Probability distributions for flood warning systems

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Abstract
Engineering design, optimal operation, evaluation of performance, and benefit‐cost analysis of a local flood warning system require an explicit and extensive characterization of uncertainties in terms of probability distributions. Such a characterization is obtained via a Bayesian Processor of Forecasts (BPF) which provides (1) a prior description of uncertainty about flood occurrence and crest height, (2) a stochastic characterization of the forecaster in terms of likelihood functions, and (3) a posterior description of uncertainty about flood occurrence and crest height, conditional on a flood crest forecast. The theoretical novelty of our BPF is that a posterior distribution can be constructed for any prior distribution, parametric or nonparametric, the generality essential in light of the variety of models used as flood crest distributions. The conceptual novelty of the BPF opens a new research paradigm (which provides distributions for real‐time decision making based on forecasts) that adjoins the classical flood frequency analysis (which has provided probability distributions for planning and design).

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