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PROBABILITY THEORY IN HYDROLOGY

PROBABILITY THEORY IN HYDROLOGY. Authors: Phd. Zekirija Idrizi , State university of Tetova, Macedonia Kujtim Zena , hidro.eng. Ministry of spatial planing, Prishtina, Kosova Phd. Isak Idrizi , civ.eng, postgratuate student in IEEES – Skopje, Macedonia. PROBABILITY THEORY IN HYDOLOGY.

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PROBABILITY THEORY IN HYDROLOGY

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  1. PROBABILITY THEORY IN HYDROLOGY • Authors: • Phd. Zekirija Idrizi, State university of Tetova, Macedonia • Kujtim Zena, hidro.eng. Ministry of spatial planing, Prishtina, Kosova • Phd. Isak Idrizi, civ.eng, postgratuate student in IEEES – Skopje, Macedonia

  2. PROBABILITY THEORY IN HYDOLOGY • Origin of probability and reliability theory • Application of probability theory in engineering • Probability theory and hidrology

  3. SITNICA WATERSHED • Central part of Kosova region • General river characteristics • Watershed size = 2816km2 • Longitudinal distance = 92,3km • Longitudinal slope = 0,054% (Valley river) • Highest altitude = 1750m • Lowest altitude = 520m • Additional parameters influencing the probability outcome of the river discharge • Climatic characteristic • Geologic characteristic • Hydrologic characteristic

  4. Hydrological analysis

  5. Probability parameters • Grouping parameters • Mean value X • Median, Me • Mode, Mo • Spreading parameters • Amplitude • Dispersion – Variance • Standard deviation • Coeficient of variation • Shape parameters • Asymmetric coefficient Cs • Ekscess Ek

  6. Graphical representation of density curve – Probability mass function

  7. Graphical representation of density curve – Probability mass function

  8. Graphical representation of density curve – Probability distribution function

  9. From frequency of occurrence to mean return value

  10. Mathematical distribution functions • Normal distribution functions • Gauss distriution • Log-normal distribution functions • Exponential distribution functions • Gumbel distribution (Two parametric) • Gamma distribution functions • Kick and Menkely • Raileigh • Weibull • Pirson III

  11. Mathematical distribution functions

  12. Probability density function

  13. Probability distribution function

  14. MAXIMUM DISCHAREGE PREDICTIONS

  15. CONCLUSION • References • Shehu B., Karanxha K. 2003: Hidrologjia Inxhinierike 1, Tiranë • Idrizi Z. 2002: Rregullimi i lumenjve, Prishtinë • Zena K. (2005):Rregullimi i lumenjve dhe rrugët lundruese – Punim diplome, Prishtinë • Zena K. (2005):Hidraulika e rrjedhjeve të ngurta në shtretërit e hapur – International symposium in Prishtina • Vukmiroviç V. 1990: Analiza verovatnoçe pojave hodroloshkih velicina,Beograd • Black P. 1996: Watershed Hydrology, USA • Jansen P., van Bendegom L., van den Berg L., de Vries M., Zanen A. 1979: Principles of river engineering, London, San Francisko, Melbourne • Jevxheviq V: 1977: Verovatnoça i statistika u hidrologiji, Sarajevo • Jovanoviç S. 1987: Primena metode matematiçka statistike u hidrologiji, Beograd

  16. To err is human, To forgive divine, but to include errors in your design, it is statistical LESLIE KISH (1910-2000)

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