SavedAdd your journal

Journals / Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi / 2026 / Cilt: 17 Sayı: 2

Copula-Based Multivariate Drought Indices: Integrating Temperature for Drought Prediction

Kopula Tabanlı Çok Değişkenli Kuraklık İndeksleri: Kuraklık Tahmini için Sıcaklığın Entegrasyonu

Tahsin Baykal(KIRIKKALE ÜNİVERSİTESİ)0000-0001-6218-0826
Pages
—
Publication Date
2026-07-18
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

MDI was found to be successful in capturing dry periods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Drought is a widespread natural hazard whose impacts can persist over long time periods.
📊
Key Findings & Data:Reliable drought prediction plays a key role in the development and assessment of effective strategies for mitigating drought-related risks.
💡
Conclusion & Impact:MDI was found to be successful in capturing dry periods.
🔬Design:Modeling & Simulation
📍Scope:2021 Verileri
⚙️Variables:Kopula tabanlı çok değişkenli kuraklık indeksi · Standartlaştırılmış Yağış İndeksi (SPI) · Hava sıcaklığı entegrasyonu

Abstract

Drought is a widespread natural hazard whose impacts can persist over long time periods. Reliable drought prediction plays a key role in the development and assessment of effective strategies for mitigating drought-related risks. There are different methods for meteorological drought assessment in literature. These methods generally require precipitation and potential evapotranspiration (PET) data. A multivariate drought index (MDI) is introduced in this study by jointly modeling the standardized precipitation index (SPI) and mean air temperature using copula functions. For this purpose, precipitation and average temperature values of the Manavgat, Korkuteli, Finike, Antalya, and Alanya meteorological stations between 1969 and 2021 were used. First, the SPI values of these stations were calculated in four different periods (3-, 6-, 9- and 12-months). Correlations between SPI values in each period and average temperature were examined, and their marginal distributions were determined. For each time scale, SPI and mean air temperature were jointly analyzed within alternative copula-based dependence structures. Model suitability was evaluated using a combination of information-based and performance-based criteria, namely AIC, BIC, RMSE, and NSE. According to the selected copula functions, the MDI of each station at 3-, 6-, 9- and 12-month periods were calculated. Finally, Standardized Precipitation Evapotranspiration Index (SPEI) values were calculated for each station, and MDI was compared with SPI and SPEI values. MDI was found to be successful in capturing dry periods.

Özet

Kuraklık, etkileri uzun süre devam edebilen yaygın bir doğal afettir. Güvenilir kuraklık tahmini, kuraklıkla ilgili riskleri azaltmaya yönelik etkili stratejilerin geliştirilmesi ve değerlendirilmesinde kilit rol oynamaktadır. Literatürde meteorolojik kuraklık değerlendirmesi için farklı yöntemler bulunmaktadır. Bu yöntemler genellikle yağış ve potansiyel buharlaşma (PET) verilerini gerektirir. Bu çalışmada, standartlaştırılmış yağış indeksi (SPI) ve ortalama hava sıcaklığının kopula fonksiyonları kullanılarak birlikte modellenmesiyle çok değişkenli bir kuraklık indeksi (MDI) tanıtılmıştır. Bu amaçla, 1969-2021 yılları arasında Manavgat, Korkuteli, Finike, Antalya ve Alanya meteoroloji istasyonlarının yağış ve ortalama sıcaklık değerleri kullanılmıştır. İlk olarak, bu istasyonların SPI değerleri dört farklı dönemde (3, 6, 9 ve 12 ay) hesaplanmıştır. Her dönemdeki SPI değerleri ile ortalama sıcaklık arasındaki korelasyonlar incelenmiş ve marjinal dağılımları belirlenmiştir. Her zaman ölçeği için, SPI ve ortalama hava sıcaklığı, alternatif kopula tabanlı bağımlılık yapıları içinde birlikte analiz edildi. Model uygunluğu, bilgi tabanlı ve performans tabanlı kriterlerin bir kombinasyonu kullanılarak değerlendirildi; bunlar AIC, BIC, RMSE ve NSE idi. Seçilen kopula fonksiyonlarına göre, her istasyonun 3, 6, 9 ve 12 aylık dönemlerdeki MDI değerleri hesaplandı. Son olarak, her istasyon için Standartlaştırılmış Yağış Buharlaşma İndeksi (SPEI) değerleri hesaplandı ve MDI, SPI ve SPEI değerleriyle karşılaştırıldı. MDI'nin kurak dönemleri yakalamada başarılı olduğu bulundu.

