Precipitation uncertainty processor for probabilistic river stage forecasting

Abstract

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 km 2 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.