Bivariate Risk Analysis of Droughts Using a Nonparametric Multivariate Standardized Drought Index and Copulas
Publication: Journal of Hydrologic Engineering
Volume 24, Issue 5
Abstract
The Nonparametric Multivariate Standardized Drought Index (NMSDI) based on precipitation and soil moisture data in conjunction with copula functions is of primary concern in this study. We are the first to investigate bivariate return periods of the NMSDI using the two typical drought characteristics (duration and severity) at 10 stations in Konya Closed Basin (KCB) in Turkey. As a result, lognormal and log-logistic distributions were identified as the most suitable distributions for drought duration and severity series according to five commonly used goodness of fit tests. Various types of copulas were considered in modeling the joint dependence between duration and severity series at each station. Our results from the five goodness of fit tests and tail dependence assessments showed that BB6, BB7, and BB8 copulas outperformed the joint modeling of duration and severity series in the KCB. The bivariate return period analysis revealed a high risk for southeastern and southwestern regions in the KCB for the 3-month NMSDI series while north to northwestern regions could be exposed to high risk for the 6-month series.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank the Editor(s) and anonymous reviewers of this paper for their thorough review and constructive comments, which have led to substantial improvements. This research was partially supported by the Scientific Research Projects Unit of Istanbul Technical University through the project (No. 39267). The authors would like to thank Turkish State Meteorological Service (TSMS) for providing the precipitation data. The upper tail dependence calculation was done by Vine copula R package by Schepsmeier et al. (2012). We also would like to appreciate NOAA/NCEP/ESRL PSD, Boulder, Colorado, USA, for making soil moisture data available for public. We finally thank Mr. Turhan Uludag, who is acting as an English instructor at The Preparatory School of Foreign Languages, ITU North Cyprus, for editing the manuscript entirely.
References
Akaike, H. 1976. “An information criterion (AIC).” Math Sci. 14 (153): 5–7.
Bačová Mitková, V., and D. Halmová. 2014. “Joint modeling of flood peak discharges, volume and duration: A case study of the Danube River in Bratislava.” J. Hydrol. Hydromech. 62 (3): 186–196. https://doi.org/10.2478/johh-2014-0026.
Borgomeo, E., G. Pflug, J. W. Hall, and S. Hochrainer-Stigler. 2015. “Assessing water resource system vulnerability to unprecedented hydrological drought using copulas to characterize drought duration and deficit.” Water Resour. Res. 51 (11): 8927–8948. https://doi.org/10.1002/2015WR017324.
Carrão, H., S. Russo, G. Sepulcre-Canto, and P. Barbosa. 2016. “An empirical standardized soil moisture index for agricultural drought assessment from remotely sensed data.” Int. J. Appl. Earth Obs. Geoinf. 48: 74–84. https://doi.org/10.1016/j.jag.2015.06.011.
Chang, J., Y. Li, Y. Wang, and M. Yuan. 2016. “Copula-based drought risk assessment combined with an integrated index in the Wei River Basin, China.” J. Hydrol. 540: 824–834. https://doi.org/10.1016/j.jhydrol.2016.06.064.
Chen, L., V. P. Singh, L. Chen, V. P. Singh, F. Asce, S. Guo, A. K. Mishra, and J. Guo. 2013. “Drought analysis using copulas.” J. Hydrol. Eng. 18 (7): 797–808. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000697.
Cheng, L., A. AghaKouchak, E. Gilleland, and R. W. Katz. 2014. “Non-stationary extreme value analysis in a changing climate.” Clim. Change 127 (2): 353–369. https://doi.org/10.1007/s10584-014-1254-5.
Daneshkhah, A., R. Remesan, O. Chatrabgoun, and I. P. Holman. 2016. “Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model.” J. Hydrol. 540: 469–487. https://doi.org/10.1016/j.jhydrol.2016.06.044.
Darling, D. A. 1957. “The Kolmogorov-Smirnov, Cramer-von Mises Tests.” Ann. Math. Stat. 28 (4): 823–838. https://doi.org/10.1214/aoms/1177706788.
De Michele, C. 2003. “A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-Copulas.” J. Geophys. Res. 108 (D2): 4067. https://doi.org/10.1029/2002JD002534.
De Michele, C., G. Salvadori, G. Passoni, and R. Vezzoli. 2007. “A multivariate model of sea storms using copulas.” Coastal Eng. 54 (10): 734–751. https://doi.org/10.1016/j.coastaleng.2007.05.007.
