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Copula-based multivariate analysis of hydro-meteorological drought

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Abstract

Droughts have far-reaching detrimental impacts on the environment, society, and economy, ranging from regional to national levels. As the drought characteristics are interrelated, multivariate analysis of those is necessary to understand the actual drought situation in a region. However, such studies are limited. Hence, this study aimed to develop a framework to investigate the meteorological and hydrological droughts using a multivariate analysis of drought characteristics in the Pennar River basin (a semi-arid region) of India, dominated by agricultural activity. Long-term observations (1980–2015) of precipitation, temperature, and streamflow were used to calculate the Standardized Precipitation Evapotranspiration Index (SPEI) and Streamflow Drought Index (SDI) at a 3-month timescale. Based on these indices, drought duration, severity, and peak were abstracted using the Run Theory. The best-fit marginal distribution was determined for every drought characteristic to establish the bivariate joint probability distribution (the copula function). Based on the best-fit copula function, the joint probabilities and the joint return periods were estimated. Results revealed that, for meteorological drought, Frank Copula and Survival Clayton copula were the best-fit copula function for the joint risk of drought duration and severity and the combination of drought duration and peak as well as drought severity and peak, respectively. The joint return period of a drought event with characteristics above the 25th percentile of the same varies between 1 and 2 years, whereas it spans between 1 and 45 years for the 50th percentile. This analysis will provide vital information for water management and planning in a region to mitigate droughts.

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Data is available upon request to the corresponding author.

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References

  • Achite M, Bazrafshan O, Wałęga A, Azhdari Z, Krakauer N, Caloiero T (2022) Meteorological and hydrological drought risk assessment using multi-dimensional copulas in the wadi ouahrane basin in Algeria. Water 14(4):653

    Google Scholar 

  • Allan RP, Hawkins E, Bellouin N, Collins B (2021) IPCC, 2021: summary for Policymakers

  • Amrit K, Pandey RP, Mishra SK, Kumre SK (2018) Long-Term meteorological drought characteristics in Southern India. In: World environmental and water resources congress 2018: Groundwater, sustainability, and hydro-climate/climate change. American Society of Civil Engineers, Reston, VA, pp 207–215

  • Ayantobo OO, Li Y, Song S (2019) Multivariate drought frequency analysis using four-variate symmetric and asymmetric archimedean copula functions. Water Resour Manag 33:103–127

    Google Scholar 

  • Ayantobo OO, Li Y, Song S, Yao N (2017) Spatial comparability of drought characteristics and related return periods in mainland China over 1961–2013. J Hydrol 550:549–567

    Google Scholar 

  • Azam M, Maeng SJ, Kim HS, Murtazaev A (2018) Copula-based stochastic simulation for regional drought risk assessment in South Korea. Water 10(4):359

    Google Scholar 

  • Brunner MI, Seibert J, Favre A-C (2016) Bivariate return periods and their importance for flood peak and volume estimation. Wires Water 3:819–833

    Google Scholar 

  • Chandrasekara SS, Kwon HH, Vithanage M, Obeysekera J, Kim TW (2021) Drought in South Asia: a review of drought assessment and prediction in South Asian countries. Atmosphere 12(3):369

    Google Scholar 

  • Chen L, Singh VP, Guo S, Mishra AK, Guo J (2013) Drought analysis using copulas. J Hydrol Eng 18(7):797–808

    Google Scholar 

  • Daneshkhah A, Remesan R, Chatrabgoun O, Holman IP (2016) Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model. J Hydrol 540:469–487

    Google Scholar 

  • Das J, Gayen A, Saha P, Bhattacharya SK (2020) Meteorological drought analysis using standardized precipitation index over Luni River Basin in Rajasthan, India. SN Applied Sciences 2:1–17

    Google Scholar 

  • Dixit S, Atla BM, Jayakumar KV (2022) Evolution and drought hazard mapping of future meteorological and hydrological droughts using CMIP6 model. Stoch Env Res Risk Assess 36:3857–3874

    Google Scholar 

  • Dixit S, Jayakumar KV (2021) A study on copula-based bivariate and trivariate drought assessment in Godavari River basin and the teleconnection of drought with large-scale climate indices. Theor Appl Climatal 146:1335–1353

