Two-Parameter Gamma-Based SUH Derivation

Abstract

Abstract-A simple procedure is suggested to compute direct runoff hydrograph (DRH) using an improved two-parameter gamma distribution (2PGD) based synthetic unit hydrograph (SUH) and it is tested on several storm events recorded in 3 different hydrometeorological catchments. When compared, the computed hydrographs were more accurate than those due to popular Gray, SCS, and Snyder methods, because of avoidance of manual, subjective, and tiresome fitting of hydrograph through few data points for their adjustments for unit runoff volume. The improved 2PGD incorporates the available approximate, but accurate, empirical relations for estimation of β and factors governing the shape of the dimensionless unit hydrograph (UH) from the Nash parameter number of reservoirs (n). The SUH peak discharge per unit area per unit effective rainfall (q p ) and time to peak (t p ) have been derived from hydrologic and geomorphologic characteristics of the watershed, which is advantageous for field use. The objective of this paper is to propose a 2PGD-based method, test it on the data of 3 watersheds, and finally carry out a sensitivity analysis for model parameters. Model results during calibration and validation are very promising with average efficiency of each watershed exceeding 92% and 72%, respectively.

Snyder-gamma synthetic unit hydrograph

“…Some of the relevant studies which are included in the References list of this manuscript will be briefly summarized in the following. Commonly, the 2-parameter gamma and the 3-parameter beta distributions are used for this purpose (e.g., Asquith et al 2005;Bhuyan et al 2015;Bhunya et al 2004Bhunya et al , 2011Ghorbani et al 2015;Haktanir and Sezen 1990;Naghibi et al 2018;Patil et al 2012;Roy and Thomas 2016;Singh 2000;Singh et al 2014). Asquith et al (2005) used measured rainfall-runoff data of 1600 storms in 93 watersheds of sizes from 0.8 to 432 km 2 in the State of Texas with the purpose of deriving synthetic unit hydrographs by four different approaches, the 2-parameter gamma distribution being one of them.…”

“…Naghibi et al (2018) studied the goodness of the distributions of 2-parameter gamma, 3-parameter beta, chi-square, and Weibull for synthetic unit hydrographs to be fitted to 14 storms in the Bar watershed in Iran, and they concluded that the 2parameter gamma distribution was the best for their cases. Patil et al (2012) presented an analytical method for computing the parameters of the 2-parameter gamma distribution as a synthetic instantaneous unit hydrograph using the dimensionless quantity β (qp × tp). Patil et al (2012) applied the 2-parameter gamma synthetic unit hydrograph first to a very small urban watershed in Cincinnati, OH (in USA) (0.0003 km 2 ), and next to two watersheds in India, whose sizes were 0.177 km 2 and 823.6 km 2 .…”

“…Patil et al (2012) presented an analytical method for computing the parameters of the 2-parameter gamma distribution as a synthetic instantaneous unit hydrograph using the dimensionless quantity β (qp × tp). Patil et al (2012) applied the 2-parameter gamma synthetic unit hydrograph first to a very small urban watershed in Cincinnati, OH (in USA) (0.0003 km 2 ), and next to two watersheds in India, whose sizes were 0.177 km 2 and 823.6 km 2 . Roy and Thomas (2016) computed a synthetic unit hydrograph in the Barathapuzha River basin (A = 6186 km 2 ) by the method of Central Water Commission (CWC) of India, and accepted this as the true unit hydrograph and compared the unit hydrographs by the 2-parameter gamma and 3-parameter beta distributions.…”

“…The models are applied to a few unit hydrographs all derived using observed rainfall-runoff data for which the numerical data needed for the Snyder method (Ct, Cp, A, L, Lc) are available. They are applied to (1) 10 unit hydrographs in Anatolia (Haktanir and Sezen 1990), (2) eight unit hydrographs developed in four watersheds in Susurluk Basin in Turkey (Usul and Birhan 1995), (3) the unit hydrograph developed for the watershed of the Yedigöze Dam in Turkey (Sanko 2007), and (4) 3f sub-zone Godavari catchment in India (Patil et al 2012). Only two of these applications will be summarized in what follows for space reason.…”