Precipitation uncertainty processor for probabilistic river stage forecasting

The precipitation uncertainty processor (PUP) is a component of the Bayesia n forecasting system which produces a short-term probabilistic river stage forecast (PRSF) based on a probabilistic quantitative precipitation forecas t (PQPF). The task of the PUP is to process a probability distribution of t he total precipitation amount through a deterministic hydrologic model (of any complexity) into a probability distribution of the model river stage. A n analytic-numerical PUP is developed based on the theory of response funct ions and empirical data simulated from the operational forecast system of t he National Weather Service for a 1430 km(2) headwater basin. The PUP outpu ts a five-parameter two-piece Weibull distribution of the model river stage . The corresponding response function is a two-piece power function. Struct ural properties of the PUP are investigated empirically, including the dete rministic equivalence principle: Under certain conditions a deterministic f orecast of the temporal disaggregation of the total precipitation amount is equivalent to a probabilistic forecast. This considerably simplifies the P QPF, without affecting the optimality of the PRSF.