Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 100

CALIBRATION PERIOD PREDICTORS OF CLIMATE SIGNAL STRENGTH

1 1

A. REF F vs R 2 B. SNR vs R 2

0.8 0.8 y = -0.300 + 1.184x R= 0.644

y = -0.184 + 1.135x R= 0.548

y = 0.195 + 0.008x R= 0.237
y = 0.242 + 0.011x R= 0.280

0.6 0.6

R 2 R 2

0.4 0.4

0.2 0.2

PVP R 2

EV1 R 2

0 0

0.45 0.5 0.55 0.6 0.65

12 14 16 18 20 22

REFF SNR

1 1

C. ESR vs R 2 D. MS v s R 2

0.8 0.8 y = 1.261 - 1.409x R= -0.650

y = 1.421 - 1.514x R= -0.621

y = 0.283 + 0.250x R= 0.104
y = 0.342 + 0.435x R= 0.161

0.6 0.6

R 2 R 2

0.4 0.4

0.2 0.2

0 0

0.6 0.64 0.68 0.72 0.76 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26

ESR MS

Fig. 4.5 Relationships between four empirical measures of signal strength (REFF, SNR, ESR,
MS) and explained variance ( R 2 ) by response functions based on the EV1 and PVP eigenvector
cutoff criteria. The signal strength and R 2 statistics are described in the text and their values come
from Tables 4.3 and 4.4

That relationship weakens considerably when SNR is used to predict R 2 (Fig. 4.5b ) ,
probably because of the strongly nonlinear behavior of SNR. Interestingly, ESR also
correlates highly with R 2

(Fig. 4.5c ) , but in an inverse sense: r equals − 0.650 for

EV1 and 0.621 for PVP. As far as we know, ESR has never been used before as

a diagnostic of chronology signal strength since Schulman ( 1956 ) first described
it, but intuitively we would have expected positive correlations like those between
REFF and R 2 . If this inverse relationship between ESR and R 2 were to hold up, it
would suggest that loss of MS in the mean-value function is good. This is coun-
terintuitive if we accept the premise that high common MS among trees in the
chronology is a true measure of signal strength. Thus, the ESR result could be
reflecting a 'species effect' here, because MS varies considerably between the tree
species used: 0.106-0.245 (Table 4.3 ) . Interestingly, the weakest relationship of all
is between chronology MS and R 2 (Fig. 4.5d ) : r equals 0.104 for EV1 and 0.161
for PVP. Again, we could have a 'species effect' here that weakens this relationship
because of differences in how conifers and hardwoods produce secondary growth in
the form of annual tree rings. In any case, the results presented here provide limited
support for REFF as a predictor of climate sensitivity. This result supports the find-
ings of Cropper ( 1982 a ), but many more test cases must be studied to determine just
how useful it really is for that purpose.

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