Derivation of low flow distribution functions using copulas

Journal of Hydrology

Volumn 508, Issue , 2014, Pages 273-288

  Yu, Kun xia ^a   Xiong, Lihua ^a   Gottschalk, Lars ^a,b  

^a WUHAN UNIVERSITY   (China)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Copula based derived distribution; Low flow distribution; Recession curve; Statistical dependence

Indexed keywords

CLIMATE CHANGE; CORRELATION THEORY; DISTRIBUTION FUNCTIONS;

COPULA-BASED DERIVED DISTRIBUTION; HUMAN ACTIVITIES; LOW FLOW; MARGINAL DISTRIBUTION; PROCESS-ORIENTED; RECESSION CURVES; RECESSION FUNCTION; STATISTICAL DEPENDENCE;

WEIBULL DISTRIBUTION;

FLOW MODELING; FLOW PATTERN; RIVER BASIN; STUDENT; WEIBULL THEORY;

CHINA;

EID: 84888422438     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2013.09.057     Document Type: Article

References (47)

1. Bardossy A. Copula-based geostatistical models for groundwater quality parameters. Water Resour. Res. 2006, 42:W11416. 10.1029/2005WR004754.
2. Brahimi, B., Chebana, F., Necir, A., 2011. Copula representation of bivariate L-moments: A new estimation method for multiparameter 2-dimentional copula models. http://arxiv.org/abs/1106.2887.
3. Caillault C., Guégan D. Empirical estimation of tail dependence using copulas: application to Asian markets. Quant. Finance 2005, 5:489-501.
4. Cunnane C. Unbiased plotting position - a review. J. Hydrol. 1978, 37:205-222.
5. De Michele C., Salvadori J. A generalized pareto intensity-duration model of storm rainfall exploiting 2-Copulas. J. Geophys. Res. 2003, 108(D2):4067. http://dx.doi.org/10.1029/2002JD002534.
6. Dupuis D. Using copulas in hydrology: benefits, cautions, and issues. J. Hydrol. Eng. 2007, 12(4):381-393.
7. Eagleson P.S. Dynamics of flood frequency. Water Resour. Res. 1972, 8(4):878-898.
8. Favre A.C., El Adlouni S., Perreault L., Thiémonge N., Bobee B. Multivariate hydrological frequency analysis using copulas. Water Resour. Res. 2004, 40:W01101. 10.1029/2003WR002456.
9. Frahm G., Junker M., Schmidt R. Estimating the tail-dependence coefficient: properties and pitfalls. Insurance: Math. Econom. 2005, 37(1):80-100.
10. Genest C., Favre A.-C. Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng. 2007, 12(4):347-368.
11. Genest C., Rémillard B. Tests of independence and randomness based on the empirical copula process. Test 2004, 13(2):335-369.
12. Genest C., Rémillard B. Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. Ann. Inst. H. Poincaré Probab. Statist. 2008, 44(6):1096-1127.
13. Genest C., Ghoudi K., Rivest L.P. A semiparametric estimation procedure of dependence parameters in multivariate families of distribution. Biometrika 1995, 82(3):543-552.
14. Genest C., Rémillard B., Beaudoin D. Goodness-of-fit tests for copulas: a review and a power study. Insurance: Math. Econom. 2009, 44(2):199-213.
15. Gottschalk L., Perzyn G. Physically based distribution function for low flow. J. Hydrol. Sci. 1989, 35(5):559-573.
16. Gottschalk L., Tallaksen L.M., Perzyna G. Derivation of low flow distribution functions using recession curves. J. Hydrol. 1997, 194(1-4):239-262.
17. Gottschalk L., Yu K.-X., Leblois E., Xiong L. Statistics of low flow: theoretical derivation of the distribution of minimum streamflow series. J. Hydrol. 2013, 481:204-219.
18. Hewa G.A., Wang Q.J., McMahon T.A., Nathan R.J., Peel M.C. Generalized extreme value distribution fitted by LH moments for low-flow frequency analysis. Water Resour. Res. 2007, 43:W06301. 10.1029/2006WR004913.
19. Hisdal H., Tallaksen L.M., Clausen B., Peters E., Gustard A. Hydrological drought characteristics. Hydrological Drought 2004, 139-198. Elsevier, Ch. 5. L. Tallaksen, H.A.J. van Lanen (Eds.).
20. Hosking J.R.M. L-moments: analysis and estimation of distributions using linear combinations of order statistics. J. Roy. Stat. Soc. Ser. B 1990, 52:105-124.
21. Hosking J.R.M., Wallis J.R. Regional Frequency Analysis 1997, Cambridge University Press, Cambridge.
