# Dissolved Oxygen Modeling by a Bayesian-Optimized Explainable Artificial Intelligence Approach
## 6 Conclusions  
Accurate modeling of DO levels in rivers is crucial for understanding ecological and biological processes. This study develops a Bayesian-optimized XAI model to uncover the underlying mechanisms of DO dynamics and predict DO concentrations. The models are applied to the lower reach of the Mississippi River, using long-term hydrological and water quality records. This study arrives at the following conclusions: \begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **Reference** & **CD** & **RMSE (mg/L)** & **MAE (mg/L)** \\ \hline
1 & Present study & 0.970 & 0.395 & 0.303 \\
2 & [PERSON] et al. [36] & – & \textless{}0.8 & – \\
3 & [PERSON] et al. [46] & 0.83 & 0.58 & 0.074 \\
4 & [PERSON] et al. [48] & 0.96 & 0.38 & 0.31 \\
5 & [PERSON] et al. [49] & 0.825 & 0.726 & 0.515 \\
6 & [PERSON] et al. [29] & – & 0.805 & 0.891 \\
7 & [PERSON] et al. [20] & – & 0.87 & – \\
8 & [PERSON] et al. [50] & 0.965 & 0.836 & – \\
9 & [PERSON] et al. [47] & – & 0.43 * & 0.255 * \\
10 & [PERSON] et al. [27] & 0.744 & 0.811 & 0.528 \\
11 & [PERSON] et al. [51] & 0.928 & 1.726 & 0.978 \\ \hline \end{tabular}
* Results from FH = 1 d.  
\end{table} 
Table 5: Comparison of ML for DO modeling by different studies. * Among the models tested, the BO-SVR exhibits superior performance with the highest goodness of fit (CD = 0.970) and the lowest errors (RMSE = 0.395 mg/L and MAE = 0.303 mg/L), making it a reliable option for practical applications. * The SHAP analysis reveals that temperature is the most influential factor in determining DO levels. Discharge and gage height also have substantial impacts. While other parameters, such as specific conductance, turbidity, and pH, are known to influence DO, their effects are more indirect and less pronounced. * Temperature, discharge, and gage height are consistently the most sensitive variables, aligning with the SHAP analysis. The model demonstrates exceptional robustness, as sensitivity values remain stable even with perturbations ranging from 5% to 30%. Specifically, temperature sensitivity values range from 1.0% to 6.1%, discharge from 0.9% to 5.2%, and gage height from 0.8% to 5.0%. * Extending prediction horizons leads to reduced accuracy. The models are capable of generating satisfactory results (CD > 0.75) with a prediction horizon of up to 30 days. This study proves that BO-optimized ML models are a valuable tool for enhancing the understanding of DO dynamics in river systems, aiding in better management of water resources and ecosystem health. However, the reliance on a limited range of influencing parameters and data from a single station constrains the spatial and environmental scope of the models. Future research could enhance accuracy by incorporating more diverse parameters, such as nutrient concentrations and biological activity, and using data from multiple monitoring points. In addition, future work could develop adaptive models that account for non-stationarity due to climate change and improve the model performance under extreme events such as floods or droughts. Q.L. : conceptualization, methodology, investigation, validation, and writing--original draft. J.H. : conceptualization, project administration, and writing--review and editing. D.M. : investigation, simulation, and visualization. H.L. : investigation, resources, and writing--review and editing. S.L. : conceptualization, methodology, supervision, and writing--review and editing. All authors have read and agreed to the published version of the manuscript. This work is supported by the National Key R&D Plan (Grant No. 2022 YFC3800505), the Key Project of Technological Innovation and Application Development of Chongqing (Grant No. CSTB2023 TIAD-KPX0086), the Open Fund of Key Laboratory of Inland Waterway Regulation Engineering of the Ministry of Communications, Chongqing Jiaotong University (Grant Nos. KLIWRE2023B02 and KLIWRE2023B03), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202400706).