• Unresolved temperature fluctuations interact with nonlinear seawater equation of state 9 to produce significant errors in large scale density • We propose two data informed, computationally efficient parameterizations to correct this error in density • The first proposed parameterization is deterministic while the second is stochastic-1-This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as

The Gent-McWilliams parameterization is commonly used in global ocean models to model the advective component of tracer transport effected by unresolved mesoscale eddies. The vertical structure of the transfer coefficient in this parameterization is studied using data from a 0.1 • resolution global ocean-ice simulation. The vertical structure is found to be well approximated by a baroclinic mode structure with no flow at the bottom, though horizontal anisotropy is crucial for obtaining a good fit. This vertical structure is motivated by reference to the vertical structure of mesoscale eddy velocity and density anomalies, which are also diagnosed from the data. Plain Language Summary Ocean mesoscale eddies transport tracers like heat, salt, and dissolved carbon dioxide, inter alia. In numerical models where these eddies are not resolved, their effects need to be parameterized. This research addresses the vertical structure of a widely used parameterization, and connects the results to vertical structure of the eddies themselves. In this combined parameterization there is one J that applies for every tracer (Bachman et al., 2015). The symmetric part of the 3 × 3 matrix J corresponds to diffusion (or anti-diffusion, depending on the sign of the

Ocean circulation models have systematic errors in large‐scale horizontal density gradients due to estimating the grid‐cell‐mean density by applying the nonlinear seawater equation of state to the grid‐cell‐mean water properties. In frontal regions where unresolved subgrid‐scale (SGS) fluctuations are significant, dynamically relevant errors in the representation of current systems can result. A previous study developed a novel and computationally efficient parameterization of the unresolved SGS temperature variance and resulting density correction. This parameterization was empirically validated but not tested in an ocean model. In this study, we implement deterministic and stochastic variants of this parameterization in the pressure‐gradient force term of a coupled ocean‐sea ice configuration of the community Earth system model‐modular ocean model version 6 and perform a suite of hindcast sensitivity experiments to investigate the ocean response. The parameterization leads to coherent changes in the large‐scale ocean circulation and hydrography, particularly in the Nordic Seas and Labrador Sea, which are attributable in large part to changes in the seasonally varying upper‐ocean exchange through Denmark Strait. In addition, the separated Gulf Stream strengthens and shifts equatorward, reducing a common bias in coarse‐resolution ocean models. The ocean response to the deterministic and stochastic variants of the parameterization is qualitatively, albeit not quantitatively, similar, yet qualitative differences are found in various regions.