I’ve got some preliminary measurement data back on several trees with Graybill tags in digital form. The dendro lab is working on cross-dating this week. The measurement data for our Tree #31 (Graybill 84-56), which Pete Holzmann posted a picture of earlier today, is very interesting. This is a strip-bark tree – remember that the NAS Panel said that strip bark trees should be avoided, a policy then disregarded in recent paleoclimate studies (Osborn and Briffa 2006; Hegerl et al 2007; anything by Mann and/or Rutherford; and, of course; Juckes et al 2007). Let’s look at some details of Tree 31 keeping strip barking in mind.
Here is a graph showing the measurement data for cores 31A (from the west) and 31B (from the southwest) for a tree that is strip-barked on the south. The dashed line shows the average ring width for all Almagre cores. There is obviously a fantastic difference between ring widths here for cores taken only 45 degrees apart: W vs SW. The maximum growth in Core 31A was in 1915 – not known as a “warm” year – when growth in the W core was about 3.7 times as much as the average for the site.
Here’s Pete’s picture of Tree 31. Tree 31 (Graybill 84-56) was sampled from the western trunk. The tree itself has TWO elongated oval trunks (split at the base). The western trunk of Tree 31 has a distinctly oval shape – it is more than two feet in one direction, less than one foot in the other. Both the south and north sides are stripped – Pete observes that you can see this at the picture gallery using the magnifying glass feature. As a preliminary interpretation, perhaps strip barking occurred in the early 19th century leading to the elliptical growth shown here.
At present, we lack a concordance to the Graybill archive numbers. I’ve experimented with various permutations and have some guesses, using the assumption that the order in the archive is consistent with the order of the tags (although it need not be.) Here is one possible overlap of the Graybill archive (ALM19 here) with our samples (match done impressionistically considering the length of the records, the “coherence” and order in the sequence of numbers. Of the 23 trees archived from Graybill’s 1983 samples, only 2 had more than one core. ALM19 had only one core – one presumes that it was drilled at the opposite side to the stripping.
One of the possible benefits of coming at this enterprise from outside is that you think about operations and calculations that dendroclimatologists don’t think about. For example, here, it is daunting to think about what kind of statistical model is needed to cope with this kind of situation. And by thinking about it, I don’t mean merely a shrill declaration that there is nothing useful – something that many readers do far more quickly than I do – there may be nothing usable, but the data is still interesting. Plus from a mathematical point of view or a crossword puzzle point of view, it doesn’t really matter whether it’s usable, it’s still interesting data.
Here’s an idea that I’m toying with. Dendrochronologists have recipes for making something called a “chronology” – these time series are then reified and then inhaled into multiproxy networks as though they were real. But what exactly is a “chronology” statistically? I’ve been mulling this over for a few years. I can get time series that correspond rather well to tree ring chronologies using traditional dendro recipes using linear mixed effects models. The advantage of such a formulation is not necessarily that you get a materially different answer, but that you get an answer about which something is known in a statistical sense (even if the Team on the Island don’t care). Leaving aside strip bark issues for a moment, the model underpinning a conventional chronology is something like:
, where is the ring width of tree i in year j, are parameters for each tree.
If you calculate the as random effects yielding values for each year, you get time series that look a lot like “conventional” chronologies of a Jacoby type. (This method corresponds to the nlsList function in the R package nlme – which would be a rather pretty paper. RCS chronologies correspond to a simple fit with an nls function.)
Now let’s suppose that you try to fit a model like this to the above cores – using ARSTAN or nlme. What happens? Well, first of all, you can’t get the negative exponential age curves to fit. What happens is that the iteration fails after a certain number of attempts and ARSTAN seems to assign a mean value in the above situation (there is also a possible assignment of a negative linear slope, but I haven’t figured out how it gets triggered in ARSTAN). For the purposes of the residuals, it really doesn’t matter whether you calculate residuals from a horizontal straight line (or from a negative exponential or any variation of such curves.) For Core 31A, you are going to have unbelievably huge residuals from any sort of model of a ARSTAN type – not only that, but the residuals are going to be unbelievably autocorrelated. The reason is obvious when you think about it – the ARSTAN type model does not model for wows in the shape of the tree from whatever is happening on the opposite side of the strip bark. This is even more so for RCS. Just looking at the above curves – how can one establish with any certainty that the sort of skew introduced by the elliptical strip barking is canceling out? You can’t. Especially if the problem isn’t addressed squarely.
