## 2 Materials and Methods
### Classification and Accuracy Assessment  
The main goals of our study were to (1) evaluate Sentinel-2 data with its particular spectral bands but also multitemporal characteristics, to (2) use and compare different machine-learning algorithms and (3) to design a semi-automated workflow that can be scaled and is optimized for processing big datasets. For this purpose, we used a hierarchical classification approach (Figure 1) and tested different band and scene combinations for PB and OBIA classifications. In a first step, we tested 14 combinations to differentiate between coniferous and broad-leaved tree types. Based on the best results acquired, we then tested 54 different approaches to distinguish between oak, beech and other broad-leaved trees within the broad-leaved subclass. Coniferous trees were not classified further as the proportions of tree species other than spruce are minor and not enough training samples were available. The ML algorithms used are an SVM classifier with a radial basis kernel function and a RF algorithm that are implemented in ArcGIS Pro as so-called raster functions. These functions, in comparison to standard geoprocessing tools, work in a dynamical way (on-the-fly) and are well-suited for distributed processing on an Image Server. This is a requirement if we envisage industrial use of the tools on large datasets. According to [PERSON] and [PERSON] [25], the RF classifier (also see [PERSON] [26] und [PERSON] [27]) consists of a combination of tree classifiers where each classifier is generated using a random vector sampled \begin{table}
\begin{tabular}{c c c} \hline \hline
**Tree Type** & **Ebersberger Forest** & **Freisinger Forest** \\ \hline Spruce & 777 & 70 \\ Pine & 2 & 1 \\ Larch & 6 & 2 \\ Fir & 1 & 2 \\ Other Coniferous & 8 & 2 \\ Beech & 75 & 4 \\ Oak & 21 & 2 \\ Other Broad-Leaved & 63 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Available pure inventory areas for training and testing. Note that each circle contains more than one sample depending on the spatial resolution of the pixel. independently from the input vector. It belongs to the ensemble methods of supervised learning and reduces overfitting effects and has become quite popular within the remote sensing community (cf. [PERSON] and [PERSON] (2018)). The maximum number of trees we eventually used was 50 and the tree depth was set to 30. As these parameters also influence classification results, we used the same parameters that we found to work well for all band combinations and tests performed in this study. SVMs, described by [PERSON] (2017), are based on the principle of Support Vector Classifiers, a linear classifier. For non-linear life phenomena, other SVMs were developed that use different kernel functions such as the radial basis function used in this study to solve non-linear problems. These kernels enlarge the feature space by using different kernel functions with e.g., polynomial kernel degrees or a radial kernel ([PERSON] et al., 2016). The radial kernel separates two classes if the Euclidean distance is large between a test observation x* and a training observation xi. Training observations that are far from x* will play no role for the prediction of the class label x*, if the kernel K is very tiny in large Euclidean distances. Kernel functions are used to separate non-linearly separable support vectors using a linear hyperplane ([PERSON], 2016). Using kernels instead of increasing the feature space using functions of the original features, the computational advantage increases ([PERSON] et al., 2016). Also, for distinct pairs i, i', it is only necessary to compute K for the training observations xi and xi' without working in the enlarged feature space which is explicitly meaningful when the enlarged feature space would be so large that computations are unpredictable. We tested both algorithm in an OBIA and a PB approach for comparison.