Abstract
The Von Mises distribution and the Pearson Type III distribution are used to describe the occurrence dates and magnitudes of annual maximum flood series, respectively. A bivariate joint distribution is developed based on Gumbel Archimedean copula. A modified inference functions for margins (MIFM) method is used to establish the marginal distribution and joint distributions with an incorporation of historical information. The conditional probabilities of flood volumes, given the flood occurrence dates (or peak discharge exceeding various values), are derived. A boundary identification method is developed to define the feasible ranges of flood peaks and volumes suitable for combination. Two combination methods, i.e., the equivalent frequency combination (EFC) method and the conditional expectation combination (CEC) method, for estimating unique bivariate flood quantiles are also proposed. The case study shows that the bivariate joint distribution can well fit both occurrence dates and magnitudes of annual maximum flood series, which can extract more flood information and provide an alternative way to conduct the multivariate frequency analysis.
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References
ASCE (American Society of Civil Engineers) (1996) Hydrology handbook. In: ASCE manuals and reports on engineering practices no. 28. American Society of Civil Engineers, New York, USA
Bayliss AC, Reed DW (2001) The use of historical data in flood frequency estimation. Report to MAFF.CEH Walingford
Black AR, Werritty A (1997) Seasonality of flooding: a case study of North Britain. J Hydrol 195:1–25
Chebana F, Quarda TBMJ (2011) Multivariate quantiles in hydrological frequency analysis. Environmetrics 22:441–455
Chen L, Guo SL, Yan BW, Liu P, Fang B (2010) A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence. Hydrol Sci J 55(8):1264–1280
Cohen AC (1976) Progressively censored sampling in the three parameters log-normal distribution. Technometrics 18(1):99–103
Coles S, Heffernan J, Tawn J (1999) Dependence measures for extreme value analysis. Extremes 2(4):339–365
Condie R (1986) Flood samples from a three-parameter lognormal population with historical information: the asymptotic standard error of estimate of the T-year flood. J Hydrol 85:139–150
Condie R, Lee K (1982) Flood frequency analysis with historical information. J Hydrol 58:47–62
CWRC (Changjiang Water Resources Commission) (1996) Hydrologic inscription cultural relics in Three Gorges Reservoir. Science Press, Bei**g (in Chinese)
De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R (2005) Bivariate statistical approach to check adequacy of dam spillway. J Hydrol Eng 1:50–57
Dupuis DJ (2007) Using copulas in hydrology: benefits, cautions, and issues. J Hydrol Eng 12(4):381–393
Fisher NI (1993) Statistical analysis of circular data. Cambridge University Press, Cambridge
Frahm G, Junker M, Schmidt R (2005) Estimating the tail dependence coefficient: properties and pitfalls. Insur Math Econ 37(1):80–100
Guo SL, Cunnane C (1991) Evaluation of the usefulness of historical and paleological floods in quantile estimation. J Hydrol 129:245–262
Hald A (1949) Maximum likelihood estimation of the parameters of a normal distribution which is truncated at a known point. Skand Aktuarietidskrift 32(1/2):119–134
Hosking JRM (1995) The use of L-moments in the analysis of censored data”. In: Balakrishnan N (ed) Recent advances in life-testing and reliability. CRC Press, Boca Raton, Fla, pp 545–564
Joe H (1997) Multivariate models and dependence concepts. Chapman & Hall, London
Joe H (2005) Asymptotic efficiency of the two-stage estimation method for copula-based models. J Multivariate Anal 94:401–419
Joe H, Xu JJ (1996) The estimation method of inference functions for margins for multivariate models. Technical Report no. 166, Department of Statistics, University of British Columbia
Leese MN (1973) Use of censored data in the estimation of Gumbel distribution parameters for annual maximum flood series. Water Resour Res 9(6):1534–1542
Li T, Guo S, Chen L, Guo J (2013) Bivariate flood frequency analysis with historical information based on Copula. J Hydrol Eng 18(8):1018–1030
Li T, Guo S, Liu Z, **ong L, Yin J (2016) Bivariate design flood quantile selection using copulas. Hydrol Res. https://doi.org/10.2166/nh.2016.049
Li X, Guo SL, Liu P, Chen G (2010) Dynamic control of flood limited water level for reservoir operation by considering inflow uncertainty. J Hydrol 391:124–132
Mardia KV (1972) Statistics of directional data. Academic Press, London
McLeish DL, Small CG (1988) The theory and applications of statistical inference functions. Lecture Notes in Statistics, 44. Springer-verlag, New York
MWR (Ministry of Water Resources) (2006) Regulation for calculating design flood of water resources and hydropower projects. Chinese Water Resources And Hydropower Press, Bei**g (in Chinese)
Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York
Poulin A, Huard D, Favre AC, Pugin S (2007) Importance of tail dependence in bivariate frequency analysis. J Hydrol Eng 12(4):L394–L403
Salvadori G, De Michele C, Durante F (2011) Multivariate design via Copulas. Hydrol Earth Syst Sci Discuss. 8:5523–5558
Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res 40:W12511. https://doi.org/10.1029/2004WR003133
Shiau JT, Wang HY, Tsai CT (2006) Bivariate frequency analysis of floods using copulas. J Am Water Resour Assoc 42(6):1549–1564
Stedinger JR, Cohn TA (1986) The value of historical and paleoflood information in flood frequency analysis. Water Resour Res 22(5):785–793
USWRC (US Water Resources Council) (1981) Guidelines for determining flow frequency, Bulletin 17B. D. C, Washington
USWRC (US Water Resources Council) (1982) Guidelines for determining flood flow frequency, Bull. 17B (revised), U.S. Gov. Print. Off., Washington, D. C
Volpi E, Fiori A (2012) Design event selection in bivariate hydrological frequency analysis. Int Assoc Sci Hydrol 57(8):1506–1515
Volpi E, Fiori A (2014) Hydraulic structures subject to bivariate hydrological loads: return period, design, and risk assessment. Water Resour Res 50(2):885–897
**ao Y, Guo SL, Liu P, Yan B, Chen L (2009) Design flood hydrograph based on multi characteristic synthesis index method. J Hydrol Eng 14(12):1359–1364
** world, IAHS Press, IAHS Publications 319, Wallingford, pp 75–82
Xu JJ (1996) Statistical Modelling and inference for multivariate and longitudinal discrete response data. Ph.D. thesis, Department of Statistics, University of British Columbia
Yue S, Quarda TBMJ, Bobée B, Legendre P, Bruneau P (1999) The Gumbel mixed model for flood frequency analysis. J Hydrol 226:88–100
Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11(2):150–164
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Chen, L., Guo, S. (2019). Copula-Based Flood Frequency Analysis. In: Copulas and Its Application in Hydrology and Water Resources. Springer Water. Springer, Singapore. https://doi.org/10.1007/978-981-13-0574-0_3
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DOI: https://doi.org/10.1007/978-981-13-0574-0_3
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