Severe analytical problems in dendroclimatology, part thirteen

Yes, I know what I said regarding moving away from tree ring analysis posts, but I will continue to put some up from time to time. If you’ve not been able to read through the series, this would be the one to read, because I think it really gets right at the heart of where and why RCS does and does not work about as clearly as I can do it. In some sense, this is a more concise version of part seven, in which tests of various conditions were made.

The background
There are twelve separate simulation results here (six graphs having two panels each, one each for increasing and one for decreasing environmental trends) in which I vary (1) the ring size response variable (widths vs areas), (2) whether “subfossil” trees are present or not (trees which do not live to the end of the analysis period; in this case, they all live only 10% of that 300 year period, 30 years), and (3) whether there is an age/size related growth trend present or not (not counting the purely geometric effect on ring widths, which is always present). Each simulation assumes two cores from each of 50 trees, and the analysis period is 300 years long. I could make this longer, but it slows down the simulations, and the results are not affected. In all cases, as in previous posts, other potentially complicating variables that would effect the results are eliminated. This means there is no inter-tree growth rate variation, no stochastic element of the ring response to the (single) environmental driver, and a positive linear association between that driver and the ring response. There is also a perfect spacing of tree start dates: each of the 50 trees begins life at perfect six year intervals over the period (i.e. 6 x 50 = 300). There is futhermore no error due to missed early rings. I show results for both stiff and flexible spline fits in the creation of the RCS regional curve. So, in summary, I’m again using best case scenarios for all non-tested variables that can and do affect actual reconstruction accuracy.

The results
I’ll present the graphs in three pairs of two graphs each. The first pair gives results when no subfossil material is present. Trees start their lives at perfectly spaced intervals and each tree lives to the very end of the 300 year analysis period. The first graph is for the ring widths and the second uses ring areas, as response variable. There is no age/size effect on the ring areas (meaning that there is only a purely geometric effect on ring widths):
Ring widths without subfossil
Ring areas with subfossil with strong size effect

One extremely important result is obvious right away: ring areas, which automatically eliminate the purely geometric effect, give a much better trend estimate than do ring widths, which do not. Also, ring widths give very different degrees of error, depending on whether the trend is positive or negative, with negative trends being more badly estimated, whereas the error using ring widths is about the same in each case.

The next pair shows results when subfossil trees make up the entire sample, with perfectly spaced (stepped) birth and death years (each tree living 30 years) over the analysis period (and again, with no age/size effect):
Ring widths with subfossil
Ring areas with subfossil

WHOA! Look at that last graph there. There is perfect overlap between the RCS-based climate estimates (for both types of splines) and the true environmental trend. The lines, both the series themselves and the linear regressions fit to them, are all perfectly coincident. This result is important: it demonstrates that the RCS method can in fact return a perfect environmental signal. But it can only do so when the trees in the sample are perfectly staggered across the analysis period with respect to the timing of both their births and deaths. And of course, that is never going to happen in the real world, although it may hopefully approximated sometimes when subfossil data is used. In reality however, it’s rarely approximated. And ring areas must be the response variable, not ring widths.

Note also that ring widths do not capture the true trend (although they are somewhat better than in the previous scenario), and that the linear trend lines to the spline fits do not actually capture the full degree of error, particularly at the beginning of the chronology for the decreasing trend scenario.

And the last pair shows the same situation, except that each tree now also has a strong age/size effect (strongly unimodal effect on ring areas, such that medium size trees grow the fastest, followed by a gradual decline to the largest trees):
Ring widths with subfossil with strong size effect
Ring areas with subfossil with strong size effect

Now that is an unpredicted result (that’s one reason you do simulation experiments!): ring widths return a more accurate signal here than they do when there is no age/size effect at all! It performs about as well as ring areas do in this situation. I am not fully sure as to why, but chance cancellation of opposing sources of error is the very likely explanation; the result likely depends on the exact nature of the size effect. This result only holds when the age structure of the sample is perfect, as it is here.

The take home messages are clear here:
(1) Whenever ring size is the response variable of interest (as opposed to density or isotopic composition), it should always be measured as ring area, not width. The reason again, is that the purely geometric decline of widths with tree size is pure nuisance/noise with no information content whatsoever, and there is accordingly no reason to include it. And yet widths are what are virtually always used.
(2) The accuracy of the RCS method is heavily dependent on the age structure of the sample (and note that the start dates of the trees in all simulations here are perfectly staggered–which they never are in real data).
(3) The magnitude of the age/size effect on ring areas (i.e. the true biological effect) is an important factor only when tree start dates are not well-staggered over the chronology (which is not the case in any of the simulations here). Unfortunately, that is a very frequent occurrence in actual tree ring data archived at the ITRDB repository.

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2 thoughts on “Severe analytical problems in dendroclimatology, part thirteen

  1. maybe this is a naive question but I know that some trees, depending on the site location etc, have strongly assymetric ring-widths – rings are not always concentric circles. Doesn’t this imply that ring area has to be the better measure to use anyway, regrdless of the analysis that you have just shown?

    • Sorry I missed your comment, due to changing how comments are approved.

      Yes, they are indeed often asymmetric, especially in windy conditions. I don’t know that that fact automatically implies that ring areas are a better measure than widths though. The real problem is that widths automatically have a non-climatic trend to them, one that *will* necessarily bias the RCS curve; ring areas by contrast, do not.

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