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Drought characterization using a new copula-based trivariate approach

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Abstract

Meteorological drought is a natural climatic phenomenon that occurs over various time scales and may cause significant economic, environmental and social damages. Three drought characteristics, namely duration, average severity and peak intensity, are important variables in water resources planning and decision making. This study presents a new method for construction of three-dimensional copulas to describe the joint distribution function of meteorological drought characteristics. Using the inference function for margins, the parameters for six types of copulas were tested to select the best-fitted copulas. According to the values of the log-likelihood function, Galambos, Frank and Clayton were the selected copula models to describe the dependence structure for pairs of duration–severity, severity–peak and duration–peak, respectively. Trivariate cumulative probability, conditional probability and drought return period were also investigated based on the derived copula-based joint distributions. The proposed model was evaluated over the observed data of a Qazvin synoptic station, and the results were compared with the empirical probabilities. For measuring the model accuracy, R 2, root mean square error (RMSE) and the Nash–Sutcliffe efficiency (NSE) criteria were used. Results indicated that R 2, RMSE and NSE were equal to 0.91, 0.098 and 0.668, respectively, which demonstrate sufficient accuracy of the proposed model. Drought probabilistic characteristics can provide useful information for water resource planning and management.

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Notes

  1. RMSE quantifies the model error in terms of the units of the variable.

References

  • Bardossy A (2006) Copula-based geostatistical models for groundwater quality parameters. Water Resour Res 42:W11416. doi:10.1029/2005WR004754

    Google Scholar 

  • Cancelliere A, Salas JD (2004) Drought length properties for periodic-stochastic hydrologic data. Water Resour Res 40:W02503. doi:10.1029/2002WR001750

    Google Scholar 

  • Chen L, Singh VP, Gao S (2011) Drought analysis based on copulas. 2011 Symposium on data-driven approaches to droughts

  • Czado C, Min A, Baumann T, Dakovic R (2008) Pair-copula constructions for modeling exchange rate dependence. Preprint, available under http://www.m4.ma.tum.de/Papers/index.html

  • De Michele C, Salvadori G (2003) A generalized Pareto intensity-duration model of storm rainfall exploiting 2-Copulas. J Geophys Res 108(D2):4067. doi:10.1029/2002JD002534

    Article  Google Scholar 

  • De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R (2005) Bivariate statistical approach to check adequacy of dam spillway. J Hydrol Eng 10(1):50–57. doi:10.1061/(ASCE)1084-0699(2005)10:1(50)

    Article  Google Scholar 

  • Dracup JA, Lee KS, Paulson EG (1980) On the statistical characteristics of drought events. Water Resour Res 16(2):289–296

    Google Scholar 

  • Favre AC, El Adlouni S, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40:01101. doi:10.1029/2003WR002456

    Google Scholar 

  • Genest C, Favre AC (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12(4):347–368. doi:10.1061/(ASCE)1084-0699(2007)12:4(347)

    Article  Google Scholar 

  • 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:W09401. doi:10.1029/2006WR005275

    Google Scholar 

  • Grimaldi S, Serinaldi F (2006a) Asymmetric copula in multivariate flood frequency analysis. Adv Water Resour 29(8):1115–1167. doi:10.1016/j.advwatres.2005.09.005

    Article  Google Scholar 

  • Grimaldi S, Serinaldi F (2006b) Design hyetograph analysis with 3-copula function. Hydrol Sci J 51(2):223–238. doi:10.1623/hysj.51.2.223

    Article  Google Scholar 

  • Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, New York

    Book  Google Scholar 

  • Kao S (2010) A copula-based joint deficit index for droughts. J Hydrol 380:121–134

    Article  Google Scholar 

  • Kao SC, Govindaraju RS (2007a) A bivariate rainfall frequency analysis of extreme rainfall with implications for design. J Geophys Res 112:D13119. doi:10.1029/2007JD008522

    Article  Google Scholar 

  • Kao SC, Govindaraju RS (2007b) Probabilistic structure of storm surface runoff considering the dependence between average intensity and storm duration. Water Resour Res 43:W06410. doi:10.1029/2006WR005564

    Google Scholar 

  • Kendall DR, Dracup JA (1992) On the generation of drought events using an alternating renewal-reward model. Stoch Hydrol Hydraul 6(1):55–68

    Article  Google Scholar 

  • Kuhn G, Khan S, Ganguly AR, Branstetter ML (2007) Geospatial-temporal dependence among weekly precipitation extremes with applications to observations and climate model simulations in South America. Adv Water Resour Res 30:2401–2423. doi:10.1016/j.advwatres.2007.05.006

