Comparative Analysis of Nonlinear Methods for Multivariable Water Level Prediction: The Case Study of the Atrato River
Authors: Renteria-Mena Jackson B. , Plaza Douglas , Giraldo Eduardo 
Published: July 2024

This paper presents an innovative multivariate forecasting application for hydrological variables, using an online model based on backpropagation (BP) neural networks. The effectiveness of this approach is verified by using the Nonlinear Autoregressive with Exogenous Inputs (NARX) and the linear Autoregressive with Exogenous Inputs (ARX) methods. The proposed methodology is implemented in two hydrological stations in the department of Chocó, Colombia, located along the Atrato River. The BP neural network structure is applied to establish correlations between water level, flow, and precipitation. This structure is designed to handle the dynamic complexity of the hydrological variables and their interconnections. In addition, a short‐term water level prediction is developed for incorporation into a flood early warning system. Validation of the approach is performed by comparing various estimation errors using regression metrics such as root mean square error (RMSE), relative mean square error (MSRE), mean absolute error (MAE), relative mean absolute error (MARE), and Nash–Sutcliffe efficiency coefficient (NSE). The computation time and the accuracy of the estimated weights versus real data are also considered. The results show that the proposed structure is the most suitable for accurately predicting water levels. It is shown that the backpropagation neural network structure of the proposed model is more effective for water level prediction. This is observed when evaluating the real data compared to the estimated data, obtaining values corresponding to the regression metrics. In particular, for output 2, the RMSE is 0.0742. Compared to the NARX model (RMSE of 0.0985) and the ARX model (RMSE of 0.1265), it is observed that the backpropagation neural network model improves the estimation by 32.6 over the NARX model and by 70.4% over the ARX model. As for the NSE coefficient for output 2 of the model, the backpropagation neural network is the closest to 1 compared to the other two models. For output 2, the backpropagation model obtains a value of 0.9966, the NARX model 0.9958, and the ARX model 0.9914. Another evaluation metric applied to this model is the Kling–Gupta efficiency coefficient (KGE), which is used to evaluate the performance of hydrological models. For the output of the two hydrological stations located in the Atrato River, we observed that for the backpropagation model a value of 0.9992 was obtained, for the NARX model a value of 0.9988 was obtained, and for the linear ARX model with nonlinear structure a value of 0.9984 was obtained. This indicates that the backpropagation neural network model provides a better estimate, as its value is closer to 1. Furthermore, the computational time executed in the algorithm of the three proposed nonlinear models is calculated, where the backpropagation obtains a calculated value of 350.9 microseconds, for the NARX model the computational time is 5908.7 microseconds and for the ARX nonlinear model, the computational time is 5172.6 microseconds. The model put forward demonstrates its effectiveness in accurately predicting water levels at two key hydrological stations along Colombia’s Atrato River. By incorporating intricate interactions among hydraulic structures and dynamic hydrological conditions, it enhances prediction accuracy. This not only aids in disaster risk management but also streamlines planning processes, particularly within flood early warning systems.