Section 5.5: "Standardization"
85
data" average chronologies contain significant bias resulting from coincidence
in the temporal distribution of equal-age sam pies , particularly the concentration of young trees forming the early sections.
Many standardization techniques have been developed to "detrend" raw
tree-ring series during chronology construction. It is not possible to give
even abrief description of the mathematical details of these here, but a good
review is given in Cook et al. (1990a). All the methods model the unwanted
(generally low-frequency) variance in the raw measurement series (using some
deterministic equation or data dependent filter) and transform the data to a
series of indices by taking either the difference (or quotients) of actual minus
(divided by) modelIed estimate for each year. The standardized tree-growth
indices are generally stationary and have generally constant variance, both
of which are desirable characteristics if data are to be averaged to form a
mean chronology. (In practice, other more robust techniques are also used
to form the mean value function and to standardize chronology variance; see
Cook et al. , 1990b; Shiyatov et al. , 1990.) The essential implication of all
of these techniques, however, is that they modify the spectral characteristics
of the tree-ring indices, imposing a low-frequency limit on the variabilityexpressed. The degree to which long-timescale variability is therefore removed
from all sampie series and from the mean chronology constructed from them
(and necessarily from any subsequent climate reconstruction made using this
chronology) is dependent on the lengths of the sampie series and the particular standardization technique employed (e.g. Briffa et al. , 1987; Cook and
Briffa, 1990).
Different methods are used for different purposes. Where the only concern is to crossdate different series (by assessing the statistical significance
of correlations calculated between series at many overlap positions), it is desirable to remove all relatively low-frequency variance in the series, perhaps
that corresponding to variability on timescales longer than a few decades.
This generally increases (even optimises) RBAR in the resulting indices and
increases the power of the comparison tests by eliminating chance, spuriously high, correlations (Le. those based on coincident trend) that would
suggest an incorrect match between two series (Munro, 1984; Wigleyet al.,
1987). Having dated the series, the original measurement data might, however, be standardized using a technique designed to maintain much longer
timescale variations in the final chronology, so preserving the potential for
reconstructing decadal-to-century timescale variations in some other signal,
such as temperature. This might then lead to a lower RBAR (and EPS) in
the chronology.
In constructing chronologies for dendroclimatic reconstruction work, there
is often a trade-off between loss of generally low-frequency variance which
might represent the theoretical signal and an increase in chronology confidence. If the required theoretical signal involves long-timescale variability, a very conservative approach must be adopted when standardizing, but
85
data" average chronologies contain significant bias resulting from coincidence
in the temporal distribution of equal-age sam pies , particularly the concentration of young trees forming the early sections.
Many standardization techniques have been developed to "detrend" raw
tree-ring series during chronology construction. It is not possible to give
even abrief description of the mathematical details of these here, but a good
review is given in Cook et al. (1990a). All the methods model the unwanted
(generally low-frequency) variance in the raw measurement series (using some
deterministic equation or data dependent filter) and transform the data to a
series of indices by taking either the difference (or quotients) of actual minus
(divided by) modelIed estimate for each year. The standardized tree-growth
indices are generally stationary and have generally constant variance, both
of which are desirable characteristics if data are to be averaged to form a
mean chronology. (In practice, other more robust techniques are also used
to form the mean value function and to standardize chronology variance; see
Cook et al. , 1990b; Shiyatov et al. , 1990.) The essential implication of all
of these techniques, however, is that they modify the spectral characteristics
of the tree-ring indices, imposing a low-frequency limit on the variabilityexpressed. The degree to which long-timescale variability is therefore removed
from all sampie series and from the mean chronology constructed from them
(and necessarily from any subsequent climate reconstruction made using this
chronology) is dependent on the lengths of the sampie series and the particular standardization technique employed (e.g. Briffa et al. , 1987; Cook and
Briffa, 1990).
Different methods are used for different purposes. Where the only concern is to crossdate different series (by assessing the statistical significance
of correlations calculated between series at many overlap positions), it is desirable to remove all relatively low-frequency variance in the series, perhaps
that corresponding to variability on timescales longer than a few decades.
This generally increases (even optimises) RBAR in the resulting indices and
increases the power of the comparison tests by eliminating chance, spuriously high, correlations (Le. those based on coincident trend) that would
suggest an incorrect match between two series (Munro, 1984; Wigleyet al.,
1987). Having dated the series, the original measurement data might, however, be standardized using a technique designed to maintain much longer
timescale variations in the final chronology, so preserving the potential for
reconstructing decadal-to-century timescale variations in some other signal,
such as temperature. This might then lead to a lower RBAR (and EPS) in
the chronology.
In constructing chronologies for dendroclimatic reconstruction work, there
is often a trade-off between loss of generally low-frequency variance which
might represent the theoretical signal and an increase in chronology confidence. If the required theoretical signal involves long-timescale variability, a very conservative approach must be adopted when standardizing, but