Skip to main content
SpringerLink
Log in

Stochastic analyses of maximum daily rainfall series recorded at two stations across the Mediterranean Sea

  • Original Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

Independence, stationarity, homogeneity, trend, and periodicity tests are applied on 48-year-long complete and 79-year-long incomplete maximum daily rainfall series recorded at Alexandria, Egypt, and on 61-year-long maximum daily rainfall series recorded at Antalya, Turkey, which are located at the southeastern and northeastern shores of the Mediterranean Sea. The results indicate no significant trend and no periodicity in mean, and both series are independent and homogeneous. Linear regression trend test applied to the 10 % highest part of the Alexandria series indicated a significant increasing trend. Next, frequency analysis is applied on each of these series by the probability distributions of Gumbel, general extreme-values, three-parameter log-normal, Pearson-3, log-Pearson-3, log-logistic, generalized Pareto, and Wakeby. The distributions, except for the generalized Pareto and Wakeby, pass the χ 2 and Kolmogorov–Smirnov goodness-of-fit tests at 90 % probability. By visual inspection of the plots of histograms together with the probability density functions, and by the results of the χ 2, Kolmogorov–Smirnov, and probability plot correlation coefficient tests, the general extreme-value distribution whose parameters are computed by the method of probability-weighted moments is deemed to be suitable for these two maximum daily rainfall series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Anderson BT, Hayhoe K, Liang X-Z (2010) Anthropogenic-induced changes in twenty-first century summertime hydroclimatology of the Northeastern U.S. Climate Change 99(3-4):403–423

    Article  Google Scholar 

  • Ball T (1992) An iconoclast’s view of climatic change. Can Water Res J 17(2):151–160

    Article  Google Scholar 

  • Bierkens MFP (2006) Stochastic hydrology (GEO4-4420). Department of Physical Geography, Utrecht University, The Netherlands

    Google Scholar 

  • Bobee B, Rasmussen PF (1995) Recent advances in flood frequency analysis. Rev Geophys, Supp, US Nat Report to Int Union of Geodesy Geophys 1991–1994:1111–1116

    Article  Google Scholar 

  • Burn DH, Mansour R, Zhang K, Whitfield PH (2011) Trends and variability in extreme rainfall events in British Columbia. Can Water Res J 36(1):67–82

    Article  Google Scholar 

  • Chargui S, Slimani M, Cudennec C (2012) Statistical distribution of rainy events characteristics and instantaneous hyetographs generation (Merguellil watershed in central Tunisia). Arabian J Geosciences, in production. doi:10.1007/s12517-011-0440-2

  • Collins MJ (2009) Evidence for changing flood risk in New England since the late 20th century. J Am Water Res Assoc 45(2):279–290

    Article  Google Scholar 

  • Cunnane, C.(1989) Statistical distributions for flood frequency analysis. WMO Operational Hydrology Report No.33. World Meteorological Organization, Geneva, Switzerland.

  • Douglas EM, Fairbank CA (2011) Is precipitation in Northern New England becoming more extreme? Statistical analysis of extreme rainfall in Massachusetts, New Hampshire, and Maine and updated estimates of the 100-year storm. J Hydrologic Eng, ASCE 16(3):203–217

    Article  Google Scholar 

  • Ehsanzade E, El Adlouni S, Bobee B (2010) Frequency analysis incorporating a decision support system for hydroclimatic variables. J Hydrologic Eng, ASCE 15(11):869–881

    Article  Google Scholar 

  • Fujibe F, Yamazaki N, Katsuyama M, Kobayashi K (2005) The increasing trend of intense precipitation in Japan based on four-hourly data for a hundred years. SOLA 1:2005–2012

    Article  Google Scholar 

  • Greenwood JA, Landwehr JM, Matalas NC, Wallis JR (1979) Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form. Water Resources Res 15(5):1049–1054

    Article  Google Scholar 

  • Groisman PY, Knight RW, Easterling DR, Karl TR, Hegerl GC, Razuvaev VN (2005) Trends in intense precipitation in the climate record. J Climate 18:1326–1350

