Erfan Abdi

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.

Reservoir management, flood control, and operational planning are the benefits of dam inflow forecasting. Decomposition algorithms can decompose complex inflow data into intrinsic components and reduce noise and fluctuations, while quantum machine learning models use features such as superposition and entanglement to manage large datasets and capture nonlinear hydrological behaviors. This study used three models: random forest (RF) as a classical benchmark, hybrid quantum neural network (HQNN) as a quantum approach, and sequential variational mode decomposition with HQNN (SVMD-HQNN) that integrates decomposition and quantum learning. The modeling was applied to forecast the inflow to Khoda Afarin Dam over 16 years (2009–2024) in two scenarios that included hydrological parameters (precipitation and evaporation) and reservoir parameters (water level, volume, and surface area). The data was divided into training and testing sets in a ratio of 70:30. The results showed that SVMD-HQNN achieved higher accuracy than the other two models with RMSE = 34.51, R² = 0.93, NSE = 0.91, MAPE = 11.48%, and KGE = 0.89 in scenario (i) and RMSE = 25.74, R² = 0.95, NSE = 0.94, MAPE = 8.98%, and KGE = 0.93 in scenario (ii). In the first scenario, this approach increased the prediction accuracy by 43.71%, and in the second scenario, it increased the prediction accuracy by 45.47% compared to the HQNN model. The proposed SVMD-HQNN framework is particularly effective under climate change conditions, where inflow fluctuations and instability are significant, and provides robust and generalizable predictions for reservoirs in similar environments.

Predicting dam inflow is critical for human life safety, water resource management, and hydroelectric power generation. While machine learning (ML) models address complex, nonlinear hydrological problems, quantum machine learning (QML) offers greater potential to overcome classical computational limits. This study compares a hybrid quantum neural network (HQNN) with the following two classical models: bidirectional CNN-LSTM and support vector regression (SVR). These models were evaluated to predict monthly inflow to the Mile Mughan Dam, a transboundary hydroelectric and irrigation dam located on the Aras River between Azerbaijan and Iran, using a 14-year dataset (2010–2023) under two scenarios. In total, 70% of data was used for training and 30% for testing. The first scenario encompassed meteorological variables plus three months of inflow lags, and the second included inflow lags only. Model performance was assessed using Coefficient of Determination (R²), Root Mean Squared Error (RMSE), Nash–Sutcliffe efficiency (NSE), Mean Absolute Percentage Error (MAPE), and graphical plots. HQNN showed superior performance across all metrics. In Scenario 1, HQNN achieved R² = 0.915, RMSE = 37.318 MCM, NSE = 0.908, MAPE = 8.343%; CNN-BiLSTM had R² = 0.867, RMSE = 46.506 MCM, NSE = 0.858, MAPE = 10.795%; SVR had R² = 0.846, RMSE = 52.372 MCM, NSE = 0.821, MAPE = 12.772%. In Scenario 2, HQNN maintained strong performance (R² = 0.855, RMSE = 48.56 MCM, NSE = 0.845, MAPE = 9.979%) and outperformed CNN-BiLSTM (R² = 0.810, RMSE = 56.126 MCM, NSE = 0.793, MAPE = 11.456%) and SVR (R² = 0.801, RMSE = 60.336 MCM, NSE = 0.761, MAPE = 12.901%). In Scenario 1 and Scenario 2, HQNN increased the prediction accuracy by 19.76% and 13.47%, respectively, compared to the CNN-BiLSTM model. These results confirm HQNN’s reliability in both multivariate and univariate modeling.

Accurate reservoir inflow predictions are critical for effective flood control and optimizing hydropower generation, thereby enhancing water resource management. This study introduces an advanced hydrological modeling approach that leverages a basic recurrent neural network (bRNN), convolutional neural network (CNN) with gated recurrent units (GRU) (bRNN-CNN-GRU), GRU with long short-term memory (LSTM) (GRU-LSTM) hybrid models, and deep neural network (DNN) to predict daily reservoir inflow at the Sefid Roud Dam. By utilizing historical data from 2018 to 2024, this study examined the following two multivariate scenarios: one incorporating water parameters such as water level, evaporation, and temperature extremes, and another focused solely on inflow delays. Training and testing sets were created from the dataset, with 80% for training and 20% for testing. For benchmarking purposes, the performance of the bRNN-CNN-GRU was evaluated against a deep neural network (DNN) and a GRU-LSTM hybrid. The evaluation metrics used were root mean square error (RMSE), correlation coefficient (r), and Nash Sutcliffe coefficient (NSE). Results demonstrated that, while all models performed better under the scenario incorporating inflow delays, the bRNN-CNN-GRU model achieved the best performance, with an RMSE of 0.71, r of 0.97, and NSE of 0.95, outperforming both the DNN and GRU-LSTM models. These findings highlight the significant advancements in hydrological modeling and affirm the applicability of the bRNN-CNN-GRU model for improved reservoir management in diverse settings.