33.1.1 Summary of the vertical convection options

In short, the handling of vertically unstable water columns in MOM can happen in one of three basic ways:

1.

Implicit A: By enabling option implicitvmix, a large vertical diffusion coefficient ( $diff\_cbt\_limit$ set in namelist) is employed between ocean cells that are gravitationally unstable. This large coefficient severely limits the model time step, and so vertical diffusion is solved implicitly to relax the restriction (see Section 37.5 for a discussion of the implicit solution to the vertical diffusion equation).

2.

Implicit B: Enabling the option kppvmix (discussed in Section 32.2.3) automatically employs implicit vertical diffusion, with vertical diffusivities prescribed from the KPP boundary layer scheme.

3.

Explicit: Explicit convection (Section 32.1.2) is MOM's default if not enabling option implicitvmix or option kppvmix. There are two choices for explicit convection, and both explicit convective schemes can be tested in a one dimensional model (refer to Section 15.1.1 for details). The two choices are the following:

• The recommended scheme is that from Rahmstorf (see Section 32.1.2.3). In MOM 2, this scheme was implemented with option fullconvect. In MOM 3, nothing needs to be enabled since this scheme is the default. All instabilities in the water column are removed on every time step.
• Option oldconvect is the old style convective adjustment (Cox 1984) which takes multiple passes through the water column, alternately looking for instability on odd and even model levels (Section 32.1.2.1). When an instability is found, tracers are mixed, with their means (weighted by cell thickness) preserved. This process may induce further instability and therefore more than one pass through the water column may be needed to remove all instability. The number of passes through the water column is controlled by variable ``ncon'' which is input through namelist. Refer to Section 14.4 for information on namelist variables. This scheme is not recommended, and is maintained for historical reasons.

The original Cox (1984) ``NCON convection scheme'' has come under a lot of scrutiny. The discussion in Section 32.1.2 from Rahmstorf, and the articles by Killworth (1989) and Marotzke (1991), provide some elaboration and motivation to not employ the NCON scheme. It is for these reasons that all releases of MOM, starting from MOM 3, use the Rahmstorf scheme for its default explicit convection sheme. The old convection remains in MOM due to historical reasons and for purposes of comparison.

It should be noted that upon encountering a vertically unstable water column, explicit convection and the 1998 MOM 3 implementation of KPP rapidly mix only the tracers, whereas option implicitvmix mixes both tracers and momentum. When momentum is not mixed, it is thought that it is simply carried along through the effects on the density field. Killworth (1989) supports this idea, so long as the purpose is large-scale ocean modeling. Basically, through the geostrophic relation, affecting density appears sufficient. Also, the vertical thermal wind shears in simulated convection regions were found by Killworth to not be too strong. Hence, mixing momentum along with density did little to affect the overall solution. These ideas, however, appear less sound for equatorial oceanography, and so the mixing of both momentum and tracers, as afforded by option implicitvmix, might be more important in this region.