If you look at the older dendro literature (even in things by Cook in the 1980s), you see much more use of “flexible” splines to fit curves like this. They were thinking of problems in canopy forests where trees can have pulses that look sort of like Core 31A. If you fit a cubic spline to these sorts of curves, you can get rid of this sort of pulse and recover the high-frequency information that is relevant to dating applications. As long as dendrochronologists were using tree cores as a service industry for other disciplines (dating Navajo pueblos or such), the ability to recover centennial scale change was irrelevant. But once climate change became the customer, then they had to modify methods to try to recover centennial-scale change and the techniques previously used to mitigate things like Core 31A were thrown out the window. One sees the development of Jacoby’s (“conservative” standardization) and Briffa-Esper “RCS” standardization which now rule the roost. Of course, none of these people worry about, and perhaps don’t even think about the hugely autocorrelated residuals or whether the residuals may point to problems.
Let’s try to posit our own model for Core 31A. What does it really mean when we talk about residuals here as a type of “error”? Yeah, there are “errors” in measurement, but that’s not really the issue. The issue is how to describe the elliptical stage of Core 31A relative to Core 31B. Or – and I’m pondering this – are we de facto modeling the reaction of a “standard” “adult” tree? And thus need to model the difference of Core 31A from a “standard adult” tree as a type of pulse with a scale of 100 years, with potentially a huge amplitude in the pulse. In this way of speaking (and I’m not sure whether this will prove useful), when a Core 31 A goes elliptical, some way needs to be figured out whereby it can be adjusted back to a “standard” tree. In this case, I don’t think that the thick rings of Core 31A in 1915 necessarily indicate fantastic growth, although perhaps they do. It doesn’t seem to make sense that the tree as a whole was somehow growing at nearly 4 times the rate of the a “standard” Almagre tree.
I don’t think that “autocorrelation” models necessarily describe the effect very well – it looks to me more like a pulse lasting nearly a century in which Core 31A is a dilation of Core 31B. How one would go about estimating the pulse and adjusting for it – I have no idea. But surely this is the sort of thing that practitioners need to be thinking about. If such pulses were somehow included in the model as some sort of random effect as a way of achieving an “honest” error estimate, it may get very hard to pick up a temperature signal.
If we find that dilation on the opposite side of strip bark is characteristic (as seems highly probable), then there may be a much simpler explanation of the 20th century trend in strip bark chronologies (reported by Graybill and Idso 1993; confirmed by Ababneh). It may have nothing to do with CO2 fertilization or any other fertilization and be nothing more than a mechanical effect from the strip barking itself. We know that Graybill went around looking for strip bark trees ( we know this because he said so!) We know that the strip bark trees constitute Mann’s PC1 (and are essential to his reconstruction.) The NAS panel said that strip bark trees should be avoided but didn’t really explain why other than possible CO2 fertilization or phosphate fertilization. In our own articles, we didn’t rely on any particular explanation of the problem with these trees – our position was more that it didn’t make any sense that climate history should depend on results from one researcher on one type of tree, about which there were many warnings.
In Ababneh’s thesis, her chronologies for whole bark trees – even in the Mannian “sweet spot” of Sheep Mountain CA – didn’t have any remarkable HS. To recap, I’m wondering if the issue is completely different from CO2 fertilization or such and something as “simple” as strip-barking itself. In this light, one would have to watch out not simply for strip bark, but for problems resulting from elliptical growth – warnings would perhaps come from growth excursions of older trees at well above population means.
Update: I looked at Pete’s Excel spreadsheet and, from the Graybill tagged trees, picked the two trees where the notes contrasted most i.e. Tree 47 was described as “mostly whole bark” while Tree 37 was described as “strip bark, hollow”. Now look at two ring widths plot that I have on hand (and I’ve only got measurements for about 7 trees so far). You should be able to guess which tree is whole bark and which tree is strip bark. Yes, on the left is Tree 47 which arguably has the sort of negative exponential growth curve presumed in tree ring studies. On the right is the strip bark tree. This would make a very strong impact on a tree ring chronology. So again the biggest effect in Tree 37 is entirely nonclimatic.