## 2 Materials and Methods
### Data
#### 2.2.1 Landsat Images  
NDVI and land surface temperature (LST) calculations were based on Landsat 5, 7, and 8 data, processed through the Google Earth Engine (GEE) cloud computing platform ([[https://code.earthegine.google.com/](https://code.earthegine.google.com/)]([https://code.earthegine.google.com/](https://code.earthegine.google.com/)) (accessed on 3 December 2022). The datasets included Landsat 5 TM, Landsat 7 ETM+, and Landsat 8 OLI/TIRS level-2 Surface Reflectance (SR) and Top of Atmosphere (TOA) data. These datasets have undergone atmospheric correction and radiometric calibration. The GEE was used to perform several preprocessing steps on Landsat 5, 7, and 8 data, including temporal filtering (focusing on images acquired from 1 July to 1 September), cloud amount filtering (selecting images with less than 5% cloud cover), masking, and spatial clipping to the study area boundary. The preprocessed data were then used to compute the annual NDVI and LST for the study period, followed by the application of a mean compositing algorithm to generate spatially averaged representations of these indices. The NDVI, a remote sensing index, is used to assess vegetation cover and growth status [37]. Its calculation formula is as follows:  
\[NDVI=\frac{NIR-RED}{NIR+RED} \tag{1}\]  
where NIR represents the reflectance of the near-infrared band and RED represents the reflectance of the red band. Typically, the reflectance in the NIR band is higher, while the reflectance in the RED band is lower. Consequently, NDVI values usually range between \(-1\) and \(1\), with higher NDVI values indicating greater vegetation cover.  
LST is an important parameter for indicating the thermal environment and is one of the primary indicators of surface conditions [38]. Based on the thermal infrared radiation transfer equation, the atmospheric effects on thermal radiation are removed during the radiation transfer process to obtain the LST [39]. Its calculation formula is as follows:  
\[LST=K_{2}/\ln[K_{1}/B(LST)+1]-273.15 \tag{2}\]  
\[B(LST)=[L_{\lambda}-L_{u}-\tau(1-\varepsilon)L_{d}]/\tau\varepsilon \tag{3}\]  
where \(B(LST)\) represents the land surface temperature (\({}^{\circ}\)C). \(K_{1}\) and \(K_{2}\) are radiometric constants. Table 1 summarizes the radiometric constants \(K_{1}\) and \(K_{2}\) for the thermal infrared bands of Landsat 5, 7, and 8. \(\tau\), \(L_{d}\), and \(L_{u}\) represent atmospheric transmittance, atmospheric downward radiance, and atmospheric upward radiance (W-m-1-sr-1-m-1), respectively. These values can be obtained from the Atmospheric Correction Parameter Calculator ([[https://atmcorr.gsfc.nasa.gov/](https://atmcorr.gsfc.nasa.gov/)]([https://atmcorr.gsfc.nasa.gov/](https://atmcorr.gsfc.nasa.gov/)) (accessed on 3 December 2022)). \(L_{\lambda}\) is the radiance value of the thermal infrared band, and \(\varepsilon\) is the surface emissivity.  
The NDVI threshold method is used to estimate surface emissivity. When the NDVI < 0.20, the pixel is considered bare soil, with an emissivity typically around 0.97.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Radiometric** & **Landsat 5** & **Landsat 7** & **Landsat 8** \\
**Constants** & **TM6 Band** & **ETM + 6 Band** & **TIRS10 Band** \\ \hline K\({}_{1}\)/(W-m\({}^{-1}\cdot\)sr-1-m\({}^{-1}\cdot\)m\({}^{-1}\)) & 607.76 & 666.09 & 774.89 \\ K\({}_{2}\)/K & 1260.56 & 1282.71 & 1321.08 \\ \hline \end{tabular}
\end{table}
Table 1: The values of the radiation constants K\({}_{1}\) and K\({}_{2}\) of the Landsat 5/7/8 thermal infrared band.  
When the NDVI > 0.50, the pixel is regarded as fully vegetated with a constant emissivity value, typically around 0.99. When 0.20 < NDVI < 0.50, the pixel is considered a mixture of bare soil and vegetation. Its calculation formula is as follows:  
\[\epsilon=0.004P_{v}+0.986 \tag{4}\]  
\[P_{v}=\left[\frac{NDVI-NDVI_{\min}}{NDVI_{\max}-NDVI_{\min}}\right]^{2} \tag{5}\]  
where \(NDVI_{min}\) is 0.20, \(NDVI_{max}\) is 0.50, and \(P_{v}\) represents the proportion of vegetation [40].