A Bayesian analysis of Generalized Pareto Distribution of runoff minima |
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| Authors: | Youcun Liu Miaojie Lu Xueli Huo Yonghong Hao Hongkai Gao Yan Liu Yonghui Fan Yuhuan Cui Francois Metivier |
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| Institution: | 1. Tianjin Key Laboratory of Water Resources and Environment, Tianjin Normal University, Xiqing District, Tianjin, PR China;2. College of Urban and Environmental Science, Tianjin Normal University, Xiqing District, Tianjin, PR China;3. Water Resources Section, Delft University of Technology, Delft, Netherlands;4. College of Mathematical Science, Tianjin Normal University, Xiqing District, Tianjin, PR China;5. School of Science, Anhui Agricultural University, Shushan District, Hefei, PR China;6. Institut de physique du globe de Paris—Sorbonne Paris Cite, Universite Paris Diderot, CNRS, UMR 7154, Paris, France |
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| Abstract: | Global climate change models have predicted the intensification of extreme events, and these predictions are already occurring. For disaster management and adaptation of extreme events, it is essential to improve the accuracy of extreme value statistical models. In this study, Bayes' Theorem is introduced to estimate parameters in Generalized Pareto Distribution (GPD), and then the GPD is applied to simulate the distribution of minimum monthly runoff during dry periods in mountain areas of the Ürümqi River, Northwest China. Bayes' Theorem treats parameters as random variables and provides a robust way to convert the prior distribution of parameters into a posterior distribution. Statistical inferences based on posterior distribution can provide a more comprehensive representation of the parameters. An improved Markov Chain Monte Carlo (MCMC) method, which can solve high‐dimensional integral computation in the Bayes equation, is used to generate parameter simulations from the posterior distribution. Model diagnosis plots are made to guarantee the fitted GPD is appropriate. Then based on the GPD with Bayesian parameter estimates, monthly runoff minima corresponding to different return periods can be calculated. The results show that the improved MCMC method is able to make Markov chains converge faster. The monthly runoff minima corresponding to 10a, 25a, 50a and 100a return periods are 0.60 m3/s, 0.44 m3/s, 0.32 m3/s and 0.20 m3/s respectively. The lower boundary of 95% confidence interval of 100a return level is below zero, which implies that the Ürümqi River is likely to cease to flow when 100a return level appears in dry periods. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | Bayesian analysis GPD MCMC runoff Ü rü mqi River |
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