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.
Although Briffa’s online response to my Yamal posts stated that CRU has “stressed” potential problems arising from “inhomogeneous” sources” in their “published work”, I have been unable to identify any CRU article that describes a procedure for testing two populations for homogeneity or any article that reports the results of such a test. (Yes, Melvin and Briffa 2008, 2009 catalogue various biases and problems associated with RCS methodology, but, as already noted, this discussion is not connected to actual statistical literature or to directly to homogeneity).
In the absence of such discussion in CRU literature, in my last post on Jaemtland, I observed that Esper et al 2003 directly considers the problem of population inhomogeneity. While Esper doesn’t describe a quantitative statistical procedure for assessing homogeneity, it describes a shall-we-say artisanal procedure which Esper used to assess inhomogeneity in a proposed combination of data.
Today I’ll apply the Esper methodology to both the Briffa 2000 Yamal data set and the extended Briffa Yamal 2009. The results are provocative.
Yamal (Briffa 2000) Esper-Style
Esper compared populations for homogeneity by plotting RCS curves on the same quadrant. The left graphic below shows (again) my close emulation of the Esper methodology for comparing two Jaemtland populations. Based on the visual difference between these two curves, Esper concluded that the biological populations were distinct, that the two populations could not be combined in a simple RCS one-size-fits-all procedure (and that the 19th century step was spurious, speaking only to a shift between populations and not to growth patterns.)
On the right, I’ve shown the corresponding graphic for the Briffa 2000 data set, again stratifying the population into two strata – this time, comparing the CRU12 to the subfossil population (plus 5 Shiyatov trees sampled in 1963 and not participating in the post-1970 “boom”). (BTW Jeff Id presented virtually the same curve within a day or two of the issue being raised – see link). I’ve added the smooth curves from fitting a negative exponential to the entire population – a variant to curve fitting after averaging widths for each age-year a la Briffa-Esper , a variant that I prefer since it is much more justifiable in statistical terms. (To date, I haven’t thoroughly canvassed the impact of this preference and I have other options in my RCS function.)
Esper et al 2003 reported that the difference between the two RCS curves on the left was sufficiently significant to establish population inhomogeneity and forestall combining the two inhomogeneous populations in a one-size-fits-all RCS chronology. What are we to make of the corresponding curve on for the Briffa 2000 Yamal population on the right?
Figure 1. Left – RCS Comparison for Jaemtland Populations. Emulating Esper et al 2003 Figure 8D. Right – same procedure applied to Briffa 2000 Yamal population, stratifying the CRU12.
The difference between curves in the right graphic “looks” just as significant to me as the difference between curves in the left graphic. Unfortunately, neither Esper (nor Briffa) establish quantitative procedures for assessing such significance. My own opinion – and I’m speaking here in purely statistical terms – is that any reasonable significance tests which rejected homogeneity for the Jaemtland populations (left) would also reject population homogeneity of the CRU12 with the Yamal subfossil population (right).
While Melvin and Briffa 2008 did not discuss procedures for testing population homogeneity, their “differing-contemporaneous-growth-rate” bias is an artisanal term for an inhomogeneity issue. They provide a passim description of this sort of bias (ironically in a reversed context to the one at hand):
In an RCS chronology, if in one period fast-grown trees outnumber slow-growing trees (or vice versa), artificial medium-frequency trends (i.e., of non-climate origin) might result. It is at the recent end of a chronology that the influence of downsloping indices, derived from fast-growing trees, may not, in general, be balanced by the upsloping index series from slower-growing trees. The result, even under constant climate conditions, is an overall negative bias, seen in the final century or most recent decades of the chronology.
Unfortunately, this somewhat blurred recognition of potential problems of population inhomogeneity did not prompt the authors to canvass statistical literature for testing procedures to evaluate such inhomogeneity.
