Uncertainty Analysis of Time of Concentration Equations based on First-Order-Analysis (FOA) Method

The time of concentration (Tc) is one the most important time parameters to predict the response of a catchment to a given rainfall and plays a key role in the hydrologic design and rainfall-runoff modeling. There are a huge number of empirical/semi-empirical equations for estimation of T_c and depending on several parameters such as rainfall attributes, topographic and land cover map scale, DEM resolution and streams delineation threshold causes significant uncertainties in the Tc value. How to quantitatively evaluate the uncertainties in model parameters and the resulting uncertainty impacts on model outputs has always been a question which has attracted much attention. In this study, the method based on the First-Order-Analysis (FOA) is used to analyze the uncertainty and the contribution of each parameter on the output of 47 T_c formulas in Kasilian and Amameh watersheds. The results show that among the 47 T_c equations, equations which are based on watershed’s characteristics, rainfall attributes and land cover-related coefficients such as Overton-Meadows, ASCE, Akan, Kinematic-Wave, McCuen et al. and Izzard have relatively high uncertainty and the average CV of these equations is about 45%. In addition, equations that are based on only geomorphological parameters have relatively low uncertainty (the average CV is about 16%). Further analysis of the effects of parameter uncertainties on the T_c equations reveals that the uncertainty associated with rainfall attributes and land cover-related coefficients have great impacts on results of the T_c equations and the uncertainty caused by these factors in humid regions relative to dry/ semi dry regions is different. Moreover, in the geomorphological-based equations, the uncertainty caused by streams delineation threshold is approximately 3-6 times of scale effects’ uncertainty.