Anisotropic Gent–McWilliams Parameterization for Ocean Models

Abstract

An anisotropic generalization of the Gent?McWilliams (GM) parameterization is presented for eddy-induced tracer transport and diffusion in ocean models, and it is implemented in an ocean general circulation model using a functional formalism to derive the spatial discretization. This complements the anisotropic viscosity parameterization recently developed by Smith and McWilliams. The anisotropic GM operator is potentially useful in both coarse- and high-resolution ocean models, and in this study the focus is on its application in high-resolution eddying solutions, for which it provides an adiabatic alternative to the more commonly used biharmonic horizontal diffusion operators. It is shown that realistically high levels of eddy energy can be simulated using harmonic anisotropic diffusion and friction operators. Isotropic forms can also be used, but these tend either to overly damp the solution when a large diffusion coefficient is used or to introduce unacceptable levels of numerical noise when a small coefficient is used. A series of numerical simulations of the North Atlantic Ocean are conducted at 0.2° resolution using anisotropic viscosity, anisotropic GM, and biharmonic mixing operators to investigate the effects of the anisotropic forms and to isolate changes in the solutions specifically associated with anisotropic GM. A high-resolution 0.1° simulation is then conducted using both anisotropic forms, and the results are compared with a similar run using biharmonic mixing. Modest improvements are seen in the mean wind-driven circulation with the anisotropic forms, but the largest effects are due to the anisotropic GM parameterization, which eliminates the spurious diapycnal diffusion inherent in horizontal tracer diffusion. This leads to significant improvements in the model thermohaline circulation, including the meridional heat transport, meridional overturning circulation, and deep-water formation and convection in the Labrador Sea.