20. Stevens Open Boundary Conditions

This chapter was contributed by Arne Biastoch (abiastoch@ifm.uni-kiel.de). Open boundary conditions have been tested successfully in the FRAM model (Stevens 1991) and in the community modeling effort (CME), (e.g. Döscher and Redler 1995). They have also been used in a GFDL-model of the North Atlantic in the framework of MAST2-DYNAMO (Dynamo 1994) as well as in a regional model of the subpolar North Atlantic (Redler and Böning 1996). The above mentioned experiments performed at Kiel were based on René Redler's^20.1 implementation in MOM 1. This chapter was written by Arne Biastoch^20.2 and describes an implementation of these open boundary conditions at the northern, southern, eastern and/or western boundary for a basin in MOM. The approach is based on the methodology of Stevens (1990).

There are two types of open boundary conditions: `active' in which the interior is forced at inflow points by data prescribed at the boundary and `passive' in which there is no forcing at the boundary and phenomena generated within the domain can propagate outward without disturbing the interior solution.

At open boundaries, baroclinic velocities are calculated using linearized horizontal momentum equations and the streamfunction is prescribed from other model results or calculated transports (e.g. directly or indirectly from the Sverdrup relation). Thus, the vertical shear of the current is free to adjust to local density gradients and internal waves are allowed to propagate out through the boundaries. Heat and salt are advected out of the domain if the normal component of the velocity at the boundary is directed outward. When the normal component of the velocity at the boundary is directed inward, heat and salt are restored to prescribed data (`active' open boundary conditions). During the course of a model integration, grid points can change from inflow to outflow (and vice-versa).

In contrast to `active' open boundary conditions, `passive' ones are characterized by not restoring tracers at inflow points. Additionally, a simple Orlanski radiation condition (Orlanski 1976) is used for the streamfunction.

In what follows, details are given for the northern and southern open boundaries. Open boundaries at the eastern and western end of the domain are handled in a similar manner except where noted.

WARNING: Tests for `active' and `passive' open boundary conditions are included as options. However, open boundary conditions is not an option which can be simply enabled to see what happens. Not only is data along the open boundaries needed (in the case of `active' open boundaries) but topography along open boundary points must be chosen carefully. Additionally, prescribing a net tranport along the open boundary (via $\psi_b$), requires that changes be made in the stream function calculation. Although open boundary conditions have been tested in simple cases, attention must be given to details to insure that specific configurations are working properly. For more details the reader is referred to Stevens (1990) and a `TO-DO' list given at the end of this chapter.