The precipitation uncertainty processor (PUP) is a component of the Bayesian forecasting system which produces a short-term probabilistic river stage forecast (PRSF) based on a probabilistic quantitative precipitation forecast (PQPF). The task of the PUP is to process a probability distribution of the total precipitation amount through a deterministic hydrologic model (of any complexity) into a probability distribution of the model river stage. An analytic-numerical PUP is developed based on the theory of response functions and empirical data simulated from the operational forecast system of the National Weather Service for a 1430 km2 headwater basin. The PUP outputs a five-parameter two-piece Weibull distribution of the model river stage. The corresponding response function is a two-piece power function. Structural properties of the PUP are investigated empirically, including the deterministic equivalence principle: Under certain conditions a deterministic forecast of the temporal disaggregation of the total precipitation amount is equivalent to a probabilistic forecast. This considerably simplifies the PQPF, without affecting the optimality of the PRSF. ¿ 2000 American Geophysical Union