Abstract
This paper uses Gumbel-Hougaard (G-H) copula, Clayton copula and Frank copula to construct joint distributions of hydrological variables of the two typical stations on the Yellow River Region, including the annual maximum flood magnitude (AMFM), the annual maximum flood occurrence date (AMFOD) and the annual runoffs (ARs). The results give the joint distribution between each pair of the variables. Also an isoline of the concurrence return periods between the AMFMs of the two stations was drawn up.
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M. H. Costa, A. Botta and J. A. Cardille, Effects of large-scale changes in land cover on the discharge of the Tocantins River, Southeastern Amazonia. J. Hydrol.283 (2003) 206–217.
Y. Lin and X. H. Wei, The impact of large-scale forest harvesting on hydrology in the Willow watershed of Central British Columbia. J. Hydrol.359 (2008)141–149.
Z. H. Zhang, B. Y. Wang W. P. Li and Z. S. Liu, Analysis of relation between floods of July 1958 and August 1982 in the Yellow River. Yellow River. 22(11) (2000) 28–30. (in Chinese)
B. Y. Wang, Y. F. Wang and H. R. Li, Study on the extraordinary rainstorm and eventual flood occurred in 1761 in Sanmenxia-Huayuankou reach of the Yellow River. Yellow River. 24(10) (2002) 14–15. (in Chinese)
L. Zhang and V. P. Singh, Bivariate rainfall frequency distributions using Archimedean copulas. J. Hydrol. 332 (2007) 93–109.
Y. Xiao, S.L. Guo, L. H. Xiong, P. Liu and B. Fang, A new Random Simulation method for constructing synthetic flood hydrographs. J. Sichuan Univ.(Eng. Sci. Ed.). 39(2) (2007) 55–60. (in Chinese)
S.-C. Kao and R. S. Govindaraju, A copula-based joint deficit index for droughts. J. Hydrol. 380 (2010) 121–134.
S. L. Guo, B. W. Yan, Y. Xiao, B. Fang and N. Zhang, Multivariate hydrological analysis and estimation. J. China Hydrol. 28(3) (2008) 1–7. ( in Chinese)
T. Lee and J. D. Salas, Copula-based stochastic simulation of hydrological data applied to Nile River flows. Hydrol. Res. 42(4) (2011) 318–330.
H. Chowdhary, L. A. Escobar and V. P. Singh, Identification of suitable copulas for bivariate frequency analysis of flood peak and flood volume data. Hydrol. Res. 42(2–3) (2011) 192–216.
J.-T. Shiau, S. Feng and S.Nadarajah, Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrol. Process. 21 (2007) 2157–2163.
Y. Y. Fu, S. W. Yan and Z. H. Ding, Study on probability between abundant and low runoffs from Weihe River and Fenhe River based on Gumble-Hougaard copula. Water Res. Hydropower Eng. 41(1) (2010) 15–17. (in Chinese)
J. A. Mooney, P. J. Heims and I. T. Jolliffe, Fitting mixture of von Mises distributions: a case study involving sudden infant death syndrome. Comput. statistics & Data Analysis. 41(3–4) (2003) 505–513.
J. A.Carta, C. Bueno and P. Ramírez, Statistical modeling of directional wind speeds using mixtures of von Mises distributions: case study. Energy Conversion & Management. 49(5) (2008) 897–907.
B. Fang, S. L. Guo, Y. Xiao, P. Liu and J. Wu, Annual maximum flood occurrence dates and magnitudes frequency analysis based on bivariate joint distribution. Adv. Water Sci. 19(4) (2008) 505–511. (in Chinese)
B. W. Yan, S. L. Guo, L. Chen and P. Liu, (2010) Flood encountering risk analysis for the Yangtze River and Qingjiang River. J. Hydraul. Eng. 41(5), 553–559. (in Chinese)
R. B. Nelsen An introduction to copulas. (Springer, New York,1999)
L. Zhang, and V. P. Singh, Bivariate flood frequency analysis using the copula method. J. Hydrol. Eng. 11(2) (2006) 150– 164.
C. Genest and A.-C. Favre, Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng. 12(4) (2007) 347– 368.
G. Kim, M. J. Silvapulle and P. Silvapulle, Comparison of semiparametric and parametric methods for estimating copulas. Comput. Stat. data Annual. 51 (2007) 2836–2850.
S. Vandenberghe, N.E.C. Werhoest and B. De Baets, Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall. Water Resour. Res. 46 (2010)W01512.
A.-C. Favre, S. E. Adlouni, L. Perreault, N. Thiémonge and B. Bobée, Multivariate hydrological frequency analysis using copulas. Water Resour. Res. 40 (2004) W01101.
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Tong, X., Wang, D., Wu, J. et al. Bivariate analysis of typical hydrological series of the yellow river. Int J Comput Intell Syst 7 (Suppl 1), 18–28 (2014). https://doi.org/10.1080/18756891.2014.853928
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DOI: https://doi.org/10.1080/18756891.2014.853928