De Michele, C., G. Salvadori, R. Vezzoli, and S. Pecora. 2013. “Multivariate assessment of droughts: Frequency analysis and dynamic return period.” Water Resour. Res. 49 (10): 6985–6994. https://doi.org/10.1002/wrcr.20551.
Dracup, J. D., and J. Keyantash. 2002. “The quantification of drought: An evaluation of drought indices.” Am. Meteorol. Soc. 83 (8): 1167–1180. https://doi.org/10.1175/1520-0477-83.8.1167.
Fan, Y., and H. van den Dool. 2004. “Climate Prediction Center global monthly soil moisture data set at 0.5° resolution for 1948 to present.” J. Geophys. Res. D Atmos. 109 (D10). https://doi.org/10.1029/2003JD004345.
Favre, A.-C., S. El Adlouni, L. Perreault, N. Thiémonge, and B. Bobée. 2004. “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res. 40 (1): 1–12. https://doi.org/10.1029/2003WR002456.
Frahm, G., M. Junker, and R. Schmidt. 2005. “Estimating the tail-dependence coefficient: Properties and pitfalls.” Insurance Math. Econ. 37 (1): 80–100. https://doi.org/10.1016/j.insmatheco.2005.05.008.
Ganguli, P. 2016. Copula theory: Introduction and application to meteorological drought. Saarbrücken, Germany: LAP LAMBERT Academic Publishing.
Ganguli, P., and A. R. Ganguly. 2016. “Space-time trends in U. S. meteorological droughts.” Biochem. Pharmacol. 8: 235–259. https://doi.org/10.1016/j.ejrh.2016.09.004.
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. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347).
Golian, S., O. Mazdiyasni, and A. AghaKouchak. 2014. “Trends in meteorological and agricultural droughts in Iran.” Theor. Appl. Climatol. 119 (3–4): 679–688. https://doi.org/10.1007/s00704-014-1139-6.
Grimaldi, S., A. Petroselli, G. Salvadori, and C. De Michele. 2016. “Catchment compatibility via copulas: A non-parametric study of the dependence structures of hydrological responses.” Adv. Water Resour. 90: 116–133. https://doi.org/10.1016/j.advwatres.2016.02.003.
Gringorten, I. I. 1963. “A plotting rule for extreme probability paper.” J. Geophys. Res. 68 (3): 813–814. https://doi.org/10.1029/JZ068i003p00813.
Grimaldi, S., and F. Serinaldi. 2006. “Asymmetric copula in multivariate flood frequency analysis.” Adv. Water Resour. 29 (8): 1155–1167. https://doi.org/10.1016/j.advwatres.2005.09.005.
Hao, Z., and A. AghaKouchak. 2013. “Multivariate standardized drought index: A parametric multi-index model.” Adv. Water Resour. 57: 12–18. https://doi.org/10.1016/j.advwatres.2013.03.009.
Hao, Z., and A. AghaKouchak. 2014. “A nonparametric multivariate multi-index drought monitoring framework.” J. Hydrometeorol. 15 (1): 89–101. https://doi.org/10.1175/JHM-D-12-0160.1.
Huang, S., Q. Huang, J. Chang, Y. Zhu, G. Leng, and L. Xing. 2015. “Drought structure based on a nonparametric multivariate standardized drought index across the Yellow River basin, China.” J. Hydrol. 530: 127–136. https://doi.org/10.1016/j.jhydrol.2015.09.042.
Janga Reddy, M., and P. Ganguli. 2012. “Application of copulas for derivation of drought severity-duration-frequency curves.” Hydrol. Process. 26 (11): 1672–1685. https://doi.org/10.1002/hyp.8287.
Jiang, C., L. Xiong, C. Y. Xu, and S. Guo. 2015. “Bivariate frequency analysis of nonstationary low-flow series based on the time-varying copula.” Hydrol. Process. 29 (6): 1521–1534. https://doi.org/10.1002/hyp.10288.
Kahya, E., M. C. Demirel, and A. O. Bég. 2008. “Hydrologic homogeneous regions using monthly streamflow in Turkey.” Earth Sci. Res. J. 12 (2): 181–193.
Kang, H., and V. Sridhar. 2017. “Description of future drought indices in Virginia.” Data Brief 14: 278–290. https://doi.org/10.1016/j.dib.2017.07.042.
Kao, S. C., and R. S. Govindaraju. 2007. “A bivariate frequency analysis of extreme rainfall with implications for design.” J. Geophys. Res. Atmos. 112 (13): https://doi.org/10.1029/2007JD008522.
