## 4 Methodology  
### Application of C-Fix to Present Environmental Conditions  
C-Fix is a Monteith type parametric model driven by temperature, radiation and the fraction of absorbed photosynthetically active radiation (_fAPAR_), quantified through its generalized relationship \begin{table}
\begin{tabular}{l c c c c c} \hline
**Index** & **Forest type** & \begin{tabular}{c} **BIOME-BGC** \\ **type** \\ \end{tabular} & \begin{tabular}{c} **Area** \\ **(km\({}^{2}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Mean altitude** \\ **(Low/High** \\ **altitudinal belt)** \\ \end{tabular} &
\begin{tabular}{c} **Mean annual** \\ **C-Fix GPP** \\ **(g C/m\({}^{2}\)/y)** \\ \end{tabular} \\ \hline FT 1 & White fir / & Evergreen & 7,742 & 1,424 m asl.(H) & 997 \\  & Norway spruce & needleleaf & & & \\ FT 2 & Chestnut & Deciduous & 8,437 & 691 m asl.(L) & 1,442 \\  & & broadleaf & & & \\ FT 4 & Beech & Deciduous & 11,602 & 1,256 m asl.(H) & 1,141 \\  & & broadleaf & & & \\ FT 7 & Holm oak & Evergreen & 7,025 & 516 m asl.(L) & 1,489 \\  & & broadleaf & & & \\ FT 8 & Deciduous oaks & Deciduous & 21,347 & 651 m asl.(L) & 1,444 \\  & & broadleaf & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Main characteristics of the forest types examined. The annual average GPP refers to the 10-year study period used as baseline (1999–2008). Figure 1: Spatial distribution of the five forest types considered in Italy. with the normalized difference vegetation index (NDVI) [20, 21]. C-Fix combines satellite-derived fAPAR with field based estimates of incoming solar radiation and air temperature, which are jointly used to simulate total photosynthesis. C-Fix is therefore conceptually simple and generally applicable, and can use inputs averaged over different time periods (most commonly ten-day to monthly). In particular, the monthly GPP (g C m\({}^{-2}\) month\({}^{-1}\)) of a forest can be computed as:  
\[GPP=\varepsilon\sum_{i=1}^{N}T_{cor.i}\textit{fAPAR}_{i}CO_{2}\textit{fertRad} _{i} \tag{1}\]  
where \(\varepsilon\) is the radiation use efficiency, \(N\) is the number of periods considered, \(T_{cori}\) is a factor accounting for the dependence of photosynthesis on air temperature \(T_{i}\), _fAPAR\({}_{i}\)_ is the fraction of absorbed PAR, _CO2 fert_ is the normalised CO\({}_{2}\) fertilisation factor, and \(Rad_{i}\) is the solar incident PAR, all referred to month \(i\). fAPAR can be derived from the top of canopy NDVI according to the linear equation proposed by [PERSON] and [PERSON], [22]. The normalized CO\({}_{2}\) fertilization factor (_CO2 fert_) is computed as [20]:  
\[CO_{2}\textit{fert}=\frac{[CO_{2}]-[O_{2}]/2\textit{s}\ast\textit{k}_{=}(1+[ O2]/\textit{k}_{o})+[CO_{2}]^{\textit{ref}}}{[CO_{2}]^{\textit{ref}}-[O_{2}]/2 \textit{s}\ast\textit{k}_{\text{m}}(1+[O_{2}]/\textit{k}_{0})+[CO_{2}]} \tag{2}\]  
where K\({}_{\text{m}}\) is the affinity constant for CO\({}_{2}\) of Rubisco (%CO\({}_{2}\)), K\({}_{0}\) is the inhibition constant for O\({}_{2}\) [%O\({}_{2}\)] and [CO\({}_{2}\)] and [O\({}_{2}\)] are the CO\({}_{2}\) and O\({}_{2}\) concentration in the mesophyll tissue of leaves, respectively. The original C-Fix does not include a specific index which accounts for the possible short-term effect of water stress on photosynthesis, as is done by other Monteith type models [e.g., 5, 23]. The need to apply C-Fix also in Mediterranean environments, that are characterized by a long summer dry season during which vegetation growth is limited by water availability [24], induced [PERSON] _et al._[25] to include such an additional water stress index. This modification is currently accompanied by the use of the MODIS temperature correction factors and radiation use efficiency [26] in place of the original coefficients proposed by [PERSON] _et al._[20]. A justification of all these choices is provided in [PERSON] _et al._[27]. Modified C-Fix was applied to simulate monthly GPP values of Italian forests for the present study period (1999-2008) following the multistep methodology which is fully described in [25].