Statistical Modeling and Analysis of Peak Flood Discharge in the Tang-e-Karzin Catchment Using Bootstrapping and Multiple Probability Distributions

Document Type : Research Paper

Authors

1 Faculty of Khorramshahr University of Science and Technology

2 Khorramshahr University of Marine Science and Technology

10.22034/gp.2025.67538.3413

Abstract

Flood frequency analysis and statistical modeling of peak discharge are essential for water resource management, hydraulic structure design, and flood hazard mitigation in semi-arid regions. This study analyzes the peak flood discharge of the Qareh-Aghaj River in the Tang-e-Karzin catchment, employing multiple probability distributions, including Gumbel Type 1, 2-parameter Gamma, 2- and 3-parameter Log-Normal, Generalized Pareto, Generalized Extreme Value (GEV), and Pearson Type 3. Parameters were estimated using methods of moments (MOM), maximum likelihood (MML), probability-weighted moments (PWM), and maximum entropy (ENT). To assess uncertainty in peak discharge predictions for return periods of 2 to 1,000 years, non-parametric bootstrapping with 1,000 random samples was applied. Peak discharge data were evaluated using foundational statistical tests: the runs test (z=0.025), Grubbs-Beck test (indicating an extreme flood event), Wald-Wolfowitz test (u=0.896), and Mann-Whitney test (p-value=0.6625), confirming data randomness, independence, and homogeneity. The Kolmogorov-Smirnov (K-S) test assessed goodness-of-fit, with the 2-parameter Log-Normal (K-S=0.089) and GEV (K-S=0.063, peak discharge 11,044.6 m³/s for a 1,000-year return period) distributions demonstrating superior performance. Bootstrapping generated 95% confidence intervals, reducing prediction uncertainty, particularly for these distributions. Comparisons using K-S and Anderson-Darling (A-D) criteria further confirmed their superiority. The findings validate bootstrapping as an effective tool for enhancing hydrological predictions and provide recommendations for designing flood-resilient structures and optimizing water resource management in the Tang-e-Karzin catchment. These results offer a foundation for flood management, hydraulic structure design, and water resource planning in this catchment and similar semi-arid regions.

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