Runoff prediction in ungauged catchments using the gamma dimensionless time-area method

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 = t c /4.24, with t c 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.