Geoscience Reference
In-Depth Information
by subtraction of the values of a straight line fitted through the single composite
series. The loss of the original 1000-year trend in the resulting index series is plain.
However, what is also clear is that the higher-frequency variance represented by
the sum of the two shorter-period sine waves (dotted line in Fig. 5.1c ) has been
severely distorted at both ends of the chronology (compare the dotted and solid
lines in Fig. 5.1c ) . This distortion comes about because of the localized influence
of the medium-frequency signal variance at the beginning and end of the composite
series on the overall fit of the standardizing line. Here the first and last values of
the signal are both zero, while the first and last values of the indices are at their
minimum and maximum, respectively. Had this example extended over another 500
years (i.e., 1500 years), the aggregate signal series would have had zero slope over-
all. Standardizing with a straight line fitted through the data would not produce any
distortion of medium-frequency signal in the index series. This potential end-effect
phenomenon, or 'trend distortion,' encountered in data-adaptive approaches to curve
fitting in tree-ring standardization is discussed in more detail in Melvin and Briffa
( 2008 ) . We return to this issue in the context of RCS later.
5.3 Background and Description of Regional Curve
Standardization
The limitations in preserving evidence of long-timescale climate change in
chronologies, led to the reintroduction of what is now generally known as regional
curve standardization. This approach scales ring measurements by comparison
against an expectation of growth for the appropriate age of ring for that type of tree
in that region (Briffa et al. 1992 ) . The tree-ring measurements acquired from mul-
tiple trees in one area are aligned by ring age (years from pith), and the arithmetic
means of ring width for each ring age are calculated. The curve created from the
mean of ring width for each ring age is smoothed by using a suitable mathematical
smoothing function (Briffa et al. 1992 ; Esper et al. 2003 ; Melvin et al. 2007 ) tocre-
ate smoothly varying RCS curve values for each ring age. In a simple application of
RCS, each ring measurement is divided by the RCS curve value for the appropriate
ring age to create a tree index (note in all cases subsequently discussed here, indices
are created by division of the expected into measured values). Chronology indices
are created as the arithmetic mean of tree indices for each calendar year. The value
of the expected growth curve is, therefore, empirically derived as the average value,
for that tree-growth parameter for the specific age of ring, based on the available
sample of trees from that site or region. The reordering of the data, from calendar
to relative life span age, is intended to remove the effect of climate variability on
expected ring growth. In the reordered alignment of the data, this climate-related
variance is assumed to be distributed randomly and expected to cancel out when the
age-aligned data are averaged to form the RCS curve.
In standardization applications where the means of index series are constrained
to be equal (e.g., approximately 1.0), a chronology formed by averaging these data
is not capable of representing variance on timescales longer than the lengths of
constituent series. The means of series of tree indices are not constrained in RCS,
Search WWH ::




Custom Search