Arabzadeh et al. (2026) Simultaneous Bayesian quantification and decomposition of structural, parameter, and forcing uncertainty in hydrologic models: A blended model approach

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-10-26
• Authors: Rezgar Arabzadeh, James Richard Craig, Bryan A. Tolson, Jonathan Romero-Cuéllar, Robert Chlumsky
• DOI: 10.1016/j.jhydrol.2026.136672

Research Groups

• Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, Canada
• Heron Hydrologic Ltd, Canada
• Hazen and Sawyer, Canada

Short Summary

This study proposes a unified Bayesian framework using a blended model to jointly quantify and temporally decompose structural, parameter, and forcing uncertainty in streamflow prediction. It found that parameter uncertainty dominates (median ~55%), followed by forcing (~25%) and structural (~20%), with significant seasonal variations.

Objective

• To quantify and temporally decompose structural, parameter, and forcing uncertainty in streamflow predictions using a unified Bayesian framework, addressing the long-standing challenge of disentangling these contributions.

Study Configuration

• Spatial Scale: 12 MOPEX catchments (subset of 438) located primarily in the eastern United States, with drainage areas ranging from 1,023 km² to 4,419 km².
• Temporal Scale: Daily data from January 1, 1948, to January 1, 2004 (56 years).

Methodology and Data

• Models used:
  • Blended model structure (Mai et al., 2020) implemented in the Raven Hydrological Modeling Framework (Craig et al., 2020).
  • Bayesian inference performed using the No-U-Turn Sampler (NUTS) (Hoffman & Gelman, 2014) from the LaplacesDemon R package.
  • Uncertainty decomposition applied using Multivariate Analysis of Variance (MANOVA).
• Data sources:
  • MOPEX dataset (Duan et al., 2006) for 12 benchmark catchments.
  • Daily meteorological forcing data (minimum temperature, maximum temperature, and precipitation) and streamflow time series, publicly available from NOAA.

Main Results

• The framework achieved CRPS skill scores of 0.84–0.92, Kling–Gupta Efficiency (KGE) values of approximately 0.63–0.85, and 95% prediction interval coverage of 0.84–0.96 across the 12 MOPEX catchments.
• Parameter uncertainty is the largest source at 11 of the 12 catchments, with a median annual contribution of approximately 55%, followed by forcing uncertainty (median ~25%) and structural uncertainty (median ~20%).
• Forcing uncertainty exhibits pronounced seasonal amplification during winter–spring high-flow periods and is positively correlated with forest cover fraction (r = 0.50) and elevation.
• Structural uncertainty is amplified during summer–fall low-flow recession periods, coinciding with when competing baseflow algorithms diverge most strongly.
• The unexplained variance component remained small and nearly constant (median ~13.5%), confirming the adequacy of the linear MANOVA model.
• The dominance of parameter uncertainty suggests that additional streamflow observations would yield greater uncertainty reduction than equivalent investment in improved forcing data or model structural refinement.
• Uncertainty envelopes in real-time streamflow forecasting should be time-varying, as structural uncertainty triples during low-flow seasons and forcing uncertainty shifts markedly between summer convective and winter frontal regimes.

Contributions

• Developed a single Bayesian calibration framework that simultaneously infers weight-generating parameters (structural uncertainty), hydrologic process parameters (parameter uncertainty), and meteorological perturbation parameters (forcing uncertainty), thereby circumventing the identifiability problem of inferring separate input and structural error models from the same streamflow record.
• Applied a multivariate variance decomposition (MANOVA) to the resulting posterior ensemble to partition total predictive uncertainty among these three sources for every Julian calendar day, yielding a time-varying uncertainty budget across the hydrological year.
• Demonstrated this framework on 12 benchmark MOPEX watersheds, providing insights into how the dominant source of uncertainty shifts seasonally and across different catchment types.

Funding

• Natural Resources Canada’s Flood Hazard Identification and Mapping Program grant (FHIMP23-27P2)
• NSERC Discovery grants: RGPIN-2017-03920, RGPIN-2023-03459 (J. Craig); RGPIN-2022-03890 (B. Tolson)
• NSERC Tier II Canada Research Chair in Hydrologic Modeling and Analysis (CRC-2020-00176) (J. Craig)

Citation

@article{Arabzadeh2026Simultaneous,
  author = {Arabzadeh, Rezgar and Craig, James Richard and Tolson, Bryan A. and Romero-Cuéllar, Jonathan and Chlumsky, Robert},
  title = {Simultaneous Bayesian quantification and decomposition of structural, parameter, and forcing uncertainty in hydrologic models: A blended model approach},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.136672},
  url = {https://doi.org/10.1016/j.jhydrol.2026.136672}
}