5.2.1.1 Fixed surface height

The key assumption with the rigid lid is that the ocean surface height is fixed

$$\eta \equiv 0.$$ (5.5)

This assumption eliminates the wave modes associated with vertical displacements of the full water column. These are the modes associated with the fast external mode gravity waves. Therefore, fixing the surface height eliminates the fast waves and consequently allows for relatively large momentum time steps. On its own, the removal of the fast modes is thought to be of minimal consequence for global ocean simulations. It does preclude the study of phenomena associated with barotropic waves, such as the barotropic tides.