🔖

Cite This Article

Baykal, T. (2026). Copula-Based Multivariate Drought Indices: Integrating Temperature for Drought Prediction. Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, Cilt: 17 Sayı: 2. https://doi.org/10.24012/dumf.1880170

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (61)

  1. L. Xing et al., “Analysis of drought characteristics in the Yangtze River Basin,” Nat. Hazards, vol. 120, pp. 3699–3718, 2024, doi: 10.1007/s11069-023-06344-9.
  2. D. Bagale, M. Sigdel, and D. Aryal, “Winter drought monitoring using standardized precipitation index over Nepal,” Nat. Hazards, vol. 120, pp. 975–988, 2024, doi: 10.1007/s11069-023-06242-0.
  3. Y. Ding et al., “Attribution of meteorological, hydrological and agricultural drought propagation in different climatic regions of China,” Agric. Water Manag., vol. 255, Art. no. 106996, 2021, doi: 10.1016/j.agwat.2021.106996.
  4. Y. Ding et al., “Propagation of meteorological to hydrological drought in different climate regions of China,” J. Environ. Manag., vol. 283, Art. no. 111980, 2021, doi: 10.1016/j.jenvman.2021.111980.
  5. W. Wei et al., “Comparative evaluation of drought indices based on remote sensing data,” Environ. Sci. Pollut. Res., vol. 28, pp. 20408–20425, 2021, doi: 10.1007/s11356-020-12120-0.
  6. L. Xu et al., “A parametric multivariate drought index under climate change,” Agric. For. Meteorol., vol. 310, Art. no. 108657, 2021, doi: 10.1016/j.agrformet.2021.108657.
  7. T. B. McKee, N. J. Doesken, and J. Kleist, “The relationship of drought frequency and duration to time scales,” in Proc. 8th Conf. Appl. Climatol., Anaheim, CA, USA, 1993, pp. 179–183.
  8. S. M. Vicente-Serrano, D. Peña-Angulo, S. Beguería, F. Domínguez-Castro, M. Tomás-Burguera, I. Noguera, et al., “Global drought trends and future projections,” Philosophical Transactions of the Royal Society A, vol. 380, no. 2238, Art. no. 20210285, 2022.
  9. G. Tsakiris, D. Pangalou, and H. Vangelis, “Regional drought assessment based on the reconnaissance drought index (RDI),” Water Resour. Manag., vol. 21, pp. 821–833, 2007, doi: 10.1007/s11269-006-9105-4.
  10. M. İ. Yüce et al., “Samsun Province Drought Analysis with SPI And SPEI,” Kahramanmaras Sutcu Imam University Journal of Engineering Sciences, 25(3), 285-295, 2022, doi: 10.17780/ksujes.1108663. (In Turkish).
  11. M. Samadian et al., “Joint analysis of drought affected by climate change in Zarinehrood watershed using copula functions,” Acta Geophys., 2024, doi: 10.1007/s11600-024-01306-6.
  12. V. Gumus et al., “Evaluating duration, severity, and peak of hydrological drought using copula,” Theor. Appl. Climatol., vol. 152, no. 3, pp. 1159–1174, 2023, doi: 10.1007/s00704-023-04445-w.
  13. M. A. Khan et al., “Modeling drought duration and severity using two-dimensional copula,” J. Atmos. Sol.-Terr. Phys., vol. 214, Art. no. 105530, 2021, doi: 10.1016/j.jastp.2020.105530.
  14. H. Ullah and M. Akbar, “Bivariate homogeneous regions and projections based on copula function using RDI and SPI indices for drought risk assessment in Pakistan,” Arab. J. Geosci., vol. 14, Art. no. 2338, 2021, doi: 10.1007/s12517-021-08645-4.
