90
Chapter 5: Interpreting High-Resolution Proxy Climate Data
mation of the selected PC-regression equations (e.g. Blasing, 1978). For a
comprehensive review of the spatial reconstruction problem, see Cook et al.
(1994).
In common with one-dimensional variable reconstruction, there is the potential for severe over-calibration of the two-dimensional transfer function.
Diagnostic statistics calculated using the calibration data, when based on
multiple predictors, invariably overestimate the true predictive power of the
calibrated equations. This is true also for measures of the goodness of fit
between actual and estimated data that take account of the effective degrees
of freedom (Cramer, 1987; HelIand, 1987) even assuming that these can be
defined properly (as discussed above). In dendroclimatology, experience has
shown that a much more realistic idea of the likely predictive power of the
calibrated regression is provided by model verification (Figure 5.4).
5.6.2 Verification of Calibrated Relationships
Verification is the testing of the validity or effectiveness of the calibrated
equation by comparing the regression estimates of the predictand data outside of the period used to fit the equation(s). Observational data (tree-ring
data where the response function is being verified, and climate data in the
case of the transfer function) are withheld from the calibration especialIy
for this purpose. A number of statistics are commonly employed to quantify
verification performance. General reviews can be found in Fritts (1976); Gordon (1982); Fritts et al. (1990) and Cook et al. (1994). They range from a
simple non-parametric test of very high-frequency association, through to a
true measure of the variance in common between the estimated and observed
data. The power of these tests, however, is proportional to the length of verification period. Where observed (instrumental) climate series are relatively
long (say 100 years), cross calibration/verification can be used on separate
halves of the data alternately and a reasonable impression is gained of the
fidelity with which interannual and decadal timescale variability is captured.
In situations where climate data for only 40-60 years are available, either
very short verification periods are used or sub-sam pIe techniques (e.g. the
jackknife - see Gordon, 1982) are employed. In both cases, the verification is
strictly limited to testing the highest frequency (i.e. interannual) performance
of the calibration model(s) and the stability of the form of the model.
A powerful procedure for testing model stability is to compare the alternative reconstructions themselves (i.e. early estimates derived separately from
equations fitted on each half of the observational data). Any serious differences in the alternative reconstructions would cast doubt on the veracity of
one or both models (e.g. Briffa et al., 1992b).
It is important to remember that even where verification is performed
using independent observational data, parametric statistics assurne normality
in the predictand and estimated data and sub se quent assumptions on the
likely predictive performance of the regression model are still strictly valid
Chapter 5: Interpreting High-Resolution Proxy Climate Data
mation of the selected PC-regression equations (e.g. Blasing, 1978). For a
comprehensive review of the spatial reconstruction problem, see Cook et al.
(1994).
In common with one-dimensional variable reconstruction, there is the potential for severe over-calibration of the two-dimensional transfer function.
Diagnostic statistics calculated using the calibration data, when based on
multiple predictors, invariably overestimate the true predictive power of the
calibrated equations. This is true also for measures of the goodness of fit
between actual and estimated data that take account of the effective degrees
of freedom (Cramer, 1987; HelIand, 1987) even assuming that these can be
defined properly (as discussed above). In dendroclimatology, experience has
shown that a much more realistic idea of the likely predictive power of the
calibrated regression is provided by model verification (Figure 5.4).
5.6.2 Verification of Calibrated Relationships
Verification is the testing of the validity or effectiveness of the calibrated
equation by comparing the regression estimates of the predictand data outside of the period used to fit the equation(s). Observational data (tree-ring
data where the response function is being verified, and climate data in the
case of the transfer function) are withheld from the calibration especialIy
for this purpose. A number of statistics are commonly employed to quantify
verification performance. General reviews can be found in Fritts (1976); Gordon (1982); Fritts et al. (1990) and Cook et al. (1994). They range from a
simple non-parametric test of very high-frequency association, through to a
true measure of the variance in common between the estimated and observed
data. The power of these tests, however, is proportional to the length of verification period. Where observed (instrumental) climate series are relatively
long (say 100 years), cross calibration/verification can be used on separate
halves of the data alternately and a reasonable impression is gained of the
fidelity with which interannual and decadal timescale variability is captured.
In situations where climate data for only 40-60 years are available, either
very short verification periods are used or sub-sam pIe techniques (e.g. the
jackknife - see Gordon, 1982) are employed. In both cases, the verification is
strictly limited to testing the highest frequency (i.e. interannual) performance
of the calibration model(s) and the stability of the form of the model.
A powerful procedure for testing model stability is to compare the alternative reconstructions themselves (i.e. early estimates derived separately from
equations fitted on each half of the observational data). Any serious differences in the alternative reconstructions would cast doubt on the veracity of
one or both models (e.g. Briffa et al., 1992b).
It is important to remember that even where verification is performed
using independent observational data, parametric statistics assurne normality
in the predictand and estimated data and sub se quent assumptions on the
likely predictive performance of the regression model are still strictly valid