Uncertainty Estimation in Predicting River Discharge Using Probabilistic Machine Learning and Conformal Prediction

Reliable streamflow forecasting with quantified uncertainty is essential for water resource management, flood mitigation, and climate adaptation in semi-arid regions. This research introduces a framework that combines three conformal prediction techniques, including Split Conformal Prediction (SplitCP), Cross Validation Plus (CV+), and conformal quantile regression, with two probabilistic machine learning algorithms, namely Natural Gradient Boosting (NGBoost) and Probabilistic Gradient Boosting Machines (PGBM), to quantify uncertainty in hydrological modeling of the Sattarkhan Dam in East Azerbaijan Province, located in north-eastern Iran. The data collected ranged from 21 March 1996 to 22 September 2022 and were divided into two chronological groups: training (70%) and testing (30%) for modeling. Probabilistic prediction quality was evaluated using the continuous ranked probability score (CRPS) and negative log-likelihood (NLL). In contrast, for conformal prediction, we used the mean predicted interval width, effective coverage, and coverage width criteria. Results in terms of correlation coefficient (CC), mean absolute error (MAE), and root mean square error (RMSE) with the test dataset suggest improved performance by NGBoost (RMSE: 0.833 m³/s, CC: 0.918, MAE: 0.375) using optimal values of user-defined parameters in comparison to PGBM (RMSE: 0.909 m³/s, CC: 0.902, MAE: 0.388). NGBoost outperforms PGBM in probabilistic prediction. Its higher coverage indicates CV+ as the most effective uncertainty estimation method for this dataset. These findings support model reliability and inform future decision-making. These findings support operational forecasting and risk-informed decision-making in semi-arid regions. Also, the framework provides a transferable template for similar hydrological uncertainty studies.