## Appendix  
### Carbon estimation and calculation of crown width using NFI data  
The carbon increment calculation require carbon estimates for each tree on a given inventory plot. For our study, we use the same method as applied by the Institute of Forest Inventory, Federal Research Centre for Forest, the agency responsible for the National Forest Inventory in Austria. The total dry carbon tree estimate of a single tree, \(C_{i}\), is calculated as follows:  
\[C_{i}=CC\times(dsm+dbm+dfm+drm) \tag{1}\]where \(CC\) is the carbon content and considered to be 0.5 for all species [26], \(dsm\) is the dry stem mass, \(dbm\) the dry branch mass, \(dfm\) the dry foliage mass and \(drm\) the dry root mass. Dry stem biomass (\(dsm\)) is calculated using stem volume and species-specific conversion factors. Stem volume (\(V_{\textit{tree}}\)) is derived from the tree measurements diameter at breast height (\(dbh\)), total tree height _(h)_ and the species-specific form factor (\(FF\)). The calculated volume represents the stem excluding aboveground part of the stump and the branches [17, 57, 58]. \[dsm=V_{\textit{tree}}\times wd\times\frac{100-sf}{100} \tag{1}\]  
\[V_{\textit{tree}}=\left(\frac{dbh}{200}\right)^{2}\times\pi\times h\times FF \tag{2}\]  
where \(V_{\textit{tree}}\) is the stem volume of a single tree [m\({}^{3}\)], \(wd\) is the dry wood density [t BM/m\({}^{3}\)], \(sf\) the shrinkage factor by tree species [%], \(dbh\) the diameter at breast height (1.3 m), \(h\) the tree height, \(d03\) the diameter at 30% of tree height and \(hc\) the crown height (height to the crown base). The form factor (\(FF\)) reduces the volume of the cylinder to the actual tree form. The Austrian Forest Inventory uses two different form factor functions: one for the trees with \(dbh\) ranging from 5-10.4 cm with the following form,  
\[FF=c_{1}+c_{2}\times\text{In}^{2}(dbh)+c_{3}/\!\!/\ h+2_{4}\ /\ dbh+c_{5}\ /\ dbh?+c_{6}\ \ dbh\ \ h+c_{7}\ \ dbh\ \ h \tag{3}\]  
and a second one for all trees with a \(dbh\)\(\geq\)10.4 cm:  
\[FF=c_{0}+c_{1}\times d03\ /\ dbh+c_{2}\times(d03\ /\ h)^{2}+c_{3}\times h\ /\ dbh+c_{4}\times h\ /\ dbh?+c_{5}\ /\ dbh+c_{6}\times hc\ /\ h \tag{4}\]  
\(c_{i}\) are species-specific parameter estimates for calculating stem volume used by the Austrian Forest Inventory given in Tables A1 and A2 [17, 57, 59]. The conversion factors \(wd\) and \(sf\) according to [PERSON] and [PERSON] [60] are given in Table A3. Note that for Equation (A3) \(dbh\) [cm] and \(h\) [m], while in Equations (A4,A5) the \(d03\), \(dbh\), \(hc\) and \(h\) [dm]. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Species Name** & **c1** & **c2** & **c3** & **c4** & **c5** & **c6** & **c7** \\ \hline Picea abies, other coniferous & 0.5634 & \(-\)0.1273 & \(-\)8.5502 & 0 & 0 & 7.6331 & 0 \\ Abies alba & 0.5607 & 0.1547 & \(-\)0.6558 & 0.0332 & 0 & 0 & 0 \\ Larix decidua & 0.4873 & 0 & \(-\)2.0429 & 0 & 0 & 5.9995 & 0 \\ Pinus sylvestris, Pinus strobus & 0.4359 & \(-\)0.0149 & 5.2109 & 0 & 0.0287 & 0 & 0 \\ Pinus nigra & 0.5344 & \(-\)0.0076 & 0 & 0 & 0 & 0 & 2.2414 \\ Pinus cembra & 0.5257 & \(-\)0.0335 & 7.3894 & \(-\)0.1065 & 0 & 0 & 3.3448 \\ Fagus sylvatica, other broadleaf & 0.5173 & 0 & \(-\)13.6214 & 0 & 0 & 9.9888 & 0 \\ Quercus sp. & 0.4171 & 0.2194 & 13.3259 & 0 & 0 & 0 \\ Carpinus betulus & 0.3247 & 0.0243 & 0 & 0.2397 & 0 & \(-\)9.9388 & 0 \\ Fraxinus sp., Sorbus sp., Prunus sp. & 0.4812 & \(-\)0.0149 & \(-\)10.831 & 0 & 0 & 9.3936 & 0 \\ Acer sp. & 0.5010 & \(-\)0.0352 & \(-\)8.0718 & 0 & 0.0352 & 0 & 0 \\ Ulmus sp. & 0.4422 & \(-\)0.0245 & 0 & 0 & 0 & 0 & 2.8771 \\ Betula sp. & 0.4283 & \(-\)0.0664 & 0 & 0 & 0 & 8.4307 & 0 \\ Almus sp. & 0.3874 & 0 & 7.1712 & 0.0441 & 0 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table A1: Coefficients used in models for volume for trees with dbh 5.0–10.4 cm ([PERSON] [59] cited in [PERSON] and [PERSON] [17]). **Table A1. **_Cont._