Estimating eddy stresses by fitting dynamics to observations using a residual-mean ocean circulation model and its adjoint

A global ocean circulation model is formulated in terms of the "residual mean" and used to study eddy-mean flow interaction. Adjoint techniques are used to compute the three-dimensional eddy stress field that minimizes the departure of the coarse-resolution model from climatological observations of temperature. The resulting 3D maps of eddy stress and residual-mean circulation yield a wealth of information about the role of eddies in large-scale ocean circulation. In eddy-rich regions such as the Southern Ocean, the Kuroshio, and the Gulf Stream, eddy stresses have an amplitude comparable to the wind stress, of order 0.2 N m(-2), and carry momentum from the surface down to the bottom, where they are balanced by mountain form drag. From the optimized eddy stress, 3D maps of horizontal eddy diffusivity kappa are inferred. The diffusivities have a well-defined large-scale structure whose prominent features are 1) large values of kappa (up to 4000 m(2) s(-1)) in the western boundary currents and on the equatorial flank of the Antarctic Circumpolar Current and 2) a surface intensification of kappa, suggestive of a dependence on the stratification N-2. It is shown that implementation of an eddy parameterization scheme in which the eddy diffusivity has an N-2 dependence significantly improves the climatology of the ocean model state relative to that obtained using a spatially uniform diffusivity.