## Materials and Methods
### Linear Spectral Mixture Analysis  
Linear Spectral Mixture Analysis (LSMA) is a widely used theory in the research of hyperspectral data and has found many applications in data analysis [41]. It describes a sample of data in a linear model that can be composed and parameterized and determined by a limited set of basic components [42]. It begins by assuming that for a given set of finite elementary substances, data samples can be modeled as a linear mixture of these substances from which data samples can be mixed into their corresponding abundance fractions. In this circumstance, the analysis of the data samples can be performed simply on these abundance fractions rather than the sample itself. The commonly used Linear Spectral Unmixing (LSU) is a technique for implementing LSMA [43].  
LSU simulates the ground as flat and the incident sunlight on the ground causes the material component to radiate a certain amount of incident energy back to the sensor. Each pixel is then modeled as a linear sum of all radiation energy curves of the components that makes up the pixel. Each component contributes to the sensor's observation in a positive linear method. In addition, energy conservation constraints are often observed, forcing the weight of the linear mixture to be positive and the sum to be one [44]. LSU usually consists of two steps: endmember extraction and computation of abundances.  
A simple constrained LSU model has the following form:  
\[\begin{array}{l}y=\sum\limits_{i=1}^{n}a_{i}f_{i}+\varepsilon\\ \sum\limits_{i=1}^{n}f_{i}=1,\text{ and }0\leq f_{i}\leq 1\end{array} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Location of RE**} & \\ \multicolumn{1}{c}{**ID**} & \multicolumn{1}{c}{**(nm)**} & \multicolumn{1}{c}{**Slope of RE**} & \multicolumn{1}{c}{**Reflectance of RE**} \\ \hline \multicolumn{2}{c}{_Pinus (Illumination)_} & & & \\ \hline  
\hline \hline \end{tabular} Note: reflectance calculated for Slope of RE was multiplied by 10,000.  
\end{table}
Table 2: Red Edge Parameters of _Pinus_ and _Larix_ with Different Illumination/Shadow Proportions. Twenty of the 80 pixels’ parameters are listed.  
where \(y\) is the measured reflectance for an image pixel, \(a_{i}\) is the measured reflectance for endmember \(i\), \(f_{i}\) is the unknown abundance or fractional cover for endmember \(i\), \(\varepsilon\) is the residual between modeled and measured reflectance of the pixel, \(n\) is the number of endmembers. In this study, number of endmembers equals three.  
In this study, mixed vegetation pixel of Sentinel-2 multispectral image can be divided into three components as illuminated vegetation canopy, shaded vegetation canopy and bare soil. Based on the LSMA theory, the three constituents can be restored or represented by solving the linear inverse problem of Equation (2) and their fractions can be weighted. It assumes that the mixed pixel is a linear mixture of a finite set of image endmembers, and the data samples are then decomposed by finding its abundance fractions of these endmembers for data analysis. Endmembers of illuminated vegetation, shaded vegetation and bare soil can be extracted using the scatterplot of two vegetation indexes (the proposed NDCSI and existing BSI in this case). The three vertexes of the 2-D scatterplot represent the samples of three endmembers respectively, which can be extracted and calculated in Equation (2) for the fractions.