*2.4. Cross-Dating*

Cross-dating is a technique used to date tree rings [23] by testing the synchronization between the individual ring-width time series. In order to verify the synchronization using statistical models, *t*-value [24] and G-value [25] in the TSAP-Win program (Rinntch, Germany) were applied. The *t*-value (Equation (1)) was developed based on the number of overlapped years between the individual ring-width time series and their correlation coefficient, while the G-value (Equation (2)) was based on the year-to-year agreement between them.

$$t = \frac{r \times \sqrt{p - 2}}{\sqrt{(1 - r^2)}}\tag{1}$$

where *r* is the correlation coefficient between the individual ring-width time series and *n* is the number of overlapped years. ݊ ݎ

$$G\_{(\mathbf{x},y)} = \frac{1}{n-1} \sum\_{i=1}^{n-1} \left[ \mathbf{G}\_{i\mathbf{\bar{x}}} + \mathbf{G}\_{i\mathbf{\bar{y}}} \right] \tag{2}$$

If (*xi*+<sup>1</sup> − *x<sup>i</sup>* ) > 0, *Gix* = +1/2, (*yi*+<sup>1</sup> − *y<sup>i</sup>* ) > 0, *Giy* = +1/2, (*xi*+<sup>1</sup> − *x<sup>i</sup>* ) = 0, *Gix* = 0, (*yi*+<sup>1</sup> − *y<sup>i</sup>* ) = 0, *Giy* = 0, (*xi*+<sup>1</sup> − *x<sup>i</sup>* ) < 0, *Gix* = –1/2, (*yi*+<sup>1</sup> − *y<sup>i</sup>* ) < 0, *Giy* = –1/2 ௬ܩ ݕ െ ାଵݕ ௫ܩ ݔ െ ାଵݔ ௬ܩ ݕ െ ାଵݕ ௫ܩ ݔ െ ାଵݔ ௬ܩ ݕ െ ାଵݕ ௫ܩ ݔ െ ାଵݔ

where *G*(*x*,*y*) is the G-value and *x<sup>i</sup>* and *y<sup>i</sup>* are the measurement ring-width values for the *i th* year. ݕ ݔ ௬ሻ,ሺ௫ܩ ݅ ௧

ୀଵ

The cross-dating was considered successful when the *t*- and/or G-values were higher than 3.5 and 65%, respectively; however, the final decision was made by synchronization between the time series through human eyes.

The local master chronologies to date the resin collection were developed using the increment cores from the opposite sides of the resin collection. The year of resin collection was assigned based on the *t*- and G-values between the individual ring-width time series and the corresponding local master chronologies.
