6.3 Gent/McWiliams/Redi SGS Eddy parameterization

There are two parts to the Redi/GM parameterization of geostrophic eddies. The first aims to mix tracer properties along isentropes (neutral surfaces) by means of a diffusion operator oriented along the local isentropic surface (Redi). The second part, adiabatically re-arranges tracers through an advective flux where the advecting flow is a function of slope of the isentropic surfaces (GM).

The first GCM implementation of the Redi scheme was by Cox 1987 in the GFDL ocean circulation model. The original approach failed to distinguish between isopycnals and surfaces of locally referenced potential density (now called neutral surfaces) which are proper isentropes for the ocean. As will be discussed later, it also appears that the Cox implementation is susceptible to a computational mode. Due to this mode, the Cox scheme requires a background lateral diffusion to be present to conserve the integrity of the model fields.

The GM parameterization was then added to the GFDL code in the form of a non-divergent bolus velocity. The method defines two stream-functions expressed in terms of the isoneutral slopes subject to the boundary condition of zero value on upper and lower boundaries. The horizontal bolus velocities are then the vertical derivative of these functions. Here in lies a problem highlighted by Griffies et al., 1997: the bolus velocities involve multiple derivatives on the potential density field, which can consequently give rise to noise. Griffies et al. point out that the GM bolus fluxes can be identically written as a skew flux which involves fewer differential operators. Further, combining the skew flux formulation and Redi scheme, substantial cancellations take place to the point that the horizontal fluxes are unmodified from the lateral diffusion parameterization.

• 6.3.1 Redi scheme: Isopycnal diffusion
• 6.3.2 GM parameterization
• 6.3.3 Griffies Skew Flux
• 6.3.4 Variable
• 6.3.5 Tapering and stability
  • 6.3.5.1 Slope clipping
  • 6.3.5.2 Tapering: Gerdes, Koberle and Willebrand, Clim. Dyn. 1991
  
  
• 6.3.6 Tapering: Danabasoglu and McWilliams, J. Clim. 1995
• 6.3.7 Tapering: Large, Danabasoglu and Doney, JPO 1997
• 6.3.8 Package Reference

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