## 2 Materials and Methods
### Overview
#### 2.1.2 FOREST Module  
The module was inspired by several existing eco-hydroological models and extensive research into the existing literature of the used equations to simulate vegetation growth and dynamic processes. Figure 2 displays main processes integrated in this model to simulate the forest growth. The model was developed using the FORTRAN 90 programming language. This was later developed considering one species per cell only and all the trees within each cell having the same characteristics. This choice was taken in order to simplify the process simulations and reduce the required inputs (considering also that for the area where this model will be used, 90% of the forest is covered with the same species). Figure 1: Scheme of the primary features common to the FEST-WB distributed-hydrological model. * Light Interception  
The amount of light available for the plant is going to define its growth rate and, together with other factors that may limit the plant growth, will be later taken into consideration. The light the plant could absorb is determined according to canopy cover. The amount of absorbed photosynthetically active radiation (_APAR_) is defined following the Lambert-Beer law [35], where:  
\[APAR=PAR\times\left(1-exp^{-K_{x}LAI}\right) \tag{1}\]  
where _PAR_ is the photosynthetically active radiation. _Kx_ is the extinction coefficient for absorption of _PAR_ by canopy, and varies between (0-1). This parameter is specific to each plant species, depending on the foliage transmissivity and leaves inclination; the _LAI_ corresponds to the leaf area index (m\({}^{2}\) m\({}^{-2}\)). The PAR can be calculated using the following formula:  
\[PAR=(1-\alpha)\times Hday \tag{2}\]  
where _Hday_ is the short-wave solar radiation and \(\alpha\) is the albedo. According to several studies, the short-wave solar radiation can be calculated as 50% of the _APAR_. These calculations are based on the assumption that the foliage is uniformly distributed. The radiation that was not intercepted by any of the vegetation crowns is going to reach the ground. * GPP and NPP Calculation  
The amount of carbon is defined through the intercepted radiation by the canopy (previously computed). Carbon assimilation is constrained by several factors such as temperature, water content, vapor pressure deficit. These factors are called modifiers. For each class the _GPP_ is calculated by the absorbed radiation and \(\varepsilon\) (gDM MJ\({}^{-1}\)) the potential radiation use efficiency or maximum quantum  
Figure 2: Flowchart of the vegetation growth functioning within the FOREST module. canopy efficiency (\(\alpha\) umol CO\({}_{2}\) umol\({}^{-1}\) PAR). The \(GPP\) for each class is calculated according to the following formula:  
\[GPP_{x}=\epsilon_{x}\times APAR_{x}\times Modifiers_{x} \tag{3}\]  
The \(GPP\) (g cm\({}^{-2}\) month\({}^{-1}\)) is calculated for each cohort. The maximum quantum canopy efficiency is species specific. \(GPP\) should be adjusted to net primary production \(NPP\) (g cm\({}^{-2}\) month\({}^{-1}\)) through a constant conversion factor \(C_{NPP}\):  
\[NPP=GPP\times C_{NPP} \tag{4}\]  
[PERSON] and [PERSON] [13] found that \(C_{NPP}\) value for wide range of forests is about 0.47 \(\pm\) 0.04. * Modifiers Calculation Increased availability of detailed forest inventory data supported the development of complex systems of differential or difference equations that simultaneously modeled change in individual components of stand growth [36; 37], including ingrowth, growth of surviving trees, mortality, and harvest. Several factors may affect the carbon allocation in forest ecosystem. This later is subject to the effect of vapor pressure deficit, soil water deficit, temperature (or frost) and the age of the trees. 1. Soil water modifier The soil water modifier (\(f_{\text{swc}\Theta}\)) implemented within the FEST-FOREST model is calculated according to the formula proposed by [PERSON] et al. [38].