We will show the existence of global weak solutions to the inviscid three-dimensional quasi-geostrophic system of equations. This system of equations models the evolution of the temperature in the atmosphere. It is widely used in geophysics and meteorology. It involves a coupling between a transport equation in the whole domain, and an other one on the boundary of the domain, at the surface of the earth. This is a joint work with Marjolaine Puel.