Kao, S. C., and R. S. Govindaraju. 2010. “A copula-based joint deficit index for droughts.” J. Hydrol. 380 (1–2): 121–134. https://doi.org/10.1016/j.jhydrol.2009.10.029.
Kendall, M. G. 1975. Rank correlation methods. London: Charles Griffin.
Lee, T., R. Modarres, and T. B. M. J. Ouarda. 2013. “Data-based analysis of bivariate copula tail dependence for drought duration and severity.” Hydrol. Process. 27 (10): 1454–1463. https://doi.org/10.1002/hyp.9233.
Ljung, G. M., and G. E. P. Box. 1978. “On a measure of lack of fit in time series models.” Biometrika 65 (2): 297–303. https://doi.org/10.1093/biomet/65.2.297.
Ma, M., S. Song, L. Ren, S. Jiang, and J. Song. 2013. “Multivariate drought characteristics using trivariate Gaussian and Student t copulas.” Hydrol. Process. 27 (8): 1175–1190. https://doi.org/10.1002/hyp.8432.
Madadgar, S., and H. Moradkhani. 2013. “Drought analysis under climate change using copula.” J. Hydrol. Eng. 18 (7): 746–759. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000532.
Madadgar, S., and H. Moradkhani. 2016. “Copula function and drought.” In Vol. 1 of Handbook of drought and water scarcity, principles of drought and water scarcity. New York: Taylor & Francis.
Mann, H. B. 1945. “Nonparametric tests against trend.” Econometrica 13 (3): 245. https://doi.org/10.2307/1907187.
Mckee, T. B., N. J. Doesken, and J. Kleist. 1993. “The relationship of drought frequency and duration to time scales.” In Proc., AMS 8th Conf. on Applied Climatology, 179–184. Boston, MA: American Meteorological Society.
Miao, C., Q. Sun, Q. Duan, and Y. Wang. 2016. “Joint analysis of changes in temperature and precipitation on the Loess Plateau during the period 1961-2011.” Clim. Dyn. 47 (9–10): 3221–3234. https://doi.org/10.1007/s00382-016-3022-x.
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. https://doi.org/10.1007/s00704-011-0524-7.
Mirakbari, M., A. Ganji, and S. R. Fallah. 2010. “Regional bivariate frequency analysis of Meteorological Droughts.” J. Hydrol. Eng. 15 (12): 985–1000. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000271.
Mishra, A. K., and V. P. Singh. 2010. “A review of drought concepts.” J. Hydrol. 391 (1–2): 202–216. https://doi.org/10.1016/j.jhydrol.2010.07.012.
Nelsen, R. B. 2006. An introduction to copulas, ser. Lecture Notes in Statistics. New York: Springer.
Pappadà, R., F. Durante, and G. Salvadori. 2017. “Quantification of the environmental structural risk with spoiling ties: Is randomization worthwhile?” Stochastic Environ. Res. Risk Assess. 31 (10): 2483–2497. https://doi.org/10.1007/s00477-016-1357-9.
Pham, M. T., H. Vernieuwe, B. de Baets, P. Willems, and N. E. C. Verhoest. 2016. “Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas.” Stochastic Environ. Res. Risk Assess. 30 (8): 2197–2214. https://doi.org/10.1007/s00477-015-1181-7.
Poulin, A., D. Huard, A.-C. Favre, and S. Pugin. 2007. “Importance of tail dependence in bivariate frequency analysis.” J. Hydrol. Eng. 12 (4): 394–403. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(394).
Rajsekhar, D., A. Mishra, and V. Singh. 2013. “Regionalization of drought characteristics using an entropy approach.” J. Hydrol. Eng. 18 (7): 870–887. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000683.
Rajsekhar, D., V. P. Singh, and A. K. Mishra. 2015. “Hydrologic drought atlas for Texas.” J. Hydrol. Eng. 20 (7): 05014023. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001074.
Renard, B., and M. Lang. 2007. “Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology.” Adv. Water Resour. 30 (4): 897–912. https://doi.org/10.1016/j.advwatres.2006.08.001.
Requena, A. I., L. Mediero, and L. Garrote. 2013. “A bivariate return period based on copulas for hydrologic dam design: Accounting for reservoir routing in risk estimation.” Hydrol. Earth Syst. Sci. 17 (8): 3023–3038. https://doi.org/10.5194/hess-17-3023-2013.
