Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 96

hickory ( Carya glabra ; CAGL), tulip poplar ( Liriodendron tulipifera ; LITU), and
black birch ( Betula lenta ; BELE). This selection covers a diverse range of conifer
and deciduous hardwood tree genera and subgenera. The tree-ring chronologies are
based on crossdated ring width series from 6 to 14 trees/12-20 cores per species
(Table 4.3 ) . In addition, 6-10 paired cores per tree were included to allow for
the calculation of within-tree correlations. The total sample size per chronology is
admittedly somewhat modest (especially for PIRI), but the selected samples allowed
for a consistent assessment of chronology signal strength over the same 1931-1996
period used for climate calibration. This enabled us to directly compare the empir-
ical signal strength statistics with the response function results. For comparative
purposes, all ring width series were also standardized with fixed 50-year smooth-
ing splines (Cook and Peters 1981 ) . In addition, the response functions and signal
strength statistics were calculated from the tree-ring chronologies after removal
of autocorrelation based on best-fit, low-order autoregressive models (the residual
chronology from programARSTAN; Cook 1985 ) . Doing so eliminated different lev-
els of autocorrelation in the original chronologies that might obscure the interspecies
comparisons presented here.
Table 4.3 provides a suite of 10 descriptive statistics for each tree-ring chronol-
ogy. MS is mean sensitivity; SD is standard deviation; R1 is first-order autocor-
relation; ESR is Edmund Schulman's R ; RTOT is the average correlation between
all series, including within-tree replicate cores; RWT is the average correlation of
the within-tree replicate cores; RBT is the average correlation of only the between-
tree cores; REFF is a weighted average correlation based on RWT and RBT; EPS
is the expressed population signal; and SNR is the signal-to-noise ratio. Refer to
our earlier discussion of these statistics and also Briffa and Jones ( 1990 ) . Explicit
mathematical definitions of these statistics are also included in an Appendix of this
chapter for those who are unfamiliar with them.
MS, SD, R1, and the correlation-based signal strength statistics for our tree
species all fall in the typical range occupied by tree-ring data from eastern North
America (ENA) (cf. Fritts and Shatz 1975 ; DeWitt and Ames 1978 ) . For exam-
ple, our average MS is 0.166, which compares well with 0.175 for ENA tree-ring
chronologies in DeWitt and Ames ( 1978 , their Table II, p. 10). In contrast, aver-
age MS for western North America chronologies is 0.365 in DeWitt and Ames
( 1978 ) and 0.390 in Fritts and Shatz ( 1975 ) . Estimates of common signal strength
for ENA chronologies (mean %Y 0.289) in DeWitt and Ames ( 1978 ) are much

lower than those presented here (mean RBT

=

0.527), but this
is an unfair comparison. Both %Y and the RBAR-based signal strength statistics
(RBT, RWT, REFF) are highly sensitive to how the tree-ring data have been pro-
cessed. Estimating signal strength from prewhitened tree-ring data, as was done
here, will in general increase those statistics. The method of detrending will also
have an effect. In contrast, MS is relatively insensitive to how the tree-ring data are
processed; e.g., MS of standardized (detrended) tree-ring indices is the same as that
of the original ring width measurements. The MS statistics in Table 4.3 also show
the danger in using this statistic as a direct measure of climate sensitivity. All of
our tree species have been subjected to the same macroclimatic effects and most are

= 0.460 and REFF =