The classical method of computing the expected annual flood damage, based on a stage-damage function and a probability distribution of the annual flood peak, has been extended by Haimes et al. [1994] in order to calculate the expected annual damage associated with solutions that combine structural flood controls and a warning system. In a case study, four alternative plans were compared: do nothing, construct levees, install a warning system, construct levees and install a warning system. The comparison was based on three criteria: average annual cost, expected annual flood damage, and restricted expectation of the annual flood damage caused by peaks higher than the T-year event (T = 10 and T = 100). This methodology is important in that it places the flood warning system on a par with structural measures and demonstrates how methods used by the U.S. Army Corps of Engineers in project feasibility studies can be supplemented with a formal multiobjective analysis.
Under the assumption that the decision rule for issuing a flood warning is of the threshold type (that is, a warning is issued whenever the forecasted flood crest exceeds a threshold), Haimes et al. [1990] have proposed a model for selecting the threshold. Imbedded in the model are four postulates. (1) The threshold currently in effect should be a function of the fraction of people in the community who responded to the previous warning. (2) This fraction decreases after a false warning and increases after a detection. (3) A fixed number of future events (marked by floods and false warnings) should be considered when selecting the threshold. (4) The selection should be Pareto-optimal with respect to the maximization of three objectives: the expected property damage reduction in the course of all events, the expected life loss reduction in the course of all events, and the expected fraction of people who will respond to the warning after the last event. A weighting method in conjunction with dynamic programming has been used to find solutions in a case study [ Li et al., 1992].
The approach leaves unanswered several methodological questions. Two of them point out the possible research directions. (1) Why is it desirable, from either the normative or the behavioral point of view, to change the warning threshold after each event? Since such a change alters the probabilities of detection and false warning, the reliability of warnings becomes nonstationary and the public can no longer rely on experience to learn appropriate responses. (2) How should one choose the number of events (stages) for the dynamic programming? Since the probabilities of detections and false warnings remain unknown until a realization of thresholds is observed, a fixed number of events does not determine the length of time over which these events occur, and thus one cannot apply the usual notion of a planning horizon.