Salvadori, G., and C. De Michele. 2004. “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events.” Water Resour. Res. 40 (12): 1–17. https://doi.org/10.1029/2004WR003133.
Salvadori, G., and C. De Michele. 2006. “Statistical characterization of temporal structure of storms.” Adv. Water Resour. 29 (6): 827–842. https://doi.org/10.1016/j.advwatres.2005.07.013.
Salvadori, G., C. De Michele, N. T. Kottegoda, and R. Rosso. 2007. Vol. 56 of Extremes in nature: an approach using copulas. New York: Springer.
Şarlak, N., E. Kahya, and A. O. Bég. 2009. “Critical drought analysis: A case study of Göksu River (Turkey) and North Atlantic oscillation influences.” J. Hydrol. Eng. 14 (8): 795–802. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000052.
Schepsmeier, U., J. Stoeber, E. C. Brechmann, B. Graeler, T. Nagler, and T. Erhardt. 2012. “VineCopula: Statistical inference of vine copulas.” In R package version 2.1.8, R-Project CRAN Repository.
Serago, J. M., and R. M. Vogel. 2018. “Parsimonious nonstationary flood frequency analysis.” Adv. Water Resour. 112: 1–16. https://doi.org/10.1016/j.advwatres.2017.11.026.
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. https://doi.org/10.1016/j.pce.2008.09.004.
Sharma, A. 2000. “Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 3—A nonparametric probabilistic forecast model.” J. Hydrol. 239 (1): 249–258. https://doi.org/10.1016/S0022-1694(00)00348-6.
She, D., A. K. Mishra, J. Xia, L. Zhang, and X. Zhang. 2016. “Wet and dry spell analysis using copulas.” Int. J. Climatol. 36 (1): 476–491. https://doi.org/10.1002/joc.4369.
Sheffield, J., G. Goteti, F. Wen, and E. F. Wood. 2004. “A simulated soil moisture based drought analysis for the United States.” J. Geophys. Res. D Atmos. 109 (24): 1–19. https://doi.org/10.1029/2004JD005182.
Shiau, J. T. 2003. “Return period of bivariate distributed extreme hydrological events.” Stochastic Environ. Res. Risk Assess. 17 (1–2): 42–57. https://doi.org/10.1007/s00477-003-0125-9.
Shiau, J. T. 2006. “Fitting drought duration and severity with two-dimensional copulas.” Water Resour. Manage. 20 (5): 795–815. https://doi.org/10.1007/s11269-005-9008-9.
Shiau, J. T., S. Feng, and S. Nadarajah. 2007. “Assessment of hydrological droughts for the Yellow River, China, using copulas.” Hydrol. Process. 21 (16): 2157–2163. https://doi.org/10.1002/hyp.6400.
Shiau, J. T., and R. Modarres. 2009. “Copula-based drought severity-duration-frequency analysis in Iran.” Meteorol. Appl. 16 (4): 481–489. https://doi.org/10.1002/met.145.
Silverman, B. W. 1986. Density estimation for statistics and data analysis. Abingdon, UK: Routledge.
Sklar, M. 1959. “Fonctions de repartition an dimensions et leurs marges.” [In French.] Publ. Inst. Statist. Univ. Paris 8: 229–231.
Smakhtin, V. U. 2001. “Low flow hydrology: A review.” J. Hydrol. 240 (3–4): 147–186. https://doi.org/10.1016/S0022-1694(00)00340-1.
Song, S., and V. P. Singh. 2010. “Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data.” Stochastic Environ. Res. Risk Assess. 24 (3): 425–444. https://doi.org/10.1007/s00477-009-0331-1.
Stephens, M. A. 1974. “EDF statistics for goodness of fit and some comparisons.” J. Am. Stat. Assoc. 69 (347): 730–737. https://doi.org/10.1080/01621459.1974.10480196.
Stone, M. 1979. “Comments on model selection criteria of Akaike and Schwarz.” J. R. Stat. Soc. Series B (Methodol.) 41 (2): 276–278.
Svoboda, M., et al. 2002. “The Drought Monitor.” Bull. Am. Meteorol. Soc. 83 (8): 1181–1190. https://doi.org/10.1175/1520-0477-83.8.1181.
Svoboda, M., B. Fuchs, Integrated Drought Management Programme (IDMP), World Meteorological Organization, Global Water Partnership, and University of Nebraska-Lincoln. 2016. Handbook of drought indicators and indices. Geneva: World Meteorological Organization.
