Geoscience Reference
In-Depth Information
of RCS. We provide some illustrative examples of potential bias issues that have
arisen in selected applications of RCS in previous published work. Finally, we sug-
gest some ways in which the potential problems we have highlighted might be
addressed in future work.
5.2 Frequency Limitation in Curve-Fitting Standardization
We now know that some types of tree-ring standardization are not ideal where there
is a specific requirement to compare the growth rates of trees over long periods of
time. The fitting of linear or curvilinear functions, or even more flexible forms of
low-pass filtering, to series of individual growth measurements and the subsequent
removal of variance associated with these trends, results in the inevitable loss of
longer-timescale information, even in relatively long measurement series; i.e., the
As an illustration of the loss of low-frequency variance incurred by fitting func-
signal comprising the arithmetic sum of three sine waves (with periods of 250, 500,
and 1000 years, each with an amplitude of two units, plotted with their phases syn-
chronized so the curves coincide every 500 years), achieved, in the original work,
Fig. 5.1
An example of the loss of long-timescale variance resulting from simple data-adaptive
standardization (in this case, linear detrending), based on the example of Fig. 1 in Cook et al.
(
1995
)
: (
a
) three sine waves with periods of 1000, 500, and 250 years; (
b
) the ideal 'signal' series
made as a composite of the three sine waves. A linear trend line is shown fitted through these data;
(
c
) indices generated by division of the signal series values by those of the trend line (
solid line
)
and a composite of the original 500- and 250-year sine waves (
dashed line
), showing the distortion
apparent near the ends of the 'chronology'
