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Comparison between Weibull and gamma distributions to derive synthetic unit hydrograph using Horton ratios
Author(s) -
Bhunya P. K.,
Berndtsson R.,
Singh P. K.,
Hubert P.
Publication year - 2008
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2007wr006031
Subject(s) - hydrograph , weibull distribution , shape parameter , scale parameter , scale (ratio) , mathematics , gamma distribution , sensitivity (control systems) , statistics , hydrology (agriculture) , geology , drainage basin , physics , geotechnical engineering , engineering , quantum mechanics , electronic engineering , geography , cartography
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.