Assessing the Performance of CMIP5 GCMs in Copula-Based Bivariate Frequncy Analysis of Drought Characteristics in the Southern Part of Karun Catchment

Document Type : Research


Assistant Professor, Climate Research Institute, Atmospheric Science and Meteorological Research Center, Mashhad, Iran


Drought is an extreme event and is a creeping phenomenon as compared with other natural disasters, which has great effects on the environment and human life. During 1997 to 2001, a severe 40-year return period drought affected half of Iran's provinces, with a loss in the agricultural sector estimated at more than US$ 10 billion (National Center for Agricultural Drought Management, and a Gross Domestic Product (GDP) reduction of about 4.4% was reported (Salami et al., 2009). A more severe drought period (2007–2009) devastated the country on a larger scale than the previous drought period. A 20% average reduction of precipitation has been reported for 2008 compared with a 30-year average (Modarres, et al. 2016). It was found that the longest and most severe drought episodes have occurred in the last 15–20 years (1998-2017) (Ghamghami and Irannejad, 2019). A drought is characterized by severity, duration and frequency. These characteristics are not independent of each other, and droughts cause significant economic, social and ecosystem impacts worldwide (IPCC, 2013). Probabilistic analysis of drought events plays an important role for an appropriate planning and management of water resources systems and agriculture, especially in arid or semi-arid regions. In particular, estimation of drought return periods can provide useful information for different water sectors under drought conditions. In this study, the capability of two CMIP5 GCMs in estimating the joint return period of severity and duration of drought using copula have been investigated in the Southern part of the Karun Basin.
In this study, three type data have been used. These include monthly precipitation and temperature observed at synoptic stations and gridded data in 1975-2005 were obtained from IRIMO (the Iranian Meteorological Organization) and CRU (http: as well as the outputs of two GCM (HadGEM2-ES and IPSL-CM5A-MR) from CMIP5 (http;// in the period of 1975-2005 for historical. Following the Intergovernmental Panel on Climate Change (IPCC, 2013), the first ensemble member (r1i1p1) from two GCMs were selected. RCPs are estimation of radiative forcing (RF), where RCP2.6 and RCP4.5 represents 2.6 and 4.5 W.m-2 and RCP8.5 represents 8.5 W.m-2 at the end of the 21th century (Goswami, 2018). Assuming a drought period as a consecutive number of intervals where SPEI (Vicente-Serrano et al. 2010) values are less than −1, two characteristics are determined, namely: extreme drought length and severity. Hydrological phenomena are often multidimensional and hence require the joint modeling of several random variables. Copulas model have become a popular multivariate modeling tool in many fields where multivariate dependence is of interest and the usual multivariate normality is in question. Among the copula-based drought frequency analysis, Elliptical and Archimedean copulas have been the most popular used equations. In this paper, we focus on copulas based multivariate drought frequency analysis considering drought duration and severity. Return period is defined as ‘‘the average time elapsing between two successive realizations of a prescribed event’’ (Salvadori et al.,2011). In the univariate setting, the return period is generally defined as (Bonaccorso, et al., 2003):
In this equation T is return period with a single variable, X (duration (D) or severity (S) of drought), greater or equal to a certain value, FX (.) are percentiles of CDF with X and E(T) is expected inter-arrival time of sequential droughts within the study period.
The bivariate analysis of drought return period is calculated as (Shiau, 2006):
Where TD∩S denotes the joint return period for D ≥ d and S ≥ s; T_  denotes the joint return period for D ≥ d or S ≥ s.
Results of a preliminary analysis based on Kendall’s correlation and upper tail dependence coefficient, computed on different datasets show significant dependence properties between the considered pair. Archimedean copulas (Clayton, Frank, and Gumbel) are fitted to the joint S-D datasets (observation, CRU, HadGEM-es and IPSL-CM4-MR) by Maximum Pseudo Likelihood Estimator (MPLE). The selected copula functions and marginal distributions were used to calculate the joint return periods of severity and duration in the conditions of "and" and "or". The results showed that HadGem has a good skill in simulating the joint probability characterization of drought. Results of the bivariate analysis using copula showed that the study area will experience droughts with greater severity and duration in future as compared with the historical period. Projected changes in characteristics of drought throughout the 21st century can help inform climate change assessments across drought‐sensitive sectors. However, the ability of global climate models (GCMs) to reproduce statistical attributes of observed drought should be investigated. We evaluated the fidelity of GCMs to simulate probabilistic characteristics of drought in Southwest of Karoun where drought plays a key climate impact.


