Abstract
The Standardized Precipitation Index (SPI) is widely used as drought meteorological index, to identify the duration and/or severity of a drought. The SPI is usually computed by fitting the gamma probability distribution to the observed precipitation data. In this work, the possibility to calculate SPI by fitting to the precipitation data the normal and the log-normal probability distributions was studied. For this purpose, 19 time series of monthly precipitation of 76 years were used, and the assumption that the gamma probability distribution would provide better representation of the precipitation data than log-normal and normal distributions, at various time scales (1, 3, 6, 12 and 24 months) was tested. It is concluded that for SPI of 12 or 24 months, the log-normal or the normal probability distribution can be used for simplicity, instead of gamma, producing almost the same results.
Similar content being viewed by others
References
Abramowitz M, Stegun A (eds) (1965) Handbook of mathematical formulas, graphs, and mathematical tables. Dover Publications Inc, New York
Anctil F, Larouche W, Viau AA (2002) Exploration of the standardized precipitation index with regional analysis. Can J Soil Sci 82(1):115–125
Beran M, Rodier J (1985) Hydrological aspects of drought, studies and reports in Hydrology 39. Unesco-WMO, Paris
Bhalme HN, Mooley DA (1980) Large scale droughts/floods and monsoon circulation. Mon Weath Rev 108:1197–1211
Bonaccorso B, Bordi I, Cancelliere A, Rossi G, Sutera A (2003) Spatial variability of drought: an analysis of the SPI in Sicily. Water Resour Manag 17:273–296
Domonkos P (2003) Recent precipitation trends in Hungary in the context of larger scale climatic changes. Nat Hazards 29:255–271
Edossa D, Babel M, Gupta A (2010) Drought analysis in the Awash river basin, Ethiopia. Water Resour Manag 24:1441–1460
Georgakakos K, Bae D-H, Jeong C-S (2005) Utility of ten-day climate model ensemble simulations for water resources applications in Korean watersheds. Water Resour Manag 19:849–872
Gibbs WJ, Maher JV (1967) Rainfall deciles as drought indicators. Bureau of Meteorology Bulletin, No. 48. Commonwealth of Australia, Melbourne
Guttman N (1999) Accepting the standardized precipitation index: a calculation algorithm. J Am Water Resour Assoc 35(2):311–322
Hayes MJ, Svoboda MD, Wilhite DA, Vanyarkho OV (1999) Monitoring the 1996 drought using the standardized precipitation index. Bull Am Meteorol Soc 80:429–438
Helsel DR, Hirsch RM (1992) Statistical methods in water resources. Elsevier, Amsterdam, 522
Jones PD, Hulme M (1996) Calculating regional climatic time series for temperature and precipitation: methods and illustrations. Int J Climatol 16:361–377
Komuscu AU (1999) Using the SPI to analyze spatial and temporal pattern of drought in Turkey. Drought Network News 11:7–13
Lana X, Burgueno A (2000) Some statistical characteristics of monthly and annual pluviometric irregularity for the Spanish Mediterranean coast. Theor Appl Climatol 65(1–2):79–97
Lloyd-Hughes B, Saunders M (2002) A drought climatology for Europe. Int J Climatol 22:1571–1592
Loukas A, Vasiliades L (2004) Probabilistic analysis of drought spatiotemporal characteristics in Thessaly region, Greece. Nat Hazards Earth Syst Sci 4:719–731
Mathieu R, Richard Y (2003) Intensity and spatial extension of drought in South Africa at different time scales. Water SA 29(4):489–500
McKee TB, Doesken NJ, Kliest J (1993) The relationship of drought frequency and duration to time scales. Proc. of the 8th Conference on Applied Climatology, American Meteorological Society, Boston, pp 179–184
Min SK, Kwon WT, Park EH, Choi Y (2003) Spatial and temporal comparisons of droughts over Korea with East Asia. Int J Climate 23(2):223–233
