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Comparison between Weibull and Gamma distributions to derive synthetic unit hydrograph using Horton order ratios

Bhunya, P K; Berndtsson, Ronny LU ; Singh, P K and Hubert, P (2008) In Water Resources Research 44(4).
Abstract
The two-parameter Weibull distribution (2PWD), similar to an instantaneous unit hydrograph (IUH), is parameterized in terms of Horton catchment ratios on the basis of a geomorphologic model of catchment response. For this the shape and scale parameters of the Weibull distribution are expressed analytically in terms of Horton's catchment ratios. The two parameters of the IUH derived using Nash's model, which is a two-parameter gamma distribution (2PGD), are also expressed analytically in terms of Horton ratios. The performance of the proposed methods is tested for describing a synthetic unit hydrograph (SUH) under limited data conditions. A comparison is made with the unit hydrographs derived from the event data of two real catchments, and... (More)
The two-parameter Weibull distribution (2PWD), similar to an instantaneous unit hydrograph (IUH), is parameterized in terms of Horton catchment ratios on the basis of a geomorphologic model of catchment response. For this the shape and scale parameters of the Weibull distribution are expressed analytically in terms of Horton's catchment ratios. The two parameters of the IUH derived using Nash's model, which is a two-parameter gamma distribution (2PGD), are also expressed analytically in terms of Horton ratios. The performance of the proposed methods is tested for describing a synthetic unit hydrograph (SUH) under limited data conditions. A comparison is made with the unit hydrographs derived from the event data of two real catchments, and with the existing geomorphological based 2PGD for developing SUH given by Rosso (1984). The sensitivity analysis of the 2PWD to the nondimensional parameter β of the UH (a product of peak discharge and time to peak) shows β to be more sensitive to the shape parameter a than the scale parameter b. Further examination to find any similarity between the behavior of 2PWD and 2PGD showed that a in 2PWD corresponds to the shape parameter n in the 2PGD, and b behaves similar to the scale parameter k in the 2PGD. Finally, practical applicability of the proposed approach to ungauged catchments is tested using field data. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Horton ratios, synthetic unit hydrograph, probability distributions
in
Water Resources Research
volume
44
issue
4
publisher
American Geophysical Union
external identifiers
  • wos:000255462800004
  • scopus:44349168806
ISSN
0043-1397
DOI
10.1029/2007WR006031
language
English
LU publication?
yes
id
e29e4410-2ea5-4a54-8fe3-7a01dff5657a (old id 587291)
date added to LUP
2007-12-12 12:41:44
date last changed
2017-07-30 04:00:52
@article{e29e4410-2ea5-4a54-8fe3-7a01dff5657a,
  abstract     = {The two-parameter Weibull distribution (2PWD), similar to an instantaneous unit hydrograph (IUH), is parameterized in terms of Horton catchment ratios on the basis of a geomorphologic model of catchment response. For this the shape and scale parameters of the Weibull distribution are expressed analytically in terms of Horton's catchment ratios. The two parameters of the IUH derived using Nash's model, which is a two-parameter gamma distribution (2PGD), are also expressed analytically in terms of Horton ratios. The performance of the proposed methods is tested for describing a synthetic unit hydrograph (SUH) under limited data conditions. A comparison is made with the unit hydrographs derived from the event data of two real catchments, and with the existing geomorphological based 2PGD for developing SUH given by Rosso (1984). The sensitivity analysis of the 2PWD to the nondimensional parameter β of the UH (a product of peak discharge and time to peak) shows β to be more sensitive to the shape parameter a than the scale parameter b. Further examination to find any similarity between the behavior of 2PWD and 2PGD showed that a in 2PWD corresponds to the shape parameter n in the 2PGD, and b behaves similar to the scale parameter k in the 2PGD. Finally, practical applicability of the proposed approach to ungauged catchments is tested using field data.},
  author       = {Bhunya, P K and Berndtsson, Ronny and Singh, P K and Hubert, P},
  issn         = {0043-1397},
  keyword      = {Horton ratios,synthetic unit hydrograph,probability distributions},
  language     = {eng},
  number       = {4},
  publisher    = {American Geophysical Union},
  series       = {Water Resources Research},
  title        = {Comparison between Weibull and Gamma distributions to derive synthetic unit hydrograph using Horton order ratios},
  url          = {http://dx.doi.org/10.1029/2007WR006031},
  volume       = {44},
  year         = {2008},
}