Starting with the first of my recent posts on Yamal, I raised the issue of whether the CRU 12 actually came from a homogeneous population to the subfossil population. This issue was related to the surprisingly small sample size of the supposedly “highly replicated” Yamal chronology, but is distinct. In his online response to Yamal posts, Briffa stated that they have “stressed” potential problems arising from “inhomogeneous” sources” in their “published work”.
Indeed, we have said so before and stressed in our published work that possible chronology biases can come about when the data used to build a regional chronology originate from inhomogeneous sources (i.e. sources that would indicate different growth levels under the same climate forcing).
Whether two populations are homogeneous is ultimately a statistical question. Consideration of this question as a statistical question has been blurred to date by the lack of understanding within the dendro community of the statistical issues involved in making a chronology (or within the statistical community of the difficult and interesting applied problems that dendros are trying to solve.) The disconnect is neatly illustrated by the references to Briffa and Melvin 2008, a highly technical article on standardization which nonetheless doesn’t include a single reference to an article or text by a non-dendro and which shows no awareness of how making a “chronology” ties into statistical literature on random effects (or how testing for population homogeneity relates to the statistical concept of “exchangeability”).
While Briffa’s articles occasionally contain caveats on population requirements for RCS standardization, I have been unable to locate any Briffa articles which he actually procedures for testing populations for homogeneity or the results of such tests, a lacuna that seems somewhat inconsistent with the idea that CRU has stressed this issue. In this instance, one wonders whether there is any practical difference between CRU stressing an issue and ignoring it.
While there doesn’t appear to be any relevant procedure in the Briffa corpus, Esper et al 2003 url does provide an on-point qualitative discussion of when two different populations can be combined in an RCS population (Tom P noted this in an earlier thread). It isn’t a formal test procedure, but it does provide a useful example (Jaemtland) where two populations were considered sufficiently distinct that they were not combined and does provide a basis for analysing Yamal homogeneity in a framework recognized by dendros.
In this post, I’ll provide a detailed description (and emulation) of the methodology described in Esper et al 2003, which, in another post, I will then attempt to apply to the “extended” Yamal data set recently presented by Briffa.
Esper’s example -see his Figure 8 – considered populations from two distinct sites: Jaemtland (swed023) and Trondelag (norw002), further distinguishing the Jaemtland site into two species PISY and PCAB. One attractive feature of this example as a precedent for analysing Yamal is that the Jaemtland population ends in the early 19th century, while the Trondelag population begins in the late18th/early 19th century, so that the techniques bear directly on the issue of population homogeneity between the Yamal subfossil and the “expanded” YAD-POR sites recently proposed by Briffa. To further accentuate the similarity, the Trondelag data set is a Schweingruber data set where each tree has two cores, while the Jaemtland data set is a non-Schweingruber data set with one core per tree.
Esper’s first step was to calculate age-dependence curves for each of the populations in question, plotting the resulting age dependence curves on the same quadrant. The following graphic shows the original Esper graphic, together with my emulation from available information (note Esper’s use of a biweight mean – which requires 4 samples). Esper observed that the (red) Trondelag (PISYsk) had a “significantly higher” growth rate and has a “rather different” slope than (black) Jaemtland. Esper’s comparison is qualitative, but nonetheless there is an obvious difference between the two age-dependence curves. One feels that this particular comparison could be worked up into a quantitative test (relatively easily if the comparison is between two negative exponential fits.)
Figure 1. Esper et al 2003 Figure 8B showing age dependence curves from two nearby sites. Left – original; right – emulation from Esper data obtained from Sciencemag. The core counts for Trondelag and Jaemtland match the reported core counts in E2003, but there is no available metadata showing which cores in swed023 are PISY and which are PCAB, the two species having been mixed in the archive. The Trondelag (PISYsk) curves should match exactly; while they are close, they don’t quite. Esper uses a biweight mean instead of a simple mean or median (this is OK.)
Esper demonstrated the impact of two non-homogeneous populations on an RCS chronology in his Figure 8D shown below at left versus my emulation shown at right, together with the core counts for Jaemtland (light gray) and Trondelag (dark gray). These show first of all that I’ve accurately emulated the key features of Esper’s methodology for this particular analysis. (Further comments below graphic.)
Figure 2. Left: Esper 2003 Figure 8D; right – Jaemtland chronology as used in Esper et al 2002, together with core counts. Light grey – Jaemtland; dark grey – Trondelag.
Look first at the early 19th century transition from Jaemtland to Trondelag data and the impact on the RCS chronology. Application of a one size fits all RCS method to this inhomogeneous population results in a inhomogeneity in the RCS chronology at the hinge point linking the two populations. Esper characterized the inhomogeneity as resulting in an “artificially shifted” mean in the early 1800s.
Esper stated that the inhomogeneity is caused by the
“rapidly growing [Trondelag] samples forcing the RCS spline [SM: would be the same for negative exponential] too high for the older, slower growing samples. This feature, namely the significantly deviating growth rates and growth decreases with aging of the Trondelag samples, indicates the existence of a different population in the sense introduced earlier. It also demonstrates the biasing effects of different populations and the fundamental requirement of the RCS method: sample homogeneity”.
There’s nothing in this paragraph that ought to be objectionable to any CA reader – it’s the sort of thing that we’re regularly concerned with. And it’s precisely the sort of thing that I’m wondering about at Yamal.
There are some other interesting features to this graphic. In the 13th century, the sample replication goes down to one core from Tornetrask, inserted into the data set as a bridge. The breakpoint in the RCS time series is pretty obvious. At the start of the record, replication falls below benchmark standards and again there is an obvious breakpoint.
In this particular analysis, Esper is at least attempting to analyse population homogeneity. In contrast, despite its length, the analysis in Briffa and Melvin 2008 fails to deal in any relevant way with the problem of population inhomogeneity (and other Briffa articles are even less helpful.)
When you have inhomogeneous populations, you can’t just add everything together. This is well understood in social science, where analysts have to take care to separate the effects of different factors. Esper’s Jaemtland-Trondelag example provides a foothold for trying to quantify population inhomogeneity within frameworks familiar to and accepted by dendros.
In a forthcoming post, I’ll apply these methods to both the Briffa 2000 Yamal data set and the “moved on” data set with some interesting and perhaps surprising results.