Improving the performance of the SPEI using four-parameter distribution function

  • Yousef RamezaniEmail author
  • Mohammad Nazeri Tahroudi
Original Paper


One of the main challenges in the present era is competition for access to water resources. Iran is also on attention due to its geopolitical and strategic location. Water scarcity is a problem which will bring the country into the next dimensions of the challenges. Reducing water resources in this country is affected by global climate change and droughts. Meteorological drought is studied by researchers using multiple indices. The Standardized Precipitation Evapotranspiration Index (SPEI) is also one of the most widely used indices in this field. The aim of this study was to investigate the meteorological drought and identify dry and wet months in the eastern stations of Iran using the SPEI. In this regard, it has been tried to select a function proportional to precipitation minus potential evapotranspiration by examining continuous and discrete statistical distribution functions. Among the 65 distribution functions examined, the results of goodness of fit tests of Anderson-Darling, Kolmogorov-Smirnov, and chi-square tests, introduced the four-parameter Burr distribution function (BDF) as the best distribution function. The results showed that the four-parameter BDF has higher accuracy than the conventional log-logistic function. The results of the extraction of SPEI showed that drought intensity in the eastern regions of Iran during the statistical period of 1973–2011 has increased and almost 26% of the months examined at all stations have faced drought. Finally, according to the results of this study, it is suggested to examine various distribution functions or use the proposed distribution function for the extraction of SPEI values. Also, as well as the existing climate change, the results of the MSPEI index appear to be better than the SPEI index.