    Article  Google Scholar 

  • Guo Y (2006) Updating rainfall IDF relationships to maintain urban drainage design standards. J Hydrologic Eng, ASCE 11(5):506–509

    Article  Google Scholar 

  • Haktanir T, Horlacher HB (1993) Evaluation of various distributions for flood frequency analysis. Hydrological Sci J 38(1):15–32

    Article  Google Scholar 

  • Haktanir T, Cobaner M, Kisi O (2010) Frequency analyses of annual extreme rainfalls from 5 min to 24 h. Hydrological Processes 24:3574–3588

    Article  Google Scholar 

  • Helsel, D. R., and Hirsch, R. M. (2002) Statistical methods in water resources, techniques of water-resources investigations of the United States, book 4, hydrologic analysis and interpretation, chapter A3, 〈http://water.usgs.gov/pubs/twri/ twri4a3/〉.

  • Hipel KW, McLeod AI (1994) Time series modeling of water resources and environmental systems. Elsevier, The Netherlands

    Google Scholar 

  • Hosking, J.R.M. and Wallis J.R. (1997). Regional frequency analysis—an approach based on L-Moments. Cambridge, Cambridge University Press.

  • IPCC (2007) Climate Change 2007: physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, 2007. [Solomon, S.: Qin, D.; Manning, M.; Chen, Z.; Marquis, M.; Averyt, K.B.; Tignor, M.; Miller, H.D., (Editors)] Cambridge Univ. Press, New York.

  • IPCC (2008) Climate change and water. Technical Paper of the Intergovernmental Panel on Climate Change, [Bates, B.C.; Kundzewicz, Z.W.; Wu, S., Palutikof, J.P. (Editors)]. IPCC Secretariat, Geneva.

  • IPCC (2011) Managing the risks of extreme events and disasters to advance climate change adaptation. A special report of Working Group I and Working Group II of the Intergovernmental Panel on Climate Change [Field, C. B.; Barros, V.; Stocker, T.F.; Qin, D.; Dokken, D.; Ebi, K.L.; Mastrandrea, M. D.; Mach, K. J.; Plattner, G.-K.; Allen, S. K.; Tignor, M. and P. M. Midgley (editors)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA

  • Iqbal MJ, Ali M (2012) A probabilistic approach for estimating return period of extreme annual rainfall in different cities of Punjab. Arabian J Geosciences, in production. doi:10.1007/s12517-012-0548-z

  • Iqbal MJ, Quamar J, Yousufzai MAK (2011) Spectral analysis of local climatic fluctuations. Arabian J Geosciences 4(1–2):291–298

    Article  Google Scholar 

  • Karim MA, Chowdhury JU (1995) A comparison of four distributions used in flood frequency analysis in Bangladesh. Hydrological Sci J 40(1):55–66

    Article  Google Scholar 

  • Kendall MG (1975) Rank Correlation Methods. Griffin, London

    Google Scholar 

  • Kite GW (1977) Frequency and risk analysis in hydrology. Water Resources Publications, Fort Collins, CO

    Google Scholar 

  • Köppen W, Geiger R (1936) Das Geographische System der Klimate. In: Köppen W, Geiger R (eds) Handbuch der Klimatologie. Verlag Gebrüder Bornträger, Berlin

    Google Scholar 

  • Kottegoda NT (1980) Stochastic water resources technology. The MacMillan Press Ltd, Hong Kong

    Google Scholar 

  • Kumar R, Chatterjee C (2005) Regional flood frequency analysis using L-moments for North Brahmatputra Region of India. J Hydrologic Eng, ASCE 10(1):1–7

    Article  Google Scholar 

  • Kundzewicz ZW, Ulbrich U, Brücher T, Graczyk D, Krüger A, Leckebusch G, Menzel L, Pińskwar I, Radziejewski M, Szwed M (2005) Summer floods in Central Europe—climate change track? Nat Hazards 36(1/2):165–189

    Article  Google Scholar 

  • Nandargi S, Dhar ON (2011) Extreme rainfall events over the Himalayas between 1871 and 2007. Hydrological Sci J 56(6):930–945

    Article  Google Scholar 

  • NZCCO (2008) Climate change effects and impacts assessment: a guidance manual for local governments in New Zealan–2nd edition, Climate Change Office of the Ministry for the Environment New Zealand.

