# Water Level Simulation in River Network by Data Assimilation Using Ensemble Kalman Filter
## 6 Experimental Evaluation
### Results and Discussion  
#### 6.4.1 Comparison of the EnKF and EKF Algorithm  
Figure 7 shows the water level error values between the simulation and the measurements among different data treatment schemes for Case 1. The evaluation metrics used for evaluating data assimilation performance are tabulated in Table 7. The data assimilation started in hour 96, and after 23 h of filtering, the data assimilation end condition had been reached for both the EnKF and EKF algorithms. The data assimilation process, whether using either EnKF or EKF, produced an instant and efficient reduction in the simulation errors. The time required for both EnKF and EKF algorithms to reach stability was minimal, indicating that both algorithms could correct the prediction results instantly for this single-river case. With the end of the assimilation phase at hour 119, the filtered water level error increased slightly but still fluctuated, mainly between \(-0.05\) m and \(0.05\) m, which was much lower than the water level error without data assimilation. The RMSE values decreased significantly by around two times after the data assimilation process was carried out using EnKF or the EKF algorithm. Although the EnKF algorithm produced a slightly lower RMSE, the difference was negligible for Case 1. However, the algorithm calculation cost for EKF was 16.7 s, which was 19.2% higher than that of EnKF, indicating that EKF was more time-consuming than EnKF. This result is similar to those found in the literature [23], namely, that the computational time of EnKF was 0.8 of that of EKF. This is because EKF requires the computation of the tangent linear state operator, whereas EnKF avoids this computation step.  
Figure 6: Schematic diagram of the Le Liu Hong plain river network.  
Note that the river in Case 1 was a mountainous single-channel river with a relatively simple water flow. This enabled a significant reduction in the algorithm calculation time and thus in the difference in calculation cost between EKF and EnKF. Indeed, for Case 2, which was a complex river network, we observed greater differences in the evaluation metrics.  
Figure 8 shows the simulated water level without data assimilation at the beginning period of the simulation (before hour 40) and with subsequent data assimilation using EKF and EnKF. Generally, the simulation error was substantially reduced and approximated to zero at the end of data assimilation using EKF or EnKF. This simulation error would spread out gradually over the long term after the end of data assimilation, indicating that the data assimilation effect could still be maintained for a relatively long period (up to 20 to 30 h) with negligible errors after the end of the data assimilation process.  
Table 8 presents a comparison of the evaluation metric results of EKF and EnKF for different stations. The calculation time required by EnKF for this river network was 4243.6 s, which was only 45% of that required by EKF (9335.4 s). Compared to the mountainous single-channel river, as expected, the calculation time increased hugely; furthermore, EnKF exhibited a much lower calculation cost value relative to EKF, i.e., the ratio of the calculation cost between EnKF and EKF decreased greatly, from 81% to 45%, indicating that the calculation efficiency of EnKF was much higher than that of EKF for a complex river network. We also found that the RMSE values of EnKF were much lower than those of EKF, regardless of the water level measuring stations selected. Particularly, Lecheng station had an RMSE value of only 9% when using EnKF compared to EKF. Interestingly, EnKF was more stable than EKF during the data assimilation period at the three stations. The high fluctuations of EKF may reduce its convergence. The filtering time (i.e., the time taken by the algorithm to reach stability after the beginning of filtering) was also much shorter for EnKF than for EKF. For example, for the Hongqiao station, EnKF took 5 h to reach stability for accurate water level calculations, whereas EKF took 20 h.