Moreira EE, Paulo AA, Pereira LS, Mexia JT (2006) Analysis of SPI drought class transitions using loglinear models. J Hydrology 331:349–359
Nalbantis I, Tsakiris G (2009) Assessment of hydrological drought revisited. Water Resour Manag 23:881–897
Ntale HK, Gan T (2003) Drought indices and their application to EastAfrica. Int J Climatol 23:1335–1357
Palmer WC (1965) Meteorological drought. Research Paper No. 45. U.S. Weather Bureau, Washington, DC
Paulo AA, Pereira LS (2007) Prediction of SPI drought class transitions using Markov chains. Water Resour Manag 21(10):1813–1827
Paulo AA, Pereira LS, Matias PG (2003) Analysis of local and regional droughts in southern Portugal using the theory of runs and the standardised precipitation index. In: Rossi G, Cancelliere A, Pereira LS, Oweis T, Shatanawi M (eds) Tools for drought mitigation in Mediterranean regions. Kluwer, Dordrecht, pp 147–157
Paulo AA, Ferreira E, Coelho C, Pereira LS (2005) Drought class transition analysis through Markov and Loglinear models, an approach to early warning. Agr Water Manag 77:59–81
Raziei T, Sagfahian B, Paulo AA, Pereira LS, Bordi I (2009) Spatial patterns and temporal variability of drought in Western Iran. Water Resour Manag 23:439–455
Rouault M, Richard Y (2003) Intensity and spatial extension of droughts in South Africa at different time scales. Water SA 29:489–500
Seiler R, Hayes M, Bressan L (2002) Using the standardized precipitation index for flood risk monitoring. Int J Climate 22:1365–1376
Shiau JT (2006) Fitting drought duration and severity with two dimensional copulas. Water Resour Manag 20:795–815
Tabrizi AA, Khalili D, Kamgar-Haghighi AA, Zand-Parsa Sh (2010) Utilization of time-based meteorological droughts to investigate occurrence of streamflow droughts. Water Resour Manag 24:4287–4306
Thom HCS (1958) A note on the gamma distribution. Mon Weather Rev 86:117–122
Tsakiris G, Vangelis H (2004) Towards a drought watch system based on spatial SPI. Water Resour Manag 18(1):1–12
Tsakiris G, Pangalou D, Vangelis H (2007) Regional drought assessment based on the Reconnaissance Drought Index (RDI). Water Resour Manag 21(5):821–833
van Rooy MP (1965) A rainfall anomaly index independent of time and space. Notos 14:43–48
Vangelis H, Spiliotis M, Tsakiris G (2011) Drought severity assessment based on bivariate probability analysis. Water Resour Manag 25:357–371
Vasiliades L, Loukas A, Liberis N (2011) A water balance derived drought index for Pinios river basin, Greece. Water Resour Manag 25:1087–1101
Vicente-Serrano S (2006) Differences in spatial patterns of drought on different time scales: an analysis of the Iberian Peninsula. Water Resour Manag 20:37–60
Wilhite DA, Hayes MJ, Svodoba MD (2000) Drought monitoring and assessment in the U.S. In: Voght JV, Somma F (eds) Drought and drought mitigation in Europe. Kluwer, Dordrecht
Wilks DS (1995) Statistical methods in the atmospheric sciences. Academic, London
Wu H, Hayes MJ, Weiss A, Hu Q (2001) An evaluation of the standardized precipitation index, the China-Z Index and the statistical Z-Score. Int J Climate 21(6):745–758
Zhao G, Hörmann G, Fohrer N, Zhang Z, Zhai J (2010) Streamflow trends and climate variability impacts in Poyang Lake Basin, China. Water Resour Manag 24:689–706
Acknowledgments
The paper is based on the research partially funded by the research programme INTERREG III B – MEDOCC - Measure – 4, Project number 2005-05-4.4-P-105 -“Acronym”– SADMO. The financing was made by 75 % from the European Social Fund and by 25 % from national resources (Greece).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Angelidis, P., Maris, F., Kotsovinos, N. et al. Computation of Drought Index SPI with Alternative Distribution Functions. Water Resour Manage 26, 2453–2473 (2012). https://doi.org/10.1007/s11269-012-0026-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-012-0026-0