Main Subjects

احمدی، ف.، رادمنش، ف.، پرهام، غ. و میرعباسی نجف‌آبادی، ر.، 1396، کاربرد توابع مفصل ارشمیدسی در تحلیل فراوانی سیلاب (مطالعه موردی: حوضه آبریز دز)، م. تحقیقات آب و خاک ایران (علوم کشاورزی ایران)، (3) 48، 477-489.
خانی تملیه، ذ.، رضایی، ح. و میرعباسی، ر.، 1399، کاربرد توابع مفصل تودرتو برای تحلیل فراوانی چهار متغیره خشکسالی­های هواشناسی (مطالعه موردی: غرب ایران)، نشریه حفاظت منابع آب و خاک، (1) 10، 93-112.
عزیزآبادی، م.، بختیاری، ب.، قادری، ک. و رضاپور، م.، 1395، بررسی تأثیر تغییر اقلیم بر منحنی‌های سختی-مدت-فراوانی خشکسالی حوزه آبریز قره‌سو با استفاده از توابع مفصل، مجله تحقیقات منابع آب ایران، (4) 47، 743-754.
کوهی، م.، 1400، پیش­نگری ویژگی­های خشکسالی­آتی تحت سناریوهای RCP در چند نمونه اقلیمی ایران، نشریه پژوهش­های اقلیم­شناسی، شماره 47، پاییز 1400.
کوهی، م.، 1396، تحلیل و بررسی خشکسالی تحت شرایط تغییر اقلیم با استفاده از توابع مفصل، پایان نامه دکتری، گروه مهندسی آب، دانشگاه فردوسی مشهد.
Amirkhani, S. and Chizari, M. 2010, Factors influencing drought management in Varamin Township. Proceedings of the Third Congress of Agricultural Extension and Natural Resources, pp. 107–118.
Bonaccorso, B., Cancelliere, A. and Rossi, G., 2003, An analytical formulation of return period of drought severity. Stochastic Environmental Research Risk, 17 (3), 157–174.
Brekke, L., Wood, A. and Pruitt, T., 2014, Downscaled CMIP3 and CMIP5 Hydrology Projections: Release of Hydrology Projections, Comparison with Preceding Information, and Summary of User Needs; US Department of the Interior Bureau of Reclamation: Denver, CO, USA.
Chakravarti, I.M., Laha, R.G. and Roy, J., 1967, Handbook of methods of applied statistics. Wiley Series in Probability and Mathematical Statistics (USA) eng.
Chen, L., Singh, V.P., Guo, S., Hao, Z. and Li, T. 2012, Flood coincidence risk analysis using multivariate Copula functions. Journal of Hydrologic Engineering 17(6), 742-755.
Chen, L., Singh, V. P., Guo, S., Mishra, A. K. and Guo, J., 2013, Drought analysis using copulas. Jouranl of  Hydrological Engineering, 18 (7), 797–808.
De Michele, C., Salvadori, G., Canossi, M., Petaccia, A. and Rosso, R., 2005, Bivariate statistical approach to check adequacy of dam spillway. Journal of Hydrologic Engineering, 10(1), 50–57.
Salvadori, G., De Michele, C. and Durante, F., 2011, On the return period and design in a multivariate framework. HYPERLINK "" Hydrology and Earth System Sciences, (11)15, 3293-3305.
Dupuis, D. J., 2007, Using Copulas in Hydrology: Benefits, Cautions, and Issues. Jouranl of Hydrologic Engineering, 12(4), 381-393.
Embrechts, P., Lindskog, F. and McNeil, A., 2003, Modelling Dependence with Copulas and Applications to Risk Management. In Rachev S. (eds),in Handbook of Heavy Tailed Distributions in Finance, 1nd ed. North Holland.
Frees, E. W. and Valdez, E. A., 1998, Understanding relationships using copulas. North American Actuarial Journal, 2(1), 1–25.
Frick, D. M., Bode, D. and Salas, J. D., 1990, Effect of drought on urban water supplies. I: Drought analysis. Journal of Hydraulic Engineering, 116(6), 733–753.
Ge, Y., Cai, X., Zhu, T. and Ringler, C., 2016, Drought frequency change:An assessment in northern India palins. Agricultural Water Management, 176, 111-121.
Genest, C. and Favre, A. C., 2007, Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering,12(4).
Genest, C., Rémillard, B. and Beaudoin, D., 2009, Goodness-of-fit tests for copulas: A review and a power study, Insurance: Mathematics and Economics, 44, 199-213.
