Romero-Cuéllar et al. (2026) Residual error modelling for process-based flood frequency analysis

Identification

• Journal: Natural hazards and earth system sciences
• Year: 2026
• Date: 2026-10-30
• Authors: Jonathan Romero-Cuéllar, James Richard Craig, Bryan A. Tolson, Rezgar Arabzadeh
• DOI: 10.5194/nhess-26-5389-2026

Research Groups

Department of Civil and Environmental Engineering, University of Waterloo, Canada.

Short Summary

This study introduces UQ-flood, a novel process-based flood frequency framework integrating a stochastic weather generator, a hydrologic model, and an annual-maximum residual error model. It demonstrates that this framework effectively corrects systematic biases in flood estimates and supports reliable flood quantile estimation, even with short data records.

Objective

• To develop and evaluate UQ-flood, a process-based flood frequency analysis framework that integrates a stochastic weather generator, a hydrologic model, and an annual-maximum residual error model, to correct systematic biases and propagate uncertainty in simulated flood peaks, particularly for sites with short data records.
• To assess if UQ-flood's central flood-quantile estimates, derived from 30 years of data, are consistent with long-record observational benchmarks.
• To quantify the impact of explicitly accounting for hydrologic model error via the residual error model on process-based flood estimates.

Study Configuration

• Spatial Scale: Three Canadian watersheds with contrasting hydroclimatic conditions: Black River (Ontario, approximately 1506 km²), Moyie River (British Columbia, approximately 1480 km²), and Lahave River (Nova Scotia, approximately 1250 km²). The study focuses on at-site flood frequency analysis.
• Temporal Scale: Hydrologic models, stochastic weather generators, and residual error models were calibrated or inferred using 30 years of daily meteorological and streamflow observations (e.g., 1 January 1991 to 31 December 2020 for Black River and Moyie River). Long-record empirical annual-maximum estimates (up to 108 years) served as the primary benchmark. The stochastic weather generator produced synthetic daily time series spanning greater than 1000 years, with sensitivity analyses conducted for simulated series lengths up to 3000 years.

Methodology and Data

• Models used:
  • Hydrologic Model: Hydrologiska Byråns Vattenbalansavdelning – Environment Canada (HBV-EC) model, implemented as a lumped representation within the Raven Hydrological Modelling Framework version 3.8.
  • Residual Error Model (REM): An additive model in Box–Cox transformed space (power parameter 0.2), utilizing Gaussian innovations and a flow-dependent error mean, with parameters inferred using the method-of-moments. This model was developed specifically for annual maxima.
  • Stochastic Weather Generator (SWG): CoSMoS (Complete Stochastic Modelling Solution) R package, adapted with bootstrap-based smoothing and physical constraints on extreme precipitation.
  • Statistical Benchmark: Bayesian Generalized Extreme Value (GEV) distribution for at-site flood frequency analysis.
• Data sources:
  • Streamflow data: Daily streamflow records from Water Survey of Canada (WSC gauges 02EC002, 08NH006, 01EF001).
  • Meteorological data: Daily precipitation, maximum temperature, and minimum temperature from Environment Canada.
  • Observation periods: 30-year records for UQ-flood development and short-record GEV analysis; full available records (up to 108 years) for empirical and long-record GEV benchmarks.

Main Results

• The central UQ-flood estimates, derived from only 30 years of observations, consistently remained within the 95 % confidence intervals for the long-record empirical discharge quantiles across all three watersheds.
• Process-based simulations without residual error correction systematically underestimated flood magnitudes, indicating a bias in models calibrated to continuous streamflow when applied to annual flood peaks.
• The application of the annual-maximum residual error model (REM) effectively corrected these systematic biases, shifting the estimated flood-frequency curves towards the long-record observational benchmarks.
• The UQ-flood framework successfully propagated residual predictive variability directly at the annual-maximum scale, providing explicit uncertainty bounds for flood quantile estimates.
• A sensitivity analysis showed that the UQ-flood interval width decreased substantially as the synthetic series length increased from 100 to approximately 1000–2000 years, stabilizing thereafter.
• The relative proximity of UQ-flood and Bayesian GEV estimates to the empirical benchmarks varied by watershed and return period, with neither approach being uniformly closest in every case.

Contributions

• Introduces UQ-flood, a novel process-based flood frequency framework that integrates a stochastic weather generator, a process-based hydrologic model, and a residual error model developed specifically at the annual-maximum scale.
• Addresses a critical mismatch in process-based flood frequency analysis by explicitly modeling residual errors at the scale of the target design variable (annual maximum flow), rather than relying solely on models calibrated for daily streamflow.
• Demonstrates that annual-maximum residual error modeling can effectively correct systematic discrepancies in process-based flood estimates and provide robust central flood-quantile estimates, even at sites with short data records, offering a practical and process-consistent alternative to conventional statistical flood frequency analysis under data-scarce conditions.
• Provides a framework for transparently propagating residual predictive variability into flood-quantile estimates, enhancing uncertainty characterization in flood risk management and engineering design.

Funding

Natural Resources Canada Flood Hazard Identification and Mapping Program (FHIMP) project FHIMP23-27P2.

Citation

@article{RomeroCuéllar2026Residual,
  author = {Romero-Cuéllar, Jonathan and Craig, James Richard and Tolson, Bryan A. and Arabzadeh, Rezgar},
  title = {Residual error modelling for process-based flood frequency analysis},
  journal = {Natural hazards and earth system sciences},
  year = {2026},
  doi = {10.5194/nhess-26-5389-2026},
  url = {https://doi.org/10.5194/nhess-26-5389-2026}
}