  In this paper we consider the 1D Green-Naghdi system over a nonflat bottom.
This system describes the evolution of water waves over an uneven bottom in the
shallow water regime in terms of the water depth $h$ and the horizontal
velocity $u$. Using a Lagrangian formulation of this system on a Sobolev type
diffeomorphism group we prove local well-posedness for $(h,u)$ in the Sobolev
space $(1+H^s(\mathbb R)) \times H^{s+1}(\mathbb R),\; s > 1/2$. This improves
the local well-posedness range.
