## 2 Decision Support System
### The Simulation Tool
#### 2.4.2 The Background Models
In the second sub-model, the NPP is distributed to foliage, stems, and roots. The third sub-model calculates density-dependent mortality using the \(-3/2\) self-thinning law to adjust the number of trees per hectare [45; 46; 47]. The water balance is calculated in the fourth sub-model, using a species-specific canopy conductance, leaf area index (LAI), and any limitations caused by VPD, soil moisture, atmospheric CO\({}_{2}\), and stand age. The fifth and final sub-model converts biomass into output variables such as tree diameter, height, basal area, and wood volume. Additionally, 3-PGmix requires the relationships governing species-mixing proportions to be provided [34]. For example, species contributions to the total stand LAI are necessary to calculate canopy interception and canopy conductance. In particular, the differentiation between deciduous and coniferous species is critical, with two parameters defining the month when leaves are produced and the month when they are lost required for deciduous trees. The original, freely available 3-PGmix model was implemented in Python and adapted to meet the specifications of the Simulation tool. The resulting model was called \"3-PGmix--Multisilva\". The novelties of the 3-PGmix--Multisilva are as follows:  
1. Management actions to improve specific ESs and modelled to represent the current practice in Luxembourgish forestry were added. Specifically: * Thinning and harvesting functions; * Stand regeneration management actions; * Management actions to promote biodiversity; * Management actions to promote forest recreation. * The forest growth model was enriched by five ES modules linking the variables from the process-based growth model and the management model with dynamic ES provision models from the literature: * Carbon storage, computing the below- and above-ground carbon stored in the biomass as well as the soil organic carbon [48]; * The air purification module, computing the tons of PM\({}_{10}\) intercepted by the canopy [49; 50]; * The water quality module, computing the tons of nitrates sequestered from or released into the soil by the forest [51]; * The forest recreation module, computing the attractiveness of the forest measured as a WTT to visit the forest [52] combined with a distance-dependent, decreasing logistic function to account for the accessibility of the forest stands;* The biodiversity module, computing three biodiversity indexes [53]: the Shannon Index based on tree species richness, the tree size diversity index at the stand level, and the habitat tree index. * A regeneration module was added to predict the regeneration success, via a generalised ordered logit model fitted to the inventory data of Luxembourgish forests. * An economic module to compute revenues, costs, and opportunity costs over the simulation. * An automatised model initialisation system. Leveraging the recent availability of species-specific parameters for European tree species [54], the tool can simulate the growth dynamics of the following species: European beech (_Fagus sylvatica_), sessile oak (_Quercus petraea_), pedunculate oak (_Quercus robur_), European ash (_Fraxinus excelsior_), sarcomore maple (_Acer pseudoplatanus_), birch (_Betula_ spp. ), Scots pine (_Pinus sylvestris_), Norway spruce (_Picea abies_), Douglas fir (_Pseudoltsuga menziesii_), European larch (_Larix decidua_), European silver fir (_Abies alba_), and Swiss pine (_Pinus embra_). These species represent most of the standing volume in Luxembourg [55]. The remaining species are assigned into one of the following species groups:  
* \"Noble broadleaves\": e.g., _Carpinus_ spp., _Juglans_ spp., _Sorbus torminalis_, and _Prunus avium_. * \"Other broadleaves\": all broadleaved species not included in the \"noble broadleaves\" group (e.g., _Alhus_ spp., _Popolus_ spp., _Salix_ spp., and _Sorbus_ spp.). * \"Other conifers\": all remaining conifer species (e.g., _Abies_ spp. and other _Pinus_ spp.).