## 2 Study Area and Materials
### Method
#### 2.3.1 Indicator Calculation  
(1) Greenness  
\(FVC\) (Fractional Vegetation Cover) is the percentage of the area covered by vegetation in relation to the total surface area. It is a simple measure of vegetation coverage and growth and a key factor in soil and water conservation and ecological assessment [35]. \(FVC\) can be used to estimate shrub biomass in high mountain or subalpine environments [36]. In this study, \(FVC\) is derived using the normalized difference vegetation index (\(NDVI\)) and pixel-based binary method [37]. The \(NDVI\) is primarily derived from MODIS data products, as shown in the following formula:  
\[NDVI=NDVI_{\text{veg}}\times FVC+NDVI_{soil}\times(1-FVC) \tag{1}\]  
\(NDVI_{\text{veg}}\) and \(NDVI_{soil}\) represent the \(NDVI\) values in areas with complete vegetation coverage and areas with complete bare soil or no vegetation coverage, respectively. The calculation formulas are as follows:  
\[NDVI_{soil}=\frac{FVC_{max}\times NDVI_{min}-FVC_{min}\times NDVI_{max}}{FVC_{ max}-FVC_{min}} \tag{2}\]  
\[NDVI_{veg}=\frac{(1-FVC_{min})\times NDVI_{max}-(1-FVC_{max})\times NDVI_{min}}{ FVC_{max}-FVC_{min}} \tag{3}\]  
Since the MODIS data used in this study were acquired from July to September, which is the period of the year with the best vegetation growth in the study area, we can approximate that \(FVC_{max}\) = 100% and \(FVC_{min}\) = 0%. Based on the pixel-based binary method, the vegetation coverage model is defined as follows:  
\[FVC=\frac{NDVI-NDVI_{min}}{NDVI_{max}-NDVI_{min}} \tag{4}\]  
In the equation, \(NDVI_{max}\) represents the normalized difference vegetation index value of pixels with vegetation coverage, while \(NDVI_{min}\) represents the normalized difference vegetation index value of pixels with complete bare soil. Since the study area is mostly inaccessible and obtaining extensive field measurements is challenging, this study uses the confidence interval values of the cumulative frequency of \(NDVI\) at 5% and 95% as the \(NDVI_{min}\) and \(NDVI_{max}\) values. The leaf area index (\(LAI\)) is a dimensionless parameter that measures the amount of foliage in the canopy and is used to reflect the vegetation growth quality in the study area [38]. In this study, the MODIS data product MOD15A3H is used to obtain \(LAI\) data for the study area. The calculation formula is as follows [39]:  
\[LAI=0.1\times DN_{A} \tag{5}\]  
\(DN_{A}\) represents the gray value of the leaf area index image except for bare land, glaciers, or water areas. Gross primary productivity (GPP) refers to the total amount of organic carbon fixed by vegetation through photosynthesis in a unit of time. The accumulation of organic carbon by vegetation is a driving force for multiple ecosystems and a key component of land carbon balance, mainly reflecting the carbon source-sink status of vegetation in the study area [40]. In this study, the MOD17A2H product of GPP is extracted at the grid level and dimensionless processing is applied to obtain the distribution of GPP in the study area. Heat  
The thermal index utilizes land surface temperature (\(LST\)), which refers to the surface temperature of the Earth's land surface that has been corrected for emissivity. It is measured in degrees Celsius (\({}^{\circ}\)C) and is an important surface parameter that controls the energy balance between the atmosphere and the land surface. The process of extracting \(LST\) involves converting the digital number (\(DN\)) values from the MOD11A2 product data into Celsius to represent the distribution of land surface temperature in the study area. The calculation formula is as follows:  
\[LST=0.02\times DN_{5}-273.15 \tag{6}\]  
Wet  
This study utilizes a modified tasseled cap transformation (Kauth-Thomas, K-T) formula [41] to extract the wetness index. The K-T transformation is a method based on image physical characteristics, which uses a linear orthogonal transformation to project and transform multi-spectral remote sensing images into three-dimensional space.