## 5 Discussion and Conclusion  
The objective of this study was to explore several allometric models for stem volume estimation of automatically delineated pine trees using ALS and multispectral line scanner data in a study site in the south-west of Germany. Independent variables that are obviously related to the stem volume were used as predictors. An allometric model with tree height and crown diameter (model 4) performed best with a RMSE of 0.2214 m\({}^{3}\) (24.02%) which is much smaller than the standard deviation of the observed variables as shown in Table 4. The results show clearly that tree height \(h\) is by far the most important predictor. Model 1 with \(h\) as the only predictor explains a high proportion of variability with \begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & **RMSE\({}_{CV}\) [m ]** & **RMSE\({}_{CV}\) [\%]** & **Bias\({}_{CV}\) [m ]** & **Bias\({}_{CV}\) [\%]** \\ \hline
1 & 0.2726 & 29.57 & 0.0203 & 2.20 \\
2 & 0.4834 & 52.44 & 0.1190 & 12.91 \\
3 & 0.5250 & 56.96 & 0.1191 & 12.92 \\
4 & 0.2214 & 24.02 & 0.0125 & 1.36 \\
5 & 0.2299 & 24.95 & 0.0146 & 1.58 \\
6 & 0.4967 & 53.88 & 0.1173 & 12.72 \\
7 & 0.2228 & 24.18 & 0.0129 & 1.40 \\ \hline \end{tabular}
\end{table} 
Table 10: Prediction accuracy of the different regression models. R\({}^{2}\) = 0.904. The height itself was estimated very precisely from the ALS point cloud with r = 0.957 (RMSE = 1.5 m and Bias = 0.08 m). Nevertheless, it was possible to increase the strength of the relationship and to improve the estimation of stem volume with the crown diameter as an additional predictor. Model 5 with tree height and crown volume performed slightly worse which might be due to the fact, that the estimation of the crown base height from the ALS point cloud is not accurate enough. However, a denser point cloud might improve the identification of the crown base which has to be analysed in future studies. Moreover, the usage of all predictors (model 7) did not reduce the RMSE. In addition model 7 (and also 6) show a non-significant coefficient for \(cv\) which indicates once more that this variable does not contribute much to the models. The RMSE of this study is in the range of the errors in most other studies carried out in Germany and Scandinavia. A selection of results is given in Table 11. However, a direct comparison is not possible due to different study sites with different forest stands and remote sensing data in addition to different validation techniques. A lower RMSE was reported by [10] for Norway spruce (_Picea abies_) and Fir (_Abies alba_) (RMSE = 16-17%). However, the prediction accuracy in this study is very close to the result of [22] who estimated the stem volume of Norway spruce (_Picea abies L. [PERSON]_), Scots pine (_Pinus sylvestris L._) and birch (_Betula spp._) with an RMSE of 22%. It was possible to delineate pine trees with an overall identification rate of \(\sim\)62%. Compared to other studies this result is quite satisfying: In [13], 40-50% coniferous trees (mainly spruces) were delineated correctly in a study site in Austria. In [11], an identification rate of 38.7-45.4% was reported for both coniferous and deciduous trees in the Bavarian Forest National Park also using DSM based segmentation algorithms. As expected the detection of trees is much worse in young forest stands (age class II with a tree age \(\leq\) 40 years) and very good for plots with an age class \(\geq\) III with 86%