Skip to main navigation menu Skip to main content Skip to site footer

Research Articles

Vol. 13 No. sp1 (2026): Recent Advances in Agriculture

Analysis of rainfall variability and spell dynamics in Coimbatore using copula function modelling

DOI
https://doi.org/10.14719/pst.11206
Submitted
9 August 2025
Published
11-03-2026

Abstract

This study investigates the coupled dynamics of rainfall and evapotranspiration in Coimbatore, a major urban and agricultural hub in southern India, over 31 years (1994–2024). Aside from areas near the Noyyal River basin and episodic overflow from the Western Ghats, the region is predominantly dry, receiving approximately 665.5 mm of annual rainfall over about 45 rainy days and exhibiting a yearly average temperature of 25.4 °C. Advanced statistical techniques, including Gaussian, t, Frank, Roch-Alegre and BB5 copula-based models, are employed to analyse key hydroclimatic indicators: the conditional probability index (CPI), moisture availability index (MAI) and potential evapotranspiration (PET). These models facilitate forecasting of wet and dry spells and provide insights relevant to drought preparedness, sustainable water management and agricultural planning in monsoon-dependent regions. Rainfall patterns and drought risk are quantified using MATLAB, enabling discrimination between low- and high-rainfall trends that are critical for rainfed agriculture. Wet and dry spell dynamics are further evaluated using the Mann-Kendall and Spearman’s Rho non-parametric tests at the 5 % significance level, supporting the identification of atmospheric demand patterns and characteristic monsoon periods. The results reveal substantial variability in hydrological regimes, characterized by abrupt transitions between extreme wet and dry spells and highlight years of pronounced moisture deficiency alongside periods of excessive moisture. This comprehensive framework, which employs the Gaussian copula function, enhances understanding of climate variability and offers actionable strategies for managing hydroclimatic risks in vulnerable regions.

