Hydrologic uncertainty processor for probabilistic stage transition forecasting

The hydrologic uncertainty processor (HUP) is a component of the Bayesian forecasting system which produces a short-term probabilistic stage transition forecast (PSTF) based on a probabilistic quantitative precipitation forecast (PQPF). The PSTF specifies a sequence of families of predictive one-step transition density functions whose product gives the predictive joint density function of the actual river stage process {H1,…,HN}. A multivariate HUP is needed to quantify hydrologic uncertainty—the aggregate of all uncertainties arising from sources other than those quantified by the PQPF. A Bayesian formulation of the multivariate HUP for a PSTF system is presented. The multivariate HUP supplies a family of posterior joint density functions of the actual river stage process {H1,…,HN}, conditional on a realization of the model river stage process {S1,…,SN} output from a deterministic hydrologic model, and an observation of the initial river stage H0. A posterior joint density function is factorized into posterior one-step transition density functions, each of which being obtained via Bayes theorem from a likelihood function and a prior one-step transition density function. To implement the HUP, a meta-Gaussian model is employed. The model is tested on data for daily river stage processes at four forecast points closing headwater basins of sizes 484, 1430, 1859, and 2372 km2, and located in the Eastern United States. The working of the HUP is illustrated, and general characteristics of the hydrologic uncertainty are inferred. The hydrologic uncertainty is significant and imposes a limit on the predictability of river stage transitions, which is currently about 48 h, given a 24-h PQPF.