## 3 Methodology
### Image Processing  
Initially, all the images are loaded into ArcGIS(r) software (Version 10.8, 2019). This system facilitates the collection, organization, management, analysis, sharing, and distribution of geographic information, creating a new template for displaying satellite images of the analyzed cities. The first step involves removing the \"background\" of bands 4, 5, and 10 using the Raster Calculator tool in the ArcToolbox/Spatial Analyst Tools/Map Algebra section (Equation (3)). This procedure is repeated for all three bands. \[BANDS_{4,5}\text{ {and} }10=\text{ {Setnull} (\"Select Band\"=0, \"Select Band\")} \tag{3}\]  
Upon completion of this step, the study area is clipped to an appropriate scale using the CLIP tool in the Windows/Image Analysis section. All bands must be selected, including those processed prior to clipping. After clipping the bands for the study area, a new red, blue, green (RGB) layer is created using the Composite Bands tool, located in Windows/Image Analysis. Only bands 2, 3, and 4, resulting from the clipping, are selected. Once the command is applied, a new RGB layer is generated, which must be configured by rearranging the bands in the order b4/b3/b2, within their properties. Following these processes, calculations are performed to obtain the radiance of the thermal images. For this calculation, bands B10 and B11 are processed using the Raster Calculator tool. The equation utilized (Equation (4)) requires the values of Bands 10 and 11, which can be found in the attribute table of the root folder, located at the beginning of the table of contents. The values are listed under the names RADIANCE MULT_BAND_10 and RADIANCE MULT_BAND_11. The constant value of 0.0003342, used in the equation, is derived from the data tables labelled RADIANCE MULT_BAND, which is the standard value for the Landsat 8 satellite. \[RADIANCE_{10}\text{ {or} }11=0.0003342\,*\text{ {\"Band} }10\text{ {or} }11^{\prime}+0.10 \tag{4}\]  
The next value required is the soil brightness temperature, derived from the previously generated bands labeled Radiance_10 or 11. Using the Raster Calculator (RC) tool again, the bands labelled Brightness_10 or 11 are computed (Equations (5) and (6)). The values of 1321.0789 and 1201.1442 are obtained from the attribute table of the root folder, specifically under the following names: (a) K2_CONSTANT_BAND_10 = 1321.0789 and (b) K1_CONSTANT_BAND_10 = 774.8853. Finally, the value of 272.15 is used to convert the final results from degrees Fahrenheit to degrees Celsius. Once both bands are generated, they are averaged using the Cell Statistics tool located in the Windows/Search/Cell Statistics section. \[BT\_10=1321.0789/Ln\text{ }(774.8853/\"RADIANCE\_10\"+1)-273.15 \tag{5}\]  
\[BT\_11=1201.1442/Ln\text{ }(480.8883/\"RADIANCE\_11\"+1)-273.15 \tag{6}\]A significant metric in understanding the thermal behavior of urban areas is the normalized difference vegetation index (NDVI), which ranges between \(1\) and \(-1\). When the spectral response of the Earth's surface is similar across both bands, NDVI values approach zero, indicating neutral values or no significant changes. Healthy vegetation, characterized by photosynthetic activity, reflects more in the near-infrared spectrum than in the visible spectrum, resulting in positive NDVI values for green vegetation. NDVI values typically range between \(0.1\) and \(-0.1\), representing areas with little or no vegetation [53; 54]. To determine the vegetation level in the study area, bands \(5\) and \(4\) are processed using the RC tool (Equation (7)). When processed correctly, selecting a color scale within the green hues is advisable. \[NDVI=(Float\ (\text{Band}5-Band4)/Float\ (Band5+Band4) \tag{7}\]  
From the NDVI, the vegetation percentage (VP) is derived.