Suitability of Gamma, Chisquare, Weibull, and Beta distributions as synthetic unit hydrographs
(2007) In Journal of Hydrology 334(12). p.2838 Abstract
 Most available methods for synthetic unit hydrograph (SUH) derivation involve manual, subjective fitting of a hydrograph through a few data points. Because of this tedious procedure, the generated unit hydrograph is often left unadjusted for unit runoff volume. During recent decades, use of probability distribution functions (pdfs) in developing SUH has received much attention because of its similarity with unit hydrograph properties. In this study, the potential of four popular pdfs, i.e., twoparameter Gamma, threeparameter Beta, twoparameter Weibull, and oneparameter Chisquare distribution to derive SUH have been explored. Simple formulae are derived using analytical and numerical schemes to compute the distribution parameters, and... (More)
 Most available methods for synthetic unit hydrograph (SUH) derivation involve manual, subjective fitting of a hydrograph through a few data points. Because of this tedious procedure, the generated unit hydrograph is often left unadjusted for unit runoff volume. During recent decades, use of probability distribution functions (pdfs) in developing SUH has received much attention because of its similarity with unit hydrograph properties. In this study, the potential of four popular pdfs, i.e., twoparameter Gamma, threeparameter Beta, twoparameter Weibull, and oneparameter Chisquare distribution to derive SUH have been explored. Simple formulae are derived using analytical and numerical schemes to compute the distribution parameters, and their validity is checked with simulation of field data. The Gamma and Chisquare distributions behave analogously, and the Beta distribution approximates a Gamma distribution in a limiting case. Application to field data shows that the Beta and Weibull distributions are more flexible in hydrograph prediction than the Gamma, Chisquare, Gray [Gray, D.M., 1961. Synthetic hydrographs for small drainage areas. In: Proceedings of the ASCE, 87, HY4, pp. 3354], SCS [SCS, 1957. Use of Storm and Watershed Characteristics in Synthetic Hydrograph Analysis and Application: V. Mockus. US Dept. of Agriculture, Soil Conservation Service, Washington, DC], and Snyder [Synder, F.F., 1938. Synthetic unit hydrographs. Trans. Am. Geophys. Union 19, 447454] methods. A sensitivity analysis of pdf parameters on peak flow estimates of an UH indicated that Gamma and Chisquare distributions overestimate the peak flow value, for any overestimation in its parameter estimates. However, for the Beta and Weibull distributions a reverse trend was observed. Both were found to behave similarly at higher @a (ratio of time to base and time to peak of UH) values. Further, an analogous triangular hydrograph approach was used to express the mean and variance of the UH in terms of time base and time to peak of the UH. This enabled a simple parameter estimation equation involving only time base and time to peak of the UH. Although the validity of this equation could not be evaluated with a proper amount of data, the results give an indication of the relationship between pdf and statistical properties of the UH to be further elaborated in future research. (Less)
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http://lup.lub.lu.se/record/587262
 author
 Bhunya, P.K.; Berndtsson, Ronny ^{LU} ; Ojha, C.S.P. and Mishra, S.K.
 organization
 publishing date
 2007
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Unit hydrograph, Probability density function (pdf), Ungauged, Time to peak, Peak discharge
 in
 Journal of Hydrology
 volume
 334
 issue
 12
 pages
 28  38
 publisher
 Elsevier
 external identifiers

 wos:000244401000003
 scopus:33846404104
 ISSN
 00221694
 DOI
 10.1016/j.jhydrol.2006.09.022
 language
 English
 LU publication?
 yes
 id
 98502f58f272483e8503fa786a32d844 (old id 587262)
 date added to LUP
 20071201 12:15:17
 date last changed
 20180617 04:51:43
@article{98502f58f272483e8503fa786a32d844, abstract = {Most available methods for synthetic unit hydrograph (SUH) derivation involve manual, subjective fitting of a hydrograph through a few data points. Because of this tedious procedure, the generated unit hydrograph is often left unadjusted for unit runoff volume. During recent decades, use of probability distribution functions (pdfs) in developing SUH has received much attention because of its similarity with unit hydrograph properties. In this study, the potential of four popular pdfs, i.e., twoparameter Gamma, threeparameter Beta, twoparameter Weibull, and oneparameter Chisquare distribution to derive SUH have been explored. Simple formulae are derived using analytical and numerical schemes to compute the distribution parameters, and their validity is checked with simulation of field data. The Gamma and Chisquare distributions behave analogously, and the Beta distribution approximates a Gamma distribution in a limiting case. Application to field data shows that the Beta and Weibull distributions are more flexible in hydrograph prediction than the Gamma, Chisquare, Gray [Gray, D.M., 1961. Synthetic hydrographs for small drainage areas. In: Proceedings of the ASCE, 87, HY4, pp. 3354], SCS [SCS, 1957. Use of Storm and Watershed Characteristics in Synthetic Hydrograph Analysis and Application: V. Mockus. US Dept. of Agriculture, Soil Conservation Service, Washington, DC], and Snyder [Synder, F.F., 1938. Synthetic unit hydrographs. Trans. Am. Geophys. Union 19, 447454] methods. A sensitivity analysis of pdf parameters on peak flow estimates of an UH indicated that Gamma and Chisquare distributions overestimate the peak flow value, for any overestimation in its parameter estimates. However, for the Beta and Weibull distributions a reverse trend was observed. Both were found to behave similarly at higher @a (ratio of time to base and time to peak of UH) values. Further, an analogous triangular hydrograph approach was used to express the mean and variance of the UH in terms of time base and time to peak of the UH. This enabled a simple parameter estimation equation involving only time base and time to peak of the UH. Although the validity of this equation could not be evaluated with a proper amount of data, the results give an indication of the relationship between pdf and statistical properties of the UH to be further elaborated in future research.}, author = {Bhunya, P.K. and Berndtsson, Ronny and Ojha, C.S.P. and Mishra, S.K.}, issn = {00221694}, keyword = {Unit hydrograph,Probability density function (pdf),Ungauged,Time to peak,Peak discharge}, language = {eng}, number = {12}, pages = {2838}, publisher = {Elsevier}, series = {Journal of Hydrology}, title = {Suitability of Gamma, Chisquare, Weibull, and Beta distributions as synthetic unit hydrographs}, url = {http://dx.doi.org/10.1016/j.jhydrol.2006.09.022}, volume = {334}, year = {2007}, }