# Water Level Simulation in River Network by Data Assimilation Using Ensemble Kalman Filter
## 1 Introduction  
River networks play an important role in watershed landscapes due to their contributions to the watershed's hydrological processes. Compared to single open-channel rivers, they are more complex and more sophisticated hydraulic simulation models are required in order to solve unsteady flow problems in river networks. In addition, due to human activity, the river network structure of basins has changed significantly, causing spatial and temporal differences in hydrological connectivity [1]. The complex nature of river networks produces challenges in flow modeling, particularly in flood forecasting for a river network. As a result, the theories and corresponding algorithms for simulating and forecasting hydraulic flow in river networks have not been well established. Although flood forecasting with machine learning or deep learning models has been attempted in relation to flood simulations [2; 3; 4; 5], a large amount of data are required as inputs for the sufficient training of model parameters. The large number of parameters and the overfitting of parameters are also great concerns when attempting to realize accurate real-time predictions [6]. The existing one-dimensional Saint-Venant equations, which include a series of nonlinear partial differential equations [7], are generally used to solve the hydrodynamic process by means of the river network hierarchical differential method [8]. However, many factors, such as the uncertainty of the model parameters and the complex boundary conditions, limit the application of the one-dimensional Saint-Venant equations for river networks; the corresponding models fail to adjust modeling errors with the data measured in real time. The use of Kalman filter (KF) real-time correction technology to improve the reliability of water simulations and the forecast accuracy of hydrodynamic models has become an important research topic in the current approach towards flood forecasting [9; 10; 11; 12; 13]. To improve the accuracy of the model, many studies have combined KF with other models. For example, [PERSON] and [PERSON] [14] developed a river flood correction model by introducing the form of the spatial distribution of the gain information into the model's error correction process, which was used to improve the form of the dynamic noise interfering matrix of the original system. [PERSON] et al. [15] combined the ensemble Kalman filter (EnKF) with a shallow water equation (SWE) to reconstruct and predict a dam break event that was experimentally reproduced. Their study indicated that filter results could be made more accurate via the estimation of parameters alongside the state. Furthermore, some studies have adopted different types of parameters to improve flood forecasting. [PERSON] et al. [16] established a data assimilation scheme based on the EnKF and a smoother containing two parameters: soil moisture and streamflow, particularly considering the time delay. By exploiting the benefits of soil moisture and streamflow, the model showed great potential for short-term flood forecasting by merging observations from ground measurements and remote-sensing data retrieval. In addition, EKF and EnKF have been used to estimate both states and parameters in stochastic differential mixed-effect models with observation noise. These algorithms are efficient, easy to implement, and require less computation time than similar methods, such as the SAEM algorithm [17]. Given that the forecasting accuracy of a hydraulic model for river networks is mainly influenced by hydraulic states, such as discharge and model parameters such as bed roughness, the combination of state and parameter assimilation has been used in hydrological data assimilation studies [12; 17]. However, it is unlikely that the joint estimation of state and parameters will fully replace batch calibration. Due to the advantages of EnKF and EKF, they are also commonly used in many other fields for numerical weather prediction, stochastic signal processing, and Bayesian state estimation.