Identical twin experiments are performed with a realistic Mediterranean general circulation model, assimilating surface pressure at the rigid lid (simulating altimeter data) in order to reproduce the three-dimensional circulation and water column structure. The first twin pair is forced with monthly varying wind stress and surface buoyancy, and the assimilation method of Cooper and Haines <1996> is used. Water columns are displaced vertically by an amount calculated to ensure that the surface pressure change required at assimilation time is reduced to zero at the seabed. The assimilation is successful with T, S and velocities having an error reduction of about 40% after 1 year, assimilating surface pressure every 15 days. A modification to this assimilation method is introduced in which a change to bottom pressure is calculated based on a balance between relative vorticity and stretching in the vertically displaced water column. A second identical twin experiment pair is forced with daily varying wind stress (from the European Centre for Medium-Range Weather Forecasts in 1992--1993) but still monthly varying surface buoyancy forcing. The variability in surface pressure is much greater when daily winds are used, with much of the high-frequency current signal being a barotropic response (with a strong signal at the seafloor). Applying the correct daily winds without any surface pressure assimilation can reduce the T, S and velocity errors by about 50% after a year, suggesting that much of the additional barotropic variability is deterministic. The additional assimilation of surface pressure every 20 days, now with the bottom pressure updated, leads to a further 30% error reduction. A further twin experiment with daily winds, in which the barotropic mode is allowed to converge first, before surface pressure assimilation begins, shows that a bottom pressure update during assimilation may be unnecessary if the correct wind stresses are known.¿ 1997 American Geophysical Union