    Google Scholar 

  • Dixit S, Jayakumar KV (2022) A non-stationary and probabilistic approach for drought characterization using trivariate and pairwise copula construction (PCC) Model. Water Resour Manag 36:1217–1236

    Google Scholar 

  • Eslamian S et al (2017) A review of drought indices. Int J Constr Res Civil Eng 3:48–66

    Google Scholar 

  • Evkaya O, Yozgatl Ci, Sevtap S-KA (2019) Drought analysis using copula approach: a case study of Turkey. Communications in Statistics: Case Studies, Data Analysis and Applications, pp 2373–7484

  • Fang Y, Madsen L, Liu L (2014) Comparison of two methods to check copula fitting. IAENG Int J Appl Math 44(1)

  • Garg V et al (2017) Assessment of land use land cover change impact on hydrological regime of a basin. Environ Earth Sci 76(18):1–17

    Google Scholar 

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

    Google Scholar 

  • Graler B et al (2013) Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. Hydrol Earth Syst Sci 17(4):1281–1296

    Google Scholar 

  • Guo Y et al (2019) Assessing socioeconomic drought based on an improved Multivariate Standardized Reliability and Resilience Index. J Hydrol 568:904–918

    Google Scholar 

  • Haied N, Foufou A, Chaab S, Azlaoui M, Khadri S, Benzahia K, Benzahia I (2017) Drought assessment and monitoring using meteorological indices in a semi-arid region. Energy Procedia 119:518–529

    Google Scholar 

  • Hao Z, AghaKouchak A (2013) Multivariate standardized drought index: a parametric multi-index model. Adv Water Resour 57:12–18

    Google Scholar 

  • Hasan HH, Razali SFM, Muhammad NS, Ahmad A (2019) Research trends of hydrological drought: a systematic review. Water 11(11):2252

    Google Scholar 

  • Hofert M et al (2014) Package ‘copula’. [Online] Available at: http://ie.archive.ubuntu.com/disk1/disk1/cran.r-project.org/web/packages/copula/copula.pdf

  • Hong X, Guo S, Zhou Y, Xiong L (2015) Uncertainties in assessing hydrological drought using streamflow drought index for the upper Yangtze River basin. Stoch Env Res Risk Assess 29(4):1235–1247

    Google Scholar 

  • Hou W, Yan P, Feng G, Zuo D (2021) A 3D copula method for the impact and risk assessment of drought disaster and an example application. Front Phys 9:656253

    Google Scholar 

  • Huang S et al (2014) Copulas-based probabilistic characterization of the combination of dry and wet conditions in the Guanzhong Plain, China. J Hydrol 519:3204–3213

    Google Scholar 

  • Kwak J, Kim S, Kim D, Kim H (2016) Hydrological drought analysis based on copula theory. River Basin Manag 2016:83–95

    Google Scholar 

  • Kogan F (1995) Application of vegetation index and brightness temperature for drought detection. Adv Space Res 15(11):91–100

    Google Scholar 

  • Kulkarni SS et al (2020) Developing a remote sensing-based combined drought indicator approach for agricultural drought monitoring over Marathwada, India. Remote Sensing 12(13):2091

    Google Scholar 

  • Kumar A, Pandey RP, Mishra SK, Kumre SK (2018) Long-Term meteorological drought characteristics in Southern India. In World Environmental and Water Resources Congress 2018: Groundwater, Sustainability, and Hydro-Climate/Climate Change, p 207–215

  • Kumar KN et al (2013) On the observed variability of monsoon droughts over India. Weather Clim Extremes 1:42–50

    Google Scholar 

  • Lee T, Modarres R, Ouarda TB (2013) Data-based analysis of bivariate copula tail dependence for drought duration and severity. Hydrol Process 27(10):1454–1463

    Google Scholar 

  • Madadgar S, Moradkhani H (2016) Copula function and drought. Taylor & Francis, New York

    Google Scholar 

  • Maity R (2018) Statistical methods in hydrology and hydroclimatology. Springer, Singapore

    Google Scholar 

  • McKee TB, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology 17(22):179–183

  • Menna BY, Mesfin HS, Gebrekidan AG, Siyum ZG, Tegene MT (2022) Meteorological drought analysis using copula theory for the case of upper Tekeze river basin, Northern Ethiopia. Theor Appl Climatol 149(1–2):621–638

