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Water 2017, 9(3), 198; doi:10.3390/w9030198

Multivariate Analysis of Joint Probability of Different Rainfall Frequencies Based on Copulas

State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
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Academic Editor: Ataur Rahman
Received: 30 December 2016 / Revised: 25 February 2017 / Accepted: 6 March 2017 / Published: 9 March 2017
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Abstract

The performance evaluation of a city’s flood control system is essentially based on accurate storm designs, where a particular challenge is the development of the joint distributions of dependent rainfall variables. When it comes to the research design for consecutive rainfall, the analytical investigation is only focused on the maximum of consecutive rainfalls, and it does not consider the probabilistic relations between the first day of rainfall and the overall rainfall included in consecutive rainfall events. In this study, the copula method is used to separate the dependence structure of multi-day rainfall from its marginal distribution and analyse the different impacts of the dependence structure and marginal distribution on system performance. Three one-parameter Archimedean copulas, including the Clayton, Gumbel, and Frank families, are fitted and compared for different combinations of marginal distributions that cannot be rejected by statistical tests. The fitted copulas are used to generate rainfall events for a system performance analysis, including the conditional probability and design values for different return periods. The results obtained in this study highlight the importance of taking into account the dependence structure of one-day and multi-day rainfall in the context of storm design evaluations and reveal the different impacts of the dependence structure and the marginal distributions on the probability. View Full-Text
Keywords: multivariate analysis; bivariate distribution; copula; frequency analysis; return period multivariate analysis; bivariate distribution; copula; frequency analysis; return period
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MDPI and ACS Style

Wang, Y.; Li, C.; Liu, J.; Yu, F.; Qiu, Q.; Tian, J.; Zhang, M. Multivariate Analysis of Joint Probability of Different Rainfall Frequencies Based on Copulas. Water 2017, 9, 198.

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