Gontara et al. (2025) Multivariate hydrological risk under heterogeneous conditions

Identification

• Journal: Journal of Hydrology
• Year: 2025
• Date: 2025-11-19
• Authors: Emna Gontara, Fateh Chebana
• DOI: 10.1016/j.jhydrol.2025.134588

Research Groups

• Institut National de la Recherche Scientifique, Centre Eau Terre et Environnement, Québec, Canada

Short Summary

This study proposes a framework for estimating multivariate quantile curves (MQCs) by directly integrating change-points (CPs) using mixture models for marginal distributions and copulas. It demonstrates that marginal CPs displace the curve, while dependence CPs alter its shape, with combined effects amplifying the impact on hydrological risk assessment.

Objective

• To develop a statistical framework for estimating multivariate quantile curves (MQCs) that explicitly integrates univariate and multivariate change-points (CPs) using mixture models for marginal distributions and copulas, thereby improving the accuracy of hydrological risk assessment under heterogeneous conditions.

Study Configuration

• Spatial Scale: Theoretical cases based on the Skootamatta basin in Ontario, Canada. Applied to three hydrometric stations in Canada: Madawaska River at Palmer Rapids (Ontario), Columbia River at Nicholson (British Columbia), and Milk River at Milk River (Alberta).
• Temporal Scale: Data records ranging from 88 to 106 years (e.g., 1930–2017 for Madawaska River, 1917–2017 for Columbia River, 1912–2017 for Milk River).

Methodology and Data

• Models used:
  • Mixture models for marginal distributions (e.g., Gumbel, Weibull, Generalized Extreme Value (GEV), two-parameter Log-Normal (LN2), Pearson type III (P3)).
  • Mixture copulas (e.g., Archimedean families like Clayton, Frank, Joe, Gumbel; Extreme-Value copulas like Galambos, Husler-Reiss).
  • Statistical tests for change-point detection: Pettitt test (univariate), Kendall’s tau-based test, Cramér–von Mises test, multivariate L-moment test (multivariate).
  • Goodness-of-fit (GOF) tests: Anderson-Darling (margins), Cramér-von Mises (copulas).
  • Model selection criteria: Akaike Information Criterion (AIC) for margins (AICmar) and copulas (AICcop).
  • Parameter estimation: Maximum Likelihood (for margins), Genetic Algorithm (for mixture copulas, optimizing Pseudo-Likelihood function).
• Data sources:
  • Theoretical cases: Generated data based on parameters from an actual hydrological dataset (flood peak and flood volume series) from the Skootamatta basin in Ontario, Canada.
  • Real-world applications: Daily streamflow records from three Canadian hydrometric stations, providing flood peak (Q, in cubic meters per second) and flood volume (V, in cubic meters).

Main Results

• Theoretical Cases:
  • Change-points (CPs) in marginal distributions (e.g., location parameters of flood peak Q or volume V) primarily cause horizontal or vertical displacements of the multivariate quantile curve (MQC) without altering its overall curvature. For example, a 70% increase in Q-location parameter shifts the MQC horizontally, increasing Q from approximately 88 m³/s to 106 m³/s at a 0.9 joint risk level.
  • CPs in the dependence structure (e.g., changes in Kendall’s τ or copula shape) primarily alter the shape and orientation of the MQC, particularly in the proper part and tail/central regions, without significant displacement. An increase in Kendall's τ tightens the curve, while a decrease expands it.
  • Combined CPs in both margins and dependence structure result in an amplified effect, causing significant shifts in both the position and shape/orientation of the MQC. Neglecting these can lead to substantial over- or underestimation of joint risk (e.g., Q from 91.68 m³/s to 110.01 m³/s and V from 2163.93 m³ to 2599.35 m³ at a given combination point for 0.9 risk level).
• Real-world Applications:
  • For Madawaska River (CP only in Q-margin, 1968), the MQC showed a horizontal shift. Neglecting the CP led to an overestimation of Q (415.54 m³/s vs 382.6 m³/s for V=1657 m³ at 0.95 level).
  • For Columbia River (CP only in dependence structure, 1986), the MQC exhibited subtle changes in shape/curvature. Neglecting the CP led to slight overestimation of Q and V (e.g., Q=686.95 m³/s, V=2761.14 m³ vs Q=678.52 m³/s, V=2747.17 m³ at 0.99 level).
  • For Milk River (CPs in V-margin (1946) and dependence structure (1931)), the MQC showed changes in both position and shape/orientation, confirming amplified effects. Neglecting the CPs led to slight overestimation of Q and V (e.g., Q=184.74 m³/s, V=304.77 m³ vs Q=176.64 m³/s, V=300.64 m³ at 0.99 level).
• The study concludes that incorporating CPs into both the modeling and quantile estimation steps is crucial for accurate and realistic risk estimation in multivariate hydrological frequency analysis.

Contributions

• Proposes an operational framework for representing heterogeneity in multivariate frequency analysis by directly integrating univariate and multivariate change-points (CPs) into the estimation of multivariate quantile curves (MQCs).
• Provides a comprehensive analysis, through twelve theoretical cases, of how different types of CPs (marginal, dependence, or both) influence the shape and position of MQCs.
• Applies the methodology to real-world hydrological datasets from Canada, demonstrating the practical impact of CPs on multivariate quantile estimates and highlighting the potential for significant misestimation if CPs are neglected.
• Enhances the understanding of the influence of CPs on the reliability of multivariate quantile estimations, particularly in hydrological regimes subject to alterations.

Funding

• National Sciences and Engineering Research Council of Canada (NSERC)
• University Mission of Tunisia in Montreal (Mission Universitaire de Tunisie en Am´erique du Nord, MUTAN)

Citation

@article{Gontara2025Multivariate,
  author = {Gontara, Emna and Chebana, Fateh},
  title = {Multivariate hydrological risk under heterogeneous conditions},
  journal = {Journal of Hydrology},
  year = {2025},
  doi = {10.1016/j.jhydrol.2025.134588},
  url = {https://doi.org/10.1016/j.jhydrol.2025.134588}
}