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

Abstract

[1] 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 b of the UH (a product of peak discharge and time to peak) shows b 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.

Synthetic Unit Hydrograph Methods: A Critical Review

“…Bhunya et al [36] explored the potential of two pdfs, two-parameter Weibull distribution (2PWD) and twoparameter Gamma distribution (2PGD) to derive SUH. Some of the important conclusions drawn from the study are as under.…”

A review of the synthetic unit hydrograph: from the empirical UH to advanced geomorphological methods

“…Their simplicity and ease of development can characterize these SUHs as they require less data and yield a smooth and single-valued shape corresponding to one unit runoff volume, which is essential for UH derivation. The SUH methods of Gray (1961), Croley (1980), Aron and White (1982), Singh and Chowdhury (1985), McCuen (1989), Haktanir and Sezen (1990), Singh (2000), Bhunya et al (2003Bhunya et al ( , 2008Bhunya et al ( , 2009 are but a few of them. Singh (1987) explored the applicability of the Weibull distribution derived from the Principal of Maximum Entropy (POME) in hydrological modelling.…”

“…The model is frequently used for determining the direct runoff hydrograph, e.g. , Boufadel (1998), Singh (2000), Jeng and Coon (2003), Agirre et al (2005) and Bhunya et al (2008). The Nash model has also been applied successfully in sedimentation and environmental engineering by Kumar and Rastogi (1987), Sharma et al (1992) and Sharma and Murthy (1996).…”

“…The IUH (equation (19)) is used to derive the resultant flood hydrograph for a given input rainfall. It is one of the most popular and widely accepted approaches to approximating the real system (Bhunya et al 2008). The model is frequently used for determining the direct runoff hydrograph, e.g.…”

“…Following Rosso's philosophy (1984), a very interesting effort was made by Bhunya et al (2008) to parameterize 2PWD and 2PGD using the GIUH approach, and simplified analytical relationships for parameter estimation in terms of Horton's ratios were developed. Discussions about the suitability and adequacy of the geomorphological descriptions for modelling purposes can be found in Gupta and Waymire (1983), Beven et al (1988) and Shamseldin and Nash (1998).…”