In reality, the ocean surface is free to deform under the influence of wind, heating and tidal forces. We find wind-driven waves and surges up to several meters high on its surface. These are typically short-lived, have short spatial scales and fast wave speeds. The surface elevations due to the large, quasi-permanent ocean currents, on the other hand, such as those associated with the Gulf Stream and its eddies, and mid-ocean gyres, are only fractions of a meter or so, and move very slowly. In order to avoid the severe limitation on the time step due to the fast gravity waves (to be discussed below), one puts a rigid lid on the ocean as this affects the large-scale motions only slightly. The first such model was formulated by Bryan . This model has been recently reformulated by Killworth et al.  to retain the free surface by treating the fast modes separately. Models that treat the fast waves implicitly have been developed by Hurlburt et al.  in connection with ``layered'' models, by Madala and Piacsek  in connection with ``level'' models, and by Blumberg and Mellor  in connection with ``sigma-coordinate'' models [for definitions of ``layered'', ``level'' and ``sigma'' see the next section].