## 3 Materials and Methods
### Land Surface Temperature  
The LST measures the skin temperature of the spatial data in the field of remote sensing. It displays the cold and hot temperature of the earth's surface through the radiant energy reflected within the surface. The thermal-infrared remote-sensing data are used for measuring the LST. The TIRS data help in recognizing the mixture of bare soil and vegetation temperatures through LST [52; 53; 54]. In our research work, we estimated the LST for the TIRS bands of Landsat 8. Equations (11)-(13) represent the estimation of LST for TIRS image 7. The conversion of the Digital Number (DN) value to the radiance of the TIRS image is calculated by using Equation (11). The conversion of radiance into the brightness temperature is shown in Equation (12). The degree conversion from Kelvin (K) to Celsius \(\copyright\) is shown in Equation (13). \[L_{\lambda}=\left(\frac{LMAX_{\lambda}-LMIN_{\lambda}}{QCALMAX-QCALMIN}\right) \ *\ \left(QCAL-QCALMIN\right)+LMIN_{\lambda} \tag{11}\]  
where \(L_{\lambda}\) represents the spectral radiance in \(\left(Watts/\left(m^{2}\ *\ sr^{2}\ *\ \mu m\right)\right),QCAL\) represents the quantized calibrated pixel value, \(QCALMAX\) represents the maximum quantized calibrated pixel value, \(QCALMIN\) represents the minimum quantized calibrated pixel value, \(LMAX_{\lambda}\) represents the spectral radiance scaled to \(QCALMAX\), and \(LMIN_{\lambda}\) represents the spectral radiance scaled to \(QCALMIN\). \[T_{K}=\frac{K2}{\ln\left(\frac{K1}{L_{\lambda}}+1\right)} \tag{12}\]  
Figure 8: LU/LC classification map of Javadi Hills for the years (**a**) 2012 and (**b**) 2015. \[C=T_{K}-273.15 \tag{13}\]  
where \(T_{K}\) represents the effectiveness at the satellite temperature in Kelvin, and \(K1\) and \(K2\) represent the calibration constants 1 and 2 in \(\left(Watts\right/(m^{2}\,*\,sr^{2}\,*\,\mu m))\), respectively. For Landsat 7, the calibration constant value of \(K1\) and \(K2\) is 666.09 and 1282.71, respectively. Equations (14)-(20) represent the estimation of LST for the TIRS image of Landsat 8. By using the radiance rescaling factor, the conversion of Top of Atmosphere (TOA) spectral radiance is shown in Equation (14). By using the thermal infrared constant values in the metadata file of the satellite image, the spectral radiance data are converted to the TOA brightness temperature, and the expression is shown in Equation (15). The \(NDVI\) is calculated for differentiating the near-infrared and visible reflectance of the vegetation cover of the satellite data. The expression for \(NDVI\) is shown in Equation (16). The Land Surface Emissivity (LSE) is derived from \(NDVI\) values for displaying the average emissivity of the earth's surface. The expressions are shown in Equations (17) and (18). By using the results of TOA brightness temperature, emitted radiance wavelength, and LSE, the LST was calculated and is shown in Equation (19). \[TL_{\lambda}=ML\,*\,QCAL+AL-O_{i} \tag{14}\]  
where \(TL_{\lambda}\) represents the TOA spectral radiance in \(\left(Watts/(m^{2}\,*\,sr^{2}\,*\,\mu m)\right)\), \(ML\) represents the radiance multiplicative band rescaling factor of the TIRS image, \(QCAL\) represents the quantized calibrated pixel value, \(AL\) represents the radiance additive band rescaling factor of TIRS image, and \(O_{i}\) represents the correction value of the TIRS band of Landsat 8. \[BT_{P}=\frac{K2}{\ln\left(\frac{K1}{TL_{\lambda}}+1\right)}-273.15 \tag{15}\]  
where \(BT_{P}\) represents TOA brightness temperature in Celsius, and \(K1\) and \(K2\) represent the calibration constant 1 and 2 in \(\left(Watts/(m^{2}\,*\,sr^{2}\,*\,\mu m)\right)\), respectively. For Landsat 8, the calibration constant value of \(K1\) and \(K2\) is 774.8853 and 1321.0789, respectively. \[NDVI=\frac{(NIR-RED)}{(NIR+RED)} \tag{16}\]  
where \(NDVI\) represents the Normalized Difference Vegetation Index, \(NIR\) represents the reflectance values of the near-infrared band, and \(RED\) represents the reflectance values of the red band.