Summing up to this stage, an Esper-style procedure for examining population inhomogeneity provides considerable evidence of inhomogeneity between the CRU12 and the Yamal subfossil population – a possibility that I raised in my initial post. I say “evidence” because I haven’t reduced the Esper procedure to a formal statistical test. However, given the importance of population homogeneity as an issue (an issue that CRU supposedly “stressed”), it is really their obligation to demonstrate population homogeneity, something that was never done for the Briffa 2000 population.
As already noted, Briffa has “moved on” to an expanded Yamal population. He presented a classic “moving on” defence i.e. that problems with the published population didn’t “matter” because they could “get” a similar result with a new population, even if the ink is barely dry on the new data set and the new population is still unpublished in the peerreviewedlitchurchur. (As previously noted, the moving-on defence never acknowledges the correctness of criticisms of the old data set; neither do they rebut the criticisms of the old data set. They just “move on” using a cloud of ink as a camouflage, sort of like a giant squid or team of giant squids in flight.)
The Briffa October 2009 Yamal Dataset
In my initial post, I observed that inclusion of the Schweingruber Khadyta River (russ035w) data set had a substantial impact on the modern portion of the Yamal RCS chronology.
In his October 2009 response, Briffa argued that he could still “get” a RCS chronology that was similar to the Briffa 2000 using an expanded Yamal data set – moving on defence. Briffa’s online response provided the first location information on the sites of the CRU12 – 2 of which came from a site on Jahak River (JAH), 5 from a site on the Porzayakha (POR) and 5 from a site on the Yadayakhodyyakha (YAD), all shown in the Location Map below. The Schweingruber Khadyta River (KHAD) site is also shown on the map below.
Yamal Location Map
It seemed implausible that only 12 cores had been taken in 1988 and 1990 from the JAH, POR and YAD sites. This proved correct. Each site had additional cores, measurement data from which was included with the online article ( JAH- 25; POR- 12; YAD -10), still rather small samples, but 4 times as many as the CRU12. The CRU10 made up 10 of 22 POR-YAD cores. A table summarizes core and tree counts is shown below.
|Site||Briffa 2000 Cores (Trees)||Briffa 2009 Cores (Trees)|
|Subfossil||235 (219)||235 (219)|
|Shiyatov||5 (5)||5 (5)|
|Jahak (JAH)||2 (2)||25 (23)|
|Porzayakha (POR)||5 (5)||12 (12)|
|Yadayakhodyyakha (YAD)||5 (5)||10 (10)|
|Khadyta River (KHAD)||0 (0)||34 (18)|
Briffa conceded that it was reasonable to include KHAD data in an RCS chronology, but also argued that the KHAD data was “atypical” and that a sensitivity reconstruction with KHAD data was “arguably the least defensible” (as compared to corresponding versions separately adding in YAD, POR and JAH data.)
Briffa agreed that the Khadyta River, Yamal (KHAD) met their selection criteria, explaining its omission on the grounds that they “simply” hadn’t considered its inclusion. However, he argued that their influence was overstated in my initial calculation. Schweingruber had taken two cores per tree, while the Russian samples typically took one core per tree. In his online response, Briffa averaged the two Schweingruber cores for each tree, thereby reducing their influence relative to the other cores (inconsistently not doing the same thing for Russian trees with duplicate cores, though they are few and it’s not a big issue.) This seems like a fair enough procedure though there seems to be a bit of opportunism – a similar situation arose when a Schweingruber series was added to Taimyr and it doesn’t appear to me that the same thing was done over there. For present purposes, let’s stipulate to KHAD averaging and the addition of the new data and once again do Esper style testing for population inhomogeneity.
In the next graphic, I report on the results of stratification tests on the expanded population. In my original post, I contrasted the chronology resulting from the combination of subfossil and KHAD data to the corresponding chronology combining subfossil and the CRU12 (primarily POR-YAD.) As noted above, Briffa vehemently argued that the KHAD data was “atypical” and provided the “least defensible” reconstruction. In the graphic below, I’ve expanded the initial comparison using the Esper-style analysis: on the left, I’ve contrasted the subfossil population (here strictly subfossil, excluding the 5 Shiyatov trees) with a modern stratum consisting of KHAD plus JAH and the 5 Shiyatov trees and JAH ( 48 trees in total), and, on the right, the same comparison of the subfossil population to a second modern stratum, extending the CRU12 to the POR-YAD combination (22 trees, including the CRU10 – there were 2 JAH in the CRU12.)
