## 3 Results
### Precipitation and Temperature Relationships with Stem Diameter Growth and Cork Growth Indices  
\(\mathrm{IC_{rw}}\) was more often and stronger correlated with climate parameters than \(\mathrm{ID_{bh}}\) (Figure 3). Correlations were mostly positive with precipitation (_p_-value \(<\) 0.05) and stronger with temperature of the autumn-winter preceding the growing season (_p_-value \(<\) 0.01) (Figure 3b), while \(\mathrm{ID_{bh}}\) showed more and stronger negative correlations with the mean temperature of late spring and autumn (Figure 3a). Figure 2: Time-series (2001–2011) plots of stem diameter growth (\(\mathrm{Di_{bh}}\)) and cork-ring width (\(\mathrm{C_{rw}}\)) (on the left) and of stem diameter growth index (\(\mathrm{ID_{bh}}\)) and cork growth (or cork-ring width) index (\(\mathrm{IC_{rw}}\)) (on the right). All the sampled 47 trees are represented by the grey lines; the black curve represents the trees’ median. Noticeably, both ID\({}_{\rm{bh}}\) and IC\({}_{\rm{rw}}\) were significantly correlated (\(p\)-value \(<\) 0.01) with precipitation (positively) and with temperature (negatively) in summer (June-August) (Figure 3). For ID\({}_{\rm{bh}}\), higher correlations were found with spring-summer precipitation, highest in June-August (r = 0.32), and with spring-summer temperature, highest in June (r = \(-\)0.30). For IC\({}_{\rm{rw}}\), higher correlations were found with summer precipitation, highest in August (r = 0.34), and with summer temperature, highest in June (r = \(-\)0.22). Influence of Tree Size on the Relationship between Climate and Stem Diameter Growth and Cork-Ring Width  
Selected mixed-effects linear models (M0-M17) were plotted against the tree size random effect, given by stem diameter at breast height under cork (Dbh) (Table 1). The fixed-effect variables were climate variables which displayed the highest bootstrap correlation coefficients (highly significant, \(p\)-value \(<\) 0.01). For ID\({}_{\rm{bh}}\): precipitation of September\({}_{\_1}  
temperature of October.1 (r = 0.26), February-April (r = 0.28), June (r = \(-\)0.30) and January-December (r = \(-\)0.24); for IC\({}_{\rm{rw}}\): precipitation of September.1 (r = 0.26), February (r = 0.28), July-August (r = 0.31) and August (r = 0.34) and mean temperature of September.1-March (r = 0.35), October.1-February) (r = 0.36), November.1-February (r = 0.37), November.1-March (r = 0.37), November.1-April (r = 0.35) and February (r = 0.37). In all the models, except M4 and M7, ID\({}_{\rm{bh}}\) and IC\({}_{\rm{rw}}\) increased with monthly precipitation and monthly temperature, and \(\alpha_{1}\) was positive. In the best ID\({}_{\rm{bh}}\) model (with the lowest AIC) (M4), ID\({}_{\rm{bh}}\) decreased about 0.115 per \({}^{\circ}\)C of increase in June temperature. In the best IC\({}_{\rm{rw}}\) model (M12), the IC\({}_{\rm{rw}}\) increased about 0.120 per \({}^{\circ}\)C of monthly winter temperature prior to the growth year (November.1-February) (Table 1). Both models for ID\({}_{\rm{bh}}\), M0 and M4, respectively with June-July precipitation and June temperature as fixed effects, explained about 10% of the total variation. Random-effect variation, related with tree stem diameter (D\({}_{\rm{bh}}\) classes), was 1% of total variation. This indicates an influence of tree size on the climate-related stem diameter growth index variations. In contrast, both models for IC\({}_{\rm{rw}}\), M8 and M12, respectively with August precipitation and November.1-February temperature as fixed effects, explained 12% (in M8) and 14% (in M12) of the total variation, and no variation was explained by the random effect related to tree stem diameter, which indicates that climate-cork growth relationships were not tree size-related. In addition, ID\({}_{\rm{bh}}\) tree size-related differences were found in the random intercept and random slope (Figure 4). Smaller trees showed steeper slopes of ID\({}_{\rm{bh}}\) with summer precipitation (June-July) and with summer (June) temperature (Figure 4, D\({}_{\rm{bh}}\).1).