## 2 Materials and Methods
### Automatic Classification of Hyperspectral Images  
In order to investigate the differences in FPAR of sunlit and shaded leaves, 150 HSI were manually classified based on composite images (wavelengths 0.605 \(\mu\)m, 0.850 \(\mu\)m, and 0.860 \(\mu\)m assigned to R, G, and B, respectively, for visual identification). The manual multispectral object-based classification was performed using the ECognition v. 9.0.1 software [44]. The composite images were used to visually classify sunlit and shaded leaf areas which were then used as target variables when training the machine learning model, using the entire 50-band spectrum as inputs. The manually classified HSI were converted into 2D arrays, with each band treated as a separate variable in the subsequent steps. For the purpose of validation, 75% of the HSI chosen randomly were used for training, and the remaining 25% were used for testing the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Range** \\ \hline Tree Species & _Adenantiera proorunina L., Khaya senegalensis A,Juss., Tabeuhia rosen DC., Albizia saman (lacq.) Merr, Peltolorium_ \\  & _pterocarpump (DC) K.Heyne, Terminala catapra L., Bauhiin x blakean Dum.,_ \\  & _Schefflera actinophylla (Endl.) Harms, Delonix regia (Boj. ex drook.) Raf., Syzygium grande (Wight) Walp_ \\ \hline  & Chlorophyll, C\({}_{\text{ab}}\) = 10–100 \(\mu\)g/cm\({}^{2}\) in 10 \(\mu\)g/cm\({}^{2}\) increments \\  & Carponenoid, C\({}_{\text{xc}}\) = 0.25C\({}_{\text{ab}}\) ug/cm\({}^{2}\) \\  & Anthocyanin, C\({}_{\text{anth}}\) = 0 \(\mu\)g/cm\({}^{2}\) \\  & Brown pigment = 0 \(\mu\)g/cm\({}^{2}\) \\ \hline  & Equivalent water thickness, EWT = 0.015 cm \\  & Leaf mass per area, LMA = 0.01 g/cm\({}^{2}\) \\  & Mesophyll leaf structure parameter, N = 1.9 \\  & Leaf Area Index, LAI = 0.0–2.0 \\ \hline Background & Grass, Concrete \\ Illumination & Ratio of direct to diffuse scene irradiance, SKYL = 0\%, 20\%, 40\%, 60\%, 80\%, 100\% \\  & Solar zenith angle, SZA = 0\({}^{\circ}\), 45\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of parameters used in PROSPECT-DART simulations. classification algorithm. The HSI in the training dataset were then appended with the target classes from the corresponding manually classified images based on the SKYL value. Since the C\({}_{\text{ab}}\) value has no impact on whether a given area of the tree is sunlit or shaded, the same target classes were assigned to HSI differing in C\({}_{\text{ab}}\), thus increasing the training dataset and reducing the risk of overfitting of the model. Since the variables are hyperspectral bands, with values within the same order of magnitude, it was not necessary to perform data normalization. The ReliefF algorithm [45] and an ensemble of decision trees (Random Forest [46]) were used to assess the feature importance in regard to data classification [47], and principal component analysis (PCA) was used to assess the possibility to reduce the dimensionality of the dataset. Machine learning was based on an artificial neural network (ANN) model from the SciKit Learn Python package (the Multi-layer Perceptron classifier v. 0.18 [48]). Rectified linear unit function (ReLu) was used for activation, and the weights were optimized using the stochastic gradient-based optimizer (Adam) [49]. The regularization term was set to 0.001. The network consisted of an input layer with 50 nodes, three hidden layers each with 32 nodes, and an output layer with a single node. The overall performance of the model was assessed based on 10-fold stratified cross-validation. In order to tentatively evaluate the classification algorithm and to check for methodological errors the entire procedure was tested on the Indian Pine HSI dataset acquired by the AVIRIS sensor in Indiana in June 1992 [50]. This dataset contains a multiband hyperspectral image of an area with each pixel classified into one of several categories (type of crop/vegetation) which makes it a good test case for the application described herein.