## 2 Materials and Methods
### Using Satellite Images to Collect Geospatial Data  
In addition to on-site sample collection, this study also includes data collection via the Sentinel-3B OLCI satellite, divided into two main steps [40; 41]. The first step involves locating collection points in Cartagena Bay during the high winds/low runoff season (summer) 2020. The satellite data were detected at 3:15 p.m. on January 19 th. The second image stage occurred during the low wind/high runoff season (winter) of 2021, and satellite data sampling was also carried out at 3:06 p.m. on October 26 th. Qualifying Sentinel-3B OLCI images were required to be free of cloud cover, as per [1; 16; 40; 41].  
Sentinel-3B OLCI satellite images used in this study present reflectance in a Neural Network (NN) with a spatial resolution of 300 m. They were normalized by ESA [9; 10; 11] to a reflectance of 0.83 ug/mg. Furthermore, they consider a maximum spectral error of 6.62%, aiming to detect the quantitative levels of concentrations of CHL_NN (m\({}^{-3}\)), TSM_NN (g m\({}^{-3}\)), and ADG_443_NN (443 m\({}^{-1}\)) during the analyzed period (2020 to 2021).  
After selecting images from the Sentinel-3B OLCI satellite, the criteria for determining the sampled points for collecting information in the waters of Cartagena Bay were based on geospatial distribution in a Triangular Irregular Network (TIN) [42; 43]. Forming an irregular mesh containing 91 collection points spaced 1000 m apart was possible. These points were distributed in the regions of Bocagrande, Isla Tierra Bomba, and Playa Blanca in Cartagena Bay, using SNAP software (Sentinel Application Platform/version 8.0.4.).  
The data collected from Sentinel-3B OLCI satellite images at the 91 sample points were organized in a data spreadsheet. K-Means clustering algorithms were used to perform quantitative analyses utilizing JASP software (Jeffreys's Amazing Statistics Program), version 3.16.7 [12; 44]. This clustering algorithm is an unsupervised technique that identifies similarities between data collected from satellite images, grouping them into clusters and allowing for the identification of hidden structures within the data sets [12; 44]. The method works iteratively, starting with an initial solution that can be a random configuration of interaction between the cluster centroids [45]. This iterative process between the cluster centroids continues until the values are smaller than the cluster mean threshold [46; 47].  
The cluster centroid data were used to calculate the Silhouette index, which evaluates the homogeneity within each cluster individually and compares them with other clusters [46; 47]. When the Silhouette index produces values closer to the upper limit of 1, this indicates greater reliability in the cluster data. Silhouette scores closer to the lower limit of \(-1\) indicate inaccuracy in the cluster data [44; 48].  
The relationship between the uses of sediment samples collected in the field, despite covering local analysis coverage, helps to accurately reveal the type of chemical elements present in the samples [1; 12; 37]. These dangerous chemical elements are transported by water currents, where satellite image sampling becomes essential, enabling a macroscale analysis of the quantitative dynamics of these chemical elements coupled in the sediments dispersed in the water [1; 12; 37].