In the tracer equations, isopycnal diffusion (Redi, 1982) with isopycnal layer thickness diffusion (Gent et al., 1995), including its modification by Visbeck et al. (1997), has become a widespread choice instead of a simple horizontal diffusion. This has led to improvements in the thermocline structure and meridional overturning (Böning et al., 1995; see Section 8.3.2). For vertical mixing of tracers, a wide variety of parametrizations is currently used, such as turbulence closures (e.g., Mellor and Yamada, 1982), non-local diffusivity profiles (Large et al., 1994) and bulk mixed-layer models (e.g., Kraus and Turner, 1967). Representation of the surface mixed layer has been much improved due to developments in these parametrizations (see Section 8.3.2). Observations have shown that deep ocean vertical mixing is enhanced over rough bottoms, steep slopes and where stratification is weak (Kraus, 1990; Polzin et al., 1997; Moum et al., 2002). While there have been modelling studies indicating the significance of such inhomogeneous mixing for the MOC (e.g., Marotzke, 1997; Hasumi and Suginohara, 1999; Otterå et al., 2004; Oliver et al., 2005, Saenko and Merryfield 2005), comprehensive parametrizations of the effects and their application in coupled climate models are yet to be seen.
Many of the dense waters formed by oceanic convection, which are integral to the global MOC, must flow over ocean ridges or down continental slopes. The entrainment of ambient water around these topographic features is an important process determining the final properties and quantity of the deep waters. Parametrizations for such bottom boundary-layer processes have come into use in some AOGCMs (e.g., Winton et al., 1998; Nakano and Suginohara, 2002). However, the impact of the bottom boundary-layer representation on the coupled system is not fully understood (Tang and Roberts, 2005). Thorpe et al. (2004) studied the impact of the very simple scheme used in the HadCM3 model to control mixing of overflow waters from the Nordic Seas into the North Atlantic. Although the scheme does result in a change of the subpolar water mass properties, it appears to have little impact on the simulation of the strength of the large-scale MOC, or its response to global warming.