## 2 Materials and Methods
### Methods  
#### 2.3.1 Calculation of Indicators  
Vegetation is the most important component of the ecosystem. Based on former studies [28; 39], this study selected five indicators related to vegetation to directly reflect the quality of the ecological environment [7]. Among them, GPP is denotes the physiological characteristics and growth status of vegetation, and the LAI reflects the growth quality of vegetation further. Based on the normalized difference vegetation index (NDVI), FVC was further extracted to represent vegetation growth status and coverage degree, and FVC is an important index to measure regional greenness directly. LST and WET represent heat and humidity in the study area, which are two factors that are closely related to vegetation growth. The formula of GPP, LAI, FVC, LST, and WET is expressed as follows:  
1. Gross primary productivity (GPP) and leaf area index (LAI)  
GPP is an indicator of plant photosynthesis [40], which is often used to quantify the quality of vegetation growth [41]. Inversion of the LAI from MODIS data products has been verified by many scholars [42; 43; 44]. According to the product description of the LAI and GPP in MODIS data products, when the digital number (DN) value of the LAI is between 253 and 255, it represents bare land, snow area, or water area. For the valid DN value, the unit of the LAI is m\({}^{2}\)/m\({}^{2}\), and the expression is as follows:  
\[\text{LAI}=0.1\times\text{DN}_{\text{LAI}} \tag{1}\]  
where DN\({}_{\text{LAI}}\) represents the DN value of leaf area index waveband images. The effective value of the GPP band is between 0 and 30,000. For the effective DN value, the unit of GPP is g C m\({}^{-2}\), and the calculation formula is:  
\[\text{GPP}=0.1\times\text{DN}_{\text{GPP}} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indicator** & **Product** & **Extracted Band** & \
\begin{tabular}{c} **Temporal** \\ **Resolution (d)** \\ \end{tabular} &
\begin{tabular}{c} **Spatial** \\ **Resolution (m)** \\ \end{tabular} \\ \hline GPP & MOD17/A2H & GPP\_500 m & 8 & 500 \\ FVC & MOD13A1 & 500m\_16\_days\_NDVI & 16 & 500 \\ LAI & MOD15A2H & Lai\_500 m & 8 & 500 \\ WET & MOD09A1 & sur\_ref\_b01 to 07 & 8 & 500 \\ LST & MOD11A2 & LST\_Day\_1 km & 8 & 1000 \\ \hline \hline \end{tabular} Note: GPP: gross primary productivity; FVC: fractional vegetation coverage; LAI: leaf area index; WET: wetness; LST: land surface temperature.  
\end{table} 
Table 1: Research indicators and MODIS data products. Many scholars have carried out several studies on vegetation coverage in ecologically fragile areas in China [45; 46]. Satellite-derived NDVI data products are an indispensable choice in large-scale investigation and research [47; 48]. Based on the MODIS product, the NDVI of Fuyun County was processed in this study, and FVC was estimated by pixel dichotomy. This method is used to calculate vegetation coverage based on the pixel linear decomposition model [49], and its expression is as follows:  
\[\text{FVC}=\frac{\text{NDVI}-\text{NDVI}_{\text{soil}}}{\text{NDVI}_{\text{ veg}}-\text{NDVI}_{\text{soil}}} \tag{3}\]  
The NDVI was selected as the parameter to calculate FVC. Since the measured data were difficult to obtain, the NDVI values of 95% and 5% of the confidence interval were used as the NDVI of the pure vegetation pixel and the pure soil pixel. The \(\text{NDVI}_{\text{soil}}\) and \(\text{NDVI}_{\text{veg}}\) values of 2008 were 0.0323 and 0.5124 in the study area, respectively. In 2018, the \(\text{NDVI}_{\text{soil}}\) and \(\text{NDVI}_{\text{veg}}\) values were 0.0827 and 0.6018 in the study area, respectively. The whole area was divided into three parts: when the NDVI was less than the NDVI of the pure soil pixel, the value of FVC was 0. When the NDVI was greater than the NDVI of the pure vegetation pixel, the value of FVC was 1. The FVC value of the pixel between the NDVI of the pure soil pixel and pure vegetation pixel was calculated by Equation (3).