This paper comparatively assesses the performance of five data assimilation techniques for three-parameter Muskingum routing with a spatially lumped or distributed model structure. The assimilation techniques used include direct insertion (DI), nudging scheme (NS), Kalman filter (KF), ensemble Kalman filter (EnKF) and asynchronous ensemble Kalman filter (AEnKF), which are applied to river reaches in Texas and Louisiana, USA. For both lumped and distributed routing, results from KF, EnKF and AEnKF are sensitive to the error specification. As expected, DI outperformed the other models in the case of lumped modelling, while in distributed routing, KF approaches, particularly AEnKF and EnKF, performed better than DI or nudging, reflecting the benefit of updating distributed states through error covariance modelling in KF approaches. The results of this work would be useful in setting up data assimilation systems that employ increasingly abundant real-time observations using distributed hydrological routing models.

Diverse hydrologic and hydraulic models of varying complexities have been proposed in the past few decades to accurately predict the water levels and discharges along rivers. Among them, the hydrologic routing models are widely used because of their simplicity, minimal data, and computational requirements. Due to their simplified assumptions, however, they are subject to various sources of uncertainty. To reduce their predictive uncertainty and improve their operational forecast abilities, data assimilation techniques have been proposed to update the states and/or parameters of the mathematic models by integrating real-time river observations with them. However, the characterization of the model errors and the location of the sensors used for data assimilation have an important effect on the model performance. The main objective of this study was to assess the effect of sensor placement and the errors of both the model and the boundary conditions on the assimilation of flow observations in the distributed hydrologic routing models. A Muskingum-Cunge routing model was applied first to a synthetic river reach with a rectangular cross section and then to a more complex natural river, the Bacchiglione River in Italy, with varying geometry of the river cross sections. The Kalman filter was used to assimilate the flow observations. Synthetic and real-world experiments were carried out. The results showed an improved model performance after the assimilation of the flow observations (e.g., a Nash index higher than 0.9 in the synthetic river and 0.85 in the Bacchiglione River); however, the procedure was sensitive to the model error and the locations of the sensors. In particular, when the model error was larger than the boundary condition error, it was suggested to place the sensors in the lower part of the river reach to maximize the model improvement at the river outlet. On average, the model performance was improved by 14% in terms of the Nash index when the sensor was located in the upstream part of the reaches of the Bacchiglione River instead of in the downstream part. Sensors placed in the upper part of the reaches enabled the improved skills to persist for additional lead time of up to 6 h for the forecasting of the water level at the reach outlet. This study presented a method that allowed identifying the optimal locations of the sensors and thus helped to improve the flood forecasts.