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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/587291
- author
- Bhunya, P K
; Berndtsson, Ronny
LU
; Singh, P K
and Hubert, P
- organization
- publishing date
- 2008
- 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 (AGU)
- 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
- 2016-04-01 13:18:17
- date last changed
- 2023-08-17 16:33:14
@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}},
keywords = {{Horton ratios; synthetic unit hydrograph; probability distributions}},
language = {{eng}},
number = {{4}},
publisher = {{American Geophysical Union (AGU)}},
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}},
doi = {{10.1029/2007WR006031}},
volume = {{44}},
year = {{2008}},
}