Warnings for natural hazards improve societal resilience and are a good example of decision-making under uncertainty. A warning system is only useful if well defined and thus understood by stakeholders. However, most operational warning systems are heuristic: not formally or transparently defined. Bayesian decision theory provides a framework for issuing warnings under uncertainty but has not been fully exploited. Here, a decision theoretic framework is proposed for hazard warnings. The framework allows any number of warning levels and future states of nature, and a mathematical model for constructing the necessary loss functions for both generic and specific end-users is described. The approach is illustrated using one-day ahead warnings of daily severe precipitation over the UK, and compared to the current decision tool used by the UK Met Office. A probability model is proposed to predict precipitation, given ensemble forecast information, and loss functions are constructed for two generic stakeholders: an end-user and a forecaster. Results show that the Met Office tool issues fewer high-level warnings compared with our system for the generic end-user, suggesting the former may not be suitable for risk averse end-users. In addition, raw ensemble forecasts are shown to be unreliable and result in higher losses from warnings.
Keywords: decision theory; early warning system; ensemble forecasting; ensemble post-processing; natural hazards.