## 2 Materials and Methods
### Data Acquisition and Processing  
The images used in this study were obtained from the Landsat 8 satellite, which captures multispectral images of 30 m resolution sampled with the OLI (Operational Land Imager) sensor. The Landsat 8 satellite also provides a 15 m panchromatic band, allowing for a greater spatial resolution. All images were geometrically corrected and acquired in level 1 (L1). The images can be directly downloaded from the EarthExplorer gateway of the United States Geological Survey (USGS) [17]. Table 1 displays the details of the images used in this study. The Landsat 8 OLI products used consist of band 2 (0.45-0.51 mm), band 3 (0.53-0.59 mm), band 4 (0.64-0.67 mm), band 5 (0.85-0.88 mm), band 6 (1.57-1.65 mm) and band 7 (2.11-2.29 mm) [42]. All images were processed using the free software Quantum GIS (QGIS) version 3.14.16. Atmospheric correction was performed through the Semi-Automatic Classification Plugin (SCP) tool based on the Dark Object Subtraction (DOS1) algorithm [43]. The panchromatic band was used to provide higher spatial resolution. This is achieved using Gram-Schmidt Pan-Sharpening to produce a high-resolution color image that improves the training set and the classification process. Google Earth images were acquired according to acquisition dates (Table 1) and geoferenced using QGIS. The closest dates to the acquisition date were selected. Field data included collection of geoferenced points \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Satellite** & **Acquisition Date** & **Bands** &
\begin{tabular}{c} **Spectral** \\ **Resolution** \\ \end{tabular} & **Path/Row** & **Cloudiness** \\ \hline Landsat 8 OLI & 14/06/2015 & 2–7 & 30 m & 023/047 & 30\% \\ Landsat 8 OLI & 26/06/2016 & 2–7 & 30 m & 023/047 & 25\% \\ Landsat 8 OLI & 02/06/2017 & 2–7 & 30 m & 023/047 & 9\% \\ Landsat 8 OLI & 23/06/2018 & 2–7 & 30 m & 023/047 & 13\% \\ Landsat 8 OLI & 10/06/2019 & 2–7 & 30 m & 023/047 & 0\% \\ Landsat 8 OLI & 12/06/2020 & 2–7 & 30 m & 023/047 & 5\% \\ Landsat 8 OLI & 23/06/2021 & 2–7 & 30 m & 023/047 & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Images of Landsat 8 OLI used in the present study. Figure 1: Location of Coatzacoalcos city in Veracruz, Mexico. and their corresponding land use for the last two years of the analyzed periods. Figure 2 shows the methodology used for the study. The DOS1 atmospheric correction method was selected, as it is the most widely used method for LULC change detection [42]. This method uses the properties of the images. For instance, pixels conforming elements such as shadows, water or forests are considered dark objects when the magnitude of the reflectance is close to zero, namely, when the reflectance is less than or equal to 1%, and all the analyzed pixels are assumed dark elements. This assumption indicates that pixels receiving low values of solar radiation (\(\sim\)100% shade) registered by the satellite correspond to atmospheric dispersion, which generally is caused by effects of the topography [44]. Once a dark object is found in the image, the minimum reflectance value of the total Digital Number (DN) histogram is assigned to the object. This minimum is then modified by the effects of atmospheric correction [45]. The surface reflectance is calculated using the following expression:  
\[\rho_{s}=\frac{\pi(L_{\lambda}-L_{p})d^{2}}{ESUIN_{\lambda}\cos\theta_{s}} \tag{1}\]  
where \(\rho_{s}\) is the surface reflectance, \(d\) is the distance to the sun, \(ESUIN_{\lambda}\) is the mean solar exo-atmospheric irradiance, \(L_{\lambda}\) is the solar spectral radiance to the satellite, \(\theta_{s}\) is the zenith angle and \(\lambda_{p}\) is the path radiance given by [46]  
\[L_{p}=L_{min}-L_{DO1\%} \tag{2}\]  
Figure 2: Flow diagram of the LULC classification methodology implemented in the SCP tool.