## 2 Materials and Methods
The terms transmission and upwelling are used to approximate the surface radiance leaving the Earth's surface for each pixel in the original cube. The plotting of transmission and upwelling (\(\tau\), Lu) and the generation of the cube are input into the ENVI 5.3 algorithm to implement thermal atmospheric correction through ISAC. In this study, ENVI 5.3 software is utilized for data pre-processing, including atmospheric correction and conversion of digital numbers to surface temperature. Atmospheric correction plays a vital role in mitigating and removing atmospheric effects on thermal infrared data. The thermal bands in Landsat 4 and 5 TM are located in Band 6. Initially,  
Figure 2: Flowchart steps to achieve the objectives of the study. the sensor captures radiance values in digital numbers, which are then processed using calculations based on previous studies [25], such as Equation (1) below:  
\[\mathrm{L_{\lambda}}=\left(\frac{\mathrm{LMAX_{\lambda}-LMIN_{\lambda}}}{\mathrm{ Q_{calm max}-Q_{calm}}}\right)-\left(\mathrm{Q_{calm}-Q_{calm}}\right)+\left( \mathrm{LMIN_{\lambda}}\right) \tag{1}\]  
As per Equation (1), the variables are defined as follows: \(\mathrm{L_{\lambda}}\) represents the pixel value as radiance in W/(m\({}^{2}\)\(\times\) sr \(\times\) um), \(\mathrm{LMAX_{\lambda}}\) is the spectral radiance scale factor to Q\({}_{calmmax}\) in W/(m\({}^{2}\)\(\times\) sr \(\times\) um), and \(\mathrm{LMIN_{\lambda}}\) is the spectral radiance scale factor to Q\({}_{calm}\) in W/(m\({}^{2}\)\(\times\) sr \(\times\) um). \(\mathrm{Q_{calm}}\) corresponds to the maximum calibrated pixel value (equivalent to LMAX) in DN, which is 255, while \(\mathrm{Q_{calm}}\) corresponds to the minimum calibrated pixel value (equivalent to LMIN) in DN. The information regarding LMAX and LMIN was obtained from the downloaded metadata accompanying the remote sensing (RS) data (Table 2). In the case of Landsat 8 OLI TIRS, surface radiance in the thermal spectrum is captured by the Thermal Infrared Sensor (TIRS) 10. To convert digital numbers to radiance spectra \(\mathrm{L_{\lambda}}\) above the atmosphere, Equation (2) is applied as follows:  
\[\mathrm{L_{\lambda}}{=}\mathrm{ML}\times\mathrm{Qcal}+\mathrm{A_{L}} \tag{2}\]  
In this study, the radiance spectrum \(\mathrm{L_{\lambda}}\) is measured in units of W/(m\({}^{2}\)-sr\(\cdot\)um), while ML represents the recalibrated gain for a specific band, also in units of W/(m\({}^{2}\)-sr\(\cdot\)um). \(\mathrm{A_{L}}\) corresponds to the path radiance, measured in units of W/(m\({}^{2}\)-sr\(\cdot\)um). The ENVI 5.3 software is employed, which provides thermal functions specifically designed for atmospheric correction purposes. Before conducting atmospheric correction, it is necessary to convert the thermal images into radiance format. The primary objective of atmospheric correction for thermal bands is to minimize and remove the atmospheric effects present in thermal infrared data. This study utilizes the in-scene atmospheric correction (ISAC) algorithm proposed by [PERSON] et al. [22]. ISAC relies on radiance data acquired at the aperture to estimate the upwelling radiance and atmospheric transmission, as described in Equation (3). Furthermore, Equation (1) is employed to calculate the radiance at the aperture, assuming that objects with the highest radiance are black. \[\mathrm{Lob}=\mathrm{\tau B(T)+Lu} \tag{3}\]  
The term \"radiance\" refers to the observed radiance at the aperture, while \(\mathrm{\tau}\) represents the atmospheric transmission. B(T) corresponds to the Planck function, and Lu represents the upwelling radiance due to the atmosphere. The in-scene atmospheric correction (ISAC) algorithm evaluates the surface radiance emitted based on the brightness temperature of each pixel. The scatter plot of radiance for each band follows the Planck formula. A linear regression line is fitted to the upper portion of the scatter plot, which represents pixels approaching an emissivity of 1.0. This process estimates the transmission (slope) and upwelling (intercept) factors.