    Article  Google Scholar 

  • Liu C, Zhang Q, Singh VP, Cui Y (2011) Copula-based evaluations of drought variations in Guangdong. South China Nat Hazards J 59:1533–1546. doi:10.1007/s11069-011-9850-4

    Article  Google Scholar 

  • Loukas A, Vasiliades L (2004) Probabilistic analysis of drought spatiotemporal characteristics in Thessaly region, Greece. Nat Hazards Earth Syst Sci 4:719–731

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • McKee TB, Doeskin NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. In: Proceedings of the 8th Conference on applied climatology, January 17–22, Anaheim, California, 179–184

  • Mirakbari M, Ganji A, Fallah SR (2010) Regional bivariate frequency analysis of meteorological droughts. J Hydrol Eng 15(12):985–1000. doi:10.1061/(ASCE)HE.1943-5584.0000271

    Article  Google Scholar 

  • Nelsen RB (2006) An introduction to copulas. Springer, New York

    Google Scholar 

  • Renard B, Lang M (2007) Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology. Adv Water Resour 30:897–912. doi:10.1016/j.advwatres.2006.08.001

    Article  Google Scholar 

  • Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res 40:W12511. doi:10.1029/2004WR003133

    Google Scholar 

  • Salvadori G, De Michele C (2006) Statistical characterization of temporal structure of storms. Adv Water Resour 29(6):827–842. doi:10.1016/j.advwatres.2005.07.013

    Article  Google Scholar 

  • Salvadori G, De Michele C, Kottegoda NT, Rosso R (2007) Extremes in nature: an approach using copulas. Water Sci Technol Library Ser, vol 56. Springer, New York

  • Shiau JT, Shen HW (2001) Recurrence analysis of hydrologic droughts of differing severity. J Water Res Plan Manage 127(1):30–40

    Google Scholar 

  • Shiau JT (2006) Fitting drought duration and severity with two-dimensional copulas. Water Resour Manage 20:795–815. doi:10.1007/s11269-005-9008-9

    Article  Google Scholar 

  • Shiau JT, Modarres R (2009) Copula-based drought severity-duration frequency analysis in Iran. J Appl Meteorol 16(4):481–489. doi:10.1002/met.145

    Article  Google Scholar 

  • Shiau JT, Wang HY, Tsai CT (2006) Bivariate frequency analysis of flood using copulas. J Am Water Resour As 42(6):1549–1564. doi:10.1111/j.1752-1688.2006.tb06020

    Article  Google Scholar 

  • Siadat H, Shiati K (2001) Overview of drought in I.R. Iran: impacts, lessons, and recommendations. A paper presented for the FAO Rep. Office in Tehran at the UNDP-Organized Regional Workshop on Drought Mitigation, Tehran, I.R. Iran, 28–29 August, p 20

  • Singh VP, Zhang L (2007) IDF curves using the frank archimedean copula. J Hydrol Eng 12(6):651–662. doi:10.1061/(ASCE)1084-0699(2007)12:6(651)

    Article  Google Scholar 

  • Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publ Inst Stat Univ Paris 8:229–231

    Google Scholar 

  • Song S, Singh VP (2010a) Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stoch Environ Res Risk Assess 24:783–805. doi:10.1007/s00477-010-0364-5

    Article  Google Scholar 

  • Song S, Singh VP (2010b) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Environ Res Risk Assess 24:425–444. doi:10.1007/s00477-009-0331-1

    Article  Google Scholar 

  • Wong G, Lambert MF, Metcalfe AV (2008) Trivariate copulas for characterization of droughts. ANZIAM J 49:306–323

    Google Scholar 

  • Wong G, Lambert MF, Leonard M, Metcalfe AV (2010) Drought analysis using trivariate copulas conditional on climatic states. J Hydrol Eng 15(2):129–141

    Article  Google Scholar 

  • Yevjevich V (1967) An objective approach to definitions and investigation of continental hydrologic droughts. Hydrology Paper 23. Colorado State University, Fort Collins, CO

  • Zelenhasic E, Salvai A (1987) A method of streamflow drought analysis. Water Resour Res 23(1):156–168

    Article  Google Scholar 

  • Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11(2):150–164. doi:10.1061/(ASCE)1084-0699(2006)11:2(150)

    Article  Google Scholar 

  • Zhang L, Singh VP (2007) Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 332(1–2):93–109. doi:10.1016/j.jhydrol.2006.06.033

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Technical and Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Bahram Saghafian & Hossein Mehdikhani

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  1. Bahram Saghafian
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  2. Hossein Mehdikhani
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Correspondence to Hossein Mehdikhani.

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Saghafian, B., Mehdikhani, H. Drought characterization using a new copula-based trivariate approach. Nat Hazards 72, 1391–1407 (2014). https://doi.org/10.1007/s11069-013-0921-6

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