Probabilistic flood forecast: Exact and approximate predictive distributions

- The exact probabilistic flood forecast (PFF) from the Bayesian forecasting system.
- An efficient numerical algorithm for calculating the exact PFF.
- A simple approximation to the PFF substantiated via comparison against the exact PFF.
- The approximate PFF may be attractive for real-time flood warnings to the public.

SummaryFor quantification of predictive uncertainty at the forecast time t0, the future hydrograph is viewed as a discrete-time continuous-state stochastic process {Hn:n=1,…,N}, where Hn is the river stage at time instance tn>t0. The probabilistic flood forecast (PFF) should specify a sequence of exceedance functions {F‾n:n=1,…,N} such that F‾n(h)=P(Zn>h), where P stands for probability, and Zn is the maximum river stage within time interval (t0,tn], practically Zn=max{H1,…,Hn}. This article presents a method for deriving the exact PFF from a probabilistic stage transition forecast (PSTF) produced by the Bayesian forecasting system (BFS). It then recalls (i) the bounds on F‾n, which can be derived cheaply from a probabilistic river stage forecast (PRSF) produced by a simpler version of the BFS, and (ii) an approximation to F‾n, which can be constructed from the bounds via a recursive linear interpolator (RLI) without information about the stochastic dependence in the process {H1,…,Hn}, as this information is not provided by the PRSF. The RLI is substantiated by comparing the approximate PFF against the exact PFF. Being reasonably accurate and very simple, the RLI may be attractive for real-time flood forecasting in systems of lesser complexity. All methods are illustrated with a case study for a 1430km2 headwater basin wherein the PFF is produced for a 72-h interval discretized into 6-h steps.