Bellos et al. (2025) An analytical methodology to assess epistemic uncertainty of 2D flood models under steady flow conditions

Identification

• Journal: Environmental Modelling & Software
• Year: 2025
• Date: 2025-12-26
• Authors: Vasilis Bellos, Vassiliοs A. Tsihrintzis
• DOI: 10.1016/j.envsoft.2025.106849

Research Groups

• Department of Environmental Engineering, Democritus University of Thrace, Xanthi, Greece
• Centre for the Assessment of Natural Hazards and Proactive Planning & Laboratory of Reclamation Works and Water Resources Management, Department of Infrastructure and Rural Development, School of Rural, Surveying and Geoinformatics Engineering, National Technical University of Athens, Athens, Greece

Short Summary

This study develops an analytical methodology to assess epistemic uncertainty in 2D flood models under steady flow conditions using an idealized benchmark setup. It proposes a new taxonomy of five uncertainty drivers (forcing, geometric, physical, computational, structural) and finds that the forcing driver has the most significant impact on model output, followed by geometric and physical drivers.

Objective

• To develop and apply an analytical methodology to assess epistemic uncertainty of 2D flood models under steady flow conditions, proposing a new taxonomy of uncertainty drivers and quantifying their hierarchical impact on model outputs and computational time using an idealized benchmark setup.

Study Configuration

• Spatial Scale: A synthetic computational domain of 1000 m × 2000 m, representing a compound trapezoidal channel with a main channel and floodplains. Water depths were measured at 13 critical points along two longitudinal profiles.
• Temporal Scale: Steady-state flow conditions.

Methodology and Data

• Models used: FLOW-R2D, a 2D flood simulator solving the 2D Shallow Water Equations (SWE) using the Finite Difference Method and McCormack numerical scheme. Manning equation was used for friction slope estimation.
• Data sources: An idealized benchmark setup (synthetic computational domain) allowing for the generation of Digital Terrain Models (DTMs) at desired resolutions. Uncertainty quantification was performed using a brute-force Monte Carlo technique with Latin Hypercube Sampling, assuming uniform distributions for input variables. Analytical solutions (Manning equation) were used to assess structural uncertainty.

Main Results

• A new taxonomy for uncertainty sources in 2D flood models was proposed, categorizing them into five drivers: forcing, geometric, physical, computational, and structural.
• Sensitivity analysis (Morris method) revealed that for the main channel, the forcing driver (discharge) is critical, followed by geometric (main channel slope, width, bank height) and physical (Manning coefficient) drivers. For floodplains, forcing (discharge) and geometric (bank height) drivers are major.
• The space step (computational driver) was identified as the most influential variable for the required computational time, exhibiting an exponential decay relationship.
• Uncertainty quantification (2000 Monte Carlo simulations) showed that the Weibull distribution is a suitable fit for the empirical distributions of water depths.
• Total uncertainty tends to decrease along the main channel but exhibits a more complex pattern (rising then falling) in the floodplains. Uncertainty in floodplains is systematically larger than in the main channel (away from upstream boundaries).
• Boundary conditions significantly influence numerical solutions, with effects observed up to 200 m from both upstream and downstream boundaries.
• Structural uncertainty (deviation from analytical solutions) is significant near boundaries (up to 200 m) and stabilizes after 400 m, typically within ±10% of water depth for a 90% confidence interval.
• The proposed Uncertainty Index (UI) indicated that the forcing driver is the most crucial factor for total uncertainty in both the main channel and floodplains. The geometric driver ranks second, and the physical driver third. Computational and structural drivers generally have minor impacts, though structural weakness was noted in floodplains near boundaries.
• Skewness analysis showed varying patterns across drivers and locations, indicating different degrees of asymmetry in the uncertainty distributions.
• The study validated that for supercritical flows (Froude number > 1), specific treatment of downstream boundaries is not required, aligning with computational hydraulics fundamentals.

Contributions

• Proposed a novel taxonomy of five uncertainty drivers (forcing, geometric, physical, computational, structural) for 2D flood models, providing a clearer framework for analysis.
• Developed an integrated framework combining sensitivity analysis and Monte Carlo-based uncertainty quantification for 2D flood models.
• Incorporated structural uncertainty analysis using analytical solutions derived from an idealized benchmark setup.
• Introduced a new metric, the Uncertainty Index (UI), to quantify the contribution of individual drivers to total uncertainty.
• Quantified the propagation of uncertainty along the flow path and explored the deviation of the mean.
• Provided generalized findings on the hierarchy of uncertainty drivers and their impact on model outputs and computational time.

Funding

• National Infrastructures for Research and Technology S.A. (GRNET S.A.)
• National HPC facility - ARIS (Project: UnFlood)

Citation

@article{Bellos2025analytical,
  author = {Bellos, Vasilis and Tsihrintzis, Vassiliοs A.},
  title = {An analytical methodology to assess epistemic uncertainty of 2D flood models under steady flow conditions},
  journal = {Environmental Modelling & Software},
  year = {2025},
  doi = {10.1016/j.envsoft.2025.106849},
  url = {https://doi.org/10.1016/j.envsoft.2025.106849}
}