Rating Curve Modeling Using Machine Learning: A Case Study in the Largest Gauging Stations in the Amazon River

Accurate estimation of river discharge is fundamental for water resources management, flood forecasting, and drought monitoring in the Amazon River Basin. Rating curves, which relate water level (stage) to discharge, are the primary tool for streamflow estimation. This study evaluates traditional curve-fitting methods and machine learning algorithms for modeling rating curves at the two largest gauging stations in the Amazon River: Itacoatiara and Óbidos. The analysis is based on 70 stage–discharge measurements at Itacoatiara (2008–2023) and 176 measurements at Óbidos (1968–2023). Five modeling approaches were compared: Power Law, Linear Regression, Decision Tree, Random Forest, XGBoost, and Multi-Layer Perceptron (MLP). Model performance was assessed against official baseline rating curves maintained by Brazil’s National Water Agency (ANA) and the Geological Survey of Brazil (SGB/CPRM) using Root Mean Square Error (RMSE), coefficient of determination (r2), Mean Bias Error (MBE), Nash–Sutcliffe Efficiency (NSE) and Kling–Gupta Efficiency (KGE). Results indicate that ensemble-based machine learning methods, particularly XGBoost (RMSE = 7463 m3/s, NSE = 0.973 at Itacoatiara; RMSE = 18,378 m3/s, NSE = 0.872 at Óbidos), outperformed traditional methods. However, the Decision Tree exhibited overfitting that could not be resolved through pruning, depth limitation, or other strategies given the sample size. Traditional methods such as the optimized Power Law remain practical and transparent alternatives for operational use. The findings suggest that machine learning can complement traditional approaches for improving rating curve accuracy in large tropical rivers, with K-fold cross-validation used to assess variability and performance.