Trivariate Uncertainty Analysis of Hydro-Climatic Drought Risk Using Bootstrap Method (Case Study: Esteghlal Dam Basin, Minab)

Pakdaman, Zohreh; Bazrasshan, Omolbanin

doi:10.22059/ije.2025.395400.1871

Trivariate Uncertainty Analysis of Hydro-Climatic Drought Risk Using Bootstrap Method (Case Study: Esteghlal Dam Basin, Minab)

Document Type : Research Article

Authors

¹ Assistant Professor, Department of statistics, Faculty of science, University of Hormozgan, Bandar Abass, Iran

² Professor, Department of Natural Resources Engineering, Faculty of Agriculture, University of Hormozgan, Bandar Abass, Iran

10.22059/ije.2025.395400.1871

Abstract

Research Topic: Trivariate Uncertainty Analysis of Hydro-Climatic Drought Risk Using Bootstrap Method (Case Study: Esteghlal Dam Basin, Minab).
Objective: The main objective was to develop a trivariate uncertainty framework for analyzing hydro-climatic drought in the Esteghlal Dam watershed (Minab), by integrating meteorological and hydrological drought indices and predicting conditional probabilities of drought severity under varying conditions.
Method: Monthly precipitation and runoff data (1991–2021) were standardized using the Gamma distribution. A Joint Drought Index (JDI) was derived by combining the Standardized Precipitation Index (SPI) and the Standardized Runoff Index (SRI). Copula functions from Archimedean and elliptical families were applied to capture dependence among drought variables. Maximum Likelihood Estimation (MLE) was used for parameter estimation, and the Sn goodness-of-fit test was employed to identify optimal copula models. Finally, trivariate conditional probabilities of drought severity were estimated, and bootstrap resampling was used to quantify the associated uncertainty.
Results: The Gumbel copula provided the best fit for modeling the dependence structure between severity, duration, and magnitude. Results showed that increasing drought duration led to higher severity, while reducing conditional probability (longer return periods) decreased severity. For example, at a 10-year return period (CP = 0.1), when duration = 20 months and magnitude = 0.33, severity was 2.47; with magnitude increased to 2.87, severity rose to 17.1. Conversely, reducing conditional probability from 0.2 to 0.005 lowered severity from 5.1 to 0.7. The most severe recorded drought exhibited severity = 93, duration = 31 months, and magnitude = 2.87.
Conclusions:
The study confirms that extreme droughts become less frequent as return periods increase, yet they can be significantly more severe. The proposed trivariate uncertainty framework, combining copula modeling and bootstrap analysis, provides a robust tool for assessing drought risks under uncertainty. This approach enhances understanding of drought dynamics and offers valuable insights for water resource management and early-warning systems in arid and semi-arid regions.

Keywords

Main Subjects

Ecohydrology

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