A bootstrap approach for the parameter uncertainty of an urban-specific rainfall-runoff model

•Evaluation of calibration parameter uncertainty is important in urban watersheds.•Bootstrap method is demonstrated for parameter uncertainty analysis of USF model.•Two data scenarios of whole data and individual flood events were considered.•Indices were proposed for the objective analysis of model parameter uncertainty.•Simulation uncertainty of USF model was analyzed using the newly defined indices. The predictions made using rainfall-runoff models are inherently uncertain and it is important to recognize and account for this uncertainty, especially in urban watersheds due to the high flood risk in these areas. Recent studies on hydrological model uncertainty mostly refer to the identification of model parameter uncertainty. However, such studies are somewhat limited using the bootstrap approach, a nonparametric method which makes less prior assumptions on the model structure and thus is more flexible. Hence, a residual-based bootstrap approach associated with the SCE-UA global optimization algorithm is demonstrated in this study for the analysis of calibrated parameter uncertainty and its subsequent effect on the model simulation of an urban-specific rainfall-runoff model, urban storage function (USF) model, under two different data scenarios of individual event-based and whole data-based scenarios. Initially, the parameter uncertainty was expressed by estimating the confidence interval (CI) of the USF model parameters obtained from bootstrapping and then the parameters from the highest to the lowest uncertainties were derived by utilizing two newly proposed parameter uncertainty indices which can make the best use of CI. Moreover, investigations on the effect of calibrated parameter uncertainty on model simulations revealed that the model was able to bracket most of the observations within the prediction range of considered scenarios. This further indicates that the residual-based bootstrap approach along with the SCE-UA method reasonably well predicted the uncertainty range of the USF model. For a better understanding of simulation uncertainty, we defined and demonstrated two model simulation uncertainty indices and these indices could be useful in future studies to analyze the simulation uncertainty of different rainfall-runoff models in the watersheds worldwide.