Fitriana et al. (2026) Non-stationary low-flow frequency analysis with mixed Weibull components and Copula-based dependence framework

Identification

• Journal: Hydrology and earth system sciences
• Year: 2026
• Date: 2026-10-27
• Authors: Farhana Sweeta Fitriana, Svenja Fischer, Gabriele Weigelhofer, Johannes Laimighofer, Gregor Laaha
• DOI: 10.5194/hess-30-6599-2026

Research Groups

• Institute of Statistics, BOKU University, Vienna, Austria (Farhana Sweeta Fitriana, Johannes Laimighofer, Gregor Laaha)
• Hydrology and Environmental Hydraulics Group, Wageningen University and Research, Wageningen, the Netherlands (Svenja Fischer)
• Institute of Hydrobiology and Water Management, BOKU University, Vienna, Austria (Gabriele Weigelhofer)

Short Summary

This study develops a non-stationary low-flow frequency analysis framework (NSLFA mixC) that accounts for temporal trends, seasonal heterogeneity, and inter-event dependence in low-flow regimes across Europe. It demonstrates that ignoring non-stationarity can lead to biased estimates of low-flow severity, especially for extreme events.

Objective

• To what extent do seasonal low flows exhibit significant trends and non-stationary behaviour in Europe?
• How can non-stationary mixture distributions and non-stationary copula-based dependence be appropriately represented within a low-flow frequency analysis framework?
• What insights do non-stationary seasonal models provide into past and present changes in low-flow behaviour?
• How does explicitly accounting for non-stationarity affect estimates of design low flows compared to stationary low-flow frequency analysis?

Study Configuration

• Spatial Scale: 721 near-natural European catchments from the ROBIN dataset, covering Austria, Switzerland, Germany, Spain, Finland, France, the United Kingdom, Ireland, Norway, Poland, and Sweden. Catchment areas range from less than 1 square kilometer to more than 10,000 square kilometers, with mean elevations between 20 meters and 3000 meters above sea level.
• Temporal Scale: Daily streamflow data harmonized to a common analysis period from 1976 to 2020.

Methodology and Data

• Models used:
  • Non-stationary seasonal low-flow frequency analysis framework (NSLFA mixC)
  • Mixed distribution (LFA mix) and mixed copula (LFA mixC) frameworks
  • Three-parameter Weibull (WEI3) distributions for seasonal low-flow minima, with linear non-stationarity in the location parameter.
  • Gumbel-Hougaard copula for modeling inter-seasonal dependence, with a time-variant parameter.
  • Maximum Likelihood (ML) estimation for model parameters.
  • Non-parametric modified Mann-Kendall test with block bootstrapping (BBSMK) for trend detection.
  • Sen slope estimator for quantifying trend magnitude.
  • Kendall's rank correlation coefficient (τ) for assessing seasonal dependence.
  • Likelihood Ratio (LR) test for model selection between stationary and non-stationary models.
  • Partitioning Around Medoids (PAM) clustering of seasonality histograms for delineating homogeneous low-flow regions.
• Data sources:
  • European Reference Observatory of Basins for INternational hydrological climate change detection (ROBIN) dataset (Level-1 network).
  • Global Runoff Data Centre (GRDC).
  • Austrian Hydrographic Service (eHYD).
  • Publicly available European CAMELS-type datasets (e.g., CAMELS-ES, CAMELS-FR, CAMELS-CH).
  • Mean daily streamflow data (cubic meters per second).

Main Results

• Non-stationary behavior is evident in approximately 10% of the near-natural European catchments studied, with varying strength across regions and return periods.
• Significant trends are more prevalent in summer low-flow series (36.1% of catchments) than in winter (18.1%). Decreasing trends dominate in summer (73.8% of significant cases), primarily in western, central, and southern Europe. Winter low flows show a more balanced mix of decreasing (59.2%) and increasing (40.8%) trends, particularly in northern Europe.
• Seasonal low flows exhibit common but generally weak to moderate dependence, with significant low to moderate Kendall's τ correlations found in 41.5% and 25.9% of catchments, respectively.
• Neglecting non-stationarity can lead to biased assessments of low-flow severity, particularly for higher return periods. For catchments with evident non-stationarity, the median relative absolute deviation in estimated 100-year return periods between 1976 and 2020 is approximately 41.7% to 41.9%.
• Comparing stationary and non-stationary estimates at the end of the observation period for non-stationary catchments reveals median relative absolute deviations of about 29.4% for 100-year return periods, indicating that stationary models can underestimate or overestimate low-flow risk by a substantial margin.
• The largest model gains come from accounting for seasonal process heterogeneity, followed by temporal non-stationarity, while the additional refinement from the mixture copula-based approach (modeling inter-seasonal dependence) is generally more modest.

Contributions

• Extends the established stationary mixed distribution and mixed copula frameworks to a non-stationary setting (NSLFA mixC), providing a unified approach for low-flow frequency analysis under changing conditions.
• Introduces a framework that jointly accounts for temporal trends, seasonal heterogeneity, and inter-event dependence, addressing key violations of traditional low-flow frequency analysis assumptions.
• Quantifies the impact of non-stationarity on design low-flow estimates across a large sample of European catchments, demonstrating that ignoring temporal changes can lead to significant biases, especially for extreme events.
• Offers new insights into the evolving nature of low-flow regimes under climate change, revealing temporal shifts in low-flow severity and seasonal dominance that are not captured by stationary models.

Funding

• Austrian Science Fund (grant no. (R/VF) 10. 55776/DOC216)
• Klima- und Energiefonds (programme “ACRP”, grant no. C265154)
• Doctoral School “Human River Systems in the 21st Century (HR21)” of BOKU University, Vienna

Citation

@article{Fitriana2026Nonstationary,
  author = {Fitriana, Farhana Sweeta and Fischer, Svenja and Weigelhofer, Gabriele and Laimighofer, Johannes and Laaha, Gregor},
  title = {Non-stationary low-flow frequency analysis with mixed Weibull components and Copula-based dependence framework},
  journal = {Hydrology and earth system sciences},
  year = {2026},
  doi = {10.5194/hess-30-6599-2026},
  url = {https://doi.org/10.5194/hess-30-6599-2026}
}