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Evaluation of the Adequacy of Statistical Distribution Functions for Deriving Unit Hydrograph

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  • R. Rai
  • S. Sarkar
  • V. Singh

Abstract

The unit hydrograph (UH) is one of the commonly employed techniques for the determination of flood hydrographs. Since the UH satisfies all the properties of a probability distribution function (PDF), it seems logical that PDFs can be employed for deriving the UH. In practice, the gamma distribution function has been commonly employed to derive the UH. In this paper, Beta (Beta), Exponential (EXP), Gamma (GM), Normal, Lognormal (LN), Weibull (WB), Logistic (LG), Generalized logistic (GLG) and Pearson Type 3 (PT 3) distribution functions were employed for the derivation of UH. Parameters of these distribution functions were estimated using the real coded genetic algorithm optimization technique. These distributions were tested on the 13 watersheds of different characteristics and it was observed that except for the EXP distribution function, most other distribution functions produced UHs which were in satisfactory agreement with observed UHs. However, three-parameter distributions GLG, PT 3 and two parameter LG were not capable of reproducing UHs for large watersheds having drainage areas of 3,360 and 4,300 km 2 . For such large watersheds WB reproduced UHs satisfactorily. Combining the overall performance of the distributions over 13 watersheds, the order of ranking the suitability of distributions were as: GM > PT 3 > Beta ≥ GLG ≥ LN > WB. Copyright Springer Science+Business Media B.V. 2009

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  • R. Rai & S. Sarkar & V. Singh, 2009. "Evaluation of the Adequacy of Statistical Distribution Functions for Deriving Unit Hydrograph," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(5), pages 899-929, March.
    • Handle: RePEc:spr:waterr:v:23:y:2009:i:5:p:899-929
    DOI: 10.1007/s11269-008-9306-0
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    References listed on IDEAS

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    1. R. Rai & M. Jain & S. Mishra & C. Ojha & V. Singh, 2007. "Another Look at Z-transform Technique for Deriving Unit Impulse Response Function," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(11), pages 1829-1848, November.
    2. Kuo, Sheng-Feng & Merkley, Gary P. & Liu, Chen-Wuing, 2000. "Decision support for irrigation project planning using a genetic algorithm," Agricultural Water Management, Elsevier, vol. 45(3), pages 243-266, August.
    3. Dooge, James C. I., 1973. "Linear Theory of Hydrologic Systems," Technical Bulletins 160041, United States Department of Agriculture, Economic Research Service.
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    5. R. Rai & S. Sarkar & Alka Upadhyay & V. Singh, 2010. "Efficacy of Nakagami-m Distribution Function for Deriving Unit Hydrograph," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(3), pages 563-575, February.

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