## 2 Decision Support System
### The Simulation Tool
#### 2.4.2 The Background Models  
At the core of the Simulation tool is the forest growth simulator. There are two main modelling families to describe the evolution of a forest stand: on the one hand, empirical models, based on statistical methods applied to observed data [30; 31; 32], and on the other hand, process-based models, based on explicit processes and interactions in forest ecosystems [33; 34]. The Simulation tool behind Multisilva is a process-based forest growth model that can represent mixed and uneven-aged forests [35; 36]. In this regard, process-based models explicit represent processes and interactions in forest ecosystems such as the carbon, water, and nutrient cycles and can capture the effects of changing climatic conditions. These processes are strictly linked with the provision of ESs, and consequently, a process-based approach was selected for the Simulation tool calculations. Considering the targeted spatial scale of the tool (forest estate level), stand-level models were preferred to tree-level models [37] in order to maintain a fast computing time and keep the model parameter set at a reasonable size. We leveraged the literature review conducted by [PERSON] et al. [36] of the existing forest growth models to identify the forest model best suited to develop the decision support system. From the list of 54 forest growth models, the 3-PGmix model [34] was selected for the following reasons: (i) it was process-based, hence capable of simulating \begin{table}
\begin{tabular}{l c l l} \hline \hline
**Ecosystem Service Indicators** & **Unit** & **Economic Values** & **Unit** \\ \hline Total extracted timber & m\({}^{3}\) & Timber revenues & EUR \\ Variation in standing volume & m\({}^{3}\)/ha & Harvesting costs & EUR \\ Air pollution deposition & t of PM\({}_{10}\) & Planting costs & EUR \\ Water purification & t of N & Young stand cleaning costs & EUR \\ Total carbon sequestered & t of CO\({}_{2}\)-eq & \begin{tabular}{l} Recreational-service-related \\ costs \\ \end{tabular} & EUR \\ Recreation (average WTT over & & \\ the simulation) & km & Set aside opportunity costs & EUR \\ Recreation (final WTT) & km & Habitat tree opportunity costs & EUR \\ Average relative true diversity & Eq. number of species & \\ Relative true diversity (min & Eq. number of species & \\ and max, final period) & \
\begin{tabular}{l} La \\ \end{tabular} & \\ Area set aside &
\begin{tabular}{l} ha \\ \end{tabular} & \\ Average number of habitat trees per hectare & Habitat trees/ha & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Indicators and economic parameters included in Multisilva. variations in forest dynamics due to management or changing climatic conditions; (ii) it was able to represent mixed-tree-species iterations; and (iii) it was equipped to describe essential processes related to radiation, water, phenology, and nutrient dynamics, which are critical for developing ecosystem service indicators. Although other models like BALANCE [38], 4C [39], and ANAFORE [40] met these criteria, 3-PGmix was preferred due to its larger number of species with pre-calibrated parameters and its lower requirement for detailed input data. This choice came at the expense of individual tree modelling; however, the cohort-level structure made it computationally efficient while retaining the capacity to model essential interspecies interactions. The 3-PGmix model derives from the 3-PG model developed by [PERSON] and [PERSON] [41], and since then, it has been validated for many species and regions around the world. The 3-PGmix model has a monthly time step and consists of five sub-models in a causal chain. These are described in detail by [PERSON] et al. [42], and only an overview is given here. The first sub-model predicts light absorption [43] and from that estimates gross primary production (GPP) with corrections imposed by temperature, frost, vapour pressure deficit (VPD), soil moisture, soil fertility, atmospheric CO\({}_{2}\), and stand age. Net primary production (NPP) is then calculated assuming NPP/GPP = 0.47 [44].