Multivariate assessment of droughts: Frequency analysis and dynamic return period

Water Resources Research

Volumn 49, Issue 10, 2013, Pages 6985-6994

  De Michele, C ^a   Salvadori, G ^b   Vezzoli, R ^c   Pecora, S ^d  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF SALENTO   (Italy)

^c CENTRO EURO MEDITERRANEO SUI CAMBIAMENTI CLIMATICI   (Italy)

^d Sezione Provinciale di Parma   (Italy)

Author keywords

copulas; drought; dynamic return period; randomization

Indexed keywords

COPULAS; FREQUENCY ANALYSIS; RANDOMIZATION; RANDOMIZATION PROCEDURE; REAL-TIME ASSESSMENT; REPEATED MEASUREMENTS; RETURN PERIODS; TEMPORAL EVOLUTION;

RANDOM PROCESSES; STREAM FLOW;

DROUGHT;

ASSESSMENT METHOD; DATA SET; DROUGHT STRESS; FLOOD; FREQUENCY ANALYSIS; MEASUREMENT METHOD; MONITORING; MULTIVARIATE ANALYSIS; RIVER FLOW; STREAMFLOW;

ITALY; PO BASIN;

EID: 84886146581     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/wrcr.20551     Document Type: Article

References (50)

1. AA. VV., (2011), Le magre del Po. Conoscerle per prevederle, cooperare per prevenirle, Fondazione CIMA, Parma (Italy), (in Italian). [Available at www.cimafoundation.org.].
2. Beran, M., and, J. Rodier, (1985), Hydrological Aspects of Drought: A Contribution to the International Hydrological Programme, Studies and Reports in Hydrology, vol. 39, UNESCO-WMO, Paris.
3. Burnham, K. P., and, D. R. Anderson, (2002), Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed., Springer, New York.
4. Byzedi, M., (2010), Analysis of hydrological drought based on daily flow series, Proc. World Acad. Sci. Eng. Technol., 70, 249-252.
5. Byzedi, M., and, B. Saghafian, (2009), Regional analysis of streamflow drought: A case study for southwestern Iran, Proc. World Acad. Sci. Eng. Technol., 57, 447-451.
6. Chambers, J. M., W. S. Cleveland, B. Kleiner, and, P. Tukey, (1983), Graphical Methods for Data Analysis, Wadsworth, Calif., Boston.
7. Claeskens, G., and, N. Hjort, (2008), Model Selection and Model Averaging, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge Univ. Press., Cambridge.
8. Clausen, B., and, C. Pearson (Pubitemid 26472261)
9. Davison, A. C., and, D. V. Hinkley, (1997), Bootstrap Methods and their Application, Cambridge Series on Statistical and Probabilistic Mathematics, Cambridge Univ. Press, Cambridge, U. K.
10. De Michele, C., and, G. Salvadori, (2003), A generalized pareto intensity-duration model of storm rainfall exploiting 2-copulas, J. Geophys. Res., 108 (D2), 4067, doi: 10.1029/2002JD002534.
11. Demuth, S., and, B. Heinrich, (1997), Temporal and spatial behaviour of droughts in South Germany, in FRIEND'97-Regional Hydrology: Concepts and models for sustainable water resources management (Proceedings of the Postojna, Slovenia, Conference, September-October 1997), vol. 246, edited by, A. Gustard, et al., pp. 151-157, IAHS, Meppel, The Netherlands.
12. Demuth, S., and, C. Külls, (1997), Probability analysis and regional aspects of droughts in southern Germany, in Sustainability of Water Resources under Increasing Uncertainty (Proceedings of Rabat Symposium SI, April 1997), vol. 240, edited by, D. Rosbjerg, et al., pp. 97-104, IAHS, Great Yamouth, UK. (Pubitemid 127553264)
13. Dracup, J., K. Lee, and, E. J. Paulson, (1980a), On the definition of droughts, Water Resour. Res., 16 (2), 297-302, doi: 10.1029/WR016i002p00297.