  15. O. Bazrafshan, H. Zamani, M. Shekari, and V. P. Singh, “Regional risk analysis and derivation of copula-based drought severity–duration curves in arid and semi-arid regions,” Theor. Appl. Climatol., vol. 141, pp. 889–905, 2020, doi: 10.1007/s00704-020-03217-0.
  16. O. O. Ayantobo, Y. Li, and S. Song, “Multivariate drought frequency analysis using four-variate symmetric and asymmetric Archimedean copula functions,” Water Resour. Manag., vol. 33, pp. 103–127, 2019, doi: 10.1007/s11269-018-2090-6.
  17. M. Jehanzaib et al., “Reassessing the frequency and severity of meteorological drought considering non-stationarity,” J. Hydrol., vol. 603, Art. no. 126948, 2021, doi: 10.1016/j.jhydrol.2021.126948.
  18. M. Montaseri, B. Amirataee, and H. Rezaie, “New approach in bivariate drought duration and severity analysis,” J. Hydrol., vol. 559, pp. 166–181, 2018, doi: 10.1016/j.jhydrol.2018.02.018.
  19. B. Saghafian and H. Mehdikhani (2014) “Drought characterization using a new copula-based trivariate approach,” Nat Hazards 72, 1391–1407, 2014, https://doi.org/10.1007/s11069-013-0921-6
  20. T. Mesbahzadeh, M. Mirakbari, M. Mohseni Saravi, F. Soleimani Sardoo and M. M. Miglietta, “Meteorological drought analysis using copula theory and drought indicators under climate change scenarios (RCP),” Meteorological Applications, 27(1), e1856, 2020, doi: 10.1002/met.1856.
  21. M. Esit and M.I. Yuce, “Copula-based bivariate drought severity and duration frequency analysis considering spatial–temporal variability in the Ceyhan Basin, Turkey,” Theoretical and Applied Climatology, 151(3), 1113-1131, 2023, doi: 10.1007/s00704-022-04317-9.
  22. I.H. Deger, M. Esıt and M.I. Yuce, M. I., “Univariate and bivariate hydrological drought frequency analysis by copula functions,” Water Resources Management, 37(12), 4881-4907, 2023, doi: 10.1007/s11269-023-03586-x.
  23. B. Shaw and N. R. Chithra, “Copula-based multivariate analysis of hydro-meteorological drought,” Theor. Appl. Climatol., vol. 153, no. 1, pp. 475–493, 2023, doi: 10.1007/s00704-023-04478-1.
  24. K. Naderi, M. Moghaddasi, and A. Shokri, “Drought occurrence probability analysis using multivariate standardized drought index and copula function under climate change,” Water Resour. Manag., vol. 36, pp. 2865–2888, 2022, doi: 10.1007/s11269-022-03186-1.
  25. S. Dixit and K. V. Jayakumar, “Spatio-temporal analysis of copula-based probabilistic multivariate drought index using CMIP6,” Int. J. Climatol., vol. 42, no. 8, pp. 4333–4350, 2022, doi: 10.1002/joc.7469.
  26. L. Xu, N. Chen, C. Yang, C. Zhang and H. Yu, “A parametric multivariate drought index for drought monitoring and assessment under climate change,” Agric. For. Meteorol., 310, 108657, 2021, https://doi.org/10.1016/j.agrformet.2021.108657
  27. V. Sahana et al., “On the rarity of the 2015 drought in India,” J. Hydrol. Reg. Stud., vol. 31, Art. no. 100727, 2020, doi: 10.1016/j.ejrh.2020.100727.
  28. Y. Liu et al., “On the mechanisms of two composite methods for construction of multivariate drought indices,” Sci. Total Environ., 647, 981-991, 2019, https://doi.org/10.1016/j.scitotenv.2018.07.273
  29. J. Yang et al., “Comprehensive drought characteristics analysis based on a nonlinear multivariate drought index,” J. Hydrol., vol. 557, pp. 651–667, 2018, doi: 10.1016/j.jhydrol.2017.12.055
