Ebrahimi (2026) A Novel Evidential Uncertainty Framework for Hybrid Models in Rainfall Simulation

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: Hamid Ebrahimi
• DOI: 10.1007/s11269-025-04386-1

Research Groups

• Civil, Water, and Environmental Engineering Faculty, Shahid Beheshti University, Tehran, Iran

Short Summary

This study develops and compares CNN-Q-learning and CNN-LSTM hybrid deep learning models, integrating Evidential Deep Learning (EDL) for uncertainty quantification, to simulate multi-station precipitation in Iran's Karkheh Basin. The CNN-Q-learning model demonstrated superior performance in capturing extreme events and quantifying uncertainty, while CNN-LSTM offered higher precision for routine predictions.

Objective

• To develop and compare two hybrid deep learning frameworks (CNN-Q-learning and CNN-LSTM) for multi-station precipitation simulation in the Karkheh Basin.
• To integrate Evidential Deep Learning (EDL) to analytically disentangle aleatoric (data-related) and epistemic (model-related) uncertainties within a single-pass predictive framework.
• To provide a comprehensive, reproducible, and uncertainty-aware precipitation forecasting framework, emphasizing rigorous training and robust uncertainty analysis.

Study Configuration

• Spatial Scale: Karkheh River Basin, Iran (approximately 50,000 km²), utilizing monthly precipitation data from five synoptic meteorological stations (Hamedan, Dashte-Abbas, Ahvaz, Ravansar, Varayne).
• Temporal Scale: Monthly precipitation data spanning 54 years (1966–2019). Input sequences used a 15-month lag to predict subsequent month's precipitation.

Methodology and Data

• Models used:
  • Hybrid Deep Learning Frameworks: Convolutional Neural Network combined with Q-learning (CNN–Q-learning), Convolutional Neural Network–Long Short-Term Memory (CNN–LSTM).
  • Uncertainty Quantification: Evidential Deep Learning (EDL) based on a Normal–Inverse–Gamma (NIG) hierarchical prior, yielding a Student-t predictive distribution.
  • Robustness and Sampling Uncertainty: Bootstrap resampling, Latin Hypercube Sampling (LHS).
  • Spatial Aggregation: Thiessen polygon method (also evaluated against Inverse Distance Weighting (IDW) and Ordinary Kriging).
• Data sources: Monthly precipitation data (1966–2019) from five synoptic stations in the Karkheh Basin, obtained from the Iranian Meteorological Organization. Data was quality-controlled, linearly interpolated for minor gaps (< 4%), and normalized via Min–Max scaling.

Main Results

• Model Performance: CNN–Q-learning more effectively captured extreme precipitation and heavy-tailed distributions (Mean RMSE ≈ 1.7 mm; NSE ≈ 0.78; CRPS ≈ 0.65; KS ≈ 0.055), showing positive skewness (≈ 1.46–1.65) and heavy tails (kurtosis ≈ 10.06). CNN–LSTM yielded sharper central predictions with slightly higher overall accuracy (Mean RMSE ≈ 1.1 mm; NSE ≈ 0.79; CRPS ≈ 0.91), maintaining near-symmetric distributions (skewness ≈ 0.17, kurtosis ≈ –0.69).
• Uncertainty Quantification (EDL): EDL successfully decomposed predictive uncertainty into aleatoric (data-related) and epistemic (model-related) components. Epistemic uncertainty generally remained below 5,000, with spikes exceeding 5 million at specific steps. Aleatoric uncertainty was near-zero, with peaks of 5–7 million. Total uncertainty was dominated by spikes around 13 million, indicating periods of high combined uncertainty.
• Calibration and Coverage: Both models achieved 100% coverage of actual data within 95% confidence bounds. CNN–Q-learning showed better calibration in the tails (KS Stat = 0.0549, A² Stat = 3.85), while CNN–LSTM exhibited narrower predictive intervals but slight underdispersion in tails (KS Stat = 0.13, A² Stat = 17.95).
• Operational Suitability: CNN–Q-learning is more suitable for risk management and extreme-event forecasting due to its heavy-tailed outputs, whereas CNN–LSTM offers higher precision for routine operational predictions.

Contributions

• Introduction of a novel CNN–Q-learning architecture for adaptive precipitation forecasting.
• Formal integration of Evidential Deep Learning (EDL) for interpretable uncertainty quantification, providing an analytical decomposition of aleatoric and epistemic uncertainties within a unified framework.
• Application of bootstrap resampling and noncentral distributions to enhance the robustness and reliability of uncertainty estimates.
• Provision of hydrologically interpretable uncertainty analyses that balance forecast sharpness with reliability, offering actionable insights for water resource management.

Funding

This research received no external funding.

Citation

@article{Ebrahimi2026Novel,
  author = {Ebrahimi, Hamid},
  title = {A Novel Evidential Uncertainty Framework for Hybrid Models in Rainfall Simulation},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04386-1},
  url = {https://doi.org/10.1007/s11269-025-04386-1}
}