Evaluation of the Time of Concentration Models for Enhanced Peak Flood Estimation in Arid Regions

Abstract

The uncertainties in the time of concentration (Tc) model estimate from contrasting environments constitute a setback, as errors in Tc lead to errors in peak discharge. Analysis of such uncertainties in model prediction in arid watersheds is unavailable. This study tests the performance and variability of Tc model estimates. Further, the probability distribution that best fits observed Tc is determined. Lastly, a new Tc model is proposed, relying on data from arid watersheds. A total of 161 storm events from 19 gauged watersheds in Southwest Saudi Arabia were studied. Several indicators of model performance were applied. The Dooge model showed the best correlation, with r equal to 0.60. The Jung model exhibited the best predictive capability, with normalized Nash–Sutcliffe efficiency (NNSE) of 0.60, the lowest root mean square error (RMSE) of 4.72 h, and the least underestimation of Tc by 1%. The Kirpich model demonstrated the least overestimation of Tc by 4%. Log-normal distribution best fits the observed Tc variability. The proposed model shows improved performance with r and NNSE of 0.62, RMSE of 4.53 h, and percent bias (PBIAS) of 0.9%. This model offers a useful alternative for Tc estimation in the Saudi arid environment and improves peak flood forecasting.