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<p>Analysis of drought, a formidable natural disaster impacting ecosystems and economies, is vital for water resources management, agriculture, and risk reduction. Drought events are typically characterized by metrics such as intensity, severity, and duration, which guide mitigation strategies. Among the numerous indices available, the Standardized Precipitation Index (SPI) stands out for its simplicity and versatility in assessing precipitation deviations from long-term averages. This paper explores the joint distribution of SPI characteristics (i.e., severity and intensity) at various time scales (1, 3, 6, and 9 months) using a new family of distributions called scale mixtures of multivariate Rayleigh (SMMR) model. Hence, this model is applied to capture the dependence structure between drought measures. For this, a dataset of SPI characteristics obtained from two rain gauge stations in Iran (i.e., Kerman and Rasht) is used to compare case studies from two regions of distinct climates. This model addresses a critical limitation in current hydrological methods, which often fail to adequately represent skewed and leptokurtic datasets. Our research introduces a specialized analytical framework for drought data, improving the accuracy and reliability of hydrological analyses. This framework effectively handles the challenges posed by high skewness and excess kurtosis. The results reveal that the bivariate Rayleigh-Laplace model consistently provides the best fit for the drought characteristics of SPI dataset in the arid Kerman station, while the bivariate Rayleigh-BS model excels for those of SPI-3 and SPI-9 in the humid Rasht station. Contour plots of the fitted distributions demonstrate that bivariate Rayleigh-Laplace and bivariate Rayleigh-BS models closely replicate the observed data patterns. By applying the SMMR distribution to assess the joint distribution of drought characteristics, this research enhances our understanding of drought behavior and offers a promising avenue for more accurate drought frequency analysis in hydrology.</p>

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Modeling drought characteristics using scale mixtures of multivariate Rayleigh distributions

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Mostafa Tamandi,
  • Farshad Fathian,
  • Anthony F. Desmond,
  • Ahad Jamalizadeh

摘要

Analysis of drought, a formidable natural disaster impacting ecosystems and economies, is vital for water resources management, agriculture, and risk reduction. Drought events are typically characterized by metrics such as intensity, severity, and duration, which guide mitigation strategies. Among the numerous indices available, the Standardized Precipitation Index (SPI) stands out for its simplicity and versatility in assessing precipitation deviations from long-term averages. This paper explores the joint distribution of SPI characteristics (i.e., severity and intensity) at various time scales (1, 3, 6, and 9 months) using a new family of distributions called scale mixtures of multivariate Rayleigh (SMMR) model. Hence, this model is applied to capture the dependence structure between drought measures. For this, a dataset of SPI characteristics obtained from two rain gauge stations in Iran (i.e., Kerman and Rasht) is used to compare case studies from two regions of distinct climates. This model addresses a critical limitation in current hydrological methods, which often fail to adequately represent skewed and leptokurtic datasets. Our research introduces a specialized analytical framework for drought data, improving the accuracy and reliability of hydrological analyses. This framework effectively handles the challenges posed by high skewness and excess kurtosis. The results reveal that the bivariate Rayleigh-Laplace model consistently provides the best fit for the drought characteristics of SPI dataset in the arid Kerman station, while the bivariate Rayleigh-BS model excels for those of SPI-3 and SPI-9 in the humid Rasht station. Contour plots of the fitted distributions demonstrate that bivariate Rayleigh-Laplace and bivariate Rayleigh-BS models closely replicate the observed data patterns. By applying the SMMR distribution to assess the joint distribution of drought characteristics, this research enhances our understanding of drought behavior and offers a promising avenue for more accurate drought frequency analysis in hydrology.