Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 95

selecting the best subset model within a given pool of candidate predictors, it does
not mean that the minimum AIC model among all competing models from differ-
ing candidate predictor pools will also select the model that verifies best. How one
chooses the candidate predictor pool for response functions matters, as Fekedulegn
et al. ( 2002 ) point out. This example also supports our contention that higher-order
eigenvectors may be less reliable predictors of tree growth because of increasing
orthogonality constraints on those extracted modes. But we have also found that
response functions of other tree species sampled near Mohonk Lake sometimes ver-
ified better using PVP (see below), so our case for using EV1 is certainly not closed.
More provocatively, the overall monthly structure (i.e., month-to-month evolution)
of the correlation function appears to be physiologically meaningful to these trees,
even when only 4 out of 32 variables pass the a priori 95% significance level. How
might this be?
We argue that the answer lies in the difference between how the monthly corre-
lations are treated statistically here versus how monthly climate actually affects tree
growth. The monthly correlations are tested in the correlation function as if adja-
cent months of climate are completely independent of each other. Yet, the positive
and negative correlations between tree rings and precipitation/temperature during
the prior and current growing season months (Fig. 4.3a ) almost certainly reflect the
sensitivity of our eastern hemlock chronology to overall changes in growing sea-
son moisture supply and evapotranspiration demand that may span adjacent months.
Response functions attempt to address this possible interaction between months both
within and between climate variables by exploiting the eigenstructure of the climate
correlation matrix, apparently with some success here. This effect is best revealed
by comparing the current growing season May-June-July correlations in Fig. 4.3a
with the coefficients of the response function for the same months based on the
single most important climate eigenvector in Fig. 4.4a . The response function coef-
ficients are more uniformly positive for precipitation and negative for temperature
over those growing season months. This result implies that the simple correlations
are not measuring the strength of the tree growth response to climate as fully as the
response function. The significant verification statistics of the final response func-
tion model support this conclusion (Table 4.2 ; EV1 results). Thus, the appearance
of more statistically significant response function coefficients during the growing
season months (Fig. 4.3b ) does not appear to be a statistical artifact of the method
in this example.
4.6 Response Functions and Empirical Signal Strength
As was noted earlier, our successful demonstration of the EV1 cutoff does not nec-
essarily mean that it will always perform better than the PVP cutoff. To demonstrate
this, we have calculated response functions for a total of seven tree species, all
located near Mohonk Lake and its cooperative weather station. The tree species
are eastern hemlock ( Tsuga canadensis ; TSCA), pitch pine ( Pinus rigida ; PIRI),
chestnut oak ( Quercus prinus ; QUPR), black oak ( Quercus velutina ; QUVE), pignut