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

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 900 R.K. Rai et al. 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.

Efficacy of Nakagami-m Distribution Function for Deriving Unit Hydrograph

“…Parameters of the Nakagami-m function μ and ω were optimized using a real-coded genetic algorithm approach (Rai et al 2008(Rai et al , 2009). Then, IUHs were derived for four watersheds from Haktanir and Sezen (1990), three watersheds from Bhunya et al (2004) and two watersheds from Bhunya et al (2003).…”

“…1. Figure 1 also includes the observed UH as well as the derived UH using various distribution functions (Rai et al 2009), such as gamma (GM), Beta, normal (NL), log-normal (LN), Weibull (WB), logistic (LG), generalized logistic (GLG), and Pearson type-3 (PT 3). Besides the visual comparison of results, the performance of the Nakagami-m distribution was also evaluated using the following statistical measures.…”

“…The shape of a probability density function (PDF) is similar to the conventional IUH. Therefore, many attempts have been made to use PDFs of different distributions for the derivation of UH (Gray 1961;Croley 1980;Haktanir and Sezen 1990;Singh 2000;Yue et al 2002;Bhunya et al 2003Bhunya et al , 2004Nadarajah 2007;Rai et al 2008Rai et al , 2009.…”

Three unit hydrographs based on the beta distribution function: a novel approach

“…Bhunya et al (2008) compared the performance of Weibull and gamma pdfs as synthetic UHs for deriving floods and compared their results with the work of Rosso (1984). Finally, Rai et al (2008Rai et al ( , 2009aRai et al ( , 2009b) presented a series of papers in which they applied the Nakagami-m, gamma, beta, normal, lognormal, Weibull, logistic, generalized logistic and Pearson Type 3 probability density functions as UHs. As apparent from the above, the use of pdfs as UHs has been very widespread and any probability density function developed from the nil value of the variable "time" also represents a unit impulse and/or pulse response of a catchment.…”

Meta-Heuristic Algorithms for Hydrologic Frequency Analysis

“…Recently, Rai et al (2009) employed the GA to derive the unit hydrograph (UH). They used nine distributions such as Beta, Exponential, Gamma, Normal, Lognormal, Weibull, Logistic, Generalized logistic and Pearson type 3 for the determination of UH.…”