Continuing from part one, first, a quick recap of the most critical points from previous posts. The first such is that the relationship between climatic driver and ring response can be very strongly non-linear, to the point of unimodal (e.g. an inverted parabola or similar shape with a single local maximum), especially when that driver is growing season temperature. This is the essential problem described by Loehle (2009), and it is very critically important. It is in no way unreasonable to expect such extreme non-linearities, based on known, general properties of biological systems with respect to temperature, for which there is much strong evidence ranging from the molecular to the population levels of organization (see here for a good discussion).
The second point is that the tree age/size effect, which is non-climatic by definition and quite strong when ring size is the response variable of interest, must be removed (mathematically), but the method devised to do this (Regional Curve Standardization, “RCS”) works well (i.e. is minimally biased) only when the sample of tree cores to which it is applied meets some pretty strict criteria. But these are essentially never met in existing tree ring samples, for reasons that have understandable historical roots (at least for older data collections). The degree to which these criteria are met in this study however, which includes relatively newly collected data, must be evaluated. A third issue would involve questions of exactly how calibration is done and the criteria for acceptance (or not) of a stable relationship between driver and response.
Another fundamental point that apparently needs to be stated, given statements sometimes seen (including in this work), is that any/all estimates of relative climatic states for particular, defined time points, are absolutely dependent on whether or not one has accurately estimated any existing long term trend in that parameter, and the importance of this point scales directly with how far apart those various time points are. But this point really should not need to be stated, it is so elementary.
The first issue, potentially extreme nonlinearity of ring response, is not addressed in this study in any way, so that is serious problem number one. More generally however, it is not even clear exactly how that issue should be addressed, or if it even can be effectively addressed, i.e. whether the problem is even tractable. It might not be, but one could, ironically enough, make a reasonable argument that those sites exhibiting the so-called divergence phenomenon between decadal-scale driver-response relationships could be useful here–or even necessary–in helping to at least provide an estimate of the uncertainty inherent in estimating past climate states from (wrongly) assumed linear relationships (if such divergence is in fact due to non-linear responses between driver and ring response, and not to analytical artifacts). That is, by purposely avoiding the inclusion of such diverging sites, in favor of sites with apparent (but not actual) linear relationship of some defined, minimum magnitude, the very information necessary to get even a first approximation of the full magnitude of past climatic uncertainty, is avoided in essentially all existing studies.
A very important related point on this issue needs to be stated here. Because positive correlations between instrumental record temperature and observed ring measures during calibration are virtually always the critical selection criterion in these studies (it being assumed that higher temperatures always lead to greater, rather than lesser, ring response), this translates directly into the fact that a true unimodal response to temperature will always potentially lead to temperature under-estimates in the pre-instrumental (historic) period, relative to the calibration period, when a linear relationship between driver and response is computed. Yes, always. I say “potentially” because there could of course be cases in which a positive linear relationship really does hold true for all times present and past; the problem is that there’s no way to definitively know this, given the data. And that is a serious problem indeed, no getting around it. If I thought there was a possible solution to it, I’d say so, but I really don’t see one.
On the issue of removing the non-climatic (i.e. age/size) trend from the data, the study is superior to many, at least at one of the two areas examined, largely due to its heavy use of sub-fossil trees (long-dead trees that have not decomposed). [This is where those interested in understanding the details may need to go back and read about the issues of RCS estimates in the presence of a climatic trend and a sub-optimal field sampling scheme, described in previous posts.] Sub-fossil trees of inherently short longevity (such as the Siberian larch, Larix sibirica, used here) have one great advantage over living trees (as sampled by typical practice) when it comes to the creation of the RCS “Regional Curve”: the tendency for an increasing mean ring (“cambial”) age over time is inherently minimized. This in turn tends to minimize the maximum possible bias in the computed Regional Curve, whenever an environmental trend is present.
The study uses both sub-fossil and living trees (as it must in order to create chronologies that extend into the instrumental record period). I looked at the age structure of the total sample, for both the Polar Urals and the southern Yamal area (separately) to see how close to the optimum they were. By optimum, I mean the tree age structure that would give an unbiased Regional Curve; that’s always going to occur when (and only when) the mean ring (cambial) age of the sample is +/- equal in each and every year sampled. Only then is it guaranteed that any existing environmental trend will not bias the Regional Curve. Conversely, the degree to which the sample contains a trend in this mean ring age is the degree to which the Regional Curve will contain some part of the environmental trend within it, which it is not supposed to do.
For now, I am just analyzing all the cores for each of the two areas together, creating a single Regional Curve for each, not separating them out by river drainage or any other potential classifying variable (and I’ll get into the problematic issue of grouping cores by their inherent growth rate, as the authors did, later). At this level of analysis, the Polar Urals sample, and its potential for problems, differs from Yamal. Here is the mean cambial age of the Polar Urals sample*:
Again, the optimal age structure would be a horizontal line in both cases, i.e. identical mean cambial ages in each and every year. Although in both cases there is a definite sawtooth-like fluctuation in mean ring age over time, it’s clear that the Yamal data has no strong, obvious trend to it, at least from about -250 to 2000. The Polar Urals, conversely, show a very definite and extreme increase in the mean cambial age after about 1750 or so, due to the sampling of the living trees, as older trees were sampled in preference to younger ones. Therefore, the Regional Curve for the Yamal data is much less likely to be trend-biased than is that for the Polar Urals, if in fact an environmental trend was really present (which of course we do not know, apriori). So, these two areas have data of different potential quality in terms of their ability to estimate relative summer temperatures over the last one to two thousand years. The sawtooth-like fluctuations on ~ century scales could still cause some potential problems in the estimate of the Regional Curve, but this is more complicated to get into, and the main point is that they will not impart a systematic trend bias in the computed Regional Curve, which is the more important issue.
* Note that these ages are computed without the “pith offset” data (data estimating the number of
cores rings missed near tree center), because the pith offset files are provided, but they are unintelligible (there are no field headers, and values given are not the integers that they should be). Therefore, it is assumed that the first measured ring of each core is the first actual ring. Since this is very often not the case, and the number of missed rings varies from core to core, some (likely small) error is introduced by this procedure.
Loehle, C. (2009). A mathematical analysis of the divergence phenomenon. Climatic Change, DOI 10.1007/s10584-008-9488-8.
twice thrice for grammar/readability, links and refs added, etc.