Abstract
In hydrological research, flood events can be analyzed by flood hydrograph coincidence. The duration of the flood hydrograph is a key variable to calculate the flood hydrograph coincidence risk probability and determining whether flood hydrograph coincidence occurs, while the actual duration of the flood hydrograph is neglected in most of existing related research. This paper creatively proposes a novel method to analyze the flood hydrograph coincidence risk probability by establishing a five-dimensional joint distribution of flood volumes, durations and interval time for two hydrologic stations. More specifically, taking the annual maximum flood of the upper Yangtze River and input from Dongting Lake as an example, the Pearson Type III and the mixed von Mises distributions were used to establish the marginal distribution of flood volumes, flood duration and interval time. Subsequently, the five-dimensional joint distribution based on vine copula was established to analyze the flood hydrograph coincidence risk probability. The results were verified by comparison with a historical flood sequence, which show that during 1951–2002, the hydrograph coincidence probabilities corresponding to its flood event coincidence volumes of 2.00 × 1011 m3, 4.00 × 1011 m3, and 6.00 × 1011 m3 are 0.213, 0.123, and 0.049, respectively. It has provided theoretical support for flood control safety and risk management in the middle and lower Yangtze River. This study also demonstrates the significant beneficial role of regulation by the Three Gorges Water Conservancy Project in mitigating flood risk of the Yangtze River. The hydrograph coincidence probability corresponding to its flood event coincidence volume of 2.00 × 1011 m3 has decreased by 0.141.
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The data that support the findings of this study are openly available in the Changjiang Water Resources Commission of The Ministry of Water Resources of China at http://www.cjw.gov.cn/.
References
Aas K, Czado C, Frigessi A, Bakken H (2006) Pair-copula constructions of multiple dependence. Insur Math Econ 44(2):182–198. https://doi.org/10.1016/j.insmatheco.2007.02.001
Bedford T, Cooke RM (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Ann Math Artif Intel 32(1):245–268. https://doi.org/10.1023/a:1016725902970
Bing JP, Deng PX, Zhang X, Lv SY, Marco M, Xiao Y (2018) Flood coincidence analysis of Poyang Lake and Yangtze River: risk and influencing factors. Stoch Env Res Risk A 32(4):879–891. https://doi.org/10.1007/s00477-018-1514-4
Brocca L, Melone F, Moramarco T (2011) Distributed rainfall-runoff modelling for flood frequency estimation and flood forecasting. Hydrol Process 25(18):2801–2813. https://doi.org/10.1002/hyp.8042
Chen L, Singh VP, Guo SL, Hao ZC, Li TY (2012) Flood coincidence risk analysis using multivariate copula functions. J Hydrol Eng 17(6):742–755. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000504
Chen YD, Zhang Q, Xiao M, Singh VP (2013) Evaluation of risk of hydrological droughts by the trivariate Plackett copula in the East River Basin (China). Nat Hazards 68(2):529–547. https://doi.org/10.1007/s11069-013-0628-8
Cheng Z, Zhang CX (2020) Analysis of the rainstorm flood process of "2020.7.7" in She County, Anhui Province. China Flood & Drought Management 30:236–240 (in Chinese) https://doi.org/10.16867/j.issn.1673-9264.2020252
Cooke BRM (2002) Vines: a new graphical model for dependent random variables. Ann Stat 30(4):1031–1068. https://doi.org/10.2307/1558694
Cooke R, Kurowicka D (2006) Uncertainty analysis with high dimensional dependence modelling. Wiley, New York
Favre AC, Adlouni SE, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(1):290–294. https://doi.org/10.1029/2003WR002456
Feng Y, Shi P, Qu SM, Mou SY, Chen C, Dong FC (2020) Nonstationary flood coincidence risk analysis using time-varying copula functions. Sci Rep 10(1):3395. https://doi.org/10.1038/s41598-020-60264-3
