Exploring potential biases in the Yamal RCS Chronology: sensitivity to the inclusion of modern data from specific sites

Overview

Here we test the robustness of published versions of the Yamal RCS chronology (Briffa, 2000; Briffa et al. 2008) shown in Figure A. We explore the sensitivity of the character of the Yamal chronology to the specific inclusion of measurements taken from living trees at each of 4 sites and compare the individual chronologies, each based on sub-fossil data combined with the modern data from each site, with the chronology created using the combined data from all sites. Chronologies are created using the RCS standardisation method incorporating the 'signal-free' technique described in Briffa and Melvin (2008), Melvin and Briffa (2008).

Background

General texts describing the basis of dendroclimatic methods include Fritts (1976) and Cook (1990). Here we summarise some relevant points.

Trees grow better in some years than in others and series of ring-width measurements from different trees at a site or across a region can show similar patterns of good and bad growth through time. The existence of this common pattern or 'signal' in series of tree-ring measurements, especially as shown in high-pass filtered data, allows the measurement series to be crossdated against each other and, provided the trees can be matched to living samples with known dates for their outer rings, the exact calendar date of each ring can be established.

Once they have been dated, ring-width data can be incorporated into a 'chronology': a time series composed of the average of many tree-ring data series. Even under the same climate conditions the growth of individual trees will vary because of different localised site conditions (e.g. soil type, aspect, competition) or other small scale factors varying within a site. The rationale for building a tree-ring chronology is to produce a robust representation of whatever underlying influence(s) is (are) expressed in the common growth pattern exhibited by a representative sample of different trees within a site or across a wider region. Averaging the records from different trees greatly reduces the variability that is not shared in common by many trees and brings out the underlying pattern of common growth changes.

The need to 'Standardise' raw measurement data to remove tree-age effects

The widths of tree rings can also vary substantially over time, according to tree age and the changing radial geometry of the tree. Radial-increment measurements generally display a characteristic pattern of rapid growth followed by a more gradual decline as the tree gets older.

If raw ring-width measurements from different trees are simply averaged together, especially when the trees germinated at roughly the same time, the chronology values would show a declining trend, expressing the narrowing of ring widths as the trees get progressively older. Standardisation methods have been developed to allow the estimation and removal of the age-related trends in tree growth measurement series, to allow the underlying tree-growth signal to be more clearly expressed. Standardisation can be accomplished by filtering the measurements with a high-pass filter (e.g. using data-adaptive or curve-fitting methods) but the inevitable consequence is that long-timescale variance in the chronology is removed.

Regional Curve Standardisation

Regional Curve Standardisation (RCS) is a simple approach to removing tree-age-related bias in chronologies. This converts measurement series into fractional deviations from a single statistical model of expected ring width as a function of tree age. Unlike the 'high-pass filter' approach, which restricts the timescale of variability in standardised series to periods shorter than the length of the tree-ring records, the RCS approach can preserve potential long-timescale variance with respect to the overall chronology mean (Cook et al. 1995, Briffa et al. 1996).

Where the focus of study is on long-term changes we believe the RCS approach remains the most promising technique, as shown by comparison with various other widely applied alternatives that demonstrably fail to preserve evidence of long-term climate trends. The methods and protocols for processing and interpreting RCS chronologies are, however, still evolving.

We have previously described how the application of this method may provide a biased indication of regional-average tree-growth changes over multi-decadal and longer timescales if the measurement data are inhomogeneous, in the sense that they are taken from trees that would have grown at different rates under the same climate conditions.

A single statistically-derived model of expected ring-width as a function of ring age may not always be an appropriate reference from which to calculate tree-growth indices for all samples and in such cases and the degree of expressed bias at any point of the chronology will depend on how specific sample biases, arising because of inhomogeneous sample data, cancel each other through time.

We are exploring ways of identifying such biases and of modifying the simple RCS approach to mitigate their effects. Further details and more extensive discussion of these issues may be found in a recent review of the status of the RCS technique (Briffa and Melvin 2008).

