historical data and the model is learned for a specific context and can hardly be generalized because of the airspace constraints, e.g. aircraft following a Standard Instrument Departure.

![The Effect of the mass parameter[]{data-label="fig:massEffect"}](./img/massEffect.pdf){width="2.5in"}

Combining both approaches is an interesting research question addressed by [@Alligier] and [@Crisostomi2008]. The latter combines Monte-Carlo Simulation and worst-case scenario for modifying the parameters of BADA while integrating a wind model. However, this work is limited to the descent phase and the experiments are performed on trajectories obtained by simulation. The main contribution of our work on this question is to show that tuning the parameters of BADA during the progress of a flight is a way to overcome the difficulties of parametric approach and avoiding to learn a model from the historical data. To the best of our knowledge, no work has answered to this question with results of the vertical plane.

Model {#Model}
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The basic idea is to create an hybrid system to generate a trajectory in the vertical plane using BADA. The system describes the transitions between the different modes in function of the states and the control laws. Following the mode, a given differential equation is integrated to obtain the 