References

  1. 1. Thyagarajan LP, Jeyanthi J, Kavitha D. Vulnerability analysis of the groundwater quality around Vellalore-Kurichi landfill region in Coimbatore. Environ Chem Ecotoxicol. 2021;3:125–30. https://doi.org/10.1016/j.enceco.2020.12.002
  2. 2. Nandhini C, Patil S. Markov Chain analysis of rainfall of Coimbatore. Mausam. 2024;75(2):501–6. https://doi.org/10.54302/mausam.v75i2.3497
  3. 3. Vimal S, Kumar NS, Kasiselvanathan M, Gurumoorthy K. Smart irrigation system in agriculture. J Phys Conf Ser. 2021;1917(1):012028. https://doi.org/10.1088/1742-6596/1917/1/012028
  4. 4. Palmer PI, Wainwright CM, Dong B, Maidment RI, Wheeler KG, Gedney N, et al. Drivers and impacts of Eastern African rainfall variability. Nat Rev Earth Environ. 2023;4(4):254–70. https://doi.org/10.1038/s43017-023-00397-x
  5. 5. Cochemé J, Franquin P. An agroclimatological survey of a semi-arid area in Africa south of the Sahara. Rome: Food and Agriculture Organization of the United Nations; 1967.
  6. 6. Panthou G, Lebel T, Vischel T, Quantin G, Sane Y, Ba A, et al. Rainfall intensification in tropical semi-arid regions: the Sahelian case. Environ Res Lett. 2018;13(6):064013. https://doi.org/10.1088/1748-9326/aac334
  7. 7. Ray M, Biswasi S, Sahoo K, Patro H. A Markov chain approach for wet and dry spell and probability analysis. Int J Curr Microbiol Appl Sci. 2018;1(6):1005–13.
  8. 8. Milan P, Wächter M, Peinke J. Turbulent character of wind energy. Phys Rev Lett. 2013;110(13):138701. https://doi.org/10.1103/PhysRevLett.110.138701
  9. 9. Saxton KE, Rawls WJ. Soil water characteristic estimates by texture and organic matter for hydrologic solutions. Soil Sci Soc Am J. 2006;70(5):1569–78. https://doi.org/10.2136/sssaj2005.0117
  10. 10. Nelsen RB. An introduction to copulas. New York: Springer; 2006.
  11. 11. Mirabbasi R, Fakheri-Fard A, Dinpashoh Y. Bivariate drought frequency analysis using the copula method. Theor Appl Climatol. 2012;108(1):191–206. https://doi.org/10.1007/s00704-011-0524-7
  12. 12. Shaw B, Chithra N. Copula-based multivariate analysis of hydro-meteorological drought. Theor Appl Climatol. 2023;153(1):475–93. https://doi.org/10.1007/s00704-023-04478-1
  13. 13. Chen L, Singh VP, Guo S, Mishra AK, Guo J. Drought analysis using copulas. J Hydrol Eng. 2013;18(7):797–808. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000697
  14. 14. Grimaldi S, Petroselli A, Salvadori G, De Michele C. Catchment compatibility via copulas: a non-parametric study of the dependence structures of hydrological responses. Adv Water Resour. 2016;90:116–33. https://doi.org/10.1016/j.advwatres.2016.02.003
  15. 15. Bazrafshan O, Zamani H, Shekari M. A copula-based index for drought analysis in arid and semi-arid regions of Iran. Nat Resour Model. 2020;33(1):e12237. https://doi.org/10.1111/nrm.12237
  16. 16. She D, Xia J, Zhang Y, Shan L. Regional frequency analysis of extreme dry spells during rainy season in the Wei River Basin, China. Adv Meteorol. 2016;2016:6427568. https://doi.org/10.1155/2016/6427568
  17. 17. Genest C, Masiello E, Tribouley K. Estimating copula densities through wavelets. Insur Math Econ. 2009;44(2):170–81. https://doi.org/10.1016/j.insmatheco.2008.07.006
  18. 18. Falhi FH, Hmood MY. Estimation of copula density using the wavelet transform. Baghdad Sci J. 2024;21(11):18. https://doi.org/10.21123/bsj.2024.9673
  19. 19. Jammazi R, Reboredo JC. Dependence and risk management in oil and stock markets: a wavelet-copula analysis. Energy. 2016;107:866–88. https://doi.org/10.1016/j.energy.2016.02.093
  20. 20. Veeraputhiran R, Karthikeyan R, Geethalakshmi V, Selvaraju R, Sundersingh S, Balasubramanian T. Crop planning-climate atlas-principles. Coimbatore: AE Publications; 2003.
  21. 21. Melo A, Pereira M, Da Silva AL. A conditional probability approach to the calculation of frequency and duration indices in composite reliability evaluation. IEEE Trans Power Syst. 1993;8(3):1118–25. https://doi.org/10.1109/59.260886
  22. 22. Goel S, Singh R. Rainfall variability and probability analysis in Tarai and mid Himalayan regions of Uttarakhand. Mausam. 2025;76(2):403–16. https://doi.org/10.54302/mausam.v76i2.6349
  23. 23. Hargreaves GH. The estimation of potential and crop evapotranspiration. St Joseph (MI): Am Soc Agric Eng; 1973.
  24. 24. Makwana JJ, Deora B, Patel C, Parmar B, Saini A. Analysis of rainfall characteristics and moisture availability index for crop planning in semi arid region of north Gujarat. J Agrometeorol. 2021;23(4):409–15. https://doi.org/10.54386/jam.v23i4.145
  25. 25. Hargreaves GH. Moisture availability and crop production. Trans ASAE. 1975;18(5):980–4. https://doi.org/10.13031/2013.36722
  26. 26. Yang Y, Roderick ML, Guo H, Miralles DG, Zhang L, Fatichi S, et al. Evapotranspiration on a greening Earth. Nat Rev Earth Environ. 2023;4(9):626–41. https://doi.org/10.1038/s43017-023-00464-3
  27. 27. Allen RG, Pereira LS, Howell TA, Jensen ME. Evapotranspiration information reporting: II. Recommended documentation. Agric Water Manag. 2011;98(6):921–9. https://doi.org/10.1016/j.agwat.2010.12.016
  28. 28. Milly PC, Dunne KA. Potential evapotranspiration and continental drying. Nat Clim Change. 2016;6(10):946–9. https://doi.org/10.1038/nclimate3046
  29. 29. Allen RG, Pereira LS, Raes D, Smith M. Crop evapotranspiration: guidelines for computing crop water requirements. FAO Irrig Drain Pap No. 56. Rome: FAO; 1998. p. 1–300.
  30. 30. Goroshi S, Pradhan R, Singh RP, Singh K, Parihar JS. Trend analysis of evapotranspiration over India observed from long-term satellite measurements. J E`arth Syst Sci. 2017;126(8):113. https://doi.org/10.1007/s12040-017-0891-2
  31. 31. Hargreaves GH, Samani ZA. Estimating potential evapotranspiration. J Irrig Drain Div ASCE. 1982;108(3):225–30. https://doi.org/10.1061/JRCEA4.0001390
  32. 32. Xu C, Wang W, Hu Y, Liu Y. Evaluation of ERA5, ERA5-Land, GLDAS-2.1 and GLEAM potential evapotranspiration data over mainland China. J Hydrol Reg Stud. 2024;51:101651. https://doi.org/10.1016/j.ejrh.2023.101651
  33. 33. Kokilavani S, Panneerselvam S, Balasubramanian T. Rainfall study for dry land areas of selected districts of Tamil Nadu for crop planning. Mausam. 2016;67(4):869–78. https://doi.org/10.54302/mausam.v67i4.1414
  34. 34. Wibig J. Dry and wet spells in Poland in the period 1966-2023. Water. 2024;16(10):1344. https://doi.org/10.3390/w16101344
  35. 35. El Hafyani M, El Himdi K. Literature review on stochastic modeling of wet and dry spells. J Environ Earth Sci. 2024;6(3):1–12. https://doi.org/10.30564/jees.v6i3.6964
  36. 36. Chen TX, Lyu HS, Horton R, Zhu YH, Chen RS, Sun MY, et al. Using copula functions to predict climatic change impacts on floods in river source regions. Adv Clim Change Res. 2024;15(3):406–18. https://doi.org/10.1016/j.accre.2024.04.006
  37. 37. Górecki J, Okhrin O. Hierarchical Archimedean copulas. Cham: Springer Nature; 2024. https://doi.org/10.1007/978-3-031-56337-9
  38. 38. Sklar A. N-dimensional distribution functions and their margins. Publ Inst Stat Univ Paris. 1959;8:229–31.
  39. 39. Heuvel EVD, Zhan Z. Myths about linear and monotonic associations: Pearson's r, Spearman's ρ and Kendall's τ. Am Stat. 2022;76(1):44–52. https://doi.org/10.1080/00031305.2021.2004922
  40. 40. Genest C, Favre AC. Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng. 2007;12(4):347–68. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347)
  41. 41. Li C, Singh VP, Mishra AK. A bivariate mixed distribution with a heavy-tailed component and its application to single-site daily rainfall simulation. Water Resour Res. 2013;49(2):767–89. https://doi.org/10.1002/wrcr.20063
  42. 42. Roch O, Alegre A. Testing the bivariate distribution of daily equity returns using copulas: an application to the Spanish stock market. Comput Stat Data Anal. 2006;51(2):1312–29. https://doi.org/10.1016/j.csda.2005.11.007

Downloads

Download data is not yet available.