Yamal Chronology History

The selection of which sites or regions from which to sample trees is usually made on the basis of the study objectives, e.g. to reconstruct temperature or precipitation. The number of sites selected is dependent on the size of the region of investigation and crucially on the availability of samples. The assessment of how many trees are needed to build a chronology is usually gauged according to the numbers required to express the statistically measured common tree-growth signal at the timescale and error levels set as objectives in the project i.e. longer timescales and smaller error margins require larger numbers of samples. Individual trees are selected for sampling on the basis of what we know about the local ecology: with the intention of maximising the potential for the ring patterns to show evidence of the common growth pattern. For living trees a representative sample is taken from what is usually a larger population of potential trees while for sub-fossil trees all samples that have sufficient rings to enable crossdating are often employed. When forming a chronology, the variance over time depends on the sample count. To avoid problems with changing variance related to differences in data replication the count of trees at the modern end of a chronology may be deliberately limited (to be consistent with the number of sub-fossil samples averaged through time) or, alternatively, statistically-based variance adjustments can be made (Osborn et al. 1997).

Over two decades our Russian colleagues collected hundreds of dead (sub-fossil) trees from sites adjacent to several river systems in the Yamal region (Hantemirov and Shiyatov 2002, Figure 1) and painstakingly crossdated many of these measurement series, to place them in exact calendrical alignment. This generated a data set of ring-widths spanning several millennia. Hantemirov and Shiyatov's intention was to use the 'corridor standardisation' (Cook et al. 1990), which can only preserve variance representing periods up to about a third of the length of a tree, and so forms a chronology which predominantly expresses the high-frequency signal of tree growth. For the "corridor-standardised" chronology produced by Hantemirov and Shiyatov, a sample replication of about 10 trees in each year is generally sufficient. To form the modern end of their chronology they also selected data from 17 trees spread over 5 sites in the region in which their sub-fossil trees were collected (see Figure B).

To retain representation over the wider area they selected a few trees from each site. With the intention of preserving some decadal and longer time scale information in their data, they selected from the longest series at each site as well as considering only trees which showed high levels of the common growth forcing signal. Their near 4,000-year chronology was published in Hantemirov and Shiyatov (2002), and the AD portion of this data set was used in Briffa (2000) and Briffa et al. (2008) without further modification or selection.

Data

The file Yamal_AD consists of measurements from 235 sub-fossil samples collected at numerous sites adjacent to the Porzayakha, Yadayakhodyyakha, Tanlovayakha and Khadytayakha rivers (Hantemirov and Shiyatov 2002, Figure 1) and samples from 17 living trees growing at 5 sites in the vicinity of the sub-fossil trees. In a second file we removed the 12 series (the same 12 series as removed by McIntyre) which came from the JAH, POR and YAD sites, to leave data from 240 trees called Yamal_SF. (See Tables 1 and 2 listing all sites used). We also produced four files containing the 'living-tree' data for each of the JAH, POR and YAD sites (measurements supplied by Rashit Hantimirov, personal communication) and a separate mean-tree file (data for 34 cores averaged to form mean series for 18 trees) named KHAD (Khadytla, Schweingruber and Briffa 1996). For the sensitivity tests we appended the cores of each of the four individual sites to those of the Yamal_SF forming four separate data sets (Yamal_YAD, Yamal_POR, Yamal_JAH and Yamal_KHAD). We also appended all series from the 4 living-tree sites to the Yamal_SF trees to form a Yamal_All chronology. The original 17 living-tree samples selected by Hantemirov and Shiyatov are in file LIVE.

Data Set Site Name Alt North East Start End Species Yamal_AD Yamal -999 6700 7000 -202 1996 LASI KHAD Khadytayakha 90 6712 6950 1782 1990 LASI POR Porzayakha 6732 7050 1580 1994 LASI JAH Jahak 25 6725 7028 1577 1991 LASI YAD Yadayakhodyyakha 6725 7048 1803 1996 LASI Table 1 – Some details of the regional and local chronologies explored in this analysis: altitude (masl), coordinates (degrees and minutes), start and end year and species (LASI is Larix siberica). The Yamal_AD file contains the measurement data used in Briffa (2000) and Briffa et al. (2008).

Derived data set Derivation details Yamal_SF Sub-fossil and 5 living trees from two sites Yamal_All Yamal_SF + KHAD + JAH + POR + YAD Yamal_KHAD Yamal_SF + KHAD YamalAD_KHAD Yamal_AD + KHAD Yamal_POR Yamal_SF + POR Yamal_JAH Yamal_SF + JAH Yamal_YAD Yamal_SF + YAD LIVE The 17 living trees of the Yamal_AD Table 2 – Details of the specific composition of data files used to create the chronologies discussed in this analysis.

