Abstract
Droughts produce a complex set of negative economic, environmental, and social impacts from regional to national scales. Drought impacts can be quantified by using drought index time series, such as the monthly Standardized Precipitation Index (SPI) time series. Drought characteristics, namely drought duration, severity, time interval and the minimum SPI values, are determined in this chapter. Five hundred years of daily rainfall data are simulated for evaluating drought characteristics. Appropriate distributions are selected for modeling drought durations, time intervals, drought severity and the minimum SPI values in different drought states. The drought episodes are quantified using multivariate copula methods. Several copulas selected from the Archimedean and meta-elliptical families are applied to constructing four-dimensional joint distributions. The dependence structure in each drought state is investigated, and drought probabilities and return periods are calculated and analyzed based on a four-dimensional copula, where the upper Han River Basin, China is used as a case study.
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References
Alley WM (1984) The palmer drought severity index: limitations and assumptions. J Clim Appl Meteor 23:1100–1109
Below R, Grover-Kopec E, Dilley M (2007) Documenting drought-related disasters: a global reassessment. J Environ Develop 16(3):328–344
Bonaccorso B, Cancelliere A, Rossi G (2003) An analytical formulation of return period of drought severity. Stoch Env Res Risk A 17(3):157–174
Cancelliere A, Salas JD (2004) Drought length properties for periodic-stochastic hydrological data. Water Resour Res 40:W02503. https://doi.org/10.1029/2002WR001750
Cancelliere A, Salas JD (2010) Drought probabilities and return period for annual streamflows series. J Hydrol 391(1–2):77–89
Chen J, Brissette PF, Leconte R (2010) A daily stochastic weather generator for preserving low-frequency of climate variability. J Hydrol 388:480–490
Chen L, Singh VP, Guo S, Mishra AK, Guo J (2013) Drought analysis based on copulas. J Hydrol Eng 18(7):797–808
Estrela T, Vargas E (2012) Drought management plans in the European Union. The case of Spain. Water Resour Manag 26(6):1537–1553
Fernández B, Salas JD (1999) Return period and risk of hydrologic events I: mathematical formulation. J Hydrol Eng 4(4):297–307
Genest C, Favre AC, Béliveau J, Jacques C (2007) Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resour Res 43(9):W09401
González J, Valdés JB (2003) Bivariate drought recurrence analysis using tree ring reconstructions. J Hydrol Eng 8(5):247–258
Guttman NB (1991) A sensitivity analysis of the Palmer hydrologic drought index. J Am Water Resour Assoc 27(5):797–807
Guttman NB (1998) Comparing the Palmer drought index and the standardized precipitation index. J Am Water Resour Assoc 34:113–121
Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc B 52:105–124
Kao SC, Govindaraju RS (2007) A bivariate frequency analysis of extreme rainfall with implications for design. J Geophys Res 112:D13119. https://doi.org/10.1029/2007JD008522
Kendall DR, Dracup JA (1992) On the generation of drought events using an alternating renewal-reward model. Stoch Hydrol Hydraul 6(1):55–68
Kim TW, Valdés JB, Yoo C (2003) Nonparametric approach for estimating return periods of droughts in arid regions. J Hydrol Eng 8(5):237–246
Mathier L, Perreault L, Bobe B, Ashkar F (1992) The use of geometric and gamma-related distributions for frequency analysis of water deficit. Stoch Hydrol Hydraul 6(4):239–254
McKee TB, Doesken NJ, Kliest J (1993) The relationship of drought frequency and duration to time scales. In: Proceedings of the 8th conference of applied climatology, 17–22 Jan, Anaheim, CA. American Meteorological Society, Boston, MA. pp 179–184
Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391(1–2):202–216
Mishra A, Singh VP, Desai V (2009) Drought characterization: a probabilistic approach. Stoch Env Res Risk A 23(1):41–55
Núñez JH, Verbist K, Wallis JR, Schaefer MG, Morales L, Cornelis WM (2011) Regional frequency analysis for mapping drought events in north-central Chile. J Hydrol 405(3–4):352–366
Palmer WC (1965) Meteorological drought. Research paper no. 45, US Department of Commerce, Weather Bureau, Washington, DC
Salas JD, Fu C, Cancelliere A, Dustin D, Bode D, Pineda A, Vincent E (2005) Characterizing the severity and risk of drought in the Poudre River, Colorado. J Water Res Plan Man 131(5):383–393
Serinaldi F, Bonaccorso B, Cancelliere A, Grimaldi S (2009) Probabilistic characterization of drought properties through copulas. Phys Chem Earth, Parts A/B/C 34(10–12):596–605
Shiau J (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resour Manag 20(5):795–815
Shiau JT, Shen HW (2001) Recurrence analysis of hydrologic droughts of differing severity. J Water Resour Plan Man 127(1):30–40
Shiau JT, Feng S, Nadarajah S (2007) Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrol Process 21(16):2157–2163
Song S, Singh VP (2010) Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stoch Env Res Risk A 24(5):783–805
Tallaksen LM, Madsen H, Clausen B (1997) On the definition and modeling of stream drought duration and deficit volume. Hydrol Sci J 42(1):15–33
Zelenhastic E, Salvai A (1987) A method of streamflow drought analysis. Water Resour Res 23(1):156–168
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). Drought Analysis Using Copulas. In: Copulas and Its Application in Hydrology and Water Resources. Springer Water. Springer, Singapore. https://doi.org/10.1007/978-981-13-0574-0_5
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DOI: https://doi.org/10.1007/978-981-13-0574-0_5
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