## 3 Methodology
### Preprocessing of Input Layers  
#### 3.1.1 Preprocessed Layers of Sentinel-2 Images  
In this study, two Sentinel-2 images from different seasons of spring and fall were used (European Space Agency (ESA), Paris, France). Figure 4a shows images from 3 May 2017, at 65.3\({}^{\circ}\) solar elevation and 143.5\({}^{\circ}\) solar azimuth while Figure 4b is from 30 October 2017, with the sun altitude of 38.5\({}^{\circ}\) and the azimuth angle of 165.5\({}^{\circ}\) (Table 1). The spectral bands defined for the Sentinel-2 used in this study are shown in Table 2. As vegetation, especially hardwoods, could have reflectivity differences depending on the season, images of both seasons were used to account for seasonal characteristics. The NDVI, NDWI, NDre maps, and the PCA texture maps were generated from the Sentinel-2 orthoimages of both seasons by using Matlab (Mathworks, Natick, MA, USA). Figure 3: Overall data processing flow to map the forest vertical structure. Sentinel-2 satellite image data were preprocessed for atmospheric correction and topographic correction. Radiant energy reaches the sensor and is affected by the atmosphere in various ways. Atmospheric correction is a method of eliminating the effects of the atmosphere that disturbs the image by reaching the sensor with unnecessary energy by the atmosphere [36]. Thus, in this study, Sentinel-2 image was converted to Bottom-Of-Atmosphere, which ignores the atmospheric effects of the original image [37]. Atmospheric correction of Sentinel images was performed with a tool called Sen2 Cor from Sentinel Application Platform (SNAP) provided by ESA. In addition, the satellite image data has a difference in reflectivity according to the sun incidence angle in a mountain area with the slope land; high mountainous region has shade and sunlit slopes. Topographic correction is necessary for mountainous area to minimize other impacts besides the forest features. In this study, a commonly used terrain correction model of statistical-empirical correction [38] was applied to Sentinel-2 optical image as follows,  
\[\rho_{h}=\rho-\{a\cdot\cos i+b\}+\overline{\rho} \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Spring** & **Fall** \\ \hline Date (YYYY.MM.DD) & 2017.05.03 & 2017.10.30 \\ Ground sample distance (m) & 10 & 10 \\ Sun altitude angle (deg.) & 65.3 & 38.5 \\ Sun azimuth angle (deg.) & 143.5 & 165.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of Sentinel-2 images used in this study. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sentinel-2 Bands** & **Central Wavelength (nm)** & **Band Width (nm)** & **Spatial Resolution (m)** \\ \hline
3 (Green) & 560 & 35 & 10 \\
4 (Red) & 665 & 30 & 10 \\ \hline
5 (Vegetation red edge) & 705 & 15 & 20 \\ \hline
6 (Vegetation red edge) & 740 & 15 & 20 \\ \hline
7 (Vegetation red edge) & 783 & 20 & 20 \\ \hline
8 (NIR) & 842 & 115 & 10 \\
11 (SWIR) & 1610 & 90 & 20 \\
12 (SWIR) & 2190 & 180 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Definition of Sentinel-2 spectral bands used in this study [36]. Figure 4: Sentinel-2 satellite ortho-rectified images acquired in the study area: (**a**) spring season; and (**b**) fall season. where \(\rho\) and \(\rho_{h}\) are pixel values from original and topographic-corrected images, respectively, \(\overline{\rho}\) is the mean value of the original image and \(i\) indicates the incidence angle. \(a\) and \(b\) are parameters of the statistical empirical model. After the topographic correction process, NDVI, NDWI, and NDre maps are generated from the topographic-corrected Sentinel-2 images, which were used for forest vertical mapping in this study instead of the original image. NDVI is an index based the reflectance difference between red and near-infrared, which increases when the vegetation activity becomes more active. The red band (Band 4) and NIR band (Band 8) are used in combination defined as follows [13].