Tosunoglu, F., and I. Can. 2016. “Application of copulas for regional bivariate frequency analysis of meteorological droughts in Turkey.” Nat. Hazards 82 (3): 1457–1477. https://doi.org/10.1007/s11069-016-2253-9.
Tosunoglu, F., and O. Kisi. 2016. “Joint modelling of annual maximum drought severity and corresponding duration.” J. Hydrol. 543: 406–422. https://doi.org/10.1016/j.jhydrol.2016.10.018.
TSMS (Turkish State Meteorological Service). 2018. “Turkish state meteorological service annual report.” Accessed March 10, 2018. https://www.mgm.gov.tr/veridegerlendirme/yagis-degerlendirme.aspx.
Van den Dool, H. 2003. “Performance and analysis of the constructed analogue method applied to U.S. soil moisture over 1981-2001.” J. Geophys. Res. 108 (D16): 8617. https://doi.org/10.1029/2002JD003114.
Üstün, A., et al. 2015. “Land subsidence in Konya Closed Basin and its spatio-temporal detection by GPS and DInSAR.” Environ. Earth Sci. 73 (10): 6691–6703. https://doi.org/10.1007/s12665-014-3890-5.
Vandenberghe, S., N. E. C. Verhoest, C. Onof, and B. De Baets. 2011. “A comparative copula-based bivariate frequency analysis of observed and simulated storm events: A case study on Bartlett-Lewis modeled rainfall.” Water Resour. Res. 47 (7): https://doi.org/10.1029/2009WR008388.
Vazifehkhah, S., and E. Kahya. 2018. “Hydrological drought associations with extreme phases of the North Atlantic and Arctic Oscillations over Turkey and northern Iran.” Int. J. Climatol. 38 (12): 4459–4475. https://doi.org/10.1002/joc.5680.
Villarini, G., J. A. Smith, F. Serinaldi, J. Bales, P. D. Bates, and W. F. Krajewski. 2009. “Flood frequency analysis for nonstationary annual peak records in an urban drainage basin.” Adv. Water Resour. 32 (8): 1255–1266. https://doi.org/10.1016/j.advwatres.2009.05.003.
Wada, Y., L. P. H. Van Beek, C. M. Van Kempen, J. W. T. M. Reckman, S. Vasak, and M. F. P. Bierkens. 2010. “Global depletion of groundwater resources.” Geophys. Res. Lett. 37 (20): https://doi.org/10.1029/2010GL044571.
Wang, C., N. B. Chang, and G. T., Yeh. 2009. “Copula-based flood frequency (COFF) analysis at the confluences of river systems.” Hydrol. Process. 23 (10): 1471–1486. https://doi.org/10.1002/hyp.7273.
Wilhite, D. A. 2000. Drought as a natural hazard: Concepts and definitions. London: Routledge.
Wong, G., M. F. Lambert, M. Leonard, and A V. Metcalfe. 2010. “Drought analysis using trivariate copulas conditional on climatic states.” J. Hydrol. Eng. 15 (2): 129–141. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000169.
Xiong, L., T. Du, C. Y. Xu, S. Guo, C. Jiang, and C. J. Gippel. 2015. “Non-stationary annual maximum flood frequency analysis using the norming constants method to consider non-stationarity in the annual daily flow series.” Water Resour. Manage. 29 (10): 3615–3633. https://doi.org/10.1007/s11269-015-1019-6.
Yevjevich, V., M. M. Siddiqui, and R. N. Downer. 1967. “Application of runs to hydrologic droughts.” Proc. Int. Hydrol. Sym. 1 (63): 496–505.
Yue, S., T. B. M. J. Ouardaa, B. Bobée, P. Legendre, and P. Bruneau. 1999. “The Gumbel mixed model for flood frequency analysis.” J. Hydrol. 226 (1): 88–100. https://doi.org/10.1016/S0022-1694(99)00168-7.
Zhang, L., and V. P. Singh. 2006. “Bivariate flood frequency analysis using the copula method.” J. Hydrol. Eng. 11 (2): 150–164. https://doi.org/10.1061/(ASCE)1084-0699(2006)11:2(150).
Zhang, L., and V. P. Singh. 2014. “Trivariate flood frequency analysis using discharge time series with possible different lengths: Cuyahoga River case study.” J. Hydrol. Eng. 19 (10): 5014012. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001003.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Apr 5, 2018
Accepted: Nov 16, 2018
Published online: Mar 6, 2019
Published in print: May 1, 2019
Discussion open until: Aug 6, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.