## 4 Results and Discussion
### Training and Validation of Machine Learning (ML) Models
#### 4.2.2 Validation of Machine Learning (ML) Models  
Data from seven stations, including Haiantong, Banjing, and Jiaogangzha stations, were selected to validate the ML water level simulation models in 2011 and 2013-2021, and the screening of the simulation factors was consistent with that of the training. The model at the time of training was adopted and input into the validation dataset to derive the simulated water level value of each model in each year, taking into consideration the completeness of the hydrological data and the accuracy of the simulation. The observed and simulated values of each station in 2011 were selected for comparison, as shown in Figure 7. The RMSE and NSE values were obtained by comparing the simulated values with the observed values at each station, and the 10-year data of each model at each station were averaged. The results are shown in Figure 8.  
Figure 7 shows that in the simulations of the ML water level simulation models in 2011, the data distribution of the RF and GBDT models are closer to the observed values. For example, at the Haiantong station, the amount of data near the median of the SVM model is considerably greater than that of the observed data, whereas the amount of data near the median of the RF and GBDT models is closer to the observed data, i.e., the water level simulation results of the RF and GBDT models are better than those of the SVM model. In terms of capturing the minimum and maximum water levels, the simulation results of the RF and GBDT models are closer to the observed minimum and maximum water levels, e.g., in Juegang station, where the difference between the minimum and maximum values of the SVM model and that of the observed data are 0.256 and 0.321, respectively, The minimum and maximum values of the RF and GBDT models are equal to the minimum and maximum values of the observed data, indicating that the RF and GBDT models are better than the SVM model.  
Figure 8: Bar chart of validation results for machine learning water level simulation models.  
Figure 7: Validation result plot of the machine learning models in 2011: (**a**) Haiantong, (**b**) Banjing, (**c**) Jiaogangzha, (**d**) Yangkouwaizha, (**e**) Juegang, (**f**) Dingyan, and (**g**) Shigang.  
Figure 8 shows that the RF and GBDT models have higher accuracy at all stations. At Yangkouwaizha station, the maximum RMSE is 0.170 and the minimum NSE is 0.725. Both models have an RMSE of less than 0.2 and an NSE greater than 0.7. The performance of the RF and GBDT models is better than that of the SVM model; for example, at Banjing station, the SVM, RF, and GBDT models have RMSE values of 0.162, 0.134, and 0.132, respectively, and NSE values of 0.762, 0.839, and 0.842, respectively, indicating that the simulation accuracies of the RF and GBDT models are higher [36]. The RMSE of the SVM model has a maximum difference of 0.089 between Yangkouwaizha and Jiaogangha stations, the RMSE of the RF model has a maximum difference of 0.045 between Yangkouwaizha and Shigang stations, and the RMSE of the GBDT model has a maximum difference of 0.049 between Yangkouwaizha and Jiaogangha stations. The NSE of the SVM model has the largest difference of 0.432 between Jiaogangzha and Juegang stations, the NSE of the RF model has the largest difference of 0.142 between Yangkouwaizha and Jiaogangzha stations, and the NSE of the GBDT model has the largest difference of 0.156 between Yangkouwaizha and Jiaogangzha stations, which indicates that the simulation results (RMSE and NSE) of the three models exhibit fluctuations, and the fluctuation of the SVM model is higher than that of the RF and GBDT models.