratable Tiljander data series. This reliance grows stronger as one goes back in time, and shorter (younger) records "drop out."

I tried to leave a remark on this subject at RealClimate.org. Apparently, that site is set to automatically fail any comment tagged with my user name, email, or IP address. Here is the local copy of what I submitted (21 Jun 3:50 PM EDT) --

I was surprised at the provenance of the paleotemperature reconstruction that was used in Kemp et al's Fig. 2A and Fig. 4A. According to Fig. 2A's legend, it is "Composite EIV global land plus ocean global temperature reconstruction, smoothed with a 30-year LOESS low-pass filter". The reference is Mann et al. (2008). In that paper's S.I., the unsmoothed version is in panel F of Fig S6, as the black line labelled "Composite (with uncertainties)".

This is one of the multiproxy reconstructions that employed the four (actually three) uncalibratable Tiljander lakebed sediment data series.

According to Gavin Schmidt, "...it's worth pointing out that validation for the no-dendro/no-Tilj is quite sensitive to the required significance, for EIV NH Land+Ocean it goes back to 1500 for 95%, but 1300 for 94% and 1100 AD for 90%" (link). Further remarks on this issue as Responses to other RC comments here (see numbers 525, 529, and 531).

The incorrect inclusion of Tiljander could well make this EIV reconstruction progressively worse, as one goes from 1500 AD back to 500 AD. This might explain the increasing divergence between the temperature recon and the sea-level recon, as one travels back from 1100 AD to the beginning of the recons at 500 AD. This pattern is shown in Kemp11's S.I. Figs. S3, S4, and S5.

Did any of the peer reviewers comment on this issue, or request that you use a no-Tiljander temperature reconstruction?