The authors would like to thank Iranian Meteorological Organization (IMO) for providing the meteorological data. Also, the authors are thankful to University of Birjand, Birjand, Iran.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Abramowitz M, Stegun IA (1965) Handbook of mathematical functions: with formulas, graphs, and mathematical tables (Vol. 55) Courier CorporationGoogle Scholar
  2. Blenkinsop SH, Fowler J (2007) Changes in drought frequency, severity and duration for the British Isles projected by the PRUDENCE regional climate models. J Hydrol 342(1):50–71CrossRefGoogle Scholar
  3. Bryant EA (1991) Natural hazards. Cambridge University Press, Cambridge, New York and MelbourneGoogle Scholar
  4. Gong DY, Ho CH (2002) Shift in the summer rainfall over the Yangtze River valley in the late 1970s. Geophys Res Lett 29(10):78–100CrossRefGoogle Scholar
  5. Hamed KH, Rao AR (1998) A modified Mann-Kendall trend test for autocorrelated data. J Hydrol 204:182–196CrossRefGoogle Scholar
  6. Intergovernmental Panel on Climate Change (IPCC) (2007) Synthesis Report 2007, AR4, Cambridge University Press, Cambridge, United Kingdomand New York, USA.Google Scholar
  7. Jones PD, Moberg A (2003) Hemispheric and large-scale surface air temperature variations: an extensive revision and an update to 2001. J Clim 16(2):206–223CrossRefGoogle Scholar
  8. Kendall M (1975) Rank correlation measures. Charles Griffin, London, 202pGoogle Scholar
  9. Keyantash J, Dracup JA (2002) The quantification of drought: an evaluation of drought indices. Bull Am Meteorol Soc 83(8):1167–1180CrossRefGoogle Scholar
  10. Khalili K, Esfandiary S, Khanmohammadi N, Nazeri Tahrudi M (2014) Half-century air temperature trends in Iran. J Middle East Appl Sci Technol 8:208–213Google Scholar
  11. Khalili K, Tahoudi MN, Mirabbasi R, Ahmadi F (2016) Investigation of spatial and temporal variability of precipitation in Iran over the last half century Stochastic environmental research and risk assessment 30(4):1205-1221.Google Scholar
  12. Khozeymehnezhad H, Tahroudi MN (2019) Annual and seasonal distribution pattern of rainfall in Iran and neighboring regions. Arab J Geosci 12(8):271CrossRefGoogle Scholar
  13. Kousari MR, Ahani H, Hendi-Zadeh R (2013) Temporal and spatial trend detection of maximum air temperature in Iran during 1960-2005. Glob Planet Chang 111:97–110CrossRefGoogle Scholar
  14. Kumar S, Merwade V, Kam J, Thurner K (2009) Streamflow trends in Indiana: effects of long term persistence, precipitation and subsurface drains. J Hydrol 374:171–183CrossRefGoogle Scholar
  15. Lorenzo-Lacruz J, Vicente-Serrano SM, López-Moreno JI, Beguería S, García-Ruiz JM, Cuadrat JM (2010) The impact of droughts and water management on various hydrological systems in the headwaters of the Tagus River (central Spain). J Hydrol 386(1):13–26CrossRefGoogle Scholar
  16. Mann H (1945) Non-parametric tests against trend. Econmetrica, 13, 245-259 Mantua, NJ, SR Hare, Y Zhang, JM Wallace, and RC Francis (1997), A Pacific decadalCrossRefGoogle Scholar
  17. Manzano A, Clemente MA, Morata A, Luna MY, Beguería S, Vicente-Serrano SM, Martín ML (2019) Analysis of the atmospheric circulation pattern effects over SPEI drought index in Spain. Atmos Res 230:104630CrossRefGoogle Scholar
  18. McKee TB, Doesken N, Kleist J (1995) Drought monitoring with multiple time scales In Proceedings of the. In: 9th Conference on Applied Climatology Dallas, Boston, MA: American Meteorological Society, pp 233–236Google Scholar
  19. Nicholls N (2004) The changing nature of Australian droughts Climatic change 63(3):323-336.CrossRefGoogle Scholar
  20. Rebetez M, Mayer H, Dupont O, Schindler D, Gartner K, Kropp JP, Menzel S (2006) Heat and drought 2003 in Europe: a climate synthesis. Ann For Sci 63(6):569–577CrossRefGoogle Scholar
  21. Ren GY, Wu H, Chen ZH (2000) Spatial patterns of change trend in rainfall of China. Q J Appl Meteor 11(3):322–330Google Scholar
  22. Saboohi R, Soltani S, Khodagholi M (2012) Trend analysis of temperature parameters in Iran. Thear Appl Climatol 109:529–547CrossRefGoogle Scholar
  23. Sen PK (1968) Estimates of the regression coefficient based on Kendall’s tau. J Am Stat Assoc 63:1379–1389CrossRefGoogle Scholar
  24. Sheffield J, Wood EF (2008) Projected changes in drought occurrence under future global warming from multi-model, multi-scenario, IPCC AR4 simulations. Clim Dyn 31(1):79–105CrossRefGoogle Scholar
  25. Solomon S, Qin D, Manning M, Marquis M, Averyt K, Tignor M, Chen Z (2007) Climate change 2007-the physical science basis: Working group I contribution to the fourth assessment report of the IPCC, vol 4. Cambridge university pressGoogle Scholar
  26. Stagge JH, Tallaksen LM, Gudmundsson L, Van Loon AF, Stahl K (2015) Candidate distributions for climatological drought indices (SPI and SPEI). Int J Climatol 35(13):4027–4040CrossRefGoogle Scholar
  27. Tabari H, Hosseinzadeh-Talaee P (2011) Analysis trends in temperature data in arid and semi-arid regions of Iran Atmospheric Research 79:1-10.Google Scholar
  28. Thiel H A rank-invariant method of linear and polynomial regression analysis, Part 3. In: Proceedings of Koninalijke Nederlandse Akademie van Weinenschatpen A, 1950. pp 1397-1412Google Scholar
  29. Vicente-Serrano SM, Beguería S, López-Moreno JA (2010) A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. J Clim 23(7):1696–1718CrossRefGoogle Scholar
  30. Wilhite DA (2000) Drought as a natural hazard: concepts and definitions A global assessment 1:3-18.Google Scholar
  31. Zarenistanak M, Dhorde AG, Kripalani RH (2014) Temperature analysis over southwest Iran: trends and projections. Thear Appl Climatol 116:103–117CrossRefGoogle Scholar
  32. Zhai P, Zhang X, Wan H, Pan X (2005) Trends in total precipitation and frequency of daily precipitation extremes over China. J Clim 18(7):1096–1108CrossRefGoogle Scholar
  33. Zhang Q, Xu CY, Zhang Z, Chen YD, Liu CL, Lin H (2008) Spatial and temporal variability of precipitation maxima during 1960–2005 in the Yangtze River basin and possible association with large-scale circulation. J Hydrol 353(3):215–227CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Water Engineering, Faculty of AgricultureUniversity of BirjandBirjandIran

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