## 4 Results and Discussion
### Comparison between Three Time Series Models  
This section analyzes the four hydrologic stations in the research area from the macroscopic perspective. Two types of indicators were used to evaluate the simulation effect of hydrological models and the correction effect of three time series models. The first is the hydrologic index NSE, R (the closer the NSE and R values are to 1, the better the simulation is, and an NSE greater than 0.7 indicates that the hydrological model simulated well). The other is the error index, that is, _MAE_, _RMSE_ and _MAPE_ (the error index of the time series model and the error index of the original BTOP model are converted to get the reduction rate, thus the larger the reduction rate, the better the model modification effect).  
A comparison of the R and NSE of the three time series models and the original BTOP model is shown in Figure 12. We can see that the R and NSE of the runoff series were improved at all four stations, among which the Prophet model has the most significant improvement effect (_NSE_ increased by an average of 30% and \(R\) increased by an average of 10%). Although the improvement effect of the LSTM and ARIMA models is not particularly obvious, mainly because they only predict the terminal error without considering the actual situation and runoff pattern characteristics, it also proves that it is effective to use the time series model to conduct runoff simulation correction for BTOP.  
The error reduction rate of _MAE_, _RMSE_ and _MAPE_ were compared. As can be seen in Figure 13, the corrections of the three models basically show positive effects in all three error indexes compared to the original BTOP simulations. The larger the triangle is, the greater the error reduction rate is, the better the model modification effect is. Finally, the correction effects of the three time models are discussed separately for different hydrological model simulation effects.  
1. At Donglin and Tuhuang stations, where BTOP simulations are better, _MAE_, _RMSE_ and _MAPE_ decreased by 6.94%-21.06%, 19.75%-25.74%, and 16.41%-24.49%, respectively, after Prophet modification. At this time, the Prophet model has a good correction effect, but the LSTM and ARIMA models have a poor effect, and the reduction rate of the corresponding error index after correction is far less than that of the Prophet model.  
Figure 11: Hydrographs from Donglin Station in 1985 with observed, simulated, and Prophet correction runoff.  
2. At Qinxi station, where the BTOP simulation is slightly less effective, _MAE_, _RMSE_, and _MAPE_ decreased by 34.91%, 19.29% and 20.3%, respectively, after Prophet modification. At this time, the Prophet model is also well modified, and the effects of LSTM and ARIMA models are improved, but the reduction rate of the corresponding error index after modification is still less than half of that of the Prophet model.
3. At Maoba station, where the BTOP simulation is the least effective, _MAE_, _RMSE_ and _MAPE_ decreased by 5.15%, 2.61% and 7.05% after Prophet modification. At this time, the modified effect of the Prophet model began to decline, and the error reduction rate after the modification of LSTM and ARIMA models was close to that of the Prophet.  
In general, the error reduction rate after correction of the Prophet model is the largest, and the reduction rate of each error indicator is about 1.7 times and 2.1 times that of the  
Figure 12: Comparison of R and NSE for four sites under different model corrections.  
Figure 13: Comparison of error reduction rate for four sites under different model corrections.  
LSTM and ARIMA models, respectively. In addition, the better the simulation effect of the hydrological model is, the more the advantages of the Prophet model effect can be reflected. Therefore, combining the hydrological and error index, we can conclude that the Prophet model has the best correction effect on BTOP, followed by the LSTM model, and the ARIMA model has the worst correction effect.