Advertisement

Modeling Earth Systems and Environment

, Volume 4, Issue 2, pp 867–879 | Cite as

Modelling of interdependence between rainfall and temperature using copula

  • P. K. Pandey
  • Lakhyajit Das
  • D. Jhajharia
  • Vanita Pandey
Original Article
  • 94 Downloads

Abstract

Temperature and rainfall are the two critical climatic parameters influence agricultural productivity and many other extreme hydrological and meteorological phenomena. Temperature and rainfall have significant temporal variation. Rainfall in many cases marginal of these two parameters known, but joint-distribution is unknown. Modelling of joint distribution or possible interdependence between these may be achieved through using Copula. In the present study, monthly rainfall and temperature time series of two stations, one from the humid region (Agartala) and another from the arid region (Bikaner) were used for copula-based analysis. Based on the AIC and BIC selection criterion best copula model was selected. The Normal copula was found to be a suitable model for rainfall and minimum temperature; rainfall and mean temperature and Clayton copula for rainfall and maximum temperature for the humid region. Similarly, for arid region Student or T copula is the best suitable model for rainfall and minimum temperature and rainfall and maximum temperature; and for rainfall and mean temperature, the Normal copula is the best suitable model. Furthermore, copula-rank correlations were obtained for the best-fit copula model to assess the inter-dependence. It was observed that the interdependence between mean temperature and rainfall is more crucial in the context of the global warming and climate change because of the occurrence of the similar types of copulas (mainly normal) in both the humid and arid climatic conditions.

Keywords

Interdependence Copula Joint distribution Temperature-rainfall Agricultural productivity 

