Fitting a Gamma Distribution Over a Synthetic Unit Hydrograph¹

Abstract

Several methods for synthetic unit hydrographs are available in the literature. Most of these methods involve the hand fitting of a curve over a set of a few hydrograph points, which can sometimes be a subjective task. Besides, the user often finds it difficult or simply neglects to adjust the generated unit graph to a runoff volume of one unit (inch, cm, or mm). It is the purpose of this paper to present to the design hydrologist a simple method to fit a smooth gamma distribution over a single point specified by the unit hydrograph peak and the time to peak with a guaranteed unit depth of runoff.

Synthetic Unit Hydrograph Methods: A Critical Review

“…Use of probability distribution functions as SUH has a long history [18][19][20][21][22]. More recently, the potential of four popular pdfs, i.e.…”

“…However, the empirical relationships (Eqs. [19][20][21][22] are watershed size specific, and should be used with in the area limits for which these are developed [1,12]. .…”

“…Due to similarity in the shape of the statistical distributions and a conventional unit hydrograph, several attempts have been made in the past to use their probability distribution function (pdfs) for derivation of the SUH [17][18][19][20][21][22]. Based on the concept of n linear reservoirs in series, Nash and Dooge [23,24] independently developed the general equation of the IUH in the form of two-parameter gamma distribution function (2PGDF).…”

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.…”

“…In this context, many studies have been completed relating UH or instantaneous unit hydrograph (IUH) parameters to their basin parameters to synthesize a UH for an ungauged basin, e.g. Bernard (1935), Snyder (1938), Taylor and Schwarz (1952), Gray (1961), Hedman (1970), Murphey et al (1977), Boyd et al (1979), Rodríguez-Iturbe and , Croley (1980), Gupta et al (1980), Aron and White (1982), Rosso (1984), , Singh (1988), Bras and Rodriguez-Iturbe (1989), Haan et al (1994), Usul and Tezcan (1995), Yen and Lee (1997), Bhadra et al (2008) and Bhunya et al (2009). Sherman (1932) was the first to see the possibilities of extending the UH theory he had developed.…”