Robust Short-Term Multivariate Water-Level Forecasting Using a Hybrid LSTM–EnKF Model Under White-Noise Disturbances
Short-term multivariate forecasting of hydrological variables remains challenging because river systems exhibit nonlinear and time-dependent dynamics, complex relationships among water level, flow, and precipitation, and uncertainty arising from measurement errors and external disturbances. Although neural network models can learn nonlinear relationships among hydrological variables, their predictive performance often deteriorates in the presence of noise. Moreover, existing approaches rarely integrate the learning of long-term temporal dependencies and cross-variable relationships with a data assimilation mechanism capable of recursively updating state estimates and reducing forecast uncertainty. This limitation reveals the need for a robust forecasting framework that combines both capabilities. Therefore, this study aimed to develop and evaluate a hybrid Long Short-Term Memory–Ensemble Kalman Filter (LSTM–EnKF) model for short-term multivariate water-level forecasting under noisy conditions. The proposed framework extends a previously developed NARX–EnKF approach by replacing the NARX network with an LSTM architecture capable of learning nonlinear temporal patterns and relationships among water level, flow, and precipitation. The model was implemented using data from two hydrological stations located along the Atrato River in Colombia and configured to generate water-level forecasts with a two-day prediction horizon. The LSTM network generated the initial forecasts, whereas the EnKF assimilated the available observations to recursively update the estimated states and reduce forecast uncertainty. Model robustness was examined by introducing Gaussian white noise with variance levels of 0.001, 0.05, 0.10, and 0.20 to represent measurement uncertainty and external disturbances. Performance was evaluated using the root mean square error (RMSE), mean absolute error (MAE), and Nash–Sutcliffe efficiency (NSE). Across all evaluated noise levels, the LSTM–EnKF model outperformed the standalone LSTM model. Its total RMSE ranged from 0.1009 to 0.1929 m, compared with 0.1740 to 0.2356 m for the standalone LSTM, representing reductions of approximately 18.1–42%. The hybrid model achieved NSE values ranging from 0.9760 to 0.9992, whereas the standalone LSTM produced values between 0.9200 and 0.9776. Furthermore, the LSTM–EnKF reduced the MAE by approximately 51.9–56.2% across both outputs. These results indicate that integrating LSTM-based temporal learning with EnKF-based data assimilation improves short-term forecasting accuracy and robustness under noisy conditions. The developed framework provides a promising tool for supporting flood early-warning systems, flood-risk management, and the protection of riverine communities.