# Water Level Simulation in River Network by Data Assimilation Using Ensemble Kalman Filter
## 1 Introduction
These fields often face high-dimensional problems and require scalable algorithms to process and make sense of the data. A comparison showed that EKF was more accurate and faster in optimizing the magnetic particle tracking (MPT) method in particle tracking [18]. Similarly, a modified EnKF was established to deal with nonlinearity in the multiple-target tracking (MTT) and multi-sensor fusion (MSF) scenarios, which was more accurate than traditional KF [19]. In stochastic signal processing (SP), high-dimensional problems are becoming more relevant in applications such as simultaneous localization and mapping (SLAM) and extended target tracking, where the state vector can contain many parameters. EnKF can be applied to these problems as it can handle nonlinear and non-Gaussian state-space models [20]. EnKF has also been applied in reservoir engineering, where the pressure, saturation, and temperature at different grid cells in the reservoir represent the state of the system. EnKF estimates the state of the system by integrating measurements from various sources such as production data, seismic data, and well-log data. EnKF has the benefit of allowing for the prediction of reservoir performance by running the simulator in a forward direction from the latest data assimilation time (analysis step) with each ensemble member [13]. One of the key aspects in river network research is flood forecasting. Flood simulation and forecasting in plain river network areas are greatly affected by the multi-level spatial river network structure, the complex water movement, the intervention of an upper dam or gate regulation, as well as the influence of uncertain factors such as boundary input conditions, riverbed variations, and model parameters. There are still more difficulties and challenges in such areas compared to single open-channel rivers in terms of calculation efficiency, the data treatment (e.g., data assimilation) process and degree, and forecasting periods (a few hours to days ahead). To date, very few studies have been conducted to investigate the performance of KF or its variants on the water flow simulation of river networks and, where available, they have simplified the river networks with the use of limited river branches and nodes [21], or short-term flow forecasting was carried out [9]. For example, [PERSON] et al. [9] developed a lumped hydrological model to propagate the discharge through the Seine river basin in France and KM was used to assimilate the discharge data to improve the simulation accuracy of flow forecasting within 72 h. However, the simulation results could be significantly influenced by the degree of river network spatialization and the spatial distribution. In this study, an EnKF algorithm was developed for performing data assimilation on simulated water level data from a river network hydraulic model for real-time water level prediction. A new data assimilation scheme was proposed for applying EnKF to simulated water level data to improve the simulation capacity, followed by a parameter analysis conducted on a simulated river network in order to understand and optimize the key parameter values. Based on the optimized parameter data, an experimental evaluation was conducted on a real single-channel river and a real plain river network with an area of 325 km\({}^{2}\). In addition, the data assimilation results obtained with EnKF were compared to those obtained with the classic Kalman filter for hydraulic simulation, i.e., the extended Kalman filter (EKF), with regard to their simulation accuracy, calculation cost, and data assimilation efficiency. In this study, we aimed to provide a data assimilation scheme using EnKF to improve the real-time simulation capacity of a river network hydraulic model.