This section resulted from the combined efforts of Stephen Griffies and Young-Gyu Park ( ygp@gfdl.gov).
The large-scale circulation in numerical models is often abbreviated in terms of its meridional-vertical plane circulation. Under certain assumptions, this circulation can be rendered by an overturning streamfunction. The streamfunction is constructed by integrating over the zonal direction between either two fixed meridional boundaries, on which the zonal velocity is assumed to vanish, or over a zonally periodic domain such as the World Ocean. Although useful, this abbreviated picture is potentially misleading due to the integration over sometimes important details of longitudinal variation. To alleviate some of the misleading characters, it is often useful to employ various vertical coordinates to construct different versions of the streamfunction. The purpose of this section is to provide a general formulation of the overturning streamfunction, and then to discuss the manners of computing this streamfunction in MOM.