14. Dracup, J., K. Lee, and, E. J. Paulson, (1980b), On the statistical characteristics of drought events, Water Resour. Res., 16 (2), 289-296, doi: 10.1029/WR016i002p00297.
15. Durante, F., and, G. Salvadori, (2010), On the construction of multivariate extreme value models via copulas, Environmetrics, 21 (2), 143-161.
16. Engeland, K., H. Hisdal, and, A. Frigessi, (2004), Practical extreme value modelling of hydrological floods and droughts: A case study, Extremes, 7, 5-30, doi: 10.1007/s10687-004-4727-5. (Pubitemid 40553882)
17. Ganguli, P., and, M. J. Reddy, (2012), Risk assessment of droughts in Gujarat using bivariate copulas, Water Resour. Manage., 26 (11), 3301-3327, doi: 10.1007/s11269-012-0073-6.
18. Genest, C., and, A. C. Favre, (2007), Everything you always wanted to know about copula modeling but were afraid to ask, J. Hydrol. Eng., 12 (4), 347-368. (Pubitemid 47023282)
19. Genest, C., and, J. Neǎlehovà, (2007), A primer on copulas for count data, Astin Bull., 37 (2), 475-515, doi: 10.2143/AST.37.2.2024077.
20. Genest, C., B. Rémillard, and, D. Beaudoin, (2009), Goodness-of-fit tests for copulas: A review and a power study, Insur. Math. Econ., 44, 199-213.
21. Gräler, B., M. J. van den Berg, S. Vandenberghe, A. Petroselli, S. Grimaldi, B. D. Baets, and, N. E. C. Verhoest, (2013), Multivariate return periods in hydrology: A critical and practical review focusing on synthetic design hydrograph estimation, Hydrol. Earth Syst. Sci., 17, 1281-1296, doi: 10.5194/hess-17-1281-2013.
22. Joe, H., (1997), Multivariate Models and Dependence Concepts, Chapman and Hall, London.
23. Kao, S.-C., and, R. S. Govindaraju, (2010), A copula-based joint deficit index for droughts, J. Hydrol., 380 (1-2), 121-134, doi: 10.1016/j.jhydrol.2009. 10.029.
24. Kjeldsen, T., A. Lundorf, and, D. Rosbjerg, (2000), Use of a two-component exponential distribution in partial duration modelling of hydrological droughts in Zimbabwean rivers, Hydrol. Sci. J., 45 (2), 285-298, doi: 10.1080/02626660009492325. (Pubitemid 30258130)
25. Kojadinovic, I., and, J. Yan, (2010), Modeling multivariate distributions with continuous margins using the copula R package, J. Stat. Software, 34 (9), 1-20.
26. Lilliefors, H. W., (1967), On the Kolmogorov-Smirnov test for normality with mean and variance unknown, J. Am. Stat. Assoc., 62, 399-402.
27. Maity, R., A. Sharma, D. Nagesh Kumar, and, K. Chanda, (2013), Characterizing drought using the reliability-resilience-vulnerability concept, J. Hydrol. Eng., 18 (7), 859-869, doi: 10.1061/(ASCE)HE.1943-5584.0000639.
28. Mirabbasi, R., A. Fakheri-Fard, and, Y. Dinpashoh, (2012), Bivariate drought frequency analysis using the copula method, Theor. Appl. Climatol., 108 (1-2), 191-206, doi: 10.1007/s00704-011-0524-7.
29. Mishra, A. K., and, V. P. Singh, (2011), Drought modeling: A review, J. Hydrol., 403 (1-2), 157-175, doi: 10.1016/j.jhydrol.2011.03.049.
30. Nelsen, R. B., (2006), An Introduction to Copulas, 2nd ed., Springer, New York.
31. Press, W., B. Flannery, S. Teukolsky, and, W. Vetterling, (1992), Numerical Recipes in C, 2nd ed., Cambridge Univ. Press, Cambridge, U. K.
32. Reddy, M. J., and, P. Ganguli, (2012), Application of copulas for derivation of drought severity-duration-frequency curves, Hydrol. Processes, 26 (11), 1672-1685, doi: 10.1002/hyp.8287.
