## 2 Materials and Methods
### Model Improvements
#### 2.3.2. Deciduous Phenology  
Similarly to [37] the phenology scheme was constrained in 3 and 5 sub-phases respectively for evergreen and deciduous species (Table 2). These phases were driven by photoperiod, thermal sum, and maximum leaf biomass (resulting from maximum attainable Leaf Area Index, LAI, m\({}^{2}\) m\({}^{-2}\)). 3D-CMCC FEM represents leaves development as a by-product of leaf biomass pool dynamics [48]. Despite being a reasonable simplification, such method leads to non-negligible excesses in growth respiration and NSC consumption during budburst. Such unrealistic demand could eventually consume all the available carbon, causing the death of the tree. For this reason, we proposed a modification of budburst phenology, to explicitly simulate the dynamic tradeoffs between demand in NSC, increase in foliar biomass, and maturation of progressively self-sufficient leaves. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Deciduous** & & **Evergreen** \\ \hline Phase & Trigger & Phase & Trigger \\ Bud Burst & GDD threshold & Bud Burst & GDD threshold \\ Leaf Development & PeakLai/2 & PeakLai & Pipe Model \\ PeakLai & Pipe Model & Leaffall & Daylength Treshold \\ Leaffall & Daylength Treshold & & \\ Unvegetative & [49] & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of the different phenological phases for deciduous and evergreen species used in 3D-CMCC PSM. We based the tradeoff function on the hypothesis that new leaf demand of NSC is higher during budburst, and gets progressively lower when maturing [50]. Idealistically, the total NSC mass (\(\mathrm{B_{R}}\)) demanded by maturing shoots and leaves could be represented by the linear differential equation (ODE):  
\[\frac{\delta B_{R}}{\delta t}-R_{NSC}(t)\cdot B_{R}(t)=\ 0 \tag{3}\]  
where \(R_{NSC}(t)\) is the instantaneous proportion of NSC demand. We assumed that C request per leaf exponentially decreases with maturity, while the total demand increases by the increasing number of leaf primordia. For simplicity, we assumed that the two components resulted in the linear reduction of \(R_{NSC}(t)\). Being a fraction, the maximum value of the integral of \(R_{5\&F\&R}(t)\) is equal to 1. Being the first vegetative day t\({}_{0}\), and the last day of budburst (\(BB_{T}\)) the last possible one to reach complete leaf development, the domain of the function was [t\({}_{0}\), \(BB_{T}\)]:  
\[1=\int_{0}^{BB_{T}}\frac{R_{NSC_{MAX}}\cdot t}{BB_{T}}\ \delta t\ \to\ R_{NSC_{MAX}}=\frac{2}{BB_{T}}\to R_{NSC}(t)=\frac{2t}{ BB_{T}}^{2}\, \tag{4}\]  
resolving the ODE, and substituting \(R_{5\&F\&R}(t)\) it gives:  
\[B_{R}(t)=\frac{B_{0}\cdot e^{\frac{2t+2}{BB_{T}}\cdot e^{-t^{2}/BB_{T}}^{2}}}{ BB_{T}}, \tag{5}\]  
where \(BB_{T}\) is the parameter used in [37], \(e^{\frac{2t+2}{BB_{T}}}\) is the biomass dependent and \(e^{\frac{-\gamma^{2}}{BB_{T}}\cdot 2}\) the maturity dependent factors (expressed in days). Graphically, the equation represents a skewed function of the amount of NSC allowed to be used by the trees of the specific class; the faster the leaves reach maturity, the more daily specific allocation is allowed (Figure 4). Another major modification we introduced involves fall leaf yellowing and senescence. Falling leaves contribute to half of annual litter production. Correctly estimating their timing has a strong impact on both GPP and Rh dynamics [32]. The 5.1 version of 3D-CMCC-FEM represents senescence  
Figure 4: Graphic representation of the C tradeoff function. The axes represent respectively bud burst days (\(BB_{T}\)), vegetative days (Veg_day), and the fraction of total NSC invested in leaf development (\(\frac{3 NSC}{\delta t}\)). The shorter \(BB_{T}\), the higher the maximum NSC fraction. by linearly decreasing leaves biomass of a predefined fraction until their pool is emptied. However, such method systematically overestimated leaf turnover at the beginning of the leaffall phase, and is poorly flexible in calculating its duration.