Hydrologic uncertainty processor for probabilistic river stage forecasting: precipitation-dependent model

The hydrologic uncertainty processor (HUP) is a component of the Bayesian forecasting system (BFS) which produces a short-term probabilistic river stage forecast (PRSF) based on a probabilistic quantitative precipitation forecast (PQPF). The task of the HUP is to quantify the hydrologic uncertainty under the hypothesis that there is no precipitation uncertainty. The hydrologic uncertainty is the aggregate of all uncertainties arising from sources other than those quantified by the PQPF. The precipitation-dependent HUP has two branches, each conditional on the hypothesized occurrence or nonoccurrence of precipitation during the period covered by the PQPF (here 24 h). Under each hypothesis, the time series of river stages (here at 24-h steps) is modeled a priori as a Markov process of order one with nonstationary transition distributions. The families of prior distributions and likelihood functions are all nonstationary (with forecast lead time) and meta-Gaussian (with respect to their multivariate dependence structure). For each lead time, Bayesian revision yields two families of posterior distributions whose mixture, determined by the probability of precipitation occurrence, characterizes the hydrologic uncertainty. Estimation and validation of the HUP are described using data from the operational forecast system (OFS) of the National Weather Service (NWS) for a 1430 km3 headwater basin.