Adequacy of two-parameter beta distribution for deriving the unit hydrograph

K., R.; Sarkar, Shibayan; Gundekar, H. G.

doi:10.2166/nh.2008.038

Cited by 9 publications

(7 citation statements)

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“…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).…”

Section: Case Imentioning

confidence: 99%

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Efficacy of Nakagami-m Distribution Function for Deriving Unit Hydrograph

Sarkar

Upadhyay

et al. 2009

Water Resour Manage

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This paper applies the Nakagami-m distribution for the derivation of unit hydrograph (UH). The applicability of this distribution was verified using the data from 13 watersheds and results were compared with other distributions, viz., Gamma (GM), Beta, normal (NL), log-normal (LN), Weibull (WB), logistic (LG), generalized logistic (GLG) and Pearson type 3 (PT3). Based on visual comparison as well as statistical measures, such as root mean square error (RMSE), coefficient of efficiency (CE), mean absolute percentage error (MAPE), and application efficiency (η dist. ), it was found that the Nakagami-m distribution yielded satisfactory UHs and direct runoff hydrographs for watersheds of various sizes.

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Section: Case Imentioning

confidence: 99%

“…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.…”

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confidence: 99%

Efficacy of Nakagami-m Distribution Function for Deriving Unit Hydrograph

Sarkar

Upadhyay

et al. 2009

Water Resour Manage

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Goñi

Gimena

López

2013

Hydrological Sciences Journal

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Three instantaneous unit hydrographs (IUH) are represented by three probability distribution functions deduced from an expression of the beta function, which depends on three parameters. The three IUHs presented, dependent on two parameters, were obtained by particularizing one of three parameters of the proposed beta function for three different values. In order to give a physical sense to the two parameters of the three presented hydrographs, these have been associated with the centroid and the time to peak. One of these three functions coincides with the gamma function. The three functions were applied for 32 direct runoff events in the Aixola (4.70 km 2 ) and Oiartzun (56.07 km 2 ) catchments, in northern Spain. The simulations performed with the three functions gave very satisfactory results. It was also observed that the two catchments had a significantly different IUH with regard to its shape.Key words instantaneous unit hydrographs; beta functions; direct runoff modelling Une approche novatrice concernant trois hydrogrammes unitaires basés sur la fonction de distribution bêta Résumé Nous avons représenté trois hydrogrammes unitaires instantanés (HUI) par des fonctions de distribution de probabilité issues de la fonction bêta, qui dépend de trois paramètres. Ces trois HUI dépendent de deux paramètres, l'un des trois paramètres de la fonction bêta proposée ayant été fixé. Afin de donner un sens physique aux deux paramètres des trois hydrogrammes, ils ont été associés au centroïde et au temps de montée des hydrogrammes. L'une des trois fonctions coïncide avec la fonction gamma. Les trois fonctions ont été appliquées à 32 épisodes de ruissellement dans les bassins de l'Aixola (4,70 km 2 ) et du Oiartzun (56,07 km 2 ), situés au Nord de l'Espagne. Les simulations effectuées avec ces trois fonctions ont donné des résultats très satisfaisants. Nous avons également observé que les deux bassins versants ont des HUI de formes significativement différentes.

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“…(Gray, 1961;Sokolov et al, 1976;Ciepielowski, 1987;Haktanir and Sezen, 1990;Yue et al, 2002;Bhunya et al, 2004Bhunya et al, , 2007. Mostly, Gamma and Beta PDFs have been used to represent the shape of UHs (Koutsoyiannis and Xanthopoulos, 1989;Haktanir and Sezen, 1990;Haan et al, 1994;Bhunya et al, 2003Bhunya et al, , 2004Rai et al, 2008). The researchers have also discussed the flexibility of the PDFs to produce different shapes by changing their parameter values (Bhunya et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…The major criterion for selection of the PDFs is the resemblance of the shape of the PDF to the shape of the observed flood hydrograph. However, to reduce the volume of the manuscript only four widely used PDFs such as: Beta, Gamma, Weibull and Lognormal were selected for the study (Koutsoyiannis and Xanthopoulos, 1989;Bhunya et al, 2004;Nadarajah, 2007;Rai et al, 2008). The portions of the continuous stream flow hydrographs having the highest peak were selected from 22 years of stream flow hydrographs at a site of the Brahmani River in the state of Orissa, India.…”

Section: Introductionmentioning

confidence: 99%

Development of design flood hydrographs using probability density functions

Pramanik

Panda

Sen

2009

Hydrological Processes

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Abstract:Probability density functions (PDFs) are used to fit the shape of hydrographs and have been popularly used for the development of synthetic unit hydrographs by many hydrologists. Nevertheless, modelling the shapes of continuous stream flow hydrographs, which are probabilistic in nature, is rare. In the present study, a novel approach was followed to model the shape of stream flow hydrographs using PDF and subsequently to develop design flood hydrographs for various return periods. Four continuous PDFs, namely, two parameter Beta, Weibull, Gamma and Lognormal, were employed to fit the shape of the hydrographs of 22 years at a site of Brahmani River in eastern India. The shapes of the observed and PDF fitted hydrographs were compared and root mean square errors, error of peak discharge (EQ P ) and error of time to peak (ET P ) were computed. The best-fitted shape and scale parameters of all PDFs were subjected to frequency analysis and the quartiles corresponding to 20-, 50-, 100-and 200-year were estimated. The estimated parameters of each return period were used to develop the flood hydrographs for 20-, 50-, 100-and 200-year return periods. The peak discharges of the developed design flood hydrographs were compared with the design discharges estimated from the frequency analysis of 22 years of annual peak discharges at that site. Lognormalproduced peak discharge was very close to the estimated design discharge in case of 20-year flood hydrograph. On the other hand, peak discharge obtained using the Weibull PDF had close agreement with the estimated design discharge obtained from frequency analysis in case of 50-, 100-and 200-year return periods. The ranking of the PDFs based on estimation of peak of design flood hydrograph for 50-, 100-and 200-year return periods was found to have the following order: Weibull > Beta > Lognormal > Gamma.

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Adequacy of two-parameter beta distribution for deriving the unit hydrograph

Cited by 9 publications

References 5 publications

Efficacy of Nakagami-m Distribution Function for Deriving Unit Hydrograph

Efficacy of Nakagami-m Distribution Function for Deriving Unit Hydrograph

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

Development of design flood hydrographs using probability density functions

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