  30. T. Varol et al., “Copula-based multivariate standardized drought index and hydrological drought characteristics in the Upper Sakarya Basin,” Nat. Hazards, vol. 116, pp. 3669–3683, 2023, doi: 10.1007/s11069-023-05830-4.
  31. H. Ullah et al., “A multi-scalar statistical approach to develop standardized copula-based drought index,” Int. J. Environ. Sci. Technol., vol. 20, no. 7, pp. 7861–7876, 2023, doi: 10.1007/s13762-022-04411-5.
  32. M.A. Khan et al., (2021) “Modeling drought duration and severity using two-dimensional copula,” J. Atmos. Sol.-Terr. Phys., 214, 105530, 2021, https://doi.org/10.1016/j.jastp.2020.105530
  33. J. Won et al., “Copula-based joint drought index using SPI and EDDI,” Sci. Total Environ., vol. 744, Art. no. 140701, 2020, doi: 10.1016/j.scitotenv.2020.140701.
  34. N. Suo, C. Xu, L. Cao, L. Song and X. Lei, “A copula-based parametric composite drought index for drought monitoring and applicability in arid Central Asia,” Catena, 235, 107624, 2024, doi: 10.1016/j.catena.2023.107624.
  35. Y. Liu, T. Hu, Q. Zuo, L. Yu and J. Yang, “Understanding copula-based multivariate standardized drought indices for characterizing meteorological, hydrological and agricultural droughts across global land areas,” Agricultural Water Management, 320, 109864, 2025, doi: 10.1016/j.agwat.2025.109864.
  36. X. Yu, X. Zeng, L. Brocca, D. Gui, D. Wang and J. Wu, “A copula‐based composite drought index for enhanced drought monitoring and analysis,” Journal of Geophysical Research: Atmospheres, 130(8), e2024JD041867, 2025, doi: 10.1029/2024JD041867.
  37. X. Lan, Y. Luo, G. Leng and J. Cao, “A novel copula-based index for agricultural drought monitoring: integrating vegetation response and meteorological drought dynamics in the middle–lower Yangtze River Basin,” Ecological Indicators, 178, 114107, 2025, doi: 10.1016/j.ecolind.2025.114107.
  38. O. Evkaya, C. Yozgatligil and A. S. Selcuk-Kestel, A. “Drought analysis using copula approach: a case study for Turkey,” Communications in Statistics: Case Studies, Data Analysis and Applications, 5(3), 243-260, 2019, doi: 10.1080/23737484.2019.1635923.
  39. T. B. Terzi and B. Önöz, “Advanced drought analysis using a novel copula-based multivariate index: a case study of the Ceyhan River Basin,” Sustainable Water Resources Management, 11(1), 11, 2025, doi: 10.1007/s40899-025-01189-5.
  40. Z. Ali, I. Hussain, M. Faisal, H. F. Nazir, M. A. Moemen, T. Hussain, and S. Shamsuddin, “A novel multi-scalar drought index for monitoring drought: The standardized precipitation temperature index,” Water Resour. Manag., vol. 31, pp. 4957–4969, 2017, doi: 10.1007/s11269-017-1788-1.
  41. E. De Martonne, “L’indice d’aridité,” Bull. Assoc. Géographes Fr., vol. 3, no. 9, pp. 3–5, 1926.
  42. T. Varol and M. Ertuğrul, “Analysis of forest fires in the Antalya region using the Keetch–Byram drought index,” J. For. Res., vol. 27, pp. 811–819, 2016, doi: 10.1007/s11676-016-0235-0.
  43. Ş. N. Erkul, Creating Antalya Drought Map and Associating it With Agricultural Lands, M.S. thesis, Grad. Sch. Nat. Appl. Sci., Akdeniz Univ., Antalya, Türkiye, 2023.
  44. H. Azizi and N. Nejatian, “Evaluation of the climate change impact on the intensity and return period for drought indices of SPI and SPEI (Varamin Plain),” Water Supply, vol. 22, no. 4, pp. 4373–4386, 2022, doi: 10.2166/ws.2022.056.
