## Appendix
### Carbon estimation and calculation of crown width using NFI data
  
**Table A5. ** Conversion factors for stem biomass [60]. \begin{tabular}{c c c} \hline
**Species Name** & **wd** & **sf** \\ \hline Picea sp. & 0.41 & 11.80 \\ Abies sp. & 0.41 & 11.85 \\ Larix sp. & 0.55 & 13.20 \\ Pinus sylvestris, other Pinus & 0.51 & 11.80 \\ Pinus nigra & 0.56 & 11.80 \\ Pinus cembra & 0.40 & 9.00 \\ Pinus strobus & 0.37 & 9.00 \\ Pseudotsuga menziesii & 0.47 & 12.00 \\ Taxus baccata & 0.64 & 8.80 \\ Fagus sylvatica, other hardwood broadleaf & 0.68 & 17.50 \\ Carpinus betulus & 0.67 & 13.60 \\ Quercus sp. & 0.75 & 18.80 \\ Fraxinus sp. & 0.67 & 13.20 \\ Acet sp. & 0.59 & 11.65 \\ Ulmus sp. & 0.64 & 12.80 \\ Castanea sativa & 0.56 & 11.45 \\ Robinia pseudaccacia & 0.73 & 11.80 \\ \hline \end{tabular}   
For the remaining biomass components (_dbm, dfm_, _drm_), we use allometric biomass functions developed for Austrian forest conditions, which are also used by the Austrian National Forest Inventory. The dry branch biomass _dbm_ [kg] for _Pinus sp._ is calculated with a _dbh_ [cm] and \(h\) [m] dependent equation [61],  
\[dbm=1.0366\cdot e^{(-2.8762+2.04516\cdot\ln(dbh)-0.07025\cdot\ln(h))} \tag{10}\]  
We use equations from [PERSON] [62] for all other tree species. If height to the life crown measurements (_hc_) are available, models using _dbh_, \(h\) and _hc_ as input variables are used according to Equation (10). If _hc_ is missing, models with _dbh_ and \(h\) are used according to Equation (11) [62]:  
\[dbm=l2\cdot e^{\frac{b_{h}+b_{2}\ln(dbh)+b_{2}-\frac{h}{dbh}}{dbh}} \tag{11}\]  
\[dbm=l3\cdot e^{\frac{b_{h}+b_{1}\ln(dbh)+b_{2}-\frac{h}{dbh}+b_{3}\ln(CR)}{dbh}} \tag{12}\]  
\[CR=\frac{h-hc}{h} \tag{13}\]  
where _CR_ is the crown ratio and all other variables as previously defined. The species-specific parameters _b\({}_{i}\),l2_ and _l3_ are given in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Species Name** & **b20** & **b21** & **b22** & **l2** & **b30** & **b31** & **b32** & **b33** & **l3** \\ \hline Picea abies, other & - & 1.7459 & - & 1.102 & - & 2.0252 & 0.1451 & 0.9154 & 1.051 \\ Abies alba & - & 2.0429 & - & 1.105 & - & 2.2066 & 0 & 0.4384 & 1.087 \\ Fagus sylvatica, other BL & - & 2.3930 & - & 1.251 & - & 2.5568 & - & 0.6002 & 1.212 \\ Quercus sp. & 1.8554 & 0.9332 & - & 1.334 & - & 1.9445 & 0 & 1.2137 & 1.280 \\ Carpinus betulus & - & 2.8913 & - & 1.181 & - & 2.8281 & 0 & 0.9318 & 1.130 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coefficients used in models for biomass in branches [62]. For coniferous trees, the foliage biomass (_dfm_) is included in the branch biomass calculations (_dbm_) as outlined above. For the deciduous trees, _dfm_ [kg] is calculated using allometric functions according to _dbh_. These functions are based on measurements collected by [PERSON] [63, 64] and are modified after [PERSON] and [PERSON] [65]. \[dfm=a_{0}\times dbh^{\alpha} \tag{10}\]  
The species-specific parameters \(a_{i}\) are given in Table 15.  
The root biomass (_drm_) in [kg] is defined as roots with a minimum diameter of 2 mm including the root stump. For _Pinus sylyestris_ and _Pinus nigra_ the allometric function of Offenthaler and Hochbichler [66] is used:  
\[drm=0.038872\times dbh^{2.066783} \tag{11}\]  
For all other species, the following dbh and age-dependent model is applied [67, 68]:  
\[drm=c_{0}\cdot e^{c_{i}+c_{2}\ln(dbh)+c_{3}\ln^{2}(dbh)+c_{4}\ln(age)} \tag{12}\]  
_dbh_ in [cm], _age_ is the tree age [a], \(c_{i}\) are species-specific parameter according to [67, 68]. The species-specific parameters \(c_{i}\) are given along with the parameters for foliage biomass in the Table 15.  
Equation (13) estimates maximum crown width of a tree assuming open-grown conditions for calculating _CCF_[27]. The species-specific parameters to calculate maximum crown width are given in Table 16.  
\[CW_{i}=e^{c_{0}+c_{1}\ln(dbh)} \tag{13}\]