Unsteady aerodynamics of a two-dimensional thin body hovering near the ground plane are studied. The effects of ground topology and height above the surface are examined. In the considered simulations, the hover kinematics are chosen to follow typical flapping motions of insects and small birds. Ground topology is expressed in terms of flat, sine, triangle, and square wave profiles, which are, in term parameterized in terms of amplitude and spatial frequency. Fully developed lift is examined for a variety of ground topologies and flapping heights. Motions near the ground plane result in enhanced and phase shifted lift; hover, recirculated vorticity can interact with the flapping body and may offset the practical gains of ground effect.