The uncertainties in the time of concentration (T_c) model estimate from contrasting environments constitute a setback, as errors in T_c 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 T_c model estimates. Further, the probability distribution that best fits observed T_c is determined. Lastly, a new T_c 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 T_c by 1%. The Kirpich model demonstrated the least overestimation of T_c by 4%. Log-normal distribution best fits the observed T_c 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 T_c estimation in the Saudi arid environment and improves peak flood forecasting.

The flood peak is commonly estimated using the rational method for the design of hydraulic structures. The method is mainly used in a deterministic context. However, there is often uncertainty in flood predictions, which should be incorporated in the design of mitigation schemes. This research proposes a methodology to cope with uncertainty in the rational method via the application of a stochastic framework. Data from 158 storms, recorded in the period 1984–1987 in 19 subbasins in the southwestern part of Saudi Arabia, were used to implement the proposed methodology. A tri-variate log-normal probability density function was used to model the joint relationship between the rational method parameters. The model considered the parameters as random variables. The uncertainty in the rainstorms was represented by intensity or depth; the uncertainty in basin delineation (due to the use of different digital elevation model resolution) was represented by the basin area; and the uncertainty in the land use/land cover was represented by the runoff coefficient. The Monte Carlo method was used to generate realizations of the peak flow and runoff volume with 95% and 99% confidence levels from the input parameters. Although the correlation between the parameters was weak, the model was capable of simulating the rational model parameters and estimating the peak flow and runoff volume relatively well, and the generated realizations fell within the confidence levels, except for a few marginal cases. The model can be used to generate peak flows and the associated confidence limits in ungauged basins from the statistics of the input parameters using the equations developed in this study.