## 2 Materials and Methods
### Modified Temperature Vegetation Wetness Index (mTVWI)  
The mTVWI [45; 46] was defined as an indirect assessment of soil moisture related to NDVI and potential surface temperatures (0s). NDVI is one of the most extensively applied vegetation indices, closely associated to leaf area index (LAI), primary production [58], and the biochemical processes underlying primary production (photosynthetic activity). Following [PERSON] et al. (2014) [46], we used the complementary values of crown defoliation \(\Gamma\), defined as 100 minus defoliation values as a proxy of NDVI.  
\[\Gamma=100-\text{Defoliation}_{\text{plot}} \tag{1}\]  
where Defoliation\({}_{\text{plot}}\) is the mean crown defoliation value in one specific plot (in %). \(\Gamma\) was calculated for all considered plots and years. The potential surface temperature (0s) was calculated in two steps, as in [45]. The first step concerned the calculation of atmospheric pressure (\(p\), in kPa), given by:  
\[p=101.3\left[\frac{293-0.0065z}{293}\right]^{5.26} \tag{2}\]where \(z\) (in m) is the plot elevation relative to sea level. This equation is based on a simplified form of the ideal gas law for a neutrally-stratified atmosphere and a temperature of 20 \({}^{\circ}\)C at a standard atmosphere (i.e., 101.3 kPa).  
Then, surface potential temperature \(\theta\)s (in K) was calculated as:  
\[\theta\text{s}=T_{s}\left[\frac{p_{0}}{p}\right]^{R/c_{p}} \tag{3}\]  
where \(T_{S}\) is the mean annual temperature (in K), \(p_{0}\) is the average pressure at mean sea level (set at 100.0 kPa), \(R\) is the gas constant (i.e., 287 J kg\({}^{-1}\) K\({}^{-1}\)), and \(c_{p}\) is the specific heat capacity of air (\(\sim\)1004 J kg\({}^{-1}\) K\({}^{-1}\)). A scatter plot between \(\theta\)s and \(\Gamma\) was generated to derive two parameters, \(\theta_{\text{dry}}\) and \(\theta_{\text{wet}}\) (Figure 1), for each considered year. \(\theta_{\text{dry}}\) (in K) indicates low levels of water availability limiting evapotranspiration; it was calculated as the straight line passing through points A and B, where A is the point with coordinates (max \(\Gamma\); max \(\theta\)s in max \(\Gamma\)) and B is the point with coordinates (max \(\Gamma\) in the 99 th percentile of \(\theta\)s; 99 th percentile of \(\theta\)s) as depicted in Figure 1 and Figure S2.  
\(\theta_{\text{wet}}\) (in K) indicates an unlimited amount of water available to sustain evapotranspiration, and was calculated as the 1 st percentile of \(\theta\)s. To derive the percentiles we considered all analyzed species together (1623 monitoring plots) for each year.  
Finally, we calculated the mTVWI as follows:  
\[\text{mTVWI}=\frac{\theta_{dry}-\theta_{s}}{\theta_{dry}-\theta_{wet}} \tag{4}\]  
where mTVWI is a dimensionless quantity varying from 0 (the case where water is not available for evapotranspiration, \(\theta_{dry}\)) and 1 (the case where water is freely available for evapotranspiration, \(\theta_{wet}\)). Consequently, the mTVWI is an index strictly linked to forest crown defoliation (\(\theta_{dry}\)), surface potential temperature, and vapor pressure deficit (VPD) conditions [46].  
All the above parameters were calculated on an annual basis during the time period 2000-2010.