Goel, N. K., Seth, S. M. and Chandra, S., 1998, Multivariate modeling of flood flows. Journal of Hydraulic Engineering, 124(2), 146–155.
Ghamghami, M. and Irannejad, P., 2019, An analysis of droughts in Iran during 1988–2017. SN Applied Sciences, 1(10), 1-21.
Intergovernmental Panel on Climate Change. 2007. The Fourth Assessment Report. Parry, M. L., Canziani, O. F., Palutikof, J. P., van der Linden, P. J., Hanson, C. E., htm" t "_blank" Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. htm" t "_blank" Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.
Intergovernmental Panel on Climate Change, 2013, Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge Univ. Press, Cambridge.
Joe, H., 1997, Multivariate Models and Dependence Concepts, Chapman & Hall, London.
Kao, S. C. and Govindaraju, R. S., 2010, A copula-historicald joint deficit index for droughts. Journal of Hydrology, 380, 121-134.
Leavitt, P. and Chen, G., 2005, Prairie Drought Limnology Project, University of Regina. Sustainable Agriculture in Western Canada: Planning for Droughts Using the Past. faculty/leavitt/drought/drought1.htm. Accessed July 2005.
Liu, M., Xu, X., Sun, A.Y., Wang, K., Liu, W. and Zhang, X., 2014, Is southwestern China experiencing more frequent precipitation extremes? Environmental Research Letters, 9, 1-12.
Madadgar, S. and Moradkhani, H., 2013, Drought analysis under climate change using copula. Journal of Hydrologic Engenieering, 18 (7), 746–759.
Modarres, R., Sarhadi, A. and Burn, D. H., 2016, Changes of extreme drought and flood events in Iran. Global and Planetary Change, 144, 67-81.
Masoud, M. B., Khaliq, M. N. and Wheater, H. S., 2015, Analysis of meteorological droughts for the Saskatchewan River Basin using univariate and bivariate approach. Journal of Hydrology, 522, 452-466.
Mesbahzadeh, T., Mirakbari, M., Mohseni Saravi, M., Soleimani Sardoo, F. and Miglietta, M. M., 2020, Meteorological drought analysis using copula theory and drought indicators under climate change scenarios (RCP). Meteorological Applications, 27(1), p.e1856.
Mirabbasi, R., Fakheri-Fard, A. and Dinpashoh, Y., 2012, Bivariate drought frequency analysis using the Copula method.Theoretical and Applied Climatology 108, 191–206.
MotevaliBashi naeini, E., Akhond Ali, A. M. Radmanesh, F., Sharifi, M. and Abedi Koupaei, J., 2019, Zoning Map of Drought Characteristics under Climate Change Scenariousing Copula Method in the Zayandeh Roud River Catchment, Irrigation Sciences and Engineering (JISE), 42 (1), 145-160. [persina]
Nelsen, R. B., 2007, An introduction to copulas. Springer. 3th edition, New York. 269 pp.
Pontes Filho, J. D., Souza Filho, F. D. A., Martins, E. S. P. R. and Studart, T. M. D. C., 2020, Copula-Historicald Multivariate Frequency Analysis of the 2012–2018 Drought in Northeast Brazil. Water, 12(3), 834.
Rahimi, L., Dehghani, A. A., Abdolhosseini, M. and Ghorbani, Kh., 2014, Flood Frequency Analysis Using Archimedean Copula Functions Historicald on Annual Maximum Series (Case Study:Arazkuseh Hydrometric Station in Golestan Province), Iranian Journal of Irrigation and Drainage No. 2, Vol. 8, May-June 2014, p. 353-365.
Reddy, M. J. and Ganguli, P., 2012, Application of copulas for derivation of drought severity –duration–frequency curves. Hydrological Process. 26, 1672–1685.
Salami, H., Shahnooshi, N. and Thomson, K. J., 2009, The economic impacts of drought on the economy of Iran: An integration of linear programming and macroeconometric modelling approaches. Ecological Economics, 68(4), 1032-1039.
Rossi, G., Benedini, M., Tsakiris, G. and Giakoumakis, S., 1992, On regional drought estimation and analysis. Water Resources Management, 6(4), 249–277.
Salvadori, G. and De Michele, C., 2007, On the use of copulas in hydrology: Theory and practice, Jouranl of Hydrologic Engneering, 12(4), 369–380.
