Radial Increment of Beech (Fagus sylvatica L.) Is under a Strong Impact of Climate in the Continental Biogeographical Region of Croatia

European beech (Fagus sylvatica L.) is an important component of forests in the alpine and continental biogeographical regions of Croatia. This study aimed to (1) analyze the long-term response of beech to climate, (2) identify potentially critical climatic conditions that could negatively affect the radial increment (RI) and vitality of beech, and (3) evaluate differences in the response of beech between the two biogeographical regions in Croatia. We used the 16 × 16 km Croatian ICP Forests Level 1 network. On a total of 25 plots, we cored between 5 and 24 trees for dendrochronological analysis. Tree-ring widths (TRW) were measured and standardized using cubic spline. TRW chronologies for the two regions were calculated and correlated to the temperature and precipitation data and Standardized Precipitation and Evapotranspiration Index (SPEI) using bootstrapped correlations. Continental region precipitation from April to August and alpine region precipitation from June to August were significantly important for RI. Temperature was less important for RI than precipitation in both regions, but the importance of the negative impact of above-average temperatures in the continental region and the positive impact of above-average precipitation in the alpine region has increased over the last two decades. A comparison with the 3-month SPEI confirmed the significant influence of high temperatures and the lack of precipitation in August on the RI of beech trees in both regions.