## 2 Materials and Methods
### Methods
#### 2.2.2 Indicators Used in the REEI  
In accordance with the literature [4], the normalized differential vegetation index (_NDVI_) representing the greenness index, the wetness component (_WET_) generated via Tassel Cap Transformation representing the wetness index, the normalized differential build-up and soil index (_NDBSI_) composed of the index-based built-up index (_IBI_) and the soil index (_SI_) as an indicator of dryness, and land surface temperature (_LST_) representing the heat index were selected as the evaluation indicators to establish the _RSEI_ evaluation model and to assess the EEQ of the study area using PCA. Then, the EEQ of the study area was classified into 5 grades of worse (0.0-0.2), poor (0.2-0.4), moderate (0.4-0.6), good (0.6-0.8), and excellent (0.8-1.0) using the Natural Breaks (Jenks) method. The primary calculation formulas are presented in Equations (1)-(9). In these equations, _PC_1 denotes the first principal component of PCA, and _bluer_, _bgrgent_, _bnd_, _bNIR_, _bSWIR1_, and _bSWIR2_ are the  
Figure 2: Methodology flow chart.  
reflectance of the blue, green, red, near-infrared, short-wave infrared 1, and short-wave infrared 2 bands of the TM and OLI sensors, respectively.  
\[RSEI=f(NDVI,WET,LST,NDBSI)_{PC1}, \tag{1}\]  
_NDVI_  
_NDVI_ can directly reflect the vegetation status in the study area. The calculation method is as shown in Equation (2) [24].  
\[NDVI=(b_{NIR}-b_{rel})/(b_{NIR}+b_{rel}), \tag{2}\]  
_WET_  
The _WET_ index generated via Tassel Cap Transformation can directly reflect the humidity conditions of vegetation and soil and is calculated by Equation (3) [25; 26]:  
\[WET=c_{1}b_{blue}+c_{2}b_{green}+c_{3}b_{red}+c_{4}b_{NIR}-c_{5}b_{SWIR1}-c_{6}b _{SWIR2}, \tag{3}\]  
where, for TM sensors, \(c_{1}\)-\(c_{6}\) are 0.0315, 0.2021, 0.3102, 0.1594, \(-\)0.6806, and \(-\)0.6109, respectively, and for OLI sensors, \(c_{1}\)-\(c_{6}\) are 0.1511, 0.1973, 0.3283, 0.3407, \(-\)0.7117, and \(-\)0.4559, respectively.  
_NDBSI_  
_NDBSI_ is characterized by the bare soil index and the index-based built-up index, expressed by Equations (4)-(6).  
\[NDBSI=(IBI+SI)/2\,, \tag{4}\]  
\[SI=[(b_{SWIR1}+b_{red})-(b_{blue}+b_{NIR})]/[(b_{SWIR1}+b_{red})+(b_{blue}+b_{ NIR})], \tag{5}\]  
\[IBI=\frac{\left\{\frac{2b_{SWIR1}}{(b_{SWIR1}+b_{NIR})}-\left[\frac{b_{NIR}}{ b_{NIR}+b_{red}}+\frac{b_{green}}{b_{SPR1}}\right]\right\}}{\left\{\frac{2b_{ SWIR1}}{(b_{SWIR}+b_{NIR})}+\left[\frac{b_{NIR}}{b_{NIR}+b_{red}}+\frac{b_{green}}{b_{ SPR1}}\right]\right\}}, \tag{6}\]  
_LST_  
The mono-window algorithm was used for the inversion of the land surface temperature, as shown in Equations (7)-(9) [27; 28]:  
\[T_{s}=[a(1-C-D)+(b(1-C-D)+C+D)T_{sensor}-DT_{a}]/C, \tag{7}\]  
\[C=\epsilon\tau, \tag{8}\]  
\[D=(1-\tau)[1+(1-\varepsilon)\tau], \tag{9}\]  
where \(a\) and \(b\) are \(-\)67.35535 and 0.458608 for TM/ETM+ sensors, respectively, but for OLI/TIRS sensors, they are \(-\)60.919 and 0.428, respectively; \(T_{sensor}\) is the brightness temperature value of the thermal infrared band; _Ta_ represents the effective average atmospheric temperature; \(C\) and \(D\) can be calculated by Equations (8) and (9); \(\varepsilon\) is the surface emissivity ratio; and \(\tau\) is the atmospheric transmittance of the thermal infrared band, which can be generated using the NASA website \"[[http://atmcorr.gsfc.nasa.gov](http://atmcorr.gsfc.nasa.gov)]([http://atmcorr.gsfc.nasa.gov](http://atmcorr.gsfc.nasa.gov))\" (accessed on 11 July 2023) by inputting the imagery date and the central latitude and longitude values of the images. Because of the limitation of imagery dates on the NASA website, the \(\varepsilon\) and \(\tau\) values for images in 1995 cannot be obtained; they can only be replaced by the values for images in 2000.