This chapter presents the continuum formulation of the free surface momentum equations. Issues related to the tracer equations are described in Chapter 8. The discrete formulation is presented in Chapter 29.
Much of the foundations for the free surface approach in MOM were established by Blumberg and Mellor (1987), Killworth et al. (1991) and Dukowicz and Smith (1994). From the perspective of global climate modeling, it is arguable that the most significant change from MOM's rigid lid is the natural ability to directly incorporate fresh water into the free surface ocean model.
Recent MOM development has focused on the explicit free surface. In particular, a new time stepping scheme for the explicit free surface has been introduced. This new scheme is more suitable for large scale modeling than that of Killworth et al. (1991) due to its enhanced stability. Additionally, the fresh water flux terms have been incorporated into the equation for the surface height only for the explicit free surface. As of Summer 1999, to provide a conservative model, the effects of an undulating surface height have been incorporated into the baroclinic and tracer equations. MOM's free surface is completely documented in the paper Griff ies, Pacanowski, Schmidt, and Balaji (2000).