Water-Level Forecasting Based on an Ensemble Kalman Filter with a NARX Neural Network Model ^†

It is fundamental, yet challenging, to accurately predict water levels at hydrological stations located along the banks of an open channel river due to the complex interactions between different hydraulic structures. This paper presents a novel application for short-term multivariate prediction applied to hydrological variables based on a multivariate NARX model coupled to a nonlinear recursive Ensemble Kalman Filter (EnKF). The proposed approach is designed for two hydrological stations of the Atrato river in Colombia, where the variables, water level, water flow, and water precipitation, are correlated using a NARX model based on neural networks. The NARX model is designed to consider the complex dynamics of the hydrological variables and their corresponding cross-correlations. The short-term two-day water-level forecast is designed with a fourth-order NARX model. It is observed that the NARX model coupled with EnKF improves the robustness of the proposed approach in terms of external disturbances. Furthermore, the proposed approach is validated by subjecting the NARX–EnKF coupled model to five levels of additive white noise. The proposed approach employs metric regressions to evaluate the proposed model by means of the Root Mean Squared Error (RMSE) and the Nash–Sutcliffe model efficiency (NSE) coefficient.