Fisher NI (1993) Statistical Analysis of Circular Data. Cambridge University Press Cambridge, UK
Gao HQ, Dai J, Shen Y, Fan HX (2017) Analysis of the flood composition and flood occurrence in Xijiang River. Pearl River 38(7):18–21 (in Chinese) https://doi.org/10.3969/j.issn.1001-9235.2017.7.004
Geyer JC (1940) New curve-fitting method for analysis of flood-records. EOS Trans Am Geophys Union 21(2):660–668. https://doi.org/10.1029/TR021i002p00660
Huang KD, Chen L, Zhou JZ, Zhang JH, Singh VP (2018) Flood hydrograph coincidence analysis for mainstream and its tributaries. J Hydrol 565:341–353. https://doi.org/10.1016/j.jhydrol.2018.08.007
Jane R, Cadavid L, Obeysekera J, Wahl T (2020) Multivariate statistical modelling of the drivers of compound flood events in south Florida. Nat Hazard 20(10):2681–2699. https://doi.org/10.5194/nhess-20-2681-2020
Joe H (1996) Families of m-variate distributions with given margins and m(m+1)/2 bivariate dependence parameters. Distributions with Fixed Marginals and Related Topics 28:120–141
Kao SC, Govindaraju RS (2010) A copula-based joint deficit index for droughts. J Hydrol 380(1–2):121–134. https://doi.org/10.1016/j.jhydrol.2009.10.029
Karmakar S, Simonovic SP (2009) Bivariate flood frequency analysis Part 2: a copula-based approach with mixed marginal distributions. J Flood Risk Manag 2(1):32–44. https://doi.org/10.1111/j.1753-318X.2009.01020.x
Klein B, Pahlow M, Hundecha Y, Schumann A (2010) Probability analysis of hydrological loads for the design of flood control systems using copulas. J Hydrol Eng 15(5):360–369. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000204
Li K, Wu S, Dai E, Xu Z (2012) Flood loss analysis and quantitative risk assessment in China. Nat Hazards 63(2):737–760. https://doi.org/10.1007/s11069-012-0180-y
Liu CL, Zhang Q, Singh VP, Cui Y (2011) Copula-based evaluations of drought variations in Guangdong. South China Nat Hazards 59(3):1533–1546. https://doi.org/10.1007/s11069-011-9850-4
Ministry of Water Resources (MWR) (2006) Regulation for Calculating Design Flood of Water Resources and Hydropower Projects. Water Resources and Hydropower Press, Beijing (in Chinese)
Peng Y, Shi YL, Yan HX, Chen K, Zhang JP (2019) Coincidence risk analysis of floods using multivariate copulas: case study of Jinsha River and Min River. China J Hydrol Eng 24(2):05018030. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001744
Prohaska S, Ilic A, Majkic B (2008) Multiple-coincidence of flood waves on the main river and its tributaries. IOP Conference 4:012013. https://doi.org/10.1088/1755-1307/4/1/012013
Reddy MJ, Ganguli P (2012) Bivariate flood frequency analysis of upper Godavari River flows using Archimedean copulas. Water Resour Manag 26(14):3995–4018. https://doi.org/10.1007/s11269-012-0124-z
Roo APJD, Hazelhoff L, Heuvelink GBM (1992) Estimating the effects of spatial variability of infiltration on the output of a distributed runoff and soil erosion model using Monte Carlo methods. Hydrol Process 6(2):127–143. https://doi.org/10.1002/hyp.3360060202
Salvadori G, Michele CD (2004) Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water Resour Res 40(12):W12511. https://doi.org/10.1029/2004WR003133
Schepsmeier U, Czado C (2016) Dependence modelling with regular vine copula models: a case-study for car crash simulation data. J Roy Stat Soc C-App 65(3):415–429. https://doi.org/10.1111/rssc.12125
Schulte M, Schumann A (2016) Evaluation of flood coincidence and retention measures by copulas. Wasserwirtschaft 106(2–3):81–87
Sklar A (1959) Fonctions de repartition a n dimensions et leurs marges. Publ Inst Stat Univ Paris:22shou9–231
Spurr BD, Koutbeiy MA (1991) A comparison of various methods for estimating the parameters in mixtures of von Mises distribution. Commun Stat-Simul C 20(2–3):725–741. https://doi.org/10.1080/03610919108812980
