Briffa et al., 2013, part two

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*:
Urals mean ring age

And here is the corresponding graph for the Yamal data:
Yamal mean ring age

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.

Reference:
Loehle, C. (2009). A mathematical analysis of the divergence phenomenon. Climatic Change, DOI 10.1007/s10584-008-9488-8.

Note: Edited twice thrice for grammar/readability, links and refs added, etc.

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6 thoughts on “Briffa et al., 2013, part two

  1. Jim

    If you cannot tell whqat temperature the ring-width is recording, how can you make any assessment of whether the RCS methodology is good or bad? Am i over-simplifying the problem? I was alluding to this problem over at real climate but I guess the discussion belongs here.

    • The “temperature the ring width is recording” is essentially the last step in the process, i.e. the calibration step against instrumental record data. Whether the RCS methodology is good or bad is completely independent of that step. It depends instead (entirely) on (1) the age/size structure of the sample, (2) the relative growth rates of the trees, and (3) the magnitude of the environmental trend over time. I explained the issue in detail, starting here and continuing with more detail in later posts in the series.

      Note that this problem remains entirely unrecognized in the peer reviewed literature.

      Edit: let me rephrase that last statement to be more precise. The issue of the potential problems caused by the interaction between the age/size structure of the tree sample, and any existing environmental trend (e.g. climatic) over time that may have existed, remains entirely unrecognized in the peer reviewed literature.

  2. Jim,

    What are your thoughts on Tom Osborn’s comments at RC http://www.realclimate.org/?comments_popup=15500, specifically:

    When I read your comments on sub-fossil trees, my mind drifted back to when Osborn said: “Our initial plan was to include the Khadyta River data in the main chronology for our new paper — even after we had inspected them and seen that they behaved differently to data from other sites in the region. Subsequently our Russian colleagues pointed out that there were issues with this particular site, that the trees were not considered ideal for dendroclimatic analysis and were not healthy. That was the basis of their exclusion from the final presented chronology.”

    and later: “In the case of the Khadyta River data, one might argue that it is better practise to leave the data in and depend on the averaging process to produce the “best estimate” of the underlying regional tree-growth signal. Without explicit knowledge that the apparent health of these trees was sub-optimal, we would probably agree with this logic. However, given the additional knowledge that the trees are unhealthy and the site not considered ideal for dendroclimatic analysis, it is reasonable in this case to exclude these data from the regional chronology. As it happens, the chronology including these data is not significantly different from our final chronology.”

    I see there is a lot of power inherent in the original author/corer declaring data as unusable (or close to it, or something to that effect), however there have been times when this has been questioned or over-ruled by other scientists that weren’t involved in the original data retrieval.

    • The second of your two quotes there comes from the comment signed by all three authors, which in toto I thought was a very good expression of the kind of reasonable decision making process involved in such a situation, including the potential tradeoff of having a larger sample size (and counting on the random variation therein to be collectively unbiased), versus having a smaller sample size (which might would be more likely to be affected by sampling error). In the latter situation (or really, any situation), when you also have some definite information about the health/responsiveness of the trees and/or about the sampling site (and with it, the likely suitability of the trees in returning a temperature signal), then yeah, I definitely agree, best not to include them.

      I definitely trust that the authors, and all dendroclimatologists for that matter, are not purposely including/excluding certain tree data in order to produce any particular desired result. There just needs to be more attention paid to certain analytical issues that can cause some real problems if ignored or misunderstood.

  3. Jim, regarding the pith offset files…

    Our pith offset is an estimate of the radius of the missing wood at sampling height in the stem, from the pith (that is presumed to be) at the centre of the stem to the first measured ring in the core sample. It is a distance, so the numbers are not necessarily integers. This estimate of missing wood radius is converted to an estimate of the missing number of rings based on measured ring widths and a calendar date. In our files, this is recorded as the estimated year that the pith grew at the sampling height (e.g. if the first measured ring is dated to 1783 and the pith offset indicates 10 missing rings plus the pith, the value recorded in our “.pth” files would be 1772).

    The pith offset information is contained in the first three columns of the “.pth” file: the core identifier, the estimated year that the pith grew, and the estimated pith offset (in units of “cm”).

    • OK, thanks a lot Tim. I thought the units must be length instead of years, since I know that the standard way of making the ring number estimate is to estimate the distance from the inner-most measured ring to the pith and then convert that to number of rings based on early growth rates, but couldn’t be sure, so thanks for clarifying.

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