Pérez et al. (2025) Beyond Deterministic Forecasts: A Scoping Review of Probabilistic Uncertainty Quantification in Short-to-Seasonal Hydrological Prediction

Identification

• Journal: Water
• Year: 2025
• Date: 2025-10-11
• Authors: David De León Pérez, Sergio Salazar-Galán, Félix Francés
• DOI: 10.3390/w17202932

Research Groups

• Research Group of Hydrological and Environmental Modelling (GIHMA), Research Institute of Water and Environmental Engineering (IIAMA), Universitat Politècnica de València, Valencia, Spain
• Agroecosystems History Laboratory, Universidad Pablo de Olavide, Sevilla, Spain

Short Summary

This scoping review synthesizes methodological trends in predictive uncertainty (PU) quantification for short-to-seasonal hydrological forecasting, identifying an exponential growth in machine learning applications, geographic concentration of studies, and persistent operational barriers.

Objective

• Evaluate contemporary methodologies for predictive uncertainty (PU) quantification in short-to-seasonal hydrological forecasting.
• Identify emerging trends, best practices, and existing gaps in statistical and machine learning-based approaches for PU quantification.
• Determine how these methodologies can bridge the gap between theoretical advancements and operational implementation in diverse hydroclimatic regions.

Study Configuration

• Spatial Scale: Global scoping review analyzing studies primarily concentrated in Chinese, North American, and European watersheds (over 65% of cases), with 97 countries mentioned across the reviewed literature.
• Temporal Scale: Forecast horizons from daily (1 day) to seasonal (up to 8 months). The review period for studies analyzed was from 2017 to 2024.

Methodology and Data

• Models used: Scoping Review (ScR) method based on De León Pérez et al. [8] protocol, aligned with PRISMA-ScR standards. Methodologies reviewed include:
  • Statistical approaches: Bayesian Forecasting System (BFS), Bayesian Model Averaging (BMA), Model Conditional Processor (MCP), Generalized Likelihood Uncertainty Estimation (GLUE), ensemble techniques, and quantile-based approaches.
  • Machine Learning/Artificial Intelligence (ML/AI) methods: Deep learning architectures (e.g., Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Bidirectional Long Short-Term Memory (BLSTM)), tree-based algorithms (e.g., Random Forest, XGBoost), and hybrid models.
  • Hybrid statistical-AI modeling frameworks.
• Data sources: Semi-automated search conducted in Scopus and Web of Science databases. A total of 572 documents were retrieved, with 92 selected for in-depth evaluation.

Main Results

• An exponential growth in the application of machine learning and artificial intelligence for predictive uncertainty quantification was observed.
• Studies are geographically concentrated in Chinese, North American, and European watersheds (over 65% of cases), leading to an underrepresentation of data-scarce tropical and arid regions.
• Persistent operational barriers hinder the adoption of advanced PU quantification, including high computational demands, interpretability constraints, and limited standardization of operational frameworks (e.g., 35% adoption rate for Bayesian frameworks).
• Hybrid statistical-AI modeling frameworks enhance forecast accuracy and PU quantification but face challenges in computational demands, interpretability, and inadequate validation for extreme events.
• Specific quantitative improvements include:
  • HUP-BMA reduced forecast interval width by 28.42% and Continuous Ranked Probability Score (CRPS) by 17.86% compared to HUP.
  • CHUP-BMA (copulas replacing Normal Quantile Transformation) further reduced interval width by 28.42% and CRPS by 17.86% versus HUP-BMA, achieving over 90% calibration for up to 7-day horizons.
  • Multi-temporal/multi-model MCP (MCP-MT) reduced forecast interval widths by 28.42% and CRPS by 17.86% compared to single-temporal approaches.
  • Gaussian Mixture Clustering Integration (GMCP) showed a 36.64% sharpness increase, 10.29% containing ratio improvement, and 16.66% Nash-Sutcliffe Efficiency (NSE) enhancement in dry catchments.
  • Multimodel MCP for reservoir inflow prediction demonstrated a 72% error reduction and NSE increase from 0.86 to 0.98 for 1-day forecasts, and a 50% error reduction and NSE increase from 0.64 to 0.93 for 3-day forecasts.
  • Bayesian deep learning (BLSTM) achieved Prediction Interval Coverage Probability (PICP) values exceeding 0.950 for 1-day forecasts.
  • XGB-GPR-BOA achieved a Root Mean Square Error (RMSE) of 1.847 cubic meters per second and an R² of 0.965 in the Yangtze River Basin.
  • RF-GPR-MV showed 15–25% improvements for 1- to 12-month forecasts.
  • PI3NN achieved 90% coverage probability for reservoir inflow forecasting while maintaining interpretability.
  • A BMA-ensemble approach achieved 80% NSE/R² improvements.
  • Copula-HUP paired with DA-LSTM-RED achieved 10–17% Mean Absolute Error (MAE) reduction and 17.86% CRPS improvement compared to traditional HUP-BMA.

Contributions

• Provides an updated field mapping of predictive uncertainty quantification in short-to-seasonal hydrological forecasting.
• Identifies systematic knowledge gaps and prioritizes research directions for the operational integration of advanced PU quantification.
• Offers a transparent presentation of information and comprehensive supplemental documentation to facilitate reproducibility and future research.
• Highlights the significance of robust frameworks integrating hydrological postprocessing from meteorological input to hydrological output to minimize uncertainty chains and support water management.

Funding

• Colombian Ministry of Science, Technology, and Innovation (MINCIENCIAS) through the Call for Doctorates Abroad 885-2 (D.D.L.P.)
• Valencian Regional Government through the WATER4CAST 2.0 (CIPROM/2023/5) research project (D.D.L.P. and F.F.)
• Spanish Ministry of Science and Innovation through TETISPREDICT (PID2022-141631OB-I00) research project (D.D.L.P. and F.F.)
• Research talent recruitment programme “EMERGIA”, Call 2021, Consejería de Universidad, Investigación e Innovación, Junta de Andalucía, Spain (EMC21_00413) (S.S.G.)
• Universitat Politècnica de València for open access (APC funding).

Citation

@article{Pérez2025Beyond,
  author = {Pérez, David De León and Salazar-Galán, Sergio and Francés, Félix},
  title = {Beyond Deterministic Forecasts: A Scoping Review of Probabilistic Uncertainty Quantification in Short-to-Seasonal Hydrological Prediction},
  journal = {Water},
  year = {2025},
  doi = {10.3390/w17202932},
  url = {https://doi.org/10.3390/w17202932}
}