Ganymede's atmosphere is produced by the interaction of the Sun and of the Jovian magnetosphere with its surface. It is a reflection of Ganymede's surface properties, but also of the complex interaction between the Ganymede and Jupiter magnetospheres. The Exospheric Global Model (EGM) has been developed in order to be able to integrate surface and magnetosphere processes with those in Ganymede's atmosphere. It is a 3D parallelized multi-species collisional model, coupled with LatHys, a hybrid multi-grid 3D multi-species model of Ganymede's magnetosphere (Leclercq et al., Geophys. Res. Let., Submitted, 2016). EGM's description of the species-dependent spatial distribution of Ganymede's atmosphere, its temporal variability during rotation around Jupiter, its connection to the surface, the role of collisions, and respective roles of sublimation and sputtering in producing Ganymede's exosphere, illustrates how modeling combined with in situ and remote sensing of Ganymede's atmosphere can contribute to our understanding of this unique surface-atmosphere-magnetosphere integrated system.