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Analysis of Probability Distributions for Modelling Extreme Rainfall Events and Detecting Climate Change: Insights from Mathematical and Statistical Methods

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  • Raúl Montes-Pajuelo

    (Department of Integrated Sciences, Applied Mathematics Section, Campus “El Carmen”, University of Huelva, 21004 Huelva, Spain)

  • Ángel M. Rodríguez-Pérez

    (Department of Engineering, University of Almería, 04120 Almería, Spain
    CIMEDES Research Center (CeiA3), University of Almería, Ctra. Sacramento, s/n, La Cañada, 04120 Almería, Spain)

  • Raúl López

    (Department of Agricultural and Forest Sciences and Engineering, University of Lleida, 25003 Lleida, Spain
    Fluvial Dynamics Research Group (RIUS), University of Lleida, 25003 Lleida, Spain)

  • César A. Rodríguez

    (Department of Mining, Mechanical, Energy and Construction Engineering, Campus “El Carmen”, University of Huelva, 21004 Huelva, Spain)

Abstract

Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions—including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, log-Gumbel, Pearson type III, log-Pearson type III, and SQRT-ET max distributions—to assess annual maximum 24 h rainfall series obtained over a long period (1972–2022) from three nearby meteorological stations. Goodness-of-fit analyses including Kolmogorov–Smirnov and chi-square tests reveal the inadequacy of exponential and normal distributions in capturing the complexity of the data sets. Subsequent frequency analysis and multi-criteria assessment enable us to discern optimal functions for various scenarios, including hydraulic engineering and sediment yield estimation. Notably, the log-Gumbel and three-parameter log-normal distributions exhibit superior performance for high return periods, while the Gumbel and three-parameter log-normal distributions excel for lower return periods. However, caution is advised regarding the overuse of log-Gumbel, due to its high sensitivity. Moreover, as our study considers the application of mathematical and statistical methods for the detection of extreme events, it also provides insights into climate change indicators, highlighting trends in the probability distribution of annual maximum 24 h rainfall. As a novelty in the field of functional analysis, the log-Gumbel distribution with a finite sample size is utilised for the assessment of extreme events, for which no previous work seems to have been conducted. These findings offer critical perspectives on extreme rainfall modelling and the impacts of climate change, enabling informed decision making for sustainable development and resilience.

Suggested Citation

  • Raúl Montes-Pajuelo & Ángel M. Rodríguez-Pérez & Raúl López & César A. Rodríguez, 2024. "Analysis of Probability Distributions for Modelling Extreme Rainfall Events and Detecting Climate Change: Insights from Mathematical and Statistical Methods," Mathematics, MDPI, vol. 12(7), pages 1-24, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1093-:d:1370115
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    References listed on IDEAS

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    1. Tassaddaq Hussain & Hassan S. Bakouch & Zafar Iqbal, 2018. "A New Probability Model for Hydrologic Events: Properties and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 63-82, March.
    2. Lauren M. Cook & Seth McGinnis & Constantine Samaras, 2020. "The effect of modeling choices on updating intensity-duration-frequency curves and stormwater infrastructure designs for climate change," Climatic Change, Springer, vol. 159(2), pages 289-308, March.
    3. Showkat Ahmad Lone & Tabassum Naz Sindhu & Marwa K. H. Hassan & Tahani A. Abushal & Sadia Anwar & Anum Shafiq, 2023. "Theoretical Structure and Applications of a Newly Enhanced Gumbel Type II Model," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    4. Yanxi Hou & Xing Wang, 2021. "Extreme and Inference for Tail Gini Functionals With Applications in Tail Risk Measurement," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1428-1443, July.
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