Theoretical and Applied Climatology

, Volume 136, Issue 1–2, pp 145–156 | Cite as

On precipitation monitoring with theoretical statistical distributions

  • Ksenija CindrićEmail author
  • Josip Juras
  • Zoran Pasarić
Original Paper


A common practice in meteorological drought monitoring is to transform the observed precipitation amounts to the standardised precipitation index (SPI). Though the gamma distribution is usually employed for this purpose, some other distribution may be used, particularly in regions where zero precipitation amounts are recorded frequently. In this study, two distributions are considered alongside with the gamma distribution: the compound Poisson exponential distribution (CPE) and the square root normal distribution (SRN). They are fitted to monthly precipitation amounts measured at 24 stations in Croatia in the 55-year-long period (1961–2015). At five stations, long-term series (1901–2015) are available and they have been used for a more detailed investigation. The accommodation of the theoretical distributions to empirical ones is tested by comparison of the corresponding empirical and theoretical ratios of the skewness and the coefficient of variation. Furthermore, following the common approach to precipitation monitoring (CLIMAT reports), the comparison of the empirical and theoretical quintiles in the two periods (1961–1990 and 1991–2015) is examined. The results from the present study reveal that it would be more appropriate to implement theoretical distributions in such climate reports, since they provide better evaluation for monitoring purposes than the current empirical distribution. Nevertheless, deciding on an optimal theoretical distribution for different climate regimes and for different time periods is not easy to accomplish. With regard to Croatian stations (covering different climate regimes), the CPE or SRN distribution could also be the right choice in the climatological practice, in addition to the gamma distribution.



Two anonymous referees are gratefully acknowledged for their constructive suggestions and comments.

Funding information

This paper has been supported in part by the Croatian Science Foundation under the 2831 (CARE) project and it is a contribution to the Hymex programme.


  1. Alexandersson H (1985) A simple stochastic model of the precipitation process. J Clim Appl Meteorol 24(12):1285–1295CrossRefGoogle Scholar
  2. Brewer MJ, Heim RR (2011) International drought workshop series. Bull Am Meteorol Soc 92(7):29–31CrossRefGoogle Scholar
  3. Cindrić K, Telišman-Prtenjak M, Herceg-Bulić I, Mihajlović D, Pasarić Z (2015) Analysis of the extraordinary 2011/2012 drought in Croatia. Theor Appl Climatol 123:503–522. CrossRefGoogle Scholar
  4. Feller W (1968) An introduction to probability theory and its application. Wiley & Sons, New YorkGoogle Scholar
  5. Fu G, Viney NR, Charles SP (2010) Evaluation of various root transformations of daily precipitation amounts fitted with a normal distribution for Australia. Theor Appl Climatol 99:229–238CrossRefGoogle Scholar
  6. Gajić-Čapka M, Cindrić K, Mihajlović D (2008) Oborina/precipitation. In: Zaninović K (ed) Klimatski atlas Hrvatske/climate atlas of Croatia 1961–1990, 1971–2000. Meteorological and Hydrological Service of Croatia (DHMZ), Zagreb, pp 43–60Google Scholar
  7. Gajić-Čapka M, Cindrić K, Pasarić Z (2014) Trends in precipitation indices in Croatia, 1961–2010. Theor Appl Climatol 121:167–177. CrossRefGoogle Scholar
  8. Guttman N (1999) Accepting the standardized precipitation index: a calculation algorithm. J Am Water Resour Assoc 35:311–322CrossRefGoogle Scholar
  9. Hayes MJ, Svoboda MD, Wall N, Widhalm M (2011) The Lincoln declaration on drought indices: universal meteorological drought index recommended. Bull Am Meteorol Soc 92(4):485–488CrossRefGoogle Scholar
  10. Juras J (1994) Some common features of probability distributions for precipitation. Theor Appl Climatol 49:69–76CrossRefGoogle Scholar
  11. Juras J, Cindrić K (2009) Analysis of precipitation quantities within different time intervals. Croatian Waters 69/70:197–352 (in Croatian)Google Scholar
  12. Livada I, Assimakopoulos VD (2007) Spatial and temporal analysis of drought in Greece using the standardized precipitation index (SPI). Theor Appl Climatol 89:143–153CrossRefGoogle Scholar
  13. McKee TB, Doeksen NJ, Kleist J (1993) The relationship of drought frequency and duration on time scales. In: Proceedings of the 8th Conference of Applied Climatology. American Meteorology Society, Anaheim, Boston, pp 179–184Google Scholar
  14. Mihajlović D (2006) Monitoring the 2003–2004 meteorological drought over Pannonian part of Croatia. Int J Climatol 26(15):2213–2225. CrossRefGoogle Scholar
  15. Öztürk A (1981) On the study of a probability distribution for precipitation totals. J Appl Meteorol 20:1499–1505CrossRefGoogle Scholar
  16. Ropelewski CF, Jelickee JB (1983) Estimating the significance of seasonal precipitation amounts using approximations of the inverse gamma function over an extended range. Preprint Eight Conf Probab Statist in Atmos Scien Hot Srings, Arkansas, AMS, pp 125–129Google Scholar
  17. Ropelewski CF, Janowiak JE, Halpert MS (1985) The analysis and display of real time surface climate data. Mon Weather Rev 13:1101–1106CrossRefGoogle Scholar
  18. Vicente-Serrano SM, González-Hidalgo JC, de Luis M, Raventós J (2004) Drought patterns in the Mediterranean area: the Valencia region (eastern Spain). Clim Res 26:5–15CrossRefGoogle Scholar
  19. Wilks DS (1990) Maximum likelihood estimation for the gamma distribution using data containing zeros. J Clim 3:1495–1501CrossRefGoogle Scholar
  20. Wilks DS (2011) Statistical methods in the atmospheric sciences. Elsevier Inc., OxfordGoogle Scholar
  21. WMO (2007) The role of climatological normals in a changing climate. WCDMP-No. 61, WMO-TD No. 1377, GenevaGoogle Scholar
  22. WMO (2009) Handbook on CLIMAT and CLIMAT TEMP reporting, Geneva. WMO/TD-No. 1188Google Scholar
  23. WMO (2012) In: Svoboda M, Hayes M, Wood D (eds) Standardized precipitation index user guide. WMO-No. 1090, GenevaGoogle Scholar
  24. Zahradníček P, Rasol D, Cindrić K, Štěpánek P (2014) Homogenisation of monthly precipitation series in Croatia. Int J Climatol 34:3671–3682. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Meteorological and Hydrological ServiceZagrebCroatia
  2. 2.Department of Geophysics, Faculty of ScienceUniversity of ZagrebZagrebCroatia

Personalised recommendations