Adequate assessment of uncertainty for prediction and simulation purposes is a current issue in hydrological research. This article describes the application of the Hydrologic Uncertainty Processor (HUP) proposed by Krzystofowicz in 1999 to a small semi-arid watershed in southern Italy. The version applied in this work is a precipitation-dependent HUP aimed at assessing the hydrologic uncertainty about actual streamflow at some future time, with lead times of a few hours, given the information available at the forecast time and assuming a perfectly known amount of precipitation. The processor is based on Bayes theorem and hence models the prior and likelihood functions to obtain the revised posterior distribution. A complete example of the modelling assumptions, estimation procedure and results is carried out in the present paper. In detail, we analysed a 26-km2 semi-arid basin, considering hourly forecasts over an almost continuous five-year period in 2000-2005. A distributed rainfall-runoff model suited to represent contributions of different runoff generation mechanisms to hydrologic response is used for deterministic predictions. Analysis of the resulting posterior distributions show that hydrologic uncertainty: (i) grows with the value of discharge predicted by the model; (ii) is higher when associated with high precipitation amounts; and (iii) increases with lead time of predictions. The predictive ability of the processor is investigated for several runoff events. The results indicate good processor performance for a lead time equal to the period covered by the precipitation forecast, and a significant deterioration for higher lead times that is heavily dominated by the presumption of null precipitation beyond the forecast period. Finally, the skill of the processor is assessed through a retrospective analysis in terms of the probability of detection and the false-alarm rate.
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