## 2 Materials and Methods
### Overview
#### 2.1.2 FOREST Module
These partitioning factors are calculated as follows:  
\[\eta_{r}=\frac{0.5}{1+2.5\times f_{age}f_{Tf}\theta} \tag{17}\]  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]0  
and  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]1  
where \(p_{fs}\) is a partition function dependent on species-specific parameters:  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]2  
with \(F_{pm}\), \(F_{pm}\), \(S_{pm}\), and \(S_{pra}\) are vegetation dependent empirical parameters and \(DBH\) is the total diameter at breast height of the sum of the individual trees of species in the pixel. After the carbon allocation, the model updates the value of \(LAI\), root mass, and the size of the trees. The increment in the \(LAI\) is function of the carbon allocated to foliage and leaf turnover due water and temperature stresses. The \(LAI\) corresponds to the gross leaf production that should be updated according to the value of leaf turnover computed as follow:  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]3  
where \(\sigma LAI\) is a specific leaf area index (m\({}^{2}\)g\({}^{-1}\)) of a vegetation, \(\delta_{f}\) is a constant leaf turnover rate for a vegetation type \(p\), \(\delta_{fw}\), and \(\delta_{ft}\) are foliage loss coefficients due to hydrologic and temperature stresses and \(\Delta t\) is time step (s). The foliage loss is mainly due to the water and temperature stresses:  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]4  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]5  
where \(\delta_{fw_{(p)max}}\) and \(\delta_{fw_{(T)max}}\) are maximum leaf decay rates (s\({}^{-1}\)) due to water and temperature factors, respectively, and \(\gamma\delta w(p)\) and \(\gamma\delta T(p)\) are dimensionless shape parameters. With water stress expressed by:  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]6  
The temperature stress is expressed by:  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]7  
The roots increment is computed by:  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]8  
where \(Root\)\(root\) is the \(root\) mass (Kg m\({}^{-2}\)) and \(\delta r_{(p)}\) is the base root turnover rate (s\({}^{-1}\)). The tree height and diameter increments are  
For \(cc\leq 0.95\)  
\[f_{age}=0.7+0.3\frac{age}{0.22 ag{}_{max}} \tag{9}\]9  
else  
\[f_{age}=1+max\Bigg{[}0,\ \bigg{(}\frac{age-0.2 ag{}_{max}}{0.95 age{}_{max}} \bigg{)}^{3}\Bigg{]} \tag{10}\]0where the height increment is computed as follows:  
\[f_{age}=1+max\Bigg{[}0,\ \bigg{(}\frac{age-0.2 ag{}_{max}}{0.95 age{}_{max}} \bigg{)}^{3}\Bigg{]} \tag{10}\]1  
The tree diameter increment is calculated:  
\[f_{age}=1+max\Bigg{[}0,\ \bigg{(}\frac{age-0.2 ag{}_{max}}{0.95 age{}_{max}} \bigg{)}^{3}\Bigg{]} \tag{10}\]2  
where \(cc\) stands for the canopy cover. This parameter value ranges between 0 and 1. This parameter is computed according to crown diameter and trees density. The tree height and diameter is afterwards updated according to the previously calculated increments:  
\[f_{age}=1+max\Bigg{[}0,\ \bigg{(}\frac{age-0.2 ag{}_{max}}{0.95 age{}_{max}} \bigg{)}^{3}\Bigg{]} \tag{10}\]3  
\[f_{age}=1+max\Bigg{[}0,\ \bigg{(}\frac{age-0.2 ag{}_{max}}{0.95 age{}_{max}} \bigg{)}^{3}\Bigg{]} \tag{10}\]4  
* Total Biomass Calculation The biomass of root, stem and foliage is updated considering the initial values of these latter. The total biomass is equal to:  
\[f_{age}=1+max\Bigg{[}0,\ \bigg{(}\frac{age-0.2 ag{}_{max}}{0.95 age{}_{max}} \bigg{)}^{3}\Bigg{]} \tag{10}\]5
* Mortality In the FEST-FOREST three types of factors that induce trees mortality were considered:
* The first mortality factor is due to the self-thinning (the one included in 3 PG), which ensures that the mean single-tree stem biomass WS does not exceed the maximum permissible single-tree stem biomass WSx [kg\(\cdot\)tree\({}^{-1}\)] [41]. * The second mortality factor is age dependent mortality following the approach of LPJ-GUESS (SMITH) [42] with aging the plants become more susceptible to the wind, diseases, etc.