The U.S. National Airspace System (NAS) has reached an extremely high level of safety in recent years. However, it will only become more difficult to maintain the current level of safety with the forecasted increase in operations, and so the FAA has been making revolutionary changes to the NAS to both expand capacity and ensure safety. Our work complements these efforts by developing a novel model-based framework for real-time monitoring and prediction of the safety of the NAS. Our framework is divided into two parts: (offline) safety analysis and modeling part, and a real-time (online) monitoring and prediction of safety. The goal of the safety analysis task is to identify hazards to flight (distilled from several national databases) and to codify these hazards within our framework such that we can monitor and predict them. From these we define safety metrics that can be monitored and predicted using dynamic models of airspace operations, aircraft, and weather, along with a rigorous, mathematical treatment of uncertainty. We demonstrate our overall approach and highlight the advantages of this approach over the current state-of-the-art through simulated scenarios.