Bayesian system for probabilistic stage transition forecasting

The second analytic-numerical Bayesian forecasting system (BFS) is presented. The purpose of this BFS is to produce a short-term probabilistic stage transition forecast (PSTF) based on a probabilistic quantitative precipitation forecast (PQPF) as an input and a deterministic hydrologic model (of any complexity) as a means of simulating the response of a headwater basin to precipitation. The river stage process is treated as a discrete-time, continuous-state stochastic process. The PSTF specifies a finite sequence of infinite families of predictive one-step transition density functions that characterize the total uncertainty about the evolution of the river stage process in time. This characterization is needed for rigorous application of stochastic decision models in flood response systems and reservoir control systems. The BFS has three structural components: the precipitation uncertainty processor (PUP), the hydrologic uncertainty processor (HUP), and the integrator (INT). Previous articles detailed the PUP and the HUP. This article presents the total system. It focuses on the INT—its derivation and properties, and the PSTF—its formats and attributes. It presents operational expressions, numerical algorithms, and a complete example using real-time input data and producing families of predictive one-step Markov transition density functions for 3 days ahead in 24- and 6-h steps. Finally, it describes a Monte Carlo scheme for generating the Bayesian ensemble forecast which is equivalent to the PSTF.