Before tracer or momentum equations can be solved, it is necessary to evaluate the vertical velocity at the ocean surface and bottom. More specifically, as discussed in Sections 22.3.1 and 22.3.2, vertical velocity at the ocean surface and bottom enters the continuity equation as an upper and lower boundary condition. Since the continuity equation is a first order differential constraint, only one boundary condition is needed to diagnose the vertical velocity w(z). Either w(0) or w(-H) may be used. For historical reasons based on the early use of the rigid lid approximation, MOM uses vertical velocity at the ocean surface and integrates downward to construct w(z) at all depths. The vertical velocity at the ocean bottom will now be given for the discrete equations. The result for integrating from the bottom up will also be given.