Series of Figures were generated showing the distribution of trees over time within each site. For each site, series of reports listing some statistics for the individual trees (or cores) are provided. Crossdating of the samples was performed using a cross-dating program, employing the same default options as used in COFECHA (Holmes 1986), to generate reports showing the levels of high-frequency common signal within the sites and between sites. Measurement data and chronology indices are available on the data page.

The Yamal data set used (Briffa 2008) differs from that used in Briffa (2000) and those used here because the last ring of the last tree was inadvertently omitted during the creation of the Yamal_AD data set in 2008. This ring is included in the Yamal_AD data set used here but the chronology shown here is as published in 2008.

Application of the RCS method in this sensitivity study

A consistent implementation of RCS standardisation is used here throughout. This involves using mean ring-width aligned by tree age to provide empirical evidence of expected ring width as a function of tree age. Where pith-offset estimates are available these were used to establish relative ring age with greater accuracy (e.g. KHAD site). The single free method (Melvin 2004, Briffa and Melvin 2008, Melvin and Briffa 2008) was used to remove the effects of the common chronology signal on the shape of the RCS curve. In this approach the estimated values of the chronology indices are removed from each measurement series by division to create series of "signal-free" measurements. The statistically-derived mean signal-free ring-width by age curve is then smoothed using an age-dependent spline (Melvin et al. 2007) fitted only to the average ring widths for tree ages represented by at least 4 trees and extrapolated linearly thereafter. Series of tree-growth indices were created by dividing measured ring-width values by the appropriate RCS curve values (for that ring age) and the chronology was created as the arithmetic mean of all tree indices. None of the chronologies created here have any form of variance stabilisation applied to them.

Results

Figure C shows the RCS curves produced using only the data from each site in turn and the chronology values (from 1800 onwards) produced using these RCS curves. Differences in index values between sites are apparent. Overall, there is good agreement in the general trends of tree growth between sites, with growth increasing markedly at all sites around 1900 and being maintained at a relatively high level afterwards, except at the KHAD site where the trees show reduced growth after 1970. The POR and YAD sites exhibit the highest levels of relative growth after 1950 with the level of growth at the JAH site somewhat lower but well above that at KHAD.

Figure D illustrates the chronology data at the same sites but standardised using individual site RCS curves that incorporate the sub-fossil data. Essentially the same picture of differing relative growth patterns between sites is revealed. These data imply that the pattern of growth changes at the KHAD site is most anomalous with respect to the growth behaviour shown at the other three sites.

On the assumption that the most conservative indication of overall tree growth patterns in this region is provided by incorporating all of the available data, Figures D, E and F present the reworked Yamal_All chronology (in black) constructed using all of the currently available data from POR, YAD, JAH and KHAD appended to the Yamal_SF data. The series of mean-tree indices, i.e. fractional deviations from the single Yamal_All RCS curve (based on all sub-fossil and available living-tree measurement data) are shown on the data page.

In Figure F, the Yamal_All chronology is compared with the Yamal_AD chronology (data as Briffa 2000), the Yamal_KHAD chronology, and the Yamal_AD_KHAD chronology (the last two based on the same data as in McIntyre's alternative versions, but for consistency processed using the same implementation of RCS used throughout this exercise). Note that the KHAD data do not extend beyond 1990 so a direct comparison is only valid up until this date.

The data in the upper panels of Figure F are shown smoothed with a 40-year low-pass cubic-smoothing spline; applied to the whole of each chronology in the left panel and truncated at 1990 in the right. The annual chronology values are shown from 1800 onwards in the lower panel. The new Yamal_All chronology presents a picture from which it is reasonable to conclude that "tree growth in the 20^th century was unusually high compared to that in previous centuries". Though the 20^th century level is lower than in our published chronologies, due to the inclusion of the KHAD data up until 1990, this conclusion better represents the balance of evidence across the different sites than any inference made on the basis of the chronology formed using only the more spatially limited, and apparently atypical data from the KHAD site.

The post-1990 values in the new Yamal_All chronology are based only on data from the POR and YAD sites, and so are likely somewhat biased by the greater increase in recent tree growth rates observed there, but we simply do not know whether the JAH, or even the KHAD site, trees exhibit high growth rates in these recent years.

Figure G presents a comparison of the published versions of the Yamal chronology with the newly created chronology (Yamal_All), incorporating all data from all 4 living-tree sites. Remembering the caveat regarding the possible positive post-1990 bias, the picture of unusually high 20^th century tree growth at the Yamal larch tree-line is essentially the same in the reworked chronology as was shown in our previously published versions.

References