Equatorial Circulation of a Global Ocean Climate Model with Anisotropic Horizontal Viscosity

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Abstract
Horizontal momentum flux in a global ocean climate model is formulated as an anisotropic viscosity with two spatially varying coefficients. This friction can be made purely dissipative, does not produce unphysical torques, and satisfies the symmetry conditions required of the Reynolds stress tensor. The two primary design criteria are to have viscosity at values appropriate for the parameterization of missing mesoscale eddies wherever possible and to use other values only where required by the numerics. These other viscosities control numerical noise from advection and generate western boundary currents that are wide enough to be resolved by the coarse grid of the model. Noise on the model gridscale is tolerated provided its amplitude is less than about 0.05 cm s−1. Parameter tuning is minimized by applying physical and numerical principles. The potential value of this line of model development is demonstrated by comparison with equatorial ocean observations. In particular, the goal of producing model equatorial ocean currents comparable to observations was achieved in the Pacific Ocean. The Equatorial Undercurrent reaches a maximum magnitude of nearly 100 cm s−1 in the annual mean. Also, the spatial distribution of near-surface currents compares favorably with observations from the Global Drifter Program. The exceptions are off the equator; in the model the North Equatorial Countercurrent is improved, but still too weak, and the northward flow along the coast of South America may be too shallow. Equatorial Pacific upwelling has a realistic pattern and its magnitude is of the same order as diagnostic model estimates. The necessary ingredients to achieve these results are wind forcing based on satellite scatterometry, a background vertical viscosity no greater than about 1 cm2 s−1, and a mesoscale eddy viscosity of order 1000 m2 s−1 acting on meridional shear of zonal momentum. Model resolution is not critical, provided these three elements remain unaltered. Thus, if the scatterometer winds are accurate, the model results are consistent with observational estimates of these two coefficients. These winds have larger westward stress than NCEP reanalysis winds, produce a 14% stronger EUC, more upwelling, but a weaker westward surface flow. In the Indian Ocean the seasonal cycle of equatorial currents does not appear to be overly attenuated by the horizontal viscosity, with differences from observations attributable to interannual variability. However, in the Atlantic, the numerics still require too large a meridional viscosity over too much of the basin, and a zonal resolution approaching 1° may be necessary to match observations. Because of this viscosity, increasing the background vertical viscosity slowed the westward surface current; opposite to the response in the Pacific.

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