Stojković et al. (2026) 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

Identification

• Journal: Journal of Hydrology Regional Studies
• Year: 2026
• Date: 2026-04-04
• Authors: Milan Stojković, Milan Dotlić, Luka Vinokić, Zoran Kapelan, Slobodan Kolaković, Veljko Prodanović
• DOI: 10.1016/j.ejrh.2026.103407

Research Groups

• The Research and Development Institute for Artificial Intelligence of Serbia
• Faculty of Civil Engineering, University of Novi Sad
• Delft University of Technology, Department of Water Management
• Faculty of Technical Science, Department of Civil Engineering, University of Novi Sad
• University of South Wales (UNSW), School of Civil and Environmental Engineering
• Faculty of Civil Engineering, University of Belgrade

Short Summary

This study develops a joint machine learning (ML)–copula framework to create adaptive stage-flow rating curves for large lowland rivers with backwater impacts. It demonstrates that Kolmogorov–Arnold Networks (KAN) outperform traditional power regression and other ML models in accuracy and robustness, especially under extreme flow conditions and synthetic data extensions.

Objective

• To develop a novel ML-based regression framework capable of estimating rating curves that could adapt to hydrological changes, trained and validated using historical datasets affected by downstream regulation.
• To validate the developed ML-based rating curve using stochastically generated flows-stage pairs derived from a site-specific bivariate copula distribution to assess performance and generalization ability for unrepresented hydrological events.
• To estimate confidence intervals for the derived rating curve using unseen observed data and testing it on stochastically generated data, providing a quantitative measure of model reliability across different flow regimes.

Study Configuration

• Spatial Scale: Lower Tisza River, specifically two hydrological stations: Senta (Serbia) and Szeged (Hungary). The river has a drainage area of 157,186 km² and is influenced by the Novi Bečej dam downstream.
• Temporal Scale: Daily flows and water levels from 1980 to 2023. Training data: 1980–2010. Verification data: 2011–2023. Homogeneity and trend analyses were conducted over 1931–2023.

Methodology and Data

• Models used: Power-law regression, Support Vector Regression (SVR), Multilayer Perceptron (MLP), Kolmogorov–Arnold Networks (KAN).
• Data sources:
  • Measured daily water levels (stage) and flows from Senta (Serbia) and Szeged (Hungary) hydrological stations (1980–2023).
  • Stochastically generated synthetic stage-flow pairs using a Gumbel copula, extending the observed data range and preserving upper-tail dependence.
  • Outlier detection using locally weighted regression (LOESS).

Main Results

• ML models (SVR, MLP, KAN) consistently outperform classical power regression for observed data, achieving RMSE values of approximately 78–163 m³/s compared to 80–173 m³/s for power regression.
• KAN demonstrates robust performance across low, mean, and high flows, particularly excelling in transition zones and at extreme conditions, avoiding underprediction observed in MLP and SVR for high flows.
• For synthetic Gumbel-generated datasets, KAN maintains performance comparable to SVR (RMSE ≈129–212 m³/s) and preserves stable behavior across flow regimes, showing an advantage in extrapolating towards high-flow conditions.
• Confidence intervals are narrower at Szeged than Senta, reflecting stronger backwater influence at Senta. KAN provides consistent estimates across both stations in the low-flow domain.
• The Gumbel copula successfully generates synthetic data preserving the observed upper-tail dependence, with stronger dependence at Szeged (Θ = 4.69) than Senta (Θ = 3.16).

Contributions

• Development of a novel joint ML–Copula framework for adaptive stage-flow rating curve estimation in large, low-slope rivers affected by backwater impacts and morphological changes.
• Introduction and evaluation of Kolmogorov–Arnold Networks (KAN) for rating curve estimation, demonstrating its superior robustness and accuracy, especially for extreme flow conditions and synthetic data extrapolation, compared to traditional methods and other ML models (SVR, MLP).
• Validation of ML models using stochastically generated data via a Gumbel copula, enhancing the assessment of generalization ability beyond observed hydrological events.
• Quantification of uncertainty through confidence intervals across different flow regimes, providing a comprehensive measure of model reliability.
• The framework offers a scalable and transferable methodological foundation for operational water management, reservoir regulation, and long-term hydrological assessment in complex river systems.

Funding

• European Union’s Horizon Europe project ARTIFACT under Grant Agreement No. 101159480.
• Interreg IPA Hungary-Serbia project ADAPTisa (HUSRB/23R/11/006).

Citation

@article{Stojković2026Towards,
  author = {Stojković, Milan and Dotlić, Milan and Vinokić, Luka and Kapelan, Zoran and Kolaković, Slobodan and Prodanović, Veljko},
  title = {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},
  journal = {Journal of Hydrology Regional Studies},
  year = {2026},
  doi = {10.1016/j.ejrh.2026.103407},
  url = {https://doi.org/10.1016/j.ejrh.2026.103407}
}