A decision-theoretic framework for probabilistic flood warnings

Early warning systems for weather-related hazards are critical tools for increasing societal resilience, but their effectiveness depends on reliability and ability to support decision-making in the face of uncertainty. While many operational contexts rely on expert judgment and predefined warning thresholds, decision-making processes rarely incorporate a formal assessment of the operational and economic impacts associated with the chosen actions. This study proposes a decision-theoretic approach for issuing flood warnings in Italy's Sieve basin (Tuscany), integrating probabilistic precipitation forecasts from the national Civil Protection system with a statistical post-processing method to explicitly evaluate predictive uncertainty. The proposed framework introduces a loss function that adapts to multiple warning levels and accommodates different risk propensities (from risk-averse to risk-prone), effectively meeting the operational needs of diverse stakeholders. The system's performance is evaluated by comparing a Bayesian decision scheme with one that explicitly accounts for precipitation forecast uncertainty, assessing cumulative economic costs against different baseline scenarios. Results demonstrate that adopting a Bayesian cost-based approach yields economic benefits and substantial improvements in the Relative Economic Value (REV). Furthermore, incorporating precipitation uncertainty drives the system toward more cost-effective warning strategies, reducing false alarms and expected losses.