Integrator of uncertainties for probabilistic river stage forecasting: precipitation-dependent model

The integrator 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 BFS decomposes the total uncertainty about the river stage into precipitation uncertainty and hydrologic uncertainty, which are quantified independently and then integrated into a predictive (Bayes) distribution of the river stage. An analytic-numerical integrator is developed using a precipitation-dependent model for the hydrologic uncertainty processor (HUP). The working of the integrator is illustrated using data from the operational forecast system (OFS) of the National Weather Service (NWS) for a 1430 km2 headwater basin. Theoretical and empirical properties of the predictive distribution are demonstrated. In general, the predictive distribution is a two-component mixture; its density is asymmetric and bimodal. Effects of hydrologic and precipitation uncertainties are examined. The superiority of the precipitation-dependent model over a simpler model is illustrated. Limitations of first-second moment analyses, Monte Carlo simulation, and ensemble forecasting are pinpointed: none of these techniques can alone produce valid PRSFs.