References

  1. Agha Kouchak A, Bárdossy A, Habib E (2010) Copula-based uncertainty modelling: application to multisensor precipitation estimates. Hydrol Process 24(15):2111–2124Google Scholar
  2. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723CrossRefGoogle Scholar
  3. Balyani S, Khosravi Y, Ghadami F et al (2017) Modeling the spatial structure of annual temperature in Iran Model. Earth Syst Environ 3:581.  https://doi.org/10.1007/s40808-017-0319-7 CrossRefGoogle Scholar
  4. Buba LF, Kura NU, Dakagan JB (2017) Spatiotemporal trend analysis of changing rainfall characteristics in Guinea Savanna of Nigeria. Model Earth Syst Environ 3:1081.  https://doi.org/10.1007/s40808-017-0356-2 CrossRefGoogle Scholar
  5. Chen Lu, Singh PV, Guo S, Mishra KA, Guo J (2013) Drought analysis using copulas. J Hydrol Eng 18(7):797–808CrossRefGoogle Scholar
  6. Ching J, Phoon KK, Chen CH (2014) Modeling piezocone cone penetration (CPTU) parameters of clays as a multivariate normal distribution. Can Geotech J 51(1):77–91CrossRefGoogle Scholar
  7. Cong RG, Brady M (2012) The interdependence between rainfall and temperature copula analysis. Sci world J.  https://doi.org/10.1100/2012/405675 Google Scholar
  8. Dupuis DJ (2007) Using copulas in hydrology: benefits, cautions, and issues. J Hydrol Eng 12(4):381–393CrossRefGoogle Scholar
  9. Fang HB, Fang KT, Kotz S (2002) The meta-elliptical distributions with given marginal. J Multivar Anal 82(1):1–16CrossRefGoogle Scholar
  10. Favre AC, Adlouni SE, Perreault L, Thiemonge N, Bobee (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(1):1–12CrossRefGoogle Scholar
  11. Huang Y, Cai J, Yin H, Cai M (2009) Correlation of precipitation to temperature variation in the Huanghe river (Yellow River) basin during 1957–2006. J Hydrol 372(1–4):1–8CrossRefGoogle Scholar
  12. Jha V, Singh RV, Bhakar SR (2003) Stochastic modeling of soil moisture. J Agric Engg 40(4):51–56Google Scholar
  13. Jhajharia D, Chattopadhyay S, Choudhary RR, Dev V, Singh VP, Lal S (2013) Influence of climate on incidences of malaria in the Thar Desert, north-west India. Int J Climatol 33:312–325CrossRefGoogle Scholar
  14. Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, LondonCrossRefGoogle Scholar
  15. Kaufmann RK, Snell SE (1997) A biophysical model of corn yield: integrating climatic and social determinants. Am J Agric Econ 79(1):178–190CrossRefGoogle Scholar
  16. Kong CY, Jamaludin S, Fadhilah Y, Hui F (2014) Bivariate copula fitting in rainfall data. In: AIP conference proceedings 1605:986Google Scholar
  17. Kreyling J, Beier C (2013) Complexity in climate change manipulation experiments. Bioscience 63(9):763–767CrossRefGoogle Scholar
  18. Laux P, Vogl S, Qiu W, Knoche RH, Kunstmann H (2011) Copula-based statistical refinement of precipitation in RCM simulations over complex terrain. Hydrol Earth Syst Sci 15(7):2401–2419CrossRefGoogle Scholar
  19. Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65(2):297–303CrossRefGoogle Scholar
  20. Lobell DB, Field CB (2007) Global scale climate-crop yield relationships and the impacts of recent warming. Environ Res Lett 2(1) (Article ID 014002)Google Scholar
  21. Nelsen RB (2001) Kendall tau metric. In: Hazewinkel M (ed) Encyclopaedia of Mathematics. Springer. ISBN 978-1556080104Google Scholar
  22. Pandey PK, Pandey V (2016) Evaluation of temperature-based Penman–Monteith (TPM) model under the humid environment. Model Earth Syst Environ 2:152.  https://doi.org/10.1007/s40808-016-0204-9 CrossRefGoogle Scholar
  23. Pandey PK, Pandey V, Singh R, Bhakar SR (2009) Stochastic modelling of actual black gram evapotranspiration. J Water Resour Protect 01(6):448–455CrossRefGoogle Scholar
  24. Pandey PK, Nyori T, Pandey V (2017) Estimation of reference evapotranspiration using data driven techniques under limited data conditions Model. Earth Syst Environ 3:1449.  https://doi.org/10.1007/s40808-017-0367-z CrossRefGoogle Scholar
  25. Rajeevan M, Pai DS, Thapliyal V (1998) Spatial and temporal relationships between global land surface air temperature anomalies and Indian summer monsoon rainfall. Meteorol Atmos Phys 66(3–4):157–171CrossRefGoogle Scholar
  26. Riha SJ, Wilks DS, Simoens P (1996) Impact of temperature and precipitation variability on crop model predictions. Clim Change 32(3):293–311CrossRefGoogle Scholar
  27. Salvadori G, Michele C (2007) On the use of copula in hydrology: theory and practice. J Hydrol Eng 12(4):369–380CrossRefGoogle Scholar
  28. Scholzel C, Friederichs P (2008) Multivariate non-normally distributed random variables in climate research—introduction to the copula approach. Nonlinear Process Geophys 15(5):761–772CrossRefGoogle Scholar
  29. Schwarz GE (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464CrossRefGoogle Scholar
  30. Serinaldi F (2008) Analysis of inter-gauge dependence by Kendall’s τK, upper tail dependence coefficient and 2-copulas with application to rainfall fields. Stoch Environ Res Risk Assess 22(6):671–688CrossRefGoogle Scholar
  31. Sethi R, Pandey BK, Krishan R et al (2015) Performance evaluation and hydrological trend detection of a reservoir under climate change condition. Model Earth Syst Environ 1:33.  https://doi.org/10.1007/s40808-015-0035-0 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • P. K. Pandey
    • 1
  • Lakhyajit Das
    • 1
  • D. Jhajharia
    • 2
  • Vanita Pandey
    • 1
  1. 1.Department of Agricultural EngineeringNorth Eastern Regional Institute of Science and TechnologyItanagarIndia
  2. 2.Department of Soil and Water EngineeringCollege of Agricultural Engineering and Post-Harvest TechnologyGangtokIndia

Personalised recommendations