Specification of eddy transfer coefficients in coarse-resolution ocean circulation models

Abstract

Parametric representations of oceanic geostrophic eddy transfer of heat and salt are studied ranging from horizontal diffusion to the more physically based approaches of Green and Stone (GS) and Gent and McWilliams (GM). The authors argue for a representation that combines the best aspects of GS and GM: transfer coefficients that vary in space and time in a manner that depends on the large-scale density fields (GS) and adoption of a transformed Eulerian mean formalism (GM). Recommendations are based upon a two-dimensional (zonally or azimuthally averaged) model with parameterized horizontal and vertical fluxes that is compared to three-dimensional numerical calculations in which the eddy transfer is resolved. Three different scenarios are considered: 1) a convective "chimney" where the baroclinic zone is created by differential surface cooling; 2) spindown of a frontal zone due to baroclinic eddies; and 3) a wind-driven, baroclinically unstable channel. Guided by baroclinic instability theory and calibrated against eddy-resolving calculations, the authors recommend a form for the horizontal transfer coefficient given by k = αf/√Ri l2 = αM2/N l2, where Ri = f2N2/M4 is the large-scale Richardson number and f is the Coriolis parameter; M2 and N2 are measures of the horizontal and vertical stratification of the large-scale flow, l measures the width of the baroclinic zone, and α is a constant of proportionality. In the very different scenarios studied here the authors find α to be a "universal" constant equal to 0.015, not dissimilar to that found by Green for geostrophic eddies in the atmosphere. The magnitude of the implied k, however, varies from 300 m2 s-1 in the chimney to 2000 m2 s-1 in the wind-driven channel.