# Water Level Simulation in River Network by Data Assimilation Using Ensemble Kalman Filter
## 6 Experimental Evaluation
### Results and Discussion
#### 6.4.2 Parameter Sensitivity
For water level prediction in practice, the accuracy and timing of water level predictions are also important. Our experiments on the Le Liu Hong plain river network showed that the EnKF-based assimilation model was able to forecast the water level after \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Treatment Scheme**} & \multicolumn{2}{c}{**Filtering Time (h)**} & \multicolumn{4}{c}{**Calculation Cost (s)**} \\ \cline{2-7}  & **Hongqiao** & **Lecheng** & **Liushi** & **Hongqiao** & **Lecheng** & **Liushi** \\ \hline  & \(\delta\) = 0.0005 m & \(\delta\) = 0.005 m & \(\delta\) = 0.05 m & \(\delta\) = 0.0005 m & \(\delta\) = 0.005 m & \(\delta\) = 0.05 m \\ EKF & 26 & 20 & 37 & 11,378 & 9335 & 15,463 \\ EnKF & 7 & 7 & 30 & 4248 & 4244 & 5415 \\ Ratio of EnKF to EKF & 27\% & 35\% & 81\% & 37\% & 45\% & 35\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Impact of observation noise level on data assimilation results based on EKF and EnKF. Figure 9: Comparison of RMSE values of EnKF and EKF at (**a**) Hongqiao station, (**b**) Lecheng station, and (**c**) Liushi station. 5 to 8 h and make predictions up to 20 to 30 h after the data assimilation process was completed. These timings are similar to those found in other research results. For example, [PERSON] et al. [25] conducted data assimilation research on the regional waters of Singapore, revealing that EnKF is efficient in short-term forecasting of water levels and currents, and the model could make better predictions up to 24 h, with the highest forecast quality within 6 h. Although increasing the initial ensemble size could lead to increased computation costs, as shown in Table 5, the overall computational cost was still relatively low. For example, the computational cost of the EnKF-based algorithm, as tested on the simulated river network, was only 223 s when using a personal computer when the ensemble size was 200, observation noise was 0.0001, and standard deviation was 0.1. Given the complex nature of a river network, more parameters, such as the water-level measurement station number and the river roughness coefficient, can be simultaneously corrected during the simulation time with hydraulic state variables. This further increases the forecasting accuracy and efficiency of the EnKF-based data assimilation model developed in this paper. Sensitivity to the type of river network and connection complexity could also be essential to testing the model's application capacity in practice. In the present study, we focused on comparing the data assimilation strategy based on the hydraulic model of a river network coupled with EKF and that coupled with EnKF. Our main objective was to understand the advantages of the data assimilation method based on EnKF. Thus, the 1D hydraulic model based on the Saint-Venant equations was used to solve the state variables of river networks. Indeed, 2D models are being developed by researchers [26; 27; 28], and future work can be carried out to develop a data assimilation strategy based on a 2D hydraulic model.