## 1 Introduction  
Chlorophyll-a (Chl-a) is an important index that can reflect phytoplankton biomass and the state of eutrophication. The concentration of Chl-a increases as the phytoplankton biomass increases, and an increase in phytoplankton may cause red tides, with the potential to threaten public health [1] and wildlife [2] and being harmful to the environment [3, 4]. The Beibu Gulf in Guangxi receives more than 120 small- and medium-sized inflows carrying a large amount of organic matter and inorganic salts, and it is likely to experience eutrophication and red tides. From 2014 to 2017, several abnormal water quality events occurred in the Beibu Gulf of Guangxi, including two red tides. Consequently, water quality monitoring in the Guangxi Beibu Gulf is of significance for protecting the water quality and environment of the Beibu Gulf and ensuring the health of its residents [5]. Traditional monitoring methods cannot completely reflect the spatial and temporal distribution of the water quality because of the small coverage of such methods, which are limited by high costs. However, satellite remote sensing enables automated monitoring of water quality parameters, including the Chl-a and total suspended solids. Such techniques benefit from lower costs and greater spatial and temporal coverage [6], and such studies have been undertaken overseas and in China [7, 8, 9, 10]. In recent years, machine learning has been used to retrieve water quality. Machine learning enhances the accuracy of inversion and the generalization ability through model training and, in turn, predicting and analyzing test data [11]. This method uses internal implicit networks and structures to determine the complex characteristics of input data and obtain explicit relationships among the output variables [12; 13]. Several approaches, including the decision tree [12; 14], BP neural network [15; 16], support vector machine model (SVM) [17; 18], and extreme machine learning approaches [19], have strong adaptability, fault tolerance, and organization of data. The optical radiometric measurement of the Chl-a concentration in coastal waters remains a challenge due to the presence of phytoplankton, suspended matter, and colored, dissolved organic matter. Some studies have revealed the advantages associated with the machine learning method applied in this field. In Galician Rias (northwest Spain), the neural network techniques were applied to estimate the Chl-a concentrations in three different water types. The results showed the capacity of the neural network to predict the Chl-a concentrations in coastal waters [20]. The Mixture Density Network (MDN) was induced for seamless retrieval of Chl-a data records in inland and coastal waters in the study of [PERSON] et al. As evidenced through image and satellite matchup analyses, the model generated realistic spatial distributions and provided a more accurate Chl-a map [21]. The Gradient-Boosting Decision Tree (GBDT) is a machine learning technique for regression, classification, and other tasks, using a decision tree flowchart approach combined with the boosting ensemble technique. The GBDT improves the capacity of the decision tree by reducing the residuals generated during the training procedure [22; 23]. It has been widely applied in social science research [24; 25; 26; 27; 28] and gradually introduced into the field of natural science [1; 2; 3; 4; 5; 6; 7; 29; 30; 31; 32; 33; 34; 35]. The GBDT exhibits much better performance in the retrieval of water depth compared with the single-band, dual-band, and BP neural network models [36]. Some studies have shown that the GBDT model can achieve higher simulation accuracy to the random forest (RF) algorithm and regression tree input with the same meteorological factors [37]. By constantly calculating the best fitting value and updating the classifier, the GBDT algorithm can obtain explicit relationships and features between different types of data with little prior knowledge.