33. Salvadori, G., and, C. De Michele, (2004), Frequency analysis via copulas: Theoretical aspects and applications to hydrological events, Water Resour. Res., 40, W12511, doi: 10.1029/2004WR003133.
34. Salvadori, G., and, C. De Michele, (2010), Multivariate multiparameter extreme value models and return periods: A copula approach, Water Resour. Res., 46, W10501, doi: 10.1029/2009WR009040.
35. Salvadori, G., and, C. De Michele, (2013), Multivariate extreme value methods, in Extremes in a Changing Climate, Water Science and Technology Library, vol. 65, edited by, A. AghaKouchak, et al., chap. 5, pp. 115-162, Springer, Dordrecht, Netherlands.
36. Salvadori, G., C. De Michele, N. Kottegoda, and, R. Rosso, (2007), Extremes in Nature. An Approach Using Copulas, Water Science and Technology Library Series, vol. 56, Springer, Dordrecht, Netherlands.
37. Salvadori, G., C. De Michele, and, F. Durante, (2011), On the return period and design in a multivariate framework, Hydrol. Earth Syst. Sci., 15, 3293-3305, doi: 10.5194/hess-15-3293-2011.
38. Salvadori, G., F. Durante, and, C. De Michele, (2013), Multivariate return period calculation via survival functions, Water Resour. Res., 49, 2308-2311, doi: 10.1002/wrcr.20204.
39. Sen, Z., (1977), Run-sums of annual flow series, J. Hydrol., 35 (3-4), 311-324, doi: 10.1016/0022-1694(77)90009-9.
40. Serinaldi, F., B. Bonaccorso, A. Cancelliere, and, S. Grimaldi, (2009), Probabilistic characterization of drought properties through copulas, Phys. Chem. Earth, 34 (10-12), 596-605, doi: 10.1016/j.pce.2008.09.004.
41. Shiau, J. T., (2006), Fitting drought duration and severity with two-dimensional copulas, Water Resour. Manage., 20 (5), 795-815, doi: 10.1007/s11269-005-9008-9. (Pubitemid 44263973)
42. Shiau, J. T., and, R. Modarres, (2009), Copula-based drought severity-duration-frequency analysis in Iran, Meteorol. Appl., 16 (4), 481-489, doi: 10.1002/met.145.
43. Song, S., and, V. P. Singh, (2010), Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm, Stochastic Environ. Res. Risk Assess., 24 (5), 783-805, doi: 10.1007/s00477-010-0364-5.
44. Tallaksen, L., H. Madsen, and, B. Clausen, (1997), On the definition and modelling of streamflow drought duration and deficit volume, Hydrol. Sci. J., 42 (1), 15-33.
45. Vandenberghe, S., N. E. C. Verhoest, and, B. De Baets, (2010), Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall, Water Resour. Res., 46, W01512, doi: 10.1029/2009WR007857.
46. VV. AA., (2013), Special Issue: Data-driven approaches to droughts, J. Hydrol. Eng., 18 (7), 735-918.
47. Wilhite, D., and, M. Glantz, (1987), Understanding the drought phenomenon: The role of definitions, in Planning for Drought: Toward a Reduction of Societal Vulnerability, edited by, D. Wilhite, W. Easterling, and, D. Wood, Westview, USA, Boulder, Colorado, pp. 11-27.
48. Wong, G., M. Lambert, M. Leonard, and, A. V. Metcalfe, (2010), Drought analysis using trivariate copulas conditional on climatic states, J. Hydrol. Eng., 15 (2), 129-141, doi: 10.1061/(ASCE)HE.1943-5584.0000169.
49. Yevjevich, V., (1967), An objective approach to definitions and investigations of continental hydrologic droughts, Hydrol. Pap. 23, Colo. State Univ., Fort Collins, Colo.
50. Zelenhasic̈, E., and, A. Salvai, (1987), A method of streamflow drought analysis, Water Resour. Res., 23 (1), 156-168, doi: 10.1029/ WR023i001p00156.