Uncertainty analysis of hydrological models is usually based on model calibration, and the Bayesian method is a popular way to evaluate the uncertainty. The traditional Bayesian method usually uses lumped model residuals to form the likelihood function, where uncertainty in inputs (rainfall) is not explicitly addressed. This paper compares three approaches based on Bayesian inferences, considering rainfall uncertainty either implicitly or explicitly in calibration. Consistent parameter estimation and reliable quantification of predictive uncertainty are mainly examined. When rainfall uncertainty is explicitly treated in calibration, several rainfall observations at one-minute time steps are grouped to share one multiplier to consider the possible observation errors. The appropriate grouping strategy that balances the representativeness and the complexity of the problem is suggested. The application of the methods considered in this study focuses on small urban catchments (<200 ha) with a small temporal scale (1 min time step), in contrast to most literature studies dealing with larger catchments monitored at larger time steps. It is found that uncertainty in rainfall has a minor contribution to the total uncertainty in runoff estimation, and this minor role can be explained by the low pass filter effect of the linear reservoir model. However, the approach explicitly accounting for input uncertainty results in more informed knowledge for uncertainties related with hydrological model calibrations, which can possibly provide an estimation of uncertainty attributed to rainfall records. It should be noted that rainfall error estimates can compensate model structural uncertainty that is not explicitly addressed in this study.
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