Sraj M, Bezak N, Brilly M (2015) Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River. Hydrol Process 29(2):225–238. https://doi.org/10.1002/lt.22388
Stein L, Pianosi F, Woods R (2020) Event-based classification for global study of river flood generating processes. Hydrol Process 34(7):1514–1529. https://doi.org/10.1002/hyp.13678
Su Q (2020) Long-term flood risk assessment of watersheds under climate change based on the game cross-efficiency DEA. Nat Hazards 104(3):2213–2237. https://doi.org/10.1007/s11069-020-04269-1
Tosunoglu F, Faruk G, Spirli MN (2020) Multivariate modeling of flood characteristics using vine copulas. Environmental Earth Sciences 79(19):1–21. https://doi.org/10.1007/s12665-020-09199-6
Try S, Tanaka S, Tanaka K, Sayama T, Oeurng C (2020) Projection of extreme flood inundation in the Mekong River basin under 4k increasing scenario using large ensemble climate data. Hydrol Process 34(22):4350–4364. https://doi.org/10.1002/hyp.13859
Wang HJ, Xiao WH, Wan YC, Zhao Y, Lu F, Yang MZ, Hou BD, Yang H (2019) Assessment of the impact of climate change on hydropower potential in the Nanliujiang River basin of China. Energy 167(JAN15):950–959. https://doi.org/10.1016/j.energy.2018.10.159
Wu ZN, He CT, Wang HL, Zhang Q (2020) Reservoir inflow synchronization analysis for four reservoirs on a mainstream and its tributaries in flood season based on a multivariate copula model. Water Resour Manag 34(9):2753–2770. https://doi.org/10.1007/s11269-020-02572-x
Yan BW, Guo SL, Yu W (2013) Coincidence risk of flood hydrographs between Yangtze River and Qing River. Journal of Hydroelectric Engineering 32(1):50–53 (in Chinese)
Yang J, Wang Y, Yao J, Chang J, Xu G, Wang X, Hu H (2020) Coincidence probability analysis of hydrologic low-flow under the changing environment in the Wei River Basin. Nat Hazards 103(2):1711–1726. https://doi.org/10.1007/s11069-020-04051-3
Yu KX, Zhang X, Li P, Li ZB, Qin Y, Sun Q (2019) Probability prediction of peak break-up water level through vine copulas. Hydrol Process 33(6):962–977. https://doi.org/10.1002/hyp.13377
Zhang L, Singh VP (2007) Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 332(1–2):93–109. https://doi.org/10.1016/j.jhydrol.2006.06.033
Zhang XT, Shao J, Guo W (2018) Analysis of flood area composition and encounter law for Yalong River and Chuanjiang River. Yangtze River 49(22):23–28
Zhang C, Peng Y, Ji CM, Shi YL (2020) Floods encountering risk analysis for upper Yangtze River and Dongting Lake. J Hydroelectric Eng 39(8):55–68
Zhu LT, Liu YC, Yan FJ, Chen LF, Li GS (2015) Flood coincidence probability analysis for Nansi Lake valley. Trans Oceanol Limnol 37(1):149–15
Acknowledgements
The study was financially supported by the Guangdong Foundation for Program of Science and Technology Research (2020B1111530001, 2019QN01L682), the GDAS Special Project of Science and Technology Development (2020GDASYL-20200102013, 2020GDASYL-20200301003). We thank LetPub (www.letpub.com) for its linguistic assistance and scientific consultation during the preparation of this manuscript.
Funding
The study was financially supported by the Guangdong Foundation for Program of Science and Technology Research (2020B1111530001, 2019QN01L682) and the GDAS Special Project of Science and Technology Development (2020GDASYL-20200102013, 2020GDASYL-20200301003).
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All authors contributed to the study conception and design. Data collection and analysis were performed by CJ and YW. The first draft of the manuscript was written by CZ, and the figures and tables were made by QX. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Zhang, C., Ji, C., Wang, Y. et al. Flood hydrograph coincidence analysis of the upper Yangtze River and Dongting Lake, China. Nat Hazards 110, 1339–1360 (2022). https://doi.org/10.1007/s11069-021-04993-2
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DOI: https://doi.org/10.1007/s11069-021-04993-2