Mesoscale eddies in the ocean have a scale of 50 to 100 km, and correspond dynamically to high and low pressure systems in the atmosphere. The role of eddies for climate change arises from their influence on the circulation by (i) transporting and mixing temperature and salinity, (ii) exchanging (usually extracting) potential energy from the mean flow, and (iii) exchanging momentum with the mean flow (in both directions). Eddy processes are of primary importance for the dynamics of intense western boundary currents, through the exchange of momentum and energy via instability and/or rectification processes, and also influence the dynamics of the Southern Ocean. The eddy contribution to the meridional transport of heat and fresh water is small in many regions but cannot be ignored on the global scale. Long lived, propagating eddies such as Agulhas rings determine a major part of the inter-basin exchange between Indian and South Atlantic Oceans. The decaying rings provide a source of warm salty water important for the global thermohaline circulation (de Ruijter et al., 1999), and variations in that exchange may generate THC variations.

Considerable progress has been made in recent years with the parametrization of eddies in climate models of coarse and medium resolution (cf., Chapter 8, Table 8.1) which do not explicitly represent eddies. New schemes are based on eddy dynamics and the physics of baroclinic instability. Lateral eddy mixing of tracers such as potential temperature and salinity is mainly directed along isopycnals, and has a small effect on the dynamics but is important for water mass properties. The traditional mixing along horizontal surfaces which is still used in several climate models leads to unrealistic upwelling in the western boundary current (Boening et al., 1995) and strongly resolution-dependent simulations of meridional overturning and heat transport (Roberts and Marshall, 1998). Isopycnal mixing is natural in models with an isopycnal vertical co-ordinate, for other models a stable and conservative algorithm for isopycnal rotation of the diffusion tensors is now available (Griffies et al., 1998).

The dynamical effects of baroclinic instability are now frequently parametrized as an additional eddy advection of tracers (Gent et al., 1995). With this parametrization, the northward heat transport in the North Atlantic Ocean is less dependent on resolution, and matches the observational estimates much better. Aspects of the Southern Hemisphere circulation are also improved by this parametrization. Theoretical studies (e.g., Killworth, 1997) suggest somewhat different formulations based on down-gradient mixing of potential vorticity. The strengths of isopycnal mixing and eddy-induced advection are usually described empirically through coefficients which are constant or dependent on grid size. For modelling climate change, it is, however, imperative to relate these coefficients to properties of the mean flow (Visbeck et al., 1997).

The parametrization of exchange of eddy momentum with the mean flow remains a challenge. Some studies suggest a substantial eddy influence on the mean barotropic flow based on the interaction of a statistical eddy field with bottom topography (Eby and Holloway, 1994; Merryfield and Holloway, 1997). However, due to the near-geostrophy of ocean currents, it is possible that these processes are not as critical as the sub-grid scale effects on tracers for the overall quality of ocean model solutions.

In summary, while the effects of ocean eddies for climate change are likely to be moderately small, a quantitative assessment will require coupled simulations with eddy-permitting ocean models.

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