water Article Nonstationary Multivariate Hydrological Frequency Analysis in the Upper Zhanghe River Basin, China Henan Gu 1,2,* ID , Zhongbo Yu 1,2,*, Guofang Li 1,2 and Qin Ju 1,2 1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China;
[email protected] (G.L.);
[email protected] (Q.J.) 2 College of Hydrology and water resources, Hohai University, Nanjing 210098, China * Correspondence:
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[email protected] (Z.Y.); Tel.: +86-135-8520-9927 (H.G.); +025-8378-6721 (Z.Y.) Received: 16 May 2018; Accepted: 11 June 2018; Published: 12 June 2018 Abstract: Design annual runoff is a classical issue in traditional univariate hydrological frequency analysis (HFA). We developed a multivariate HFA approach for designs for a study region covering the confluence of two streams. HFA relies on the assumption that probability distribution is consistent in the past, present, and future; however, it has been asserted as incorrect under an uncertain and changing environment. A change-point was detected in our study and adopted to divide runoff into two periods, with no significant trends in all subseries. The post-change design annual runoff witnessed dramatic mean value decline by about half at four frequencies (50%, 75%, 90% and 95%), which were selected in the bivariate analysis. Probability distribution models were constructed with univariate p-III distributions through Clayton, Frank, and Gumbel copulas and independence. Frank copula showed a generally better match with observations than others. The traditional approach, adding up the same-frequency results from both tributaries independently, was disproved by the systematically smaller design values in independence model than copulas and the 40% asynchronous encounter probability.