Towards adaptive stage-flow rating curve for large lowland river streams on the lower Tisza River with backwater impacts using deep learning and copula approach

Study region and rationale: The case study focuses on two hydrological stations on the lower Tisza River (Serbia and Hungary), located on a large lowland river stream strongly influenced by the downstream Novi Bečej reservoir (Serbia), where backwater effects and long-term hydraulic variability pose significant challenges for accurate flow estimation. Conventional approaches that assume a stable stage-flow relationship fail to capture rating curve complexity. To address these limitations, this study introduces a joint machine learning (ML)–copula framework in which ML-based rating models are developed and verified on measured data and stochastically generated synthetic stage-flow pairs using a Gumbel copula. The framework integrates traditional power-law regression with Support Vector Regression (SVR), Multilayer Perceptron (MLP), and Kolmogorov–Arnold Networks (KAN), and evaluates uncertainty through confidence intervals and performance metrics (MAE, RMSE, MAPE, R², PICP). ML models outperform classical power regression across low, mean, and high flows, with SVR, MLP, and KAN achieving RMSE ≈ 78–163 m³ /s compared to RMSE ≈ 80–173 m³ /s for power regression. Under synthetic Gumbel-generated datasets, KAN maintains performance comparable to SVR (RMSE ≈ 129–212 m³/s) and preserves stable behavior across flow regimes, avoiding the underprediction observed in MLP. Consequently, KAN demonstrates the robustness necessary for adaptive stage-flow rating curve estimation under changing hydraulic conditions. • A joint ML–copula framework for stage–flow rating curve estimation in lowland rivers affected by backwater. • ML models (SVR, MLP, KAN) outperform power-law regression with uncertainty quantification and multiple performance metrics. • KAN shows robust performance on Gumbel-generated datasets, maintaining accuracy across flow regimes without underprediction.