Hydrologic uncertainty processor for probabilistic river stage forecasting

The hydrologic uncertainty processor (HUP) is a component of the Bayesian forecasting system that produces a short‐term probabilistic river stage forecast 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; these sources include the hydrologic model (model and parameter uncertainties), inputs estimated deterministically (measurement, estimation, and prediction uncertainties), and inputs not forecasted (e.g., precipitation beyond the period covered by the PQPF). Bayesian theory for the HUP is presented, and a meta‐Gaussian model is developed. This parametric model allows for (1) any form of marginal distributions of river stages, (2) a nonlinear and heteroscedastic dependence structure between the model river stage and the actual river stage, and (3) an analytic solution of the Bayesian revision process. Estimation and validation of the model are described using data from the operational forecast system of the National Weather Service for a 1430‐km 2 headwater basin.