Taimyr – Linear or Nonlinear?

While I’ve got Esper open, here’s some thoughts on the division of cores and sites between "linear" and "nonlinear" – where I’ve been seeking an operational definition for some time. Herr Esper told Science:

The split into linear and non-linear ring width series is shown in a supplementary figure accompanying the Science paper. The methods of this widely accepted, approach are described in the paper cited below and in the Science paper. It is possible to make this an operational approach, for example, by fitting growth curves to the single measurement series (e.g. straight line and negative exponential fits) and group the data accordingly. We didn’t do this in the Science paper, but rather investigated the data with respect to the meta information (i.e. for a particular site; data from living trees, and clusters of sub-fossil data), which I believe is a much stronger approach. This, however, requires experience with dendrochronological samplings and chronology development. Esper J, Cook ER, Krusic PJ, Peters K, Schweingruber FH (2003) Tests of the RCS method for preserving low-frequency variability in long tree-ring chronologies. Tree-Ring Research 59, 81-98.

So how is this split described in the Science paper itself:

To build RCS chronologies from the whole data set containing different sites and species, we analyzed the growth levels and trends of the individual ring width series after aligning them by cambial age and classifying them into two groups, one with age trends having a weakly "linear" form and one with age trends that are clearly "nonlinear" (see Web fig. 1). This classification was used to calculate two mean chronologies representing 443 linear and 762 nonlinear individual series. It is necessary to divide the overall data set this way because differences in growth levels and slopes can bias resulting RCS chronologies [Esper et al, eventually 2003].

This states that the cores were divided into linear and nonlinear, but this statement is not a description of the "methods", as stated in the response from Science. The article itself contains no other discussion that could be construed as description of this method. Hockey Team members tend to think that merely asserting something is a proof.

What does Web fig 1 show? I’ve excerpted it below. It shows the number of cores in "linear" and "non-linear" sites, but again is not an exposition of the method. Here though is something interesting – "Tai" (Taymir) is shown as a "linear" site – based on what Esper says is a "widely accepted" approach.

So let’s see what Esper et al [2003] says about the division between linear and nonlinear. Actually nothing. It actually does not mention the distinction anywhere. It does say (not very helpfully for Esper, it seems to me):

RCS is clearly sensitive to the effects of different subsample populations entering into the calculation of single RC. Including samples from different biological-growth populations in one RCS run could bias the resulting chronologies (e.g. TRW in Figure 8C) thus affecting interpretations of climate made from the resulting chronologies. However opportunities to test the data for the existence of different populations are limited.

OK, there’s nothing in Esper et al [2002] or Esper et al [2003] which provides a definition of linear versus nonlinear. As a test case, let’s see what Naurzbaev et al [2002] said about RCS as applied to their site. This is a "linear" site. Schweingruber is a common co-author to the two articles. This should be an ideal place to see "linear" trees in action. Here is their Figure 2.

Original caption: Figure 2 The two “‹Å“regional’ age curves (1) obtained for cores and stem wood samples taken at a height of 0.5–1.0 m above ground and (2) as derived from discs of dead trees where the lower part of the stem is preserved. An offset in the curves is required to account for the sampling height bias and to produce a single valid standardization reference curve.

Wait a minute – I thought that this was supposed to be a "linear" site using a "widely accepted" approach. Let’s see what Naurzbaev et al [2002] actually said about this figure and their RCS procedure:

To remove the effect of increasing tree age on the measured ring widths in individual samples, the measurement data were converted to indices by taking anomalies from the appropriate years of a single reference curve, a function of expected ring width against tree age for trees in this region. This was derived by fitting a negative exponential function through the simple averages of all the measured series, after aligning them by cambial age from the tree pith (that is according to the life cycle of the tree as opposed to any calendrical date): the so-called “‹Å“Regional Curve Standardization’ or RCS (Briffa et al., 1996). However, rather than assume that a single RCS reference curve was suitable for all the data, the sample measurement series were first divided into two groupings and RCS curves calculated for each: one derived from the living-tree and dead-tree samples where these were cored between 0.5 and 1.0 m above the ground; the second derived from the best-preserved subfossil samples and using growth right at the base of the tree (Figure 2). The age curves for the tree-base measurements show how the increase in radial diameter is slow for up to about 70 years before the long period of later diminishing ring width begins. These early years are not represented in the living-tree core samples because of the height of coring in the stem. Assuming that the pith (i.e., innermost) ring at this height was equivalent to the year of tree germination would obviously lead to a rather large error in assigning the relative life cycle age of the living samples. The slow early growth of these trees might be associated with competition by other low-level vegetation as well as the inàƒ’€šà uence of snow cover (Gorchakovskii and Shiyatov, 1985; Abaimov et al., 1997a). However, by aligning the living trees correctly, making allowance for the initial slow growth in these data, it is possible to derive a single appropriate RCS curve, as shown in Figure 2. This curve is also confirmed by reference to other material from living trees collected previously in the region (Vaganov et al., 1996b).

I guess Naurzbaev didn’t get the memo. Naurzbaev et al [2002] gave a detailed description of a nonlinear age profile, with as usual for Naurzbaev, a completely convincing account. Esper on the other hand used undisclosed "meta-information", "which I [Esper] believe is a much stronger approach. This, however, requires experience with dendrochronological samplings and chronology development."

Even requests from Science to explain his methodology doesn’t seem to have got Esper’s attention, who seems quite content to blow off Science rather than actually describe his methodology. This is as bad as Mann. Now with all these guys, there’s an innate orneriness. Just because they are being ornery doesn’t necessarily mean that there’s any big problem at the end of the day. But it does make you wonder why there’s such a big problem getting the data.


  1. TCO
    Posted Apr 22, 2006 at 1:07 PM | Permalink

    As expected the division of linear and nonlinear serves to emphasize hockey sticks. And they haven’t given the mathematical test for grouping (or justification for the division).

  2. Posted Apr 22, 2006 at 2:47 PM | Permalink

    I agree that these people clearly think that if a statement gets through peer review and is published, then it’s not only proved but it becomes a proof itself. Many of them will tell you about this principle quite explicitly.

  3. jae
    Posted Apr 23, 2006 at 8:45 AM | Permalink

    I don’t think these guys have many “standardized procedures.” It looks to me like they each make up new procedures as they go along, to help with the cherry picking. Different recipes for cherry pie!

  4. Posted Apr 23, 2006 at 10:16 AM | Permalink

    Just because they are being ornery doesn’t necessarily mean that there’s any big problem at the end of the day.

    Its more of a big problem for them. I wouldn’t be surprised if it wasn’t a major factor in the decision to convene the NAS panel. If they had been transparent and cooperative from the start, it wouldn’t have been necessary.

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