Data-driven eddy closure for oceanic eastward jets

Closed parameterizations (aka turbulence closures) are needed for representing the effects of unresolved oceanic mesoscale eddies in non-eddy-resolving and eddy-permitting oceanic general circulation models, such as those used for climate modeling studies. One of the most significant difficulties for parameterizing eddy effects is eddy backscatter, which largely maintains eastward jet extensions of the western-boundary currents and their adjacent recirculation zones. In this paper, we focus on the classical wind-driven, quasigeostrophic double-gyre ocean dynamics and propose and test a novel data-driven eddy closure. For this, the eddy effects are defined as the coarse-grid model errors arising from the approximation of the given eddy-resolving reference solution containing an energetic and coherent eastward jet. Without the eddy effects being taken into account, the coarse-grid non-eddy-resolving version of the model yields no eastward jet at all. These missing eddy effects are restored approximately by the implemented eddy closure that interactively corrects the dynamically resolved potential vorticity field. The closure is data-driven because it utilizes some important information about the actual eddies in the reference solution, which is treated as a substitute for the oceanic observational data. The systematically assessed closure skills are significant because the eddy-parameterized solutions qualitatively correctly recover the eastward jet, which is completely missed otherwise. First, our results serve as a proof of concept for implementing a closure extension into the primitive equations, which are used routinely in comprehensive oceanic general circulation models. Second, our results emphasize the fundamental importance of representing the key eddy/large-scale correlations by any parameterization of the eastward jet eddy backscatter.