A Closer Look at Regional Curve Standardization of Tree-Ring Records: Justification of the Need, aWarning of Some Pitfalls, and Suggested Improvements in Its Application - Dendroclimatology - page 118

problems with the use of RCS when he stated, ' all individuals of a species rarely

attain optimum growth at the same age, and individual trees differ in their growth
rates because of differences in soil factors, competition, microclimate, and other
factors governing the productivity of a site.'
In practice, the simple application of RCS as described above makes sweeping
assumptions about the validity of using a single, empirically derived curve to rep-
resent 'expected' radial tree growth as a function of tree age under constant climate
conditions, and that this simple curve is an appropriate benchmark for scaling mea-
sured ring widths throughout the entire time span of a chronology. It is assumed that
the mean of tree-growth deviations from this expectation, as observed in multiple
tree samples at any one time, represents the net tree-growth response to variations in
climate forcing alone. It is assumed that the form of the RCS curve is unbiased by
the presence of residual climate variability in the stacked average of cambial-age-
aligned samples, and that through time the growth of sample trees is not biased by
some factors other than climate that would lead to a misinterpretation of the RCS
chronology variability. In practice, these assumptions are unlikely to be entirely
valid. The purpose of this review is to draw attention to several examples of how
different potential sources of bias can affect RCS chronologies.

...

5.4.1 'Trend-in-Signal' Bias

The first distortion of underlying common forcing signal occurs in RCS when that
signal has variance on timescales that approach or are longer than the length of
the chronology. As a hypothetical example, let us say that the climate affecting
tree growth has a trend over 600 years (Fig. 5.2a ; actually, this series represents a
negative trend with added white noise smoothed with a 10-year spline to represent
short-timescale climate forcing superimposed on the long-term forcing trend). This
signal series can be subdivided into five 200-year-long series, each overlapping by
100 years, to represent a set of pseudo-tree-ring measurement series (Fig. 5.2b ) .
Aligning these series by ring age (Fig. 5.2c ) , averaging and smoothing, produces
the RCS curve (shown in Fig. 5.2d ) . This RCS curve displays the mean slope of all
sample series. As they all contain the underlying long-term forcing signal, the RCS
curve must do likewise. Each sample measurement series is then indexed by dividing
by the appropriate age value of the RCS curve. Each of the resulting standardized
series (Fig. 5.2e ) has no substantial overall trend (i.e., the mean series of the age-
aligned index series has zero trend).
When the index series are realigned by calendar year, each series systematically
underestimates the magnitude of the ideal forcing in its early section and overesti-
mates the signal later, a potential medium-frequency bias. In the average chronology
(Fig. 5.2f ) , the original overall signal trend is captured by the differences in the
means of the index series. In our simplified example, the bias in the trends of indi-
vidual index series cancel to some extent by virtue of the compensating biases in
overlaps between early sections of some index series and late sections of others. In