## 5 Summary and Conclusions  
This study used three time series models to correct the hydrological model BTOP runoff simulation in the Xuanhan Section of the Zhou River, China. The error between the simulated and observed flow of the BTOP was taken as a random variable, and the Prophet, ARIMA, LSTM models were used to predict the error series. Finally, the predicted error was used to correct the simulated flow to achieve the effect of correcting the runoff simulation accuracy of the BTOP hydrological model. The corrected results were elaborated from the perspective of the overall effect and the individual analysis of causes. The summary and conclusions are as follows:  
1. The simulation of the BTOP model in the Zhou River basin is excellent. When the BTOP hydrological model is used for simulation in the study area, the law of error can be followed. We can see that the simulated flow of BTOP is generally slightly higher than the observed flow during the low-flow periods, while the simulated flood peak flow is smaller than the observed flow in high-flow periods.
2. The integration of the BTOP model and three time series models, Prophet, LSTM, and ARIMA, effectively improved the simulated runoff from the BTOP model. Among them, the prophet model performed best.
3. The LSTM model has a poor correction effect in high-flow periods due to its lack of scenario prediction. The ARIMA model does not consider seasonal factors and outlier processing and lacks physical analysis of the causes, leading to poor simulation results in both high-flow and low-flow periods.
4. In this study, the holiday function \(h_{(t)}\) in the Prophet model is improved to the flow function \(f_{(t)}\), which makes the sequence more consistent with the runoff pattern and makes up for the poor effect of the comparison models in the high-flow periods. The improved model can better predict the hydrological time series and greatly improve the runoff simulation accuracy of the hydrological model.  
It can be concluded that the improved Prophet model proposed in this study can effectively modify the runoff simulation of the BTOP hydrological model. However, some shortcomings of the study can be considered, as the lack of hydrological stations in the watershed, and the model training period can be extended appropriately. In the application of the time series model, it is a trend in model development for analysts to integrate their domain expertise. More effective correction of the high-flow periods of the hydrological model should be considered in the future, and attention should also be paid to the pre-processing of data and scenario prediction.  
Q.X.: Conceptualization, Software, Methodology, Formal analysis, Data Curation, Visualization, Writing--original draft. L.Z.: Conceptualization, Methodology, Formal analysis, Writing--review and editing. X.X.: Formal analysis, Visualization. L.L.: Methodology, Formal analysis. X.L. ([PERSON]): Data Curation, Visualization. X.L. ([PERSON]): Data Curation. T.A.: Funding acquisition, Supervision. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Regional Innovation Cooperation Program (2020 YPQ0013) and Key R&D Project (2021 YFS028) from the Science& Technology Department of Sichuan Province, Key R&D Project (XZ202101 ZY0007G) from the Science and Technology Department of Tibet.  
**Acknowledgments:** We gratefully acknowledge the anonymous reviewers for their comments and suggestions that improved this manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.