Section 5.6: Quantifying Climate Signals
87
relationship between the tree-ring chronology and the climate data of interest.
This is achieved empirically by the use of regression analyses. For general
references that review various techniques used in dendroclimatology see for
example: Fritts (1976, 1991); Guiot (1990); Cook et al. (1994).
Most analyses use series of monthly mean climate parameters, principally
because of their relevance to climatologists and their general availability.
However, this must always be a compromise as trees do not respond directly
to such crude variables. Rather they integrate much more subtle changes in
many micro-environmental factors such as available soil moisture, radiation,
humidity etc., all of which vary over very short timescales (as short as minutes and even seconds). These variations are only indirectly represented by
available meteorological data.
.
Linear equations are used even though they may not be entirely appropriate
for modelling the full range of tree-growthj climate relationships. This further
compromise is necessary because non-linear expressions could not be inverted
to give unique estimates of past climate. Acutely aware of these facts and
of the pitfalls that await the unwary user of regression analysis (Draper and
Smith, 1981; Rencher and Pun, 1980), dendroclimatologists employ a rigorous
approach involving the validation or "verification" of fitted or "calibrated"
regressions.
5.6.1 Calibration of Theoretical Signal
Calibration in this context may involve deriving an equation which expresses
variability in some tree-growth parameter as function of an ensemble of climate variables (e.g., monthly mean temperatures and precipitation totals).
This is the so-called response function: a set of regression coeflicients whose
signs and magnitudes suggest the pattern of climate influence on growth (Figure 5.2). Discussions of the use of response functions may be found in Fritts
et al. (1971); Fritts (1976); Guiot et al. (1982); Blasing et al. (1984); Briffa
and Cook (1990) and Serre-Bachet and Tessier (1990). Response function
analyses are often used to identify the climate variable or season over which
this variable may be averaged to produce an optimum "season" for reconstruction. The equation which expresses this variable as a function of tree
growth (at one or more sites) is the "transfer function": a set of regression
weights which, when multiplied by past tree growth data, provide estimates
of past climate (Fritts et al., 1971; Blasing, 1978; Lofgren and Hunt, 1982).
A range of regression techniques is employed: from simple linear regression,
through multiple regression with a single predictand up to the most complex
spatial problem where multiple predictands are estimated using multiple predictors.
The use of multiple regression is most often the norm in dendroclimatology and the danger of artificial predictability in calibrated regressions is very
real. Even when using tree-ring data from a single si te to estimate a single
climate variable, simple regression may not be appropriate. This is because
87
relationship between the tree-ring chronology and the climate data of interest.
This is achieved empirically by the use of regression analyses. For general
references that review various techniques used in dendroclimatology see for
example: Fritts (1976, 1991); Guiot (1990); Cook et al. (1994).
Most analyses use series of monthly mean climate parameters, principally
because of their relevance to climatologists and their general availability.
However, this must always be a compromise as trees do not respond directly
to such crude variables. Rather they integrate much more subtle changes in
many micro-environmental factors such as available soil moisture, radiation,
humidity etc., all of which vary over very short timescales (as short as minutes and even seconds). These variations are only indirectly represented by
available meteorological data.
.
Linear equations are used even though they may not be entirely appropriate
for modelling the full range of tree-growthj climate relationships. This further
compromise is necessary because non-linear expressions could not be inverted
to give unique estimates of past climate. Acutely aware of these facts and
of the pitfalls that await the unwary user of regression analysis (Draper and
Smith, 1981; Rencher and Pun, 1980), dendroclimatologists employ a rigorous
approach involving the validation or "verification" of fitted or "calibrated"
regressions.
5.6.1 Calibration of Theoretical Signal
Calibration in this context may involve deriving an equation which expresses
variability in some tree-growth parameter as function of an ensemble of climate variables (e.g., monthly mean temperatures and precipitation totals).
This is the so-called response function: a set of regression coeflicients whose
signs and magnitudes suggest the pattern of climate influence on growth (Figure 5.2). Discussions of the use of response functions may be found in Fritts
et al. (1971); Fritts (1976); Guiot et al. (1982); Blasing et al. (1984); Briffa
and Cook (1990) and Serre-Bachet and Tessier (1990). Response function
analyses are often used to identify the climate variable or season over which
this variable may be averaged to produce an optimum "season" for reconstruction. The equation which expresses this variable as a function of tree
growth (at one or more sites) is the "transfer function": a set of regression
weights which, when multiplied by past tree growth data, provide estimates
of past climate (Fritts et al., 1971; Blasing, 1978; Lofgren and Hunt, 1982).
A range of regression techniques is employed: from simple linear regression,
through multiple regression with a single predictand up to the most complex
spatial problem where multiple predictands are estimated using multiple predictors.
The use of multiple regression is most often the norm in dendroclimatology and the danger of artificial predictability in calibrated regressions is very
real. Even when using tree-ring data from a single si te to estimate a single
climate variable, simple regression may not be appropriate. This is because