## 1 Introduction
This algorithm experienced a significant decrease in predictive accuracy when the PC concentrations are below 300 \(\mathrm{\SIUnitSymbolMicro g}\)/L, with the model's coefficient of determination (R\({}^{2}\)) dropping from 0.99 to 0.65 [19]. These empirical algorithms or semi-analytical algorithms showed high errors in predicting PC concentration, such as the model proposed by [PERSON] [19], which had a relative error of up to 30.7% for PC concentration prediction. Recent comparative studies between empirical statistical models and machine learning models indicated that machine learning algorithms achieve higher prediction accuracy for PC concentration [20; 21]. Moreover, these algorithms demonstrate improved capability in capturing the mapping relationship between PC concentrations \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Time** & **Descriptions** \\ \hline
1 & January 2015–March 2015 & Wide-ranging and long-lasting impacts \\
2 & November 2015–December 2015 & Area not available \\
3 & December 2016 & Area not available \\
4 & January 2017–March 2017 & Dull water color and unknown size \\
5 & November 2017–December 2017 & Area not available \\
6 & January 2018 & Concentrations reach high levels \\
7 & January 2019–February 2019 & Area not available \\ \hline \hline \end{tabular} Based on information from the Marine Disaster Bulletin, the Guangci Marine Environmental Quality Bulletin and publicly available literature from both domestic and international sources.  
\end{table} 
Table 1: Statistical table of _P. glo_ red tide events in Qinzhou Bay, Guangxi. and spectral characteristics. It is worth considering whether the accuracy of the model is higher when using high spatial resolution and high spectral resolution images for PC concentration retrieval [22; 23; 24]. It is well known that many inland lakes are severely affected by cyanobacterial blooms. Previous studies on PC concentration retrieval have mainly focused on areas with high PC concentrations in inland waters bodies, leading to the poor performance of these models in the low PC concentration range. In the absence of exogenous input, PC concentration in nearshore waters is usually low ([0, 20] \(\mathrm{\SIUnitSymbolMicro g/L}\)), resulting in limited investigation of PC concentration retrieval in these nearshore areas. Combining machine learning algorithms has the potential to fill the research gap in remote sensing monitoring of low PC concentrations in nearshore regions. To address the issue of low PC concentration in Qinzhou Bay, Guangxi, we attempted to construct a series of spectral indices based on the bands after image preprocessing. Subsequently, we comprehensively analyzed the correlation between these spectral indices and PC concentrations. Ultimately, we identified the optimal spectral bands/indices to be used as independent variables for input into the Particle Swarm Optimization-based Backpropagation Neural Network model (PSO-BPNN). This model utilized high spatial resolution data from Sentinel-2 MSI for accurate prediction of PC concentrations. Based on these findings, the paper proposed an early warning threshold for predicting _P. glo_ red tide outbreaks in Qinzhou Bay. This method can roughly infer the risk of _P. glo_ red tide outbreak based on the distribution of PC concentration, providing a scientific basis for water environmental management in coastal areas.