22. IPCC Climate Change 2007: Impacts, Adaptation and Vulnerability. Contributions of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change 2007, Cambridge University Press, Cambridge.
23. Joe H., Xu J. The estimation method of inference functions for margins for multivariate models. Technical Report 166 1996, Department of Statistics, University of British Columbia, Vancouver, Canada.
24. Kim G., Silvapulle M.J., Silvapulle P. Comparison of semiparametric and parametric methods for estimating copulas. Comp. Stat. Data Anal. 2007, 51(6):2836-2850.
25. Kojadinovic I., Holmes M. Tests of independence among continuous random vectors based on Cramér-von Mises functionals of the empirical copula process. J. Multivariate Anal. 2009, 100(6):1137-1154.
26. Kojadinovic I., Yan J. Modeling multivariate distributions with continuous margins using the copula R package. J. Stat. Softw. 2010, 34(9):1-20.
27. Lee K.S., Kim S.U. Identification of uncertainty in low flow frequency analysis using Bayesian MCMC method. Hydrol. Process. 2008, 22(12):1949-1964.
28. Luo X.L., Zeng E.Y., Ji R.Y., Wang C.P. Effects of in-channel sand excavation on the hydrology of the Pearl River Delta, China. J. Hydrol. 2007, 343:230-239.
29. Madsen, H., Rosbjerg, D., 1995. On the modeling of extreme droughts. In: Modelling and Management of Sustainable Basin-scale Water Resources Systems (Proc. Boulder Symp., July 1995), 377-385. IAHS Publ. no. 231.
30. Mamun A.A., Hashim A., Daoud J.I. Regionalisation of low flow frequency curves for the Peninsular Malaysia. J. Hydrol. 2010, 381(1-2):174-180.
31. McMahon T.A., Finlayson B.L. Droughts and anti-droughts: the low-flow hydrology of Australian rivers. Freshwater Biol. 2003, 48:1147-1160.
32. Michiels F., De Schepper A. A copula test space model how to avoid the wrong copula choice. Kybernetika 2008, 44(6):864-878.
33. Nelsen R.B. An Introduction to Copulas 2006, Springer, New York. second ed.
34. Oakes D. Multivariate survival distributions. J. Nonparam. Stat. 1994, 3(3-4):343-354.
35. Pacheco A., Gottschalk L., Krasovskaia I. Regionalization of low flow in Costa Rica. Climate Variability and Change-Hydrological Impacts. Proceedings of the Fifth FRIEND World Conference Havana, Cuba, November 2006. IAHS Publ. 308 2006, 111-116. IAHS Press, Wallingford, UK.
36. Perzyna J.G., Gottschalk L. Derived frequency distribution for low flows. Extreme Values: Floods and Droughts 1995, vol. 1:139-149. Kluwer, Dordrecht. K.W. Hipel (Ed.).
37. Poulin A., Huard D., Favre A., Pugin S. Importance of tail dependence in bivariate frequency analysis. J. Hydrol. Eng. 2007, 12(4):394-403.
38. Salvadori G., De Michele C. Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour. Res. 2004, 40(12):W12511. 10.1029/2004WR003133.
39. Salvadori G., De Michele C. On the use of copulas in hydrology: theory and practice. J. Hydrol. Eng. 2007, 12(4):369-380.
40. Seráing R., Xiao P. A Contribution to multivariate L-moments, L-comoment matrices. J. Multivariate Anal. 2007, 98(9):1765-1781.
41. Shi C., Zhou Y., Fan X., Shao W. A study on the annual runoff change and its relationship with water and soil conservation practices and climate change in the middle Yellow River basin. CATENA 2013, 100:31-41.
42. Shih J.H., Louis T.A. Inferences on the association parameter in copula models for bivariate survival data. Biometrics 1995, 51(4):1384-1399.
43. Sklar A. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 1959, 8:229-231.
44. Tallaksen L.M., Madsen H., Clausen B. On the definition and modelling of streamflow drought duration and deficit volume. Hydrol. Sci. J. 1997, 42(1):15-33.
45. Tsakiris G., Nalbantis I., Cavadias G. Regionalization of low flows based on Canonical Correlation Analysis. Adv. Water Resour. 2011, 34(7):865-872.
46. WMO (World Meteorological Organization), 2008. Manual on Low-flow Estimation and Prediction. Operational Hydrology Report No.50, WMO-No.1029. Geneva, Switzerland.
47. Zhang L., Singh V.P. Trivariate flood frequency analysis using the Gumbel-Hougaard copula. J. Hydrol. Eng. 2007, 12(4):431-439.