## 4 Discussion  
### Comparison of Different Models  
Two machine learning models were used for comparison in this study. An artificial neural network is a machine learning model that can explore the nonlinear relationship between the input variables and target data though training and adjusting the inside interconnected processing neurons [41]. The features of high prediction accuracy, self-adaptation, and robustness make it widely used for retrieval in waters with complex optical characteristics [42]. The support vector machine (SVM) is a useful tool for nonlinear statistical learning and regression analysis [43], whose training provides the support vectors to separate the classes in a multidimensional attribute space (the inland water's trophic status classification is based on machine learning and remote sensing data). The artificial neural network and SVM model were trained in MATLAB software. Given the same input variables as the GBDT model, the performance of them for the estimation of the Chl-a concentration in the coastal waters of the Beibu Gulf in Guangxi were evaluated. The results from verifying the accuracies of different models are compared in Figure 10 and Table 7.  
The GBDT model performed well, as indicated in the statistical metrics. The results of the analyses of the accuracy demonstrated that the GBDT model exhibited the highest inversion accuracy for the Chl-a concentration, with an RMSE of 1.626; the remote sensing inversion model for the Chl-a concentration based on the GBDT algorithm exhibited advantages in the inversion accuracy. The GBDT model performed better than the B4/B1 model and the other models tested. While the B4/B1 model reasonably estimated the Chl-a concentration (R\({}^{2}\) = 0.706; Figure 10b), it exhibited deviations at high and low Chl-a concentrations. The floating algae index (FAI), a water index strongly correlated with Chl-a which was proposed by [PERSON] in 2009 [44], exhibited a relatively large deviation from the in situ data (R\({}^{2}\) = 0.591, RMSE = 2.226 \(\upmu\)g/L, MAPE = 35.884%, and MAE = 1.843 \(\upmu\)g/L) (Table 6; Figure 10f). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Variables** & **MAE** & **MAPE** & **RMSE** & **R2** \\  & & **(\(\upmu\)g/L)** & **(\%)** & **(\(\upmu\)g/L)** & **R2** \\ \hline Single band & B3 & 3.381 & 65.758 & 3.705 & 0.563 \\  & B4 & 3.006 & 58.470 & 2.903 & 0.719 \\ \hline Band ratio & B4/B1 & 1.967 & 38.261 & 1.935 & 0.706 \\ \hline Band & B2 + B3 & 2.035 & 39.582 & 2.248 & 0.637 \\  & B2 + B4 & 1.898 & 36.927 & 2.029 & 0.671 \\  & B3 + B4 & 1.795 & 34.913 & 1.959 & 0.698 \\ \hline Water index & FAI & 1.843 & 35.884 & 2.226 & 0.591 \\ \hline SVM & B4, B3 + B4, B3, B1 \(-\) B4, B2 \(+\) B4 & 2.085 & 39.784 & 2.986 & 0.527 \\ \hline GBDT model & B4, B3 + B4, B3, B1 \(-\) B4, B2 \(+\) B4 & 0.998 & 19.414 & 1.626 & 0.778 \\ \hline Neural network & B4, B3 + B4, B3, B1 \(-\) B4, B2 \(+\) B4 & 1.492 & 28.472 & 1.974 & 0.714 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of model accuracies. Among the machine learning algorithms tested, the GBDT algorithm exhibited the best performance, while the SVM had the poorest performance (R\({}^{2}\) = 0.527, RMSE = 2.986 \(\upmu\)g/L, MAPE = 39.784%, and MAE = 2.085 \(\upmu\)g/L). Given the same input variables as the GBDT model, the neural network had a higher inversion accuracy than the traditional statistical models (R\({}^{2}\) = 0.706), showing a capacity to estimate the concentration of Chl-a in the coastal water. In general, the neural network tended to underestimate the Chl-a concentration, and the reason for this might be that the samples used to train and validate the neural network were inadequate. In a previous study ([PERSON] et al. [45]), the artificial neural network performed well for the estimation of the TSM and Chl-a concentration, but it required a large dataset for training.