## 4 Experiment I--DSM Quality Evaluation
### Comparison of DSMs to the Top Height H100 at Forest Inventory Plots  
In this section, the normalized canopy heights extracted from the DSMs are evaluated with the aid of Forest inventory plots introduced in Section 2.3. The top height H100 is used as reference height for each inventory plot. Nine CHMs were generated by subtracting the terrain height from the DSMs. For this purpose, a digital terrain model (DTM) was generated from the last returns of the 2010 airborne laser scanning data. The H100 height from 2008 and 2013 are used as reference heights for each inventory plot. The locations of these inventory plots are indicated by black dots in Figure 3. Thus, for each inventory plot, the corresponding pixels in the CHMs represented by the inventory plots are used for the evaluation. The DSMs acquired before 2010 were compared against the H100 heights from 2008. The DSMs acquired after 2010 were compared against the H100 heights from 2013. The maximum heights from the CHMs yielded the highest correlation coefficients with the H100 heights in [37]. Thus, following the same workflow, we plot the maximum CHM heights separately for all datasets against the H100 height of the field plots in Figure 6. The CHMs from LiDAR2010, WorldView2012, and Aerial2012 match much better the H100 heights than the other datasets. The main scatter points from LiDAR2001 and HRSC2003 cluster lower values than the center 1:1 line, which means that, due to the time difference the H100 heights are significantly higher than the height from these two DSMs. ALOS2008, Cartosat2008, RapidEye2009 and TanDEM-X2013 show many inventory plots with lower height estimation and therefore less correlation to the H100 heights. Besides the maximum CHM values, the mean, 68.3% and 95% quantiles within the forest inventory plot regions are derived. The Pearson's correlation coefficients of these DSM metrics with the H100 heights are listed in Table 4. By taking the H100 heights (\(h\)) as reference, the relative root mean square error (RRMSE) is calculated for each CHM as:  
\[\text{RRMSE }(\hat{h})=\sqrt{\frac{1}{n}\sum_{j=1}^{n}\left(\frac{\hat{h}-h}{h} \right)^{2}} \tag{4}\]  
where \(n\) is the total number of inventory plots, \(\hat{h}\) represents the canopy height calculated from the CHMs by taking the maximum, mean, 68.3% or 95% quantiles of the pixels covered by the inventory plot, and \(h\) is the H100 height of the corresponding plot. In Table 4, the best results with highest \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Pairs** & **Mean** & **Max** & **68.3\% Quantile** & **95\% Quantile** \\ \hline
500 m\({}^{2}\) & & & & \\ \hline HRSC2003 & 0.982 & 0.969 & 0.978 & 0.973 \\ ALOS2008 & 0.970 & 0.931 & 0.953 & 0.941 \\ Cartosat2008 & 0.966 & 0.959 & 0.959 & 0.961 \\ RapidEye2009 & **0.940** & **0.922** & **0.923** & **0.922** \\ WorldView2012 & 0.987 & 0.972 & 0.980 & 0.976 \\ Aerial2122 & **0.991** & **0.990** & **0.985** & **0.989** \\ TanDEM-X2013 & 0.969 & 0.952 & 0.959 & 0.955 \\ \hline \hline
1 Hectare & & & & \\ \hline HRSC2003 & 0.993 & 0.989 & 0.992 & 0.991 \\ ALOS2008 & 0.993 & 0.950 & 0.982 & 0.967 \\ Cartosat2008 & 0.992 & 0.973 & 0.989 & 0.981 \\ RapidFye2009 & **0.974** & **0.940** & **0.959** & **0.946** \\ WorldView2012 & 0.997 & 0.983 & 0.994 & 0.987 \\ Aerial2012 & **0.998** & **0.995** & **0.997** & **0.994** \\ TanDEM-X2013 & 0.995 & 0.961 & 0.989 & 0.975 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation coefficients between height metrics of image- and LiDAR-derived DSMs for 500 m\({}^{2}\) and 1 ha grid cells (highest and lowest values are marked in bold). correlation and lowest RRMSE are marked in bold black, while the worst result with lowest correlation and highest RRMSE are marked in bold grey.