Terzi et al. (2026) Probabilistic Risk Assessment of Meteorological and Hydrological Droughts with Copula Functions: A Multivariate Framework

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-01-01
• Authors: Tolga Barış Terzi, Osman Üçüncü
• DOI: 10.1007/s11269-025-04464-4

Research Groups

• Department of Civil Engineering, Faculty of Engineering, Karadeniz Technical University, Trabzon, Turkey

Short Summary

This study develops a sequential, copula-based framework to assess meteorological and hydrological drought risk in the Çoruh River Basin, demonstrating that this integrated multivariate approach provides more accurate estimates of drought duration, severity, and joint return periods compared to traditional univariate methods.

Objective

• To evaluate and compare drought behavior using the Standardized Precipitation Evapotranspiration Index (SPEI) and Standardized Streamflow Index (SSFI).
• To construct a copula-based Multivariate Standardized Drought Index (MSDI) by integrating meteorological and hydrological variables.
• To model the dependence between drought duration and severity using copula functions to estimate joint return periods.
• To compare the MSDI-based assessment with univariate results to demonstrate the added value of the multivariate approach.

Study Configuration

• Spatial Scale: Çoruh River Basin (northeastern Turkey), covering an area of 20,265 square kilometers, extending 183 kilometers in length and 251 kilometers in width, with elevations ranging from 550 meters to 3397 meters.
• Temporal Scale: 38 years of monthly data from 1973 to 2011.

Methodology and Data

• Models used:
  • Standardized Precipitation Evapotranspiration Index (SPEI)
  • Standardized Streamflow Index (SSFI)
  • Multivariate Standardized Drought Index (MSDI)
  • Copula functions (Clayton, Frank, Galambos, Gaussian, Gumbel, Plackett, Student-t) for modeling dependence.
  • Run theory for drought event characterization (threshold of -1).
  • Hargreaves method for Potential Evapotranspiration (PET) calculation.
  • Maximum Likelihood Estimation (MLE) for copula and marginal distribution parameter estimation.
  • Model selection criteria: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood.
  • Goodness-of-fit tests: Kolmogorov–Smirnov, Anderson–Darling, Cramér-von Mises.
• Data sources:
  • Monthly precipitation, mean minimum temperature, mean maximum temperature data from the Turkish State Meteorological Service.
  • Monthly streamflow data from the General Directorate of State Hydraulic Works.

Main Results

• Univariate indices (SPEI and SSFI) showed broad temporal coherence but significant discrepancies in the timing and magnitude of drought events, with hydrological droughts exhibiting delayed onset and greater persistence.
• The copula-based MSDI provided a more coherent representation of drought conditions, identifying major drought events and accounting for discrepancies between individual indices. For example, the 2000 drought event was estimated by MSDI-12 to have a duration of 28 months and a severity of -55.64, substantially higher than SPEI-12 (11 months, -22.83) and SSFI-12 (25 months, -45.07).
• Pearson correlation coefficients between MSDI and univariate indices ranged from 0.71 to 0.90, predominantly exceeding 0.80.
• The Exponential distribution was consistently the best fit for drought duration for all indices. For drought severity, the Exponential distribution was best for SPEI-12 and SSFI-12, while the Lognormal distribution best modeled MSDI-12 severity.
• The Gaussian copula provided the best fit for MSDI-12, the Frank copula for SPEI-12, and the Galambos copula for SSFI-12 in bivariate frequency analysis of drought duration and severity.
• MSDI-12 consistently produced higher estimates of drought duration and severity for given return periods compared to univariate indices. For a 50-year return period, MSDI-12 indicated a duration of 25 months and a severity of 54, compared to 15 months and 23 for SPEI-12, and 21 months and 35 for SSFI-12.
• Joint return periods for simultaneous exceedance were 56 years for MSDI-12 at the 50-year level, indicating that concurrent extreme duration and severity are more likely for MSDI-12 than for SPEI-12 (73 years).

Contributions

• Presents a novel sequential, copula-based framework that integrates the development of a multivariate drought index (MSDI) with subsequent bivariate frequency analysis of its derived characteristics, addressing a gap in existing literature.
• Demonstrates that accounting for the dependence between meteorological and hydrological conditions fundamentally changes the characterization of drought risk, revealing markedly higher durations, severities, and joint return levels for compound droughts than suggested by univariate indices.
• Provides a more realistic assessment of multiyear drought persistence and compound risk, offering actionable insights for early warning systems, hydropower scheduling, and reservoir carry-over planning in vulnerable regions.
• Highlights the potential for univariate indices to underestimate the severity and frequency of extreme droughts, leading to an optimistic bias in water resources risk assessment.

Funding

• The Scientific and Technological Research Council of Türkiye (TÜBİTAK) provided open access funding.

Citation

@article{Terzi2026Probabilistic,
  author = {Terzi, Tolga Barış and Üçüncü, Osman},
  title = {Probabilistic Risk Assessment of Meteorological and Hydrological Droughts with Copula Functions: A Multivariate Framework},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-025-04464-4},
  url = {https://doi.org/10.1007/s11269-025-04464-4}
}