Mixture Probability Models with Covariates: Applications in Estimating Risk of Hydroclimatic Extremes
Publication: Journal of Hydrologic Engineering
Volume 28, Issue 4
Abstract
Modeling of extreme events is important in many scientific fields, including environmental and civil engineering, and impacts and risk assessments. Among available methods, statistical models that allow estimating extremes’ frequency and intensity are regularly used in procedures to anticipate potential changes in extreme events. Extreme value theory provides a theoretical basis for statistical estimation of extreme events using frequency analysis. The challenge in modeling is knowing when to use the block maxima method or the peaks-over-threshold (POT) method. Each has its drawbacks. POT describes the main characteristics of the observed extreme series; the threshold selection is always challenging and might affect the accuracy of the simulated results and the credibility of changes in extreme values. To encompass this challenge, mixture models offer more flexibility to represent samples with nonhomogeneous data. This study presents the gamma generalized Pareto (GGP) mixture model for estimating risk occurrence of hydroclimatic extremes. The model was developed in its general form, whereas the observed hydrometeorological extreme events depend on multidimensional covariates. A maximum likelihood algorithm is proposed to estimate the parameters with a constraint on the shape parameter of the generalized Pareto (GP) distribution. A Monte Carlo (MC) simulation compared the proposed model with the classical POT approach, with a fixed threshold, and the annual maximum series of streamflow. The approach was applied using a daily hydrological data set from an observed station located in the Saint John River at Fort Kent (01AD002), New Brunswick, Canada. The results show a flexibility to model extremes for dependent or nonstationary time series and adequately describes the central part of the observed frequencies, as well as the tails.
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Data Availability Statement
Hydrometric data used in this study are available on the official site of Environment Canada (Environnement et Changement Climatique Canada 2018). MATLAB codes were developed by the authors; direct requests for these codes can be made to the corresponding author.
Acknowledgments
We acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), individual grants of Professor Philippe Gachon (NSERC-RGPIN-2016-06436 and NSERC-RGPIN-2022-05032) and of Professor Salah El Adlouni (NSERC-RGPIN-2019-05746). We also acknowledge other financial supports from the Strategic Research Chair of the University of Québec in Montreal (UQAM) held by Professor Philippe Gachon, by UQAM under the scholarship for the exemption of additional tuition fees for foreign students, and by UQAM’s Faculty of Sciences under the faculty financial support program.
Author contributions: Nawres Yousfi contributed to the methodology, investigation, data curation, formal analysis, and writing of the original draft. Salaheddine El Adlouni contributed to the conceptualization, methodology, and writing of the original draft. Simon Michael Papalexiou contributed to the conceptualization, methodology, and writing review and editing. Philippe Gachon contributed to the conceptualization, methodology, and writing review and editing.
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Journal of Hydrologic Engineering
Volume 28 • Issue 4 • April 2023
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© 2023 American Society of Civil Engineers.
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Received: May 20, 2022
Accepted: Dec 28, 2022
Published online: Feb 14, 2023
Published in print: Apr 1, 2023
Discussion open until: Jul 14, 2023
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