In order to quantify the degree of correspondence in tree-growth trend changes on time scales ranging from multi-decadal to centennial, we have compared the temporal growth patterns across all RCS chronologies using the Kendall's (1975)
concordance coefficient, applied over different moving time windows (appendix B
). In effect, this is similar to calculating a moving Spearman rank correlation coefficient but enables more than two series to be compared at once (Siegel & Castellan 1988
; Zar 1999
). Unlike the more frequently applied Pearson correlation coefficient, with a range of −1 to +1, the concordance coefficient varies from 0 to 1, with 0 indicating no common signal between the time series being compared and a value of 1 indicating perfect parallel ordering of the elements being compared. Here, the concordance coefficient was used because previous work using simulated data (Shishov & Ivanovsky 2006
) had shown that it reveals measures of the similarity in variability between series even in the presence of significant levels of white and even red noise. Similarly, the concordance coefficient is less sensitive to the length of the analysis period (or moving window) when this is short (Shishov & Ivanovsky 2006
), in comparison with average Pearson correlations (sliding RBar).
shows the results of alternative applications of the concordance coefficient for comparing 101-year growth trends across the three regional RCS chronologies: first, using the year-to-year data and second, using the SSA smoothed chronology data in each region (). In the smoothed data, high values of concordance are achieved for the comparison of the most recent section of the chronologies (for windows centred between approx. 1890 and 1930, corresponding to a range of comparisons spanning approx. 1840–1980), though they have since fallen slightly, probably associated with the extreme growth increase in Yamal that is not matched in Fennoscandia or Avam–Taimyr. However, even higher concordance values are found in the smoothed data between 840 and 880 (comparisons spanning 790–930), but these are associated with a series of oscillations following a widespread cool period approximately 800 ( and ) and not with the warm period approximately 1000. In the unsmoothed data, relatively high concordance is apparent again in medieval times, but the highest values in 2000 years are recorded for windows spanning the most recent century or so. In b
, concordance is calculated for different length windows using the raw RCS indices, but the results for each window length are smoothed (using the negative exponential least-squares method; Mclain 1974
), which is roughly equivalent to using a 200-year spline. In the unsmoothed concordance series, except for the shortest (51 years) window results which clearly show high concordance approximately 900, there is evidence of rising and unprecedented similarity in tree growth across northwest Eurasia in the most recent century. This is accentuated in the smoothed series for 101- and 201-year window lengths.
Figure 8 (a) Kendall's concordance coefficients calculated for overlapping 101-year windows using the RCS chronologies of Fennoscandia, Yamal and Avam–Taimyr, as SSA-filtered data (red line) and unfiltered data (blue line); (b) concordance coefficients (more ...)
shows the standardized distribution of 1846 concordance coefficients (plotted within one standard deviation classes) calculated between the three RCS regional curves for overlapping 101-year windows (the thin red line in b; data have a mean concordance of 0.4 with a standard deviation of 0.08). The values are distinguished according to whether they derive from one of three periods: moving windows centred between 764 and 960 (n=197), and so roughly incorporating the medieval period; modern values, including windows centred between 1900 and 1946 (n=47); and the values for the remaining windows (n=1602). The medieval values generally lie between 0 and 2 standard deviations of the mean, but the recent values all lie between 1 and 3 standard deviations, most between 2 and 3 standard deviations. This is strongly indicative of an unprecedented level of agreement in centennial tree-growth trends across the whole of northwest Eurasia in a context of at least 2000 years. This is suggestive of very unusual, near continental scale, common forcing of northern tree growth and probably the result of an increasingly widespread similarity in summer warming.
Figure 9 Distribution of (standardized) concordance coefficients (mean=0.40, s.d.=0.08) between the RCS chronologies of Fennoscandia, Yamal and Avam–Taimyr (derived for 101-year moving windows) and separated into three time periods with windows centred (more ...)
As a final comparison, we investigated the changes in the concordance coefficient of summer temperatures at locations equivalent to those of the three chronology regions that are the focus of this paper, but using simulated rather than observed or inferred temperature data. Mean summer temperature data were extracted from two simulations made with the UK Hadley Centre fully coupled atmosphere/ocean GCM (HadCM3, see Tett et al. 2007
). These simulations were run as part of the European project SO&P (http://www.cru.uea.ac.uk/cru/projects/soap/
). One of these simulations, run for the last 500 years (AD 1500–2000), uses only ‘natural’ forcings (a combination of orbital, land use and estimated irradiance changes and volcanic activity). The other, run only for the period 1750–2000, uses the same natural forcings but includes the additional influence of increasing atmospheric GHG concentrations (the so-called ‘all forcings’ run). Changing concordance values for these simulations are also shown plotted, for overlapping 51- and 101-year periods, in c
The concordance values clearly increase steadily throughout the duration of the all forcings simulation, but the magnitude of the values is low, even by the end of the experiment. Indeed even the maximum concordance values calculated for the series 101-year windows reach only just above 0.3, barely significant, while values approaching 0.4 occur in the naturally forced experiment. These results imply either that an interpretation of strong external forcing of recent widespread high warmth over northern Eurasia, perhaps the consequence of increased atmospheric GHGs, cannot be supported or, alternatively, that this particular GCM simulation of the last 250 years is not consistent with the observational temperature and dendroclimatically implied evidence of unusual warming that has been experienced in the real world.