    Google Scholar 

  • Mesbahzadeh T, Mirakbari M, Mohseni Saravi M, Soleimani Sardoo F, Miglietta MM (2020) Meteorological drought analysis using copula theory and drought indicators under climate change scenarios (RCP). Meteorol Appl 27(1):e1856

  • Mirabbasi R, Fard AF, Dinpashoh Y (2012) Bivariate drought frequency analysis using the copula method. Theoret Appl Climatol 108(1):191–206

    Google Scholar 

  • Mirakbari M, Ganji A, Fallah SR (2010) Regional bivariate frequency analysis of meteorological droughts. J Hydrol Eng 15(12):985–1000

    Google Scholar 

  • Mishra AK, Singh VP, Desai VR (2009) Drought characterization: a probabilistic approach. Stoch Environ Res Risk Assess 23(1):41–55

    Google Scholar 

  • Nalbantis I, Tsakiris G (2009) Assessment of hydrological drought revisited. Water Resour Manag 23(5):881–897

    Google Scholar 

  • Nelsen RB (2007) An introduction to copulas. Springer Science & Business Media

  • Palmer W (1965) Meteorological drought. US Department of Commerce, Weather Bureau, Washington, DC

    Google Scholar 

  • Pandey RP, Dhama YK (2000) Drought characterization in arid and semi arid climatic regions of India. National Institute of Hydrology

  • Panu U, Sharma T (2009) Analysis of annual hydrological droughts: the case of Northwest Ontario, Canada. Hydrol Sci J 54(1):29–42

    Google Scholar 

  • Pathak AA, Dodamani BM (2016) Comparison of two hydrological drought indices. Perspect Sci 8:626–628

    Google Scholar 

  • Pontes Filho JD, Souza Filho FDA, Martins ESPR, Studart TMDC (2020) Copula-based multivariate frequency analysis of the 2012–2018 drought in Northeast Brazil. Water 12(3):834

    Google Scholar 

  • Poonia V et al (2021a) Drought occurrence in Different River Basins of India and blockchain technology based framework for disaster management. J Clean Prod 312:127737

    Google Scholar 

  • Poonia V, Jha S, Goyal MK (2021b) Copula based analysis of meteorological, hydrological and agricultural drought characteristics across Indian river basins. Int J Climatol 41(9):4637–4652

    Google Scholar 

  • Pörtner H-O et al (2022) Climate change 2022: Impacts, adaptation and vulnerability. IPCC, Geneva

    Google Scholar 

  • Qin F, Ao T, Chen T (2021) Bivariate frequency of meteorological drought in the upper Minjiang River based on copula function. Water 13(15):2056

    Google Scholar 

  • Rajsekhar D, Singh VP, Mishra AK (2015) Multivariate Drought Index: an information theory based approach for integrated drought assessment. J Hydrol 526:164–182

    Google Scholar 

  • Rose MAJ, Chithra NR (2020) Evaluation of temporal drought variation and projection in a tropical river basin of Kerala. J Water Clim Chang 11(S1):115–132

    Google Scholar 

  • Sajeev A, Deb Barma S, Mahesha A, Shiau JT (2021) Bivariate drought characterization of two contrasting climatic regions in India using copula. J Irrig Drain Eng 147(3):05020005

  • Shafer BA (1982) Developement of a surface water supply index (SWSI) to assess the severity of drought conditions in snowpack runoff areas. In Proceedings of the 50th Annual Western Snow Conference, Colorado State University, Fort Collins, 1982

  • Shiau J (2006) Fitting drought duration and severity with two-dimensional Copulas. Water Resour Manag 20:795–815

    Google Scholar 

  • Shiau J-T, Modarres Rb (2009) Copula-based drought severity-duration-frequency analysis in Iran. Meteorol Appl 16(4):481–489

    Google Scholar 

  • Shiau J-T, Shen HWa (2001) Recurrence analysis of hydrologic droughts of differing severity. J Water Resour Plan Manag 127(1):30–40

    Google Scholar 

  • Shukla S, Wood AW (2008) Use of a standardized runoff index for characterizing hydrologic drought. Geophys Res Lett 35(2)

