## 4 Results and Analysis
### Addressing Stand Density Effects  
The results in Figures 3 and 4 show a clear stand density related trend. We apply a logarithmic trend curve to correct for stand density effects similar to [PERSON] _et al._[3]:  
\[\Delta\mathit{NPP}=a+b\times\ln(\mathit{SDI})\pm\varepsilon \tag{15}\]  
\[\Delta\mathit{NPP}=a+b\times\ln(CCF)\pm\varepsilon \tag{16}\]  
\(a\) and \(b\) are the corresponding coefficient estimates and \(\varepsilon\) the remaining error and all other variables as previously defined. We apply Equations (15) and (16) to all data and again separately for the three MODIS forest land cover types relevant for Austrian forests (\"evergreen needleleaf forest\", \"mixed forest\" and \"deciduous broadleaf forest\". Note that the stand density measures _SDI_ and _CCF_ are calculated based on the stand situation at the end of the growth period. Plotting the results of the fitted trend curves show that all exhibit the same pattern whether they are grouped according to _SDI_ or _CCF_ (left images in Figure 5). The regression results are given in Table 2.  
Figure 4: Difference between MODIS NPP and NFI NPP (MODIS minus NFI) grouped by MODIS land cover types (ENF = evergreen needleleaf forest, MF = mixed forest) and stand density measures: SDI (**top**); CCF (**bottom**). Properties of illustration analogous to Figure 2.  
A variance analysis reveal no significant differences in the parameter estimates \(a\) and \(b\) given in Table 2 between the major forest biome types represented by the MODIS land cover types. This suggests that for Austrian forests no biome type specific parameters are needed (Figure 5).  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Depending Variable** & & \multicolumn{1}{c}{**a**} & \multicolumn{1}{c}{**SE a**} & \multicolumn{1}{c}{**b**} & \multicolumn{1}{c}{**SE b**} & \multicolumn{1}{c}{**r\({}^{2}\)**} & \multicolumn{1}{c}{**n**} \\ \hline SDI & ENF & 908.3 & 83.0 & \(-\)143.0 & 13.1 & 0.30 & 277 \\  & DBF & 1265.8 & 194.7 & \(-\)192.2 & 31.6 & 0.34 & 71 \\  & MF & 1203.3 & 38.1 & \(-\)181.3 & 6.0 & 0.26 & 2516 \\  & all & 1181.0 & 19.4 & \(-\)178.7 & 3.0 & 0.28 & 8716 \\ CCF & ENF & 694.8 & 60.0 & \(-\)141.3 & 12.2 & 0.33 & 277 \\  & DBF & 951.3 & 145.1 & \(-\)159.5 & 26.5 & 0.34 & 71 \\  & MF & 841.9 & 30.1 & \(-\)148.8 & 30.1 & 0.21 & 2516 \\  & all & 812.4 & 15.1 & \(-\)147.6 & 2.9 & 0.22 & 8716 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coefficients and statistics of trend curves displayed in Figure 5 a,b coefficients for Equations (15) and (16), SE standard error of coefficients, r\({}^{2}\) coefficient of determination, n degrees of freedom.  
Figure 5: Scatterplots of NPP difference (\(\Delta\)NPP) and stand density dependent trend curves using SDI **(top left)** and CCF (**bottom left)**, the trend curves are calculated for MODIS forest land cover types separately (ENF = evergreen needleaf forest, DBF = deciduous broadleaf forest, MF = mixed forest) and for all land cover types together (all). The images on the right side (Corr. \(\Delta\)NPP) show the NPP difference after correcting for stand density given by the trend lines using all plots (all).  
We remove the stand density bias from MODIS NPP using Equation (15), where \(a\) equals 1181.0 and \(b\) -178.7, and Equation (16), where \(a\) equals 812.4 and \(b\) -147.6 (Table 2). The detrended MODIS NPP features a mean of 515.5 gC/m\({}^{2}\)/year, standard deviation 181.7 gC/m\({}^{2}\)/year and compared to terrestrial NPP a RMSE of 227.8 gC/m\({}^{2}\)/year. After removing the stand density related trend, the difference between the two NPP assessment methods do not exhibit a bias as shown in the right-hand images in Figure 5 (_SDI_\(r^{2}\leq 0.01\), _CCF_\(r^{2}\leq 0.01\)) than when using the original MODIS NPP results on the left side of Figure 5.