  • Onoz B, Bayazit M (2003) The power of statistical tests for trend detection. Turkish J Eng Environ Sci, Tubitak 27:247–251

    Google Scholar 

  • Peel MC, Wang QC, Vogel RM, McMahon TA (2001) The utility of L-moment ratio diagrams for selecting a regional probability distribution. Hydrological Sci J 46(1):147–155

    Article  Google Scholar 

  • Rao AR, Hamed KH (2000) Flood frequency analysis. CRC Press, Washington

    Google Scholar 

  • Rao AR, Azli M, Pae LJ (2011) Identification of trends in Malaysian monthly runoff under the scaling hypothesis. Hydrological Sci J 56(6):917–929

    Article  Google Scholar 

  • Ross SM (2004) Introduction to probability and statistics for engineers and scientists, 3rd edn. Elsevier Academic Press, USA

    Google Scholar 

  • Saf B (2009) Regional flood frequency analysis using L-moments for the Buyuk and Kucuk Menderes River Basins of Turkey. J Hydrologic Eng, ASCE 14(8):783–794

    Article  Google Scholar 

  • Seckin N, Yurtal R, Haktanır T, Doğan A (2010) Comparison of probability weighted moments and maximum likelihood methods used in flood frequency analysis for Ceyhan River Basin. Arabian J Sci Eng 35(1B):49–69

    Google Scholar 

  • Seckin N, Haktanir T, Yurtal R (2011) Flood frequency analysis of Turkey using L-moments method. Hydrological Processes 25:3499–3505

    Article  Google Scholar 

  • Sen Z, Khiyami HA, Al-Harty SG, Al-Ammawi FA, Al-Balkhi AB, Al-Zahrani MI, Al-Hawsawy HM (2012a) Flash flood inundation map preparation for wadis in arid regions. Arabian J Geosciences, in production. doi:10.1007/s12517-012-0614-6, 1-10

  • Sen Z, Al AlSheikh A, Al-Turbak A, Al-Bassam A, Al-Dakheel A (2012b) Climate change impact and runoff harvesting in arid regions. Arabian J Geosciences, in production. doi:10.1007/s12517-011-0354-z, 1-9

  • Subyani AM (2011) Hydrologic behaviour and flood probability for selected arid basins in Makkah Area, western Saudi Arabia. Arabian J Geosciences 4(5–6):817–824

    Article  Google Scholar 

  • Villarini G, Smith JA, Baeck ML, Krajewski WF (2011) Examining flood frequency distributions in the Midwest U.S. J Am Water Res Assoc 47(3):447–463

    Article  Google Scholar 

  • WMO (2009) Guide to hydrological practices, volume II, management of water resources and application of hydrological practices. WMO-No. 168, sixth edition, World Meteorological Organization, P.O. Box 2300, CH-1211, Geneva 2, Switzerland.

  • Yevjevich, V. (1972) Stochastic processes in hydrology. Water Resources Publns, Fort Collins. CO.

  • Yue S, Pilon P, Caradias G (2002) Power of the Mann-Kendall and Spearman’s rho tests for detecting monotonic trends in hydrological series. J Hydrology 259:254–271

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. King Abdulaziz University, Water Research Centre, Jeddah, Saudi Arabia

    Tefaruk Haktanir, Saleh Bajabaa & Milad Masoud

Authors
  1. Tefaruk Haktanir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saleh Bajabaa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Milad Masoud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tefaruk Haktanir.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haktanir, T., Bajabaa, S. & Masoud, M. Stochastic analyses of maximum daily rainfall series recorded at two stations across the Mediterranean Sea. Arab J Geosci 6, 3943–3958 (2013). https://doi.org/10.1007/s12517-012-0652-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12517-012-0652-0

Keywords

Search

Navigation