Briffa et al., 2013, part three

This post is almost a notes-to-self; I’m putting it up to illustrate the kinds of issues that have to be considered and worked through in tree ring analysis as one confronts real data sets.

In part two I posted a couple of graphs showing the mean ring (“cambial”) age, by calendar year, for each of the Polar Ural and Yamal data sets given in Briffa et al., 2013. From that I concluded that that the Yamal data was superior to the Urals data, because there was no strong, long-term trend in the same for Yamal, whereas there is for the Polar Urals. To reiterate, the critical concept here is that if, for example, the younger (innermost) rings in the sample tend to occur in early calendar years, while the older rings tend to occur in later years, then the computed regional curve will be biased, if there is in fact a climatic trend over that time. It will not then be a true reflection of the effect of age/size alone on the ring response, but instead contain environmental signal information within it. And since the regional curve is the reference standard against which all rings of all cores are measured (to estimate the environmental parameter of interest (e.g. temperature)), the entire climate estimation (“reconstruction”) process is directly affected.

But in doing some more analysis and thinking, I realized that the issue was a little more complex than just that. In particular, I also computed the mean year of occurrence for each ring age, at each of the Urals and Yamal areas. For example, at Yamal the maximum age reached by any tree in the sample was 416 years (measured rings only, not including those missed near the pith during coring, due to the problems with the pith offset data I mentioned in part two). So, for each of the 416 possible ring ages, I computed the mean year of occurrence, i.e. the average calendar year in which the 1st, 2nd…416th rings occur. I also computed a couple other things, including the frequency of occurrence of each ring age.

Here is the frequency of ring ages, and the mean year of occurrence for each such age, for the Yamal data:
Yamal cambial ages
Yamal mean year of ring occurrence

The corresponding graphics for the Polar Urals data are quite similar to these, but I’ll just focus on Yamal here, since I had said earlier that I thought the Yamal data was superior, in terms of removing the age/size trend and thereby extracting a better environmental signal.

I thought I would see a more constant distribution of ring ages in the Yamal data, but it’s the second graph that was the most surprising result; I expected it to also be closer (much closer) to some roughly constant value, or at least fluctuating but not strongly trending, instead of steeply and continually increasing as it is. I assumed this based on the result from the second graph shown in part two. This is not a good result, because it shows that the early (innermost) rings definitely occurred in earlier calendar years, and late rings correspondingly in later years, which is the really critical concern, relative to the potential problem I just mentioned.

But, what the actual effect will be on the Regional Curve is complicated by the graph in part two I just linked to, and so the question immediately arises: If earlier rings occurred preferentially in earlier calendar years, and later rings in later years, how does that fact interact, mathematically, with the fact that the mean cambial age of the rings in each calendar year more or less fluctuates around a constant value over most of the full chronology length?

The short answer is don’t know exactly, without doing some more thorough investigations. Indeed, I can’t even know in any meaningful way, without subjecting the specific age structure of these Yamal data to a tree growth model, in which I can vary a number of important things, particularly the magnitude and direction of the imposed environmental trend, and the exact nature of the tree growth response to those trends (including deterministic and stochastic responses). Then I can examine systematically how accurate any resulting climate reconstructions are, when produced by standard analytical practices (or non-standard for that matter), relative to their true, known values. And from previous work doing just that, I know that you can’t have a tree ring sample with a poor temporal distribution of the ring ages, in a trending environment, and expect any type of accurate climatic reconstruction. These kinds of questions need to be addressed.

The take home message is that this detrending/standardizing step is complicated. It’s not formulaic–there are a lot of considerations to make if you want to get it right. And I’m only referring to one step in the full climate reconstruction process.

This stuff is complex; it’s not a black box process.

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