  This paper is devoted to the study of water waves under the influence of the
gravity and the Coriolis force. It is quite common in the physical literature
that the rotating shallow water equations are used to study such water waves.
We prove a local wellposedness theorem for the water waves equations with
vorticity and Coriolis force, taking into account the dependence on various
physical parameters and we justify rigorously the shallow water model. We also
consider a possible non constant pressure at the surface that can be used to
describe meteorological disturbances such as storms or pressure jumps for
instance.
