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Maximum Entropy-Copula Method for Hydrological Risk Analysis under Uncertainty: A Case Study on the Loess Plateau, China

1
State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an 710048, China
2
College of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056038, China
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(11), 609; https://doi.org/10.3390/e19110609
Received: 25 September 2017 / Revised: 3 November 2017 / Accepted: 11 November 2017 / Published: 15 November 2017
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
Copula functions have been extensively used to describe the joint behaviors of extreme hydrological events and to analyze hydrological risk. Advanced marginal distribution inference, for example, the maximum entropy theory, is particularly beneficial for improving the performance of the copulas. The goal of this paper, therefore, is twofold; first, to develop a coupled maximum entropy-copula method for hydrological risk analysis through deriving the bivariate return periods, risk, reliability and bivariate design events; and second, to reveal the impact of marginal distribution selection uncertainty and sampling uncertainty on bivariate design event identification. Particularly, the uncertainties involved in the second goal have not yet received significant consideration. The designed framework for hydrological risk analysis related to flood and extreme precipitation events is exemplarily applied in two catchments of the Loess plateau, China. Results show that (1) distribution derived by the maximum entropy principle outperforms the conventional distributions for the probabilistic modeling of flood and extreme precipitation events; (2) the bivariate return periods, risk, reliability and bivariate design events are able to be derived using the coupled entropy-copula method; (3) uncertainty analysis highlights the fact that appropriate performance of marginal distribution is closely related to bivariate design event identification. Most importantly, sampling uncertainty causes the confidence regions of bivariate design events with return periods of 30 years to be very large, overlapping with the values of flood and extreme precipitation, which have return periods of 10 and 50 years, respectively. The large confidence regions of bivariate design events greatly challenge its application in practical engineering design. View Full-Text
Keywords: hydrological risk analysis; maximum entropy-copula method; uncertainty; Loess Plateau hydrological risk analysis; maximum entropy-copula method; uncertainty; Loess Plateau
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Guo, A.; Chang, J.; Wang, Y.; Huang, Q.; Guo, Z. Maximum Entropy-Copula Method for Hydrological Risk Analysis under Uncertainty: A Case Study on the Loess Plateau, China. Entropy 2017, 19, 609.

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