  45. J. Laimighofer and G. Laaha, “How standard are standardized drought indices?” J. Hydrol., vol. 613, Art. no. 128385, 2022, doi: 10.1016/j.jhydrol.2022.128385.
  46. P. Ghasemi et al., “Application of Gaussian process regression to forecast multi-step ahead SPEI drought index,” Alexandria Eng. J., vol. 60, no. 6, pp. 5375–5392, 2021, doi: 10.1016/j.aej.2021.04.022.
  47. C. Liu, C. Yang, Q. Yang and J. Wang, “Spatiotemporal drought analysis by the standardized precipitation index (SPI) and standardized precipitation evapotranspiration index (SPEI) in Sichuan Province, China,” Sci. Rep., 11(1), 1280, 2021, https://doi.org/10.1038/s41598-020-80527-3
  48. A. Sklar, “Fonctions de répartition à n dimensions et leurs marges,” Publ. Inst. Statist. Univ. Paris, vol. 8, pp. 229–231, 1959.
  49. M. Seyedabadi, M. Kavianpour, and S. Moazami, “Multivariate drought risk analysis based on copula functions,” Water Supply, vol. 20, no. 6, pp. 2375–2388, 2020, doi: 10.2166/ws.2020.153.
  50. M. Sadegh, E. Ragno, and A. AghaKouchak, “Multivariate Copula Analysis Toolbox (MvCAT): describing dependence and underlying uncertainty using a Bayesian framework,” Water Resour. Res., vol. 53, no. 6, pp. 5166–5183, 2017, doi: 10.1002/2016WR020242.
  51. B. Zhang, S. Wang and Y. Wang, (2019). “Copula‐based convection‐permitting projections of future changes in multivariate drought characteristics,” J. Geophys. Res. Atmos., 124(14), 7460-7483.
  52. F. Wang et al., “A new copula-based standardized precipitation evapotranspiration streamflow index,” J. Hydrol., vol. 585, Art. no. 124793, 2020, doi: 10.1016/j.jhydrol.2020.124793.
  53. World Meteorological Organization, Standardized Precipitation Index User Guide, WMO-No. 1090, Geneva, Switzerland, 2012.
  54. R. B. Nelsen, An Introduction to Copulas, 2nd ed. New York, NY, USA: Springer, 2006.
  55. Republic of Türkiye Ministry of Agriculture and Forestry, Executive Summary of the Antalya Basin Drought Management Plan, General Directorate of Water Management, Dept. Flood and Drought Management, Ankara, Türkiye, 2018.
  56. H. Wu, X. Su, V.P. Singh, K. Feng K and J. Niu, “Agricultural drought prediction based on conditional distributions of vine copulas,” WATER RESOUR RES 57(8):e2021WR029562, 2021, doi:10.1029/2021WR029562
  57. Z. Zhong, Q. Zhao, G. Sang, J. Xue, J. Wang, F. Lin, F. “Copula-based composite drought index combining precipitation, temperature, and NDVI used for drought monitoring,” Theoretical and Applied Climatology, 157:103 2026, doi:10.1007/s00704-026-06033-0
  58. M. Dikici and M. Aksel, “Comparison of SPI, SPEI and SRI drought indices for Seyhan Basin,” International Journal of Electronics Mechanical and Mechatronics Engineering, 9(4), 1751-1762, 2019.
  59. M. Dikici, “Drought analysis with different indices for the Asi Basin (Turkey),” Sci Rep 10, 20739, 2020, doi: 10.1038/s41598-020-77827-z.
  60. M. Dikici, H.I. Burgan, “Exploring the Effect of Meteorological and Hydrological Trends on Groundwater Drought Index: The Case of Seyhan Basin,” Ecohydrology, 18(6), e70110, 2025, doi: 10.1002/eco.70110.
  61. M. Dikici, “Drought Analysis for the Seyhan Basin with Vegetation Indices and Comparison with Meteorological Different Indices,” Sustainability, 14, 4464, 2022, doi: 10.3390/su14084464.