Scholz, F. W. and Stephens, M. A., 1987, K-sample Anderson-Darling tests. Journal of the American Statistical Association, 82(399), 918– 924.
Schweizer, B. and Wolff, E. F., 1981, On Nonparametric Measures of Dependence of Random Variables. The Annals of Statistics, 9(4), 879-885.
Shahabfar, A. and Eitzinger, J., 2008, Spatial and temporal analysis of drought in Iran by using drought indices, European Meteorological Society (EMS), Proceedings of the 7th European Conference on Applied Climatology (ECAC) (EMS2008), Amsterdam, The Netherlands, SEP 29th–OCT 3rd, 2008.
Shi, H., Li, T. and Wei, J., 2017, Evaluation of the gridded CRU TS precipitation dataset with the point raingauge records over the Three-River Headwaters Region. Journal of Hydrology, 548, 322–332.
Shiau, J., 2003, Return period of bivariate distributed extreme hydrological events. Stochastic Environmental Research Risk Assessment, 17 (1–2), 42–57.
Shiau, J. T., 2006, Fitting drought duration and severity with two-dimensional copulas. Water Resources Management 20, 795–815.
Shiau, J. T., Feng, S. and Nadarajah, S., 2007, Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrological Processes, 21(16), 2157–2163.
Shiau, J.T. and Modarres, R., 2009, Copula-based drought severity-duration-frequency analysis in Iran. Meteorological Applications, 16, 481–489.
Sibuya, M., 1960, Bivariate extreme statistics. Annals of the Institute of Statistical Mathematics (Tokyo) 11, 195–210.
Sklar, A., 1959, Distribution functions of n Dimensions and Margins, Publications of the Institute of Statistics of the University of Paris 8, 229-231. (in French).
Song, S. and Singh, V. P., 2010, Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stochastic Environmental Research and Risk Assessment, 24, 783–805.
Song, S. and Singh, V. P., 2009, Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stochastic Environmental Research and Risk Assessment, 24 (3), 425–444.
Taylor, K. E., Stouffer, R. J. and Meehl, G. A., 2012, An overview of CMIP5 and the experiment design. Bulletin of the American Meteorological Society. 93, 485–498.
Touma, D., Ashfaq, M., Nayak, M. A., Kao, S. and Diffenbaugh, N. S., 2015, A multi-model and multi-index evaluation of drought characteristics in the 21st century. Journal of Hydrology, 526, 196–207.
Tsakiris, G. and Vangelis, H. J. E. W., 2005, Establishing a drought index incorporating evapotranspiration. European water, 9(10), 3-11.
United States Department of Agriculture, Foreign Agricultural Serrvice, 2008, IRAN: Wheat Production Declines Due to Drought, Commodity Intelligence Report, May9, 2008.
Vandenberghe, S.,Verhoest, N.E.C. and De Baets, B., 2010, Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis, historicald on 105 year 10 min rainfall. Water Resources Research,46, 1-17.
Vicente-Serrano, S. M., Beguería, S. and López-Moreno, J. I., 2010, A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. Journal of climate, 23(7), 1696-1718.
Won, J., Choi, J., Lee, O. and Kim, S., 2020, Copula-historicald Joint Drought Index using SPI and EDDI and its application to climate change. Science of the Total Environment, 744, p.140701.
Wong, G., Lambert, M. F., Leonard, M. and Metcalfe, A. V., 2010, Drought Analysis Using Trivariate Copulas Conditional on Climatic States. Journal of Hydrologic Engineering, 15(2), 129-141.
World Meteorological Organization, 2011, Weather extremes in a changing climate: hindsight on foresinght. WCDMP, 63, 11075-6.
Xu, K., Yang, D., Yang, H., Li, Z., Qin, Y. and Shen, Y., 2015, Spatio-temporal variation of drought in China during 1961–2012: a climatic perspective. Journal of Hydrololgy. 526, 253–264.
Yevjevich, V., 1967, An objective approach to definitions and investigations of continental hydrologic droughts. Colorado State University.
Yue, S., Ouarda, T. B. M. J., Bobée, B., Legendre, P. and Bruneau, P., 1999, The Gumbel mixed model for flood frequency analysis. Journal of Hydrology, 226(1-2), 88–100.
Yue, S., 2001., A Bivariate Extreme Value Distribution Applied to flood Frequency Analysis. Nordic Hydrology, 32(1), 49-64.
Zhang, L. and Singh, V. P. 2007, Gumbel-Hougaard copula for trivariate rainfall frequency analysis. Journal of  Hydrologic Engineering. 12, 409–419.