There has been growing interest in air transportation community to develop a routing decision model based on probabilistic characterization of severe weather. In the probabilistic air traffic management (PATM), decisions are made based on the stochastic weather information in the expected total cost sense. Probabilistic approach aims to enhance routing flexibility and reduce the risks associated with uncertainty of the future weather.

In this research, a geometric model is adopted to generate optimal route choice when the future weather is stochastic. The geometric recourse model (GRM) is a strategic PATM model that incorporates route hedging and en-route recourse options to respond to weather change. Hedged routes are routes other than the nominal or detour route, and aircraft is re-routed to fly direct to the destination, which is called recourse, when the weather restricted airspace become flyable. Aircraft takes either the first recourse or the second recourse: The first recourse occurs when weather clears before aircraft reaches it flying on the initial route. The second recourse occurs when the aircraft is at the weather region.

There are two variations of GRM: Single Recourse Model (SRM) with first recourse only and Dual Recourse Model (DRM) with both the first and second recourse options. When the weather clearance time follows a uniform distribution, SRM becomes convex with optimal route being either the detour or a hedged route. The DRM has a special property when the maximum storm duration time is less than the flight time to the tip of the storm on the detour route: it is always optimal to take the nominal route. The performance study is conducted by measuring the cost saving from either SRM or DRM. The result shows that there are cases with substantial cost saving, reaching nearly 30% with DRM.

The ground-airborne hybrid model is an extension of the GRM, where both ground holding as well as route hedging are considered. The optimal combination of ground delay and route choice is determined by weather characteristics as well as the ground-airborne cost ratio. The numerical analysis reveals that whenever ground delay is required, the optimal route choice is the nominal one, while a non-nominal route is optimal when the ground delay is zero. There exists a unique critical cost ratio associated with given weather condition, which determines whether ground holding is optimal or not.