Runoff prediction in ungauged catchments using the gamma dimensionless time-area method
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ORIGINAL PAPER
Runoff prediction in ungauged catchments using the gamma dimensionless time-area method T. Sabzevari 1
Received: 9 June 2016 / Accepted: 18 January 2017 # Saudi Society for Geosciences 2017
Abstract Time-area (TA), which constitutes the basis for rainfall-runoff transformation in the Clark model, is conventionally derived from the tedious procedure of delineating isochrones. In the present study, by combining the Nash instantaneous unit hydrograph (IUH), in terms of the gamma function, and the Clark model, a new TA relationship (TAR) is introduced. This equation involves the Nash models’ parameters (i.e., the number of reservoirs, n, and the storage coefficient, k). Considering that n = 5 for ungauged catchments, the following equation for estimating k was obtained: k = tc/4.24, with tc being the time of concentration of the catchment. Finally, a gamma time-area (GTA) function was derived for estimating the time-area diagram (TAD) of catchments. The TADs derived from the GTA function were compared to the GIS-based TADs and those derived from the US Army Corps of Engineers (USACE) method and the kinematic wave (KW) model in four catchments, namely, Kasilian, Ajay, Jafarabad, and Shourandika. In the Kasilian catchment, the direct runoff hydrograph (DRH) was simulated using the Clark model based on the GTA and USACE methods and compared with the observed hydrographs. Results indicate that the coefficient of efficiency (CE) in the Kasilian catchment for the two methods is approximately 0.8, while the errors in the peak discharge prediction are 9 and 11.2% in the GTA and USACE methods, respectively. Keywords Time-area . Gamma distribution . Ungauged catchment . Nash model . Clark model
* T. Sabzevari [email protected]; [email protected] 1
Department of Civil Engineering, Estahban Branch, Islamic Azad University, Estahban, Iran
Introduction The Clark unit hydrograph (UH) method (Clark 1945) incorporates the processes of attenuation and the translation of runoff through a time-area (TA) relationship (TAR). In this technique, the catchment is divided into a number of subareas via isochrones, i.e., the contours of equal travel time to the catchment outlet. The histogram of contributing catchment subareas is known as the TA histogram (TAH) and provides the basis for the excess rainfall-runoff transformation. To construct the TAH, the catchment time of concentration must be divided into a number of equal time intervals, which represent the time difference between adjacent isochrones (Ajward and Muzik 2000). Ever since Clark (1945) introduced the TA concept, there has been a significant interest in using the TA method and its variants (Kull and Feldman 1998; Saghafian et al. 2002), due to their capacity for considering the spatial variation in catchment characteristics and the spatiotemporal variation in rainfall for the purposes of hydrologic simulation. Between 40 and 60% of US Army Corps of Engineers (USACE) projects are handled by the TA method and its variants (Kull and Feldman 1988).
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