The results are self-evident. The age-dependence curve of the KHAD-JAH-Shiyatov population is, remarkably, similar, (and remarkably similar) to the corresponding subfossil curve, while the POR-YAD population isn’t. In respect to the POR-YAD comparison, it appears to me, that as with the CRU12, any significance test that distinguishes between the Jaemtland populations a la Esper will also determine inhomogeneity between the Yamal subfossil population and the POR-YAD population (but not for the KHAD-JAH-Shiyatov population.) The Esper-style test indicates that it is the KHAD-JAH combination and not the POR-YAD combination that offers a homogeneous extension of the subfossil population to the modern period. And that a simplistic attempt to use “all” the data is merely a backdoor method of getting the inhomogeneous POR-YAD cores into the mix – a line of argument that we’ve seen previously with bristlecones.
Figure 2. Yamal Esper-style RCS Comparisons. Left – Subfossil vs KHAD, JAH and Shiyatov living population; Right – subfossil versus YAD and POR sites (extending the CRU12)
Although the KHAD-JAH population is evidently much more homogeneous with the subfossil population than the POR-YAD population, Briffa’s online article commentary gives the opposite impression, stating of my initial sensitivity test using KHAD data:
exclusive use of the KHAD data (i.e. the most ‘extreme’ of McIntyre’s alternative chronologies) likely provides an atypical representation of the more general long-term course of changing tree growth, as represented by the data from the other sites.
Briffa’s argument, in effect, entirely ignored the problem of population inhomogeneity – notwithstanding CRU claims to have “stressed” this issue. They dumped all the data into the hopper including the inhomogeneous YAD-POR data (extending the CRU12) and got a chronology that was sort of similar to the original chronology. They argued that there was:
“no additional information with which to justify the exclusion of any of these data”
This is obviously not correct. There is enough information to carry out an Esper-style test for population homogeneity, a test that indicates that the KHAD-JAH population is relatively homogeneous with the subfossil population, while the POR-YAD population isn’t. Contrary to Briffa’s claim, this inhomogeneity test mandates either a substantial adjustment to the POR-YAD population, or, if that is unavailable, the exclusion of the data, as Esper did with Trondelag and Jaemtland. Calculating the resulting chronology, here is the 20th century portion:
Here is the corresponding graphic going back through the medieval period.
Adding the apparently inhomogeneous POR-YAD populations will, of course, result in a HS. The issue is, of course, the inhomogeneity of the POR-YAD population with the Yamal subfossil population. Briffa said that they “stressed” the importance of population homogeneity.
But it’s not enough to pay lip service to the concept. It needs to be demonstrated.
The Esper-style test is, by no means, revealed truth and doubtless there are better ways of testing for population homogeneity well known within conventional statistical literature. But at least the Esper method is recognized within dendro literature and, to my knowledge, the only test for population homogeneity reported in the dendro literature (I’d be happy to test any other methods drawn to my attention).
Application of the Esper-style test demonstrates Briffa’s failure to carry out any test for population inhomogeneity and demonstrates the futility of the analysis in Briffa’s online post. It also supports the surmise made in my original post – that there was a serious issue with the population inhomogeneity of both the CRU12, now seen to extend into the expanded POR-YAD 22.
A note that I’ll be following up on – in carrying out the above analysis, the age-RW plots compare age to average ring widths for each age. These values do not reconcile to values at Briffa’s online article (even where core counts are matched exactly.) It appears that the age-ring width plots in Briffa’s online article do not show actual average ring widths but adjusted average ring widths- the adjustments might be based on the algorithm described in Melvin and Briffa 2008, but this is just a guess.