## 2 Methods
### Terrestrial NPP--\"Ground Based\" Approach
#### 2.2.1 Increment Estimation  
Originally forest growth data was intended to provide volume increment in m\({}^{3}\)/ha per growth period [6]. The growth period varies depending on the temporal measurement interval of terrestrial sample plots. We develop a consistent and comparable terrestrial productivity data set by deriving NPP estimates using forest inventory data starting with:  
\[NPP=inc_{plot}+C_{Litter} \tag{3}\]  
where \(C_{Litter}\) is the flow of dry carbon into litter [gC/m\({}^{2}\)/year] as defined in Equation (9), \(inc_{plot}\) is the dry carbon increment of trees (above and below ground biomass) [gC/m\({}^{2}\)/year] resulting from repeated plot observations taken at the end \(C_{Forest\_2}\) minus those observations taken at the beginning \(C_{Forest\_1}\) of the growth period  
\[inc_{plot}=C_{Forest\_2}-C_{Forest\_1} \tag{4}\]  
Equation (4) gives the common way to calculate increment for repeated observations and terrestrial plot data, the carbon values (\(C_{Forest\_1}\) and \(C_{Forest\_2}\)) being the sum of the tree carbon estimates calculated from repeatedly measured diameters at breast height (_dbh_) and tree heights (_h_) for a given tree. The National Forest Inventory of Austria use a combined recording system with (i) fixed area plots for trees ranging in _dbh_ from 5 cm to 10.4 cm and (ii) an angle count sampling system [20] for all trees with a _dbh\(>\)_10.4 cm. In angle count sampling the stem number represented by a sample tree changes by diameter and thus the represented tree population changes too, which differs from fixed-area plots (e.g., used in the National Forest Inventory system of Norway [4] or permanent research plots like the \"Austrian Waldboden-Zustandsinventur\" [21]). This affects volume or biomass stocks as well as periodic increment and thus the results from fixed area plot sampling are quite different compared to angle count sampling [6].  
In principle, three different approaches in estimating increment form angle count sample data exist: (i) the starting value method; (ii) the end value method and (iii) the difference method.  
For details we refer to [PERSON] [22] and [PERSON] and [PERSON] [6]. All three methods are statistically sound and deliver unbiased results [23, 24].  
For our study, we use the starting value method, which is also used by the Austrian National Forest Inventory:  
\[inc_{plot}=\Sigma inc_{survivors}+\Sigma inc_{ingrowth} \tag{5}\]  
where \(inc_{plot}\) is the periodic increment on each plot resulting from \(\Sigma inc_{survivors}\) the \"survivor trees\", which were also sampled in the last measurement, and \(\sum inc_{ingrowth}\) the \"ingrowth trees\" or trees, which have reached the threshold during the re-measurement period and are thus selected [6,22,25]. The carbon increments of the \"survivor trees\" are calculated as  
\[\Sigma inc_{survivors}=\Sigma((C_{{}_{2}}-C_{{}_{1}})\times nrep_{{}_{1}}) \tag{6}\]  
and the carbon increments of the \"ingrowth trees\" are  
\[\Sigma inc_{ingrowth}=\Sigma(C_{{}_{2}}\times nrep_{{}_{2}}) \tag{7}\]  
\(nrep_{i}\) is the \"represented\" stem number per hectare at time 1 or time 2 and depends on the basal area factor \(k\) and the individual tree basal area \(g\) (for trees with \(dbh>\)10.4 cm \(nrep_{i}=k/g\) and for trees with \(dbh\) 5-10.4 cm \(nrep_{i}=10\),000/(2.6\({}^{2}\pi\)) = 470.9). \(C_{i}\) are the carbon estimates for this \"representative\" tree at time 1 or time 2.