Determinants of evacuation timing in response to probabilistic forecasts

Examined are determinants of the time to issue an evacuation statement in an operational environment for a local or regional life-threatening hazard, whose probability of occurrence is forecast in real time. Adaptive decisions to issue such a statement at each time are analyzed through Monte Carlo simulation experiments that explicitly consider parametric uncertainty and embed an adaptive stochastic decision methodology. Given a set of values of the uncertain component model parameters, the target of the decision methodology is whether to issue the statement at the current decision time or to delay for a later time. Considered are: (a) the forecast sequence of the probability of event occurrence as a function of lead time including the estimate at the initial time, and a measure of the forecast uncertainty; (b) a probabilistic characterization of the evolving anticipated public response as a function of forecast lead time; (c) the uncertain level of forecast probability threshold below which the public is not anticipated to respond; and (d) the estimate of the time interval of evacuation completion. Within the simulation framework, quantitative analysis is afforded by casting the decision problem in a constrained optimization form with due account for uncertainty. For each simulation scenario, both expected value and high-percentile value functions are used for the objective function of the constraint optimization problem. Their inclusion allows consideration of the level of risk aversion of the evacuating public and of the agency issuing the evacuation statement. Simulation of various parametric scenarios is performed with a sensitivity analysis of the results, with dimensionless-time measures used for broad applicability. Broadly applied conclusions are derived, and an example is provided to illustrate the impact of the adaptive nature of the decision component on the decision results.