# Supplemental Data

Low-Frequency Signals in Long Tree-Ring Chronologies for Reconstructing Past Temperature VariabilityJan Esper, Edward R. Cook, and Fritz H. Schweingruber |

## Supplementary Material

**The difficulty in differentiating climate trends from biological trends.**

If, for example, the trees of a millennia-long chronology that existed at the beginning of the Little Ice Age (LIA), say ~800 years ago, recorded long-term decreasing temperature trends, these individual trends might be regarded as biological growth trends and eliminated once the trends were removed. In this situation, one cannot decide whether a portion of the decreasing trends (into the beginning LIA) is a climatic signal superimposed on the biological noise. That is why it can be particularly difficult to preserve the transition from the MWP into the LIA, even if the living trees from the same site are proven to be temperature sensitive. The decrease in temperature from the MWP to the LIA mimics the growth trend expected from biological aging effects.

**The difficulty of differentiating large-scale spatial averages of warm-season and annual temperatures.**

Annual (January-December) and warm-season (April-September) temperatures for the 30° to 70°N latitude Northern Hemisphere (NH) extratropics have a correlation of 0.87 over the period 1856-2000 on an inter-annual basis and 0.93 after decadal smoothing. The 10-year high-pass residuals have a correlation of 0.74. These correlations increase to 0.94, 0.97, and 0.83, respectively, when the region is expanded to 0° to 90°N. The correlations of annual and warm-season 30° to 70°N temperatures with those of the full NH (0° to 90°N) are also high. For annual temperatures, the unfiltered, 10-year low-pass, and 10-year high-pass correlations are 0.94, 0.98, and 0.84, respectively. For warm-season temperatures, they are 0.91, 0.96, and 0.79, respectively. Only on the inter-annual to decadal time scale do the two area averages differ appreciably. Because the temporal scale of variability being examined here is multi-decadal or longer, and the spatial scale is hemispheric, calibrating the tree-ring data in terms of warm-season or annual temperatures gives nearly identical results for either the full NH or the NH extratropics. These data were kindly provided by P. D. Jones and T. Osborn of the Climatic Research Unit (University of East Anglia, Norwich, UK).

**Estimating the mean biological growth curves for the RCS method.**

Regional curve standardization (RCS) requires aligning the individual tree ring series by cambial age, i.e., the innermost
ring of each series is set to a biological age of "1" if all rings are present to the pith or given a starting age >1 if a
specified number of rings are missing from the pith (the "pith offset"). Experiments have shown that the RCS method is not
very sensitive to even relatively large inaccuracies in the estimates of pith offsets (*1*). This biological age re-alignment of the ring-width series means that they are not dated by calendar years anymore. RCS
presumes that the age-aligned series describe an average behavior typical for this data set, and that this behavior reflects
the biological age-related noise. This non-climatic term can be estimated by calculating a mean value function of the cambial
age-aligned data, i.e., the regional curve (RC). Because the data being averaged are not correctly aligned by calendar year,
the mean value function averages out the misaligned, high-frequency signals due to climate and emphasizes the signal due to
biological aging. The resulting RC is then fitted with a smooth curve to remove remaining stochastic "wiggles" still present
in the average, and the smoothed RC is used to detrend all of the individual ring-width series. The ring-width departures
from the RC are then re-aligned back to their correct calendar years and averaged into a mean chronology for dendroclimatic
studies [see (*2*) for details]. A recent study (*1*) shows that RCS can be used to combine tree-ring data from different species and sites. Different species, sites, and sub-samples
(e.g., from living trees, archeological wood, and natural sub-fossil wood) may bias resulting RCS chronologies if the growth
levels and trends of these categories are not similar, i.e., the series represent varying populations. However, if similarity
in growth level and trend is proven, an unlimited number of individual series from different species and sites can be used
in the RCS procedure (*1*). 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 (*1*).

**Changing individual site contributions to the RCS chronologies.**

The temporal distribution of the nine sites from North America, Europe and Asia contributing to the nonlinear data set, and the eight sites from North America and Asia contributing to the linear data set (see Web fig. 2). Athabasca, Mangazeja, and Polar Urals are represented in both data sets because some of the trees belong to the linear and others to the nonlinear data sets. Average sample depth is higher in the nonlinear than in the linear data set, and declines in both data sets back in time. This decline indicates that the resulting chronologies are more uncertain in the early periods, particularly before the year 1200.

**Sources of the MBH data. **

The MBH temperature reconstruction was downloaded from ftp://ftp.ngdc.noaa.gov/paleo/contributions_by_author/mann1999/recons/nhem-recon.dat and the 40-year low-pass MBH series and its confidence intervals were kindly supplied by M. E. Mann.

**Estimating the bootstrap 95% confidence intervals.**

In order to avoid biases in the calculation of the combined mean value function due to different sample sizes at the different
sites, we first reduced each site data set to its own RCS mean value function. Each site RCS chronology was then weighted
by the cosine of the latitude band (centered in either 30° to 50°N or 50° to 70°N) to provide more realistic regional weighting
and smoothed with a 20-year low-pass filter to emphasize low-frequency variations that are of most interest here. Lastly,
the grand mean of the 14 site chronologies, with bootstrap confidence intervals (*2*), was calculated. The available smoothed indices were sampled with replacement 1000 times and the arithmetic means calculated.
The empirical distribution of these 1000 bootstrap means for each year serve as the basis for estimating the two-tailed 95%
confidence limits. The confidence limits include corrections for bias and skew, which provide second-order correctness (*2*).

**References**

1. J. Esper *et al.*, *Tree-Ring Res.*, in press.

2. K. R. Briffa *et al.*, *Clim. Dyn.***7**, 111 (1992)

**Supplemental Figure 1.** Arithmetic mean curves of individual ring width series from different sites after aligning by cambial age. Athabasca, Mangazeja
and Polar Urals are represented in both data sets, because some of the series from these sites belong to the linear and others
to the nonlinear data set.

Medium version | Full size version

**Supplemental Figure 2.** Sites and sample depths of the linear and nonlinear data sets. (Ath, Athabasca; Bor, Boreal; Mac, Mackenzie; Que, Quebec;
Upp, Upperwright; Got, Gotland; Jae, Jaemtland; Tir, Tirol; Tor, Tornetraesk; Man, Mangazeja; Mon, Mongolia; Pol, Polar Urals;
Tai, Taimir; Zha, Zhaschiviersk). See the map for the exact site locations (main text, Fig. 1).