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Nonstationary Analysis for Bivariate Distribution of Flood Variables in the Ganjiang River Using Time-Varying Copula

1,2, 3,* and 2
1
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2
Jiangxi Provincial Institute of Water Sciences, Nanchang 310029, China
3
School of Environmental Studies, China University of Geosciences, Wuhan 430074, China
*
Author to whom correspondence should be addressed.
Water 2019, 11(4), 746; https://doi.org/10.3390/w11040746
Received: 11 March 2019 / Revised: 1 April 2019 / Accepted: 8 April 2019 / Published: 10 April 2019
(This article belongs to the Section Hydrology)
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Abstract

Nonstationarity of univariate flood series has been widely studied, while nonstationarity of some multivariate flood series, such as discharge, water stage, and suspended sediment concentrations, has been studied rarely. This paper presents a procedure for using the time-varying copula model to describe the nonstationary dependence structures of two correlated flood variables from the same flood event. In this study, we focus on multivariate flood event consisting of peak discharge (Q), peak water stage (Z) and suspended sediment load (S) during the period of 1964–2013 observed at the Waizhou station in the Ganjiang River, China. The time-varying copula model is employed to analyze bivariate distributions of two flood pairs of (Z-Q) and (Z-S). The main channel elevation (MCE) and the forest coverage rate (FCR) of the basin are introduced as the candidate explanatory variables for modelling the nonstationarities of both marginal distributions and dependence structure of copula. It is found that the marginal distributions for both Z and S are nonstationary, whereas the marginal distribution for Q is stationary. In particular, the mean of Z is related to MCE, and the mean and variance of S are related to FCR. Then, time-varying Frank copula with MCE as the covariate has the best performance in fitting the dependence structures of both Z-Q and Z-S. It is indicated that the dependence relationships are strengthen over time associated with the riverbed down-cutting. Finally, the joint and conditional probabilities of both Z-Q and Z-S obtained from the best fitted bivariate copula indicate that there are obvious nonstationarity of their bivariate distributions. This work is helpful to understand how human activities affect the bivariate flood distribution, and therefore provides supporting information for hydraulic structure designs under the changing environments. View Full-Text
Keywords: nonstationary; flood; main channel elevation; forest cover rate; time-varying copula; the Ganjiang River nonstationary; flood; main channel elevation; forest cover rate; time-varying copula; the Ganjiang River
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Wen, T.; Jiang, C.; Xu, X. Nonstationary Analysis for Bivariate Distribution of Flood Variables in the Ganjiang River Using Time-Varying Copula. Water 2019, 11, 746.

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