Scale Dependent Surface Horizontal Eddy Diffusivity and Its Linkage to Kinetic Energy Spectra

Oceanic tracer distributions are modified by ocean motions of all scales, but only the large scale motions are resolved by the present day Earth System Models. In these models the unresolved sub-gridscale tracer transport is generally parameterized through diffusive closures with a scale-independent constant diffusion coefficient. However, evidence from observations and basic theory suggest that diffusivity should be scale dependent. Here we use a recently developed MicroInverse method to diagnose the diffusion tensor at the ocean surface from sea surface temperature and sea level observations, as well as from idealized model simulations. We compare these results to existing parameterizations of stirring by shear and strain in the large scale currents, as well as mixing by sub-gridscale velocity fluctuations. We find that the spatial pattern of diffusivity is linked to the kinetic energy of the flow, and that the large scale stirring explains most of the diagnosed diffusivity below 2º scale, while the small scale mixing becomes important at larger scales. We also find that between 0.5º-2º resolution the diffusivity scales as the length scale (grid size) to the power of 4/3 in the tropics and close to the boundary currents, while the scaling is closer to 2/3 in the gyre interiors. We discuss the (non-trivial) linkage between the diffusivity-wavenumber spectra and the kinetic energy-wavenumber spectra, and emphasize the need for scale aware diffusivity parameterizations.