  • Sinha J, Sharma A, Khan M, Goyal MK (2018) Assessment of the impacts of climatic variability and anthropogenic stress on hydrologic resilience to warming shifts in Peninsular India. Sci Rep 8:13833

    Google Scholar 

  • Song S, Singh VP (2010a) Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stoch Env Res Risk Assess 24(5):783–805

    Google Scholar 

  • Song S, Singh VP (2010b) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Env Res Risk Assess 24(3):425–444

    Google Scholar 

  • Spinoni J et al (2019) A new global database of meteorological drought events from 1951 to 2016. J Hydrol Reg Stud 22:100593

    Google Scholar 

  • Swain S, Mishra SK, Pandey A (2020) Assessment of meteorological droughts over Hoshangabad district, India. In IOP conference series: earth and environmental science, vol 491, No 1. IOP Publishing, p 012012

  • Swain S, Mishra SK, Pandey A (2021) A detailed assessment of meteorological drought characteristics using simplified rainfall index over Narmada River Basin, India. Environ Earth Sci 80:1–15

    Google Scholar 

  • Tigkas D, Vangelis H, Tsakiris G (2015) DrinC: a software for drought analysis based on drought indices. Earth Sci Inf 8(3):697–709

    Google Scholar 

  • Tootoonchi F et al (2021) Copulas for hydroclimatic analysis: a practice-oriented overview. Wiley Interdiscip Rev Water 9(2):e1579

    Google Scholar 

  • Tsakiris G et al (2016) Analysing drought severity and areal extent by 2D Archimedean copulas. Water Resour Manag 30(15):5723–5735

    Google Scholar 

  • Udayar S et al (2019) Analysis of drought from humid, semi-arid and arid regions of India using DrinC model with different drought indices. Water Resour Manag 33:1521–1540

    Google Scholar 

  • Vandenberghe S et al (2012) Joint return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. Hydrol Earth Syst Sci 9(5):6781–6828

    Google Scholar 

  • Vazifehkhah S, Tosunoglu F, Kahya E (2019) Bivariate risk analysis of droughts using a nonparametric multivariate standardized drought index and copulas. J Hydrol Eng 24(5):05019006

  • Vicente-Serrano S et al (2012) Accurate computation of a streamflow drought index. J Hydrol Eng 17(2):318–332

    Google Scholar 

  • Villarini G et al (2009) Flood frequency analysis for nonstationary annual peak records in an urban drainage basin. Adv Water Resour 32(8):1255–1266

    Google Scholar 

  • Wang L, Zhang X, Wang S, Salahou MK, Fang Y (2020) Analysis and application of drought characteristics based on theory of runs and copulas in Yunnan, Southwest China. Int J Environ Res Public Health 17(13):4654

    Google Scholar 

  • Wu R, Zhang J, Bao Y, Guo E (2019) Run theory and copula-based drought risk analysis for Songnen grassland in Northeastern China. Sustainability 11(21):6032

    Google Scholar 

  • Xu K et al (2015) Spatio-temporal variation of drought in China during 1961–2012: a climatic perspective. J Hydrol 526:253–264

    Google Scholar 

  • Yan J (2007) Enjoy the joy of copulas: with a package copula. J Stat Softw 21(4):1–21

    Google Scholar 

  • Yevjevich V (1967) An objective approach to definitions and investigations of continental hydrologic droughts. Hydrol Pap Colo State Univ 23:382–391

    Google Scholar 

  • Zhang L, Wang Y, Chen Y, Bai Y, Zhang Q (2020) Drought risk assessment in Central Asia using a probabilistic copula function approach. Water 12(2):421

    Google Scholar 

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  1. Department of Civil Engineering, National Institute of Technology Calicut, Calicut, Kerala, India

    Balaram Shaw &  Chithra N R

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  1. Balaram Shaw
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Both authors contributed to the study conception and design. The analysis was done by Balaram Shaw under the supervision of Dr. Chithra NR. The first draft of the manuscript was written by Balaram Shaw, and it was revised by Dr. Chithra NR. Both authors have read and approved the final manuscript.

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Correspondence to Balaram Shaw.

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Shaw, B., Chithra N R Copula-based multivariate analysis of hydro-meteorological drought. Theor Appl Climatol 153, 475–493 (2023). https://doi.org/10.1007/s00704-023-04478-1

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