Abstract
The coincidence of flood flows of the mainstream and its tributaries may determine flood peaks. This study analyzed the risk of flooding caused by such flood coincidences in consideration of flood magnitudes and the time (dates) of occurrence. The Pearson Type III distribution and the Log Pearson Type III are selected as the marginal distributions of flood magnitudes for annual maximum flood series, and the mixed von Mises distribution is selected as the marginal distribution of flood occurrence dates. Two four-dimensional copula functions are developed for the joint distribution of flood magnitudes and occurrence dates. The upper Yangtze River in China and the Colorado River in the U.S. are selected to evaluate the computation method for risk analysis. The coincidence probabilities of flood magnitudes and occurrence dates are calculated, and the conditional probabilities for the Three Gorges Reservoir (TGR) are analyzed. Results show that the von Mises distribution can fit the observed flood dates data well. The X-Gumbel copula is selected for risk analysis. Based on the proposed model, the coincidence and conditional probabilities for any return period can be obtained.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
De Michele C, Salvadori G (2003) A generalized Pareto intensity duration model of storm rainfall exploiting 2-copulas. J Geophys Res 108(D2):4067. https://doi.org/10.1029/2002JD002534
De Michele C, Salvadori G, Passoni G, Vezzoli R (2007) A multivariate model of sea storms using copulas. Coastal Eng 54(10):734–751
Dupuis DJ (2007) Using copulas in hydrology: benefits, cautions, and issues. J Hydrol Eng 12(4):381–393
Enright M, Wilberg DE, Tibbetts JR (2008) Water Resources Data, Utah, Water Year 2004. U.S. Geological Survey: 120
Favre AC, Adlouni S, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(W01101):12
Grimaldi S, Serinaldi F (2006) Design hyetographs analysis with 3-copula function. Hydrol Sci J 51(2):223–238
Interagency Advisory Committee on Water Data (IACWD) (1982) Guidelines for determining flood flow frequency: bulletin 17B of the Hydrology Subcommittee. Office of Water Data Coordination, U.S. Geological Survey, Reston, Virginia
Kao SC, Govindaraju RS (2008) Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resour Res 44(2):W02415. https://doi.org/10.1029/2007WR006261
Kao SC, Govindaraju RS (2010) A copula-based joint deficit index for droughts. J Hydrol 380(1–2):121–134
Ministry of Water Resources (MWR) (1993) Regulation for calculating design flood of water resources and hydropower projects. Chinese Water Resource Hydro Press, Beijing, China (in Chinese)
Munro P (1992) A Mojave dictionary. UCLA, Los Angeles
Prohaska S, Ilic A, Majkic B (2008) Multiple-coincidence of flood waves on the main river and its tributaries. IOP Conf Ser Earth Environ Sci 4:012013
Reed D (1999) The flood estimation handbook-1: overview. Institute of Hydrology, Wallingford
Robson A, Reed D (1999) Flood estimation handbook, vol.3: statistical procedure for flood frequency estimation. Institute of Hydrology, Wallingford, UK
Salvadori G, Michele CD (2010) Multivariate multiparameter extreme value models and return periods: A copula approach. Water Resour Res 46, W10501, https://doi.org/10.1029/2009WR009040
Serinaldi F, Grimaldi S (2007) Fully nested 3-copula: procedure and application on hydrological data. J Hydrol Eng 12(4):420–430
Serinaldi F, Bonaccorso B, Cancelliere A, Grimaldi S (2009) Probabilistic characterization of drought properties through copulas. Phys Chem Earth 34(10–12):596–605
Shiau JT, Wang HY, Chang TT (2006) Bivariate frequency analysis of floods using copulas. J Am Water Resour Assoc 42(6):1549–1564
Song S, Singh VP (2010) Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stoch Environ Res Risk Assess 24(5):783–805. https://doi.org/10.1007/s00477-010-0364-5
U.S. Geological Survey (2011) National hydrography dataset high-resolution flowline data. The National Map
Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11(2):150–164
Zhang L, Singh VP (2007a) Gumbel-Hougaard copula for trivariate rainfall frequency analysis. J Hydrol Eng 12(4):409–419
Zhang L, Singh VP (2007b) Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 332:93–109
Zhang L, Singh VP (2007c) Trivariate flood frequency analysis using the Gumbel-Hougaard copula. J Hydrol Eng 12(4):431–439
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Chen, L., Guo, S. (2019). Flood Coincidence Risk Analysis Using Multivariate Copula Functions. In: Copulas and Its Application in Hydrology and Water Resources. Springer Water. Springer, Singapore. https://doi.org/10.1007/978-981-13-0574-0_6
Download citation
DOI: https://doi.org/10.1007/978-981-13-0574-0_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-0573-3
Online ISBN: 978-981-13-0574-0
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)