Terzi et al. (2025) A novel statistical framework for constructing multivariate standardized drought indices

Identification

• Journal: Theoretical and Applied Climatology
• Year: 2025
• Date: 2025-09-27
• Authors: Tolga Barış Terzi, Osman Üçüncü
• DOI: 10.1007/s00704-025-05779-3

Research Groups

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

Short Summary

This study developed a novel copula-based framework for the Multivariate Standardized Drought Index (MSDI) using month-specific probability distributions and copulas to better account for seasonal variability and inter-variable dependence. The proposed methodology demonstrated improved drought detection and characterization, particularly for extreme and compound events, in two distinct Turkish river basins.

Objective

• To develop an improved statistical methodology for MSDI calculation that incorporates monthly-specific marginal distributions tailored to seasonal variability.
• To preserve the comparability of the multivariate drought index across different regions by maintaining a consistent dependence structure through copula modeling.
• To apply the proposed approach to long-term hydrometeorological datasets to evaluate its performance in capturing the spatial and temporal characteristics of drought.
• To demonstrate the advantages of the methodology over conventional univariate and multivariate drought indices, particularly in terms of sensitivity to seasonal patterns and robustness in multivariate contexts.

Study Configuration

• Spatial Scale: Two climatically and geographically distinct river basins in Turkey: the Çoruh River Basin (humid) and the Seyhan River Basin (semi-arid Mediterranean). One meteorological and one hydrological station were selected within each basin.
• Temporal Scale: Long-term hydrometeorological datasets.

Methodology and Data

• Models used:
  • Novel copula-based Multivariate Standardized Drought Index (MSDI) framework.
  • Standardized Precipitation Index (SPI) and Standardized Streamflow Index (SSFI) for univariate comparison.
  • Empirical Multivariate Standardized Drought Index (MSDIe) for comparison.
  • Probability Distribution Functions (PDFs): Normal, Lognormal, Weibull, Gamma, Exponential, Logistic, Pearson Type III, Fisk (month-specific best-fit).
  • Copula functions: Clayton, Frank, Gaussian, Gumbel, Student’s t (basin-specific selection).
  • Goodness-of-fit tests: Kolmogorov-Smirnov (K-S) test, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood.
  • Drought event identification: Run theory with a threshold of -1.
• Data sources:
  • Meteorological data (precipitation) from the General Directorate of Meteorology (MGM).
  • Hydrological data (streamflow) from the State Hydraulic Works (DSİ).

Main Results

• The use of month-specific best-fit probability distribution functions significantly enhanced the accuracy of marginal transformations and improved the representation of seasonal dynamics.
• Copula-based dependency modeling revealed distinct basin-specific structures: the Gumbel copula was optimal for the semi-arid Seyhan River Basin (E1801–17866), indicating upper-tail dependence, while the Gaussian copula was optimal for the humid Çoruh River Basin (E2304–17089), suggesting symmetric dependence.
• Compared to the empirical MSDI (MSDIe), the proposed copula-based MSDI exhibited smoother temporal transitions and improved detection of drought extremes, particularly in the tails of the distribution, capturing deeper deficits during severe events.
• Drought duration, severity, and recovery characteristics derived from the proposed MSDI more accurately reflected hydrological stress and identified compound drought events that might be overlooked by univariate indices (SPI or SSFI) alone.
• The MSDI consistently captured a broader spectrum of drought behavior, with detected events tending to exhibit longer durations and higher severities compared to those identified by individual univariate indices.

Contributions

• Introduction of a novel copula-based statistical framework for MSDI construction that explicitly accounts for seasonal variability by employing month-specific best-fit probability distribution functions for marginal transformation.
• Ensures the comparability of the multivariate drought index across different regions by maintaining a consistent dependence structure through the copula framework, despite using distinct PDFs for each monthly group.
• Provides a more robust and realistic characterization of compound drought events, their onset, severity, and recovery, by integrating precipitation and streamflow anomalies.
• Demonstrates improved sensitivity to seasonal patterns and enhanced detection of extreme drought events compared to both univariate indices and existing empirical multivariate methods.
• Offers a valuable tool for integrated drought risk assessment, supporting proactive water resource management, agricultural planning, and ecological monitoring in diverse climatic settings.

Funding

• Not applicable.

Citation

@article{Terzi2025novel,
  author = {Terzi, Tolga Barış and Üçüncü, Osman},
  title = {A novel statistical framework for constructing multivariate standardized drought indices},
  journal = {Theoretical and Applied Climatology},
  year = {2025},
  doi = {10.1007/s00704-025-05779-3},
  url = {https://doi.org/10.1007/s00704-025-05779-3}
}