Cautionary Tales from the Mesoscale Eddy Transport Tensor

The anisotropic mesoscale eddy transport tensor is diagnosed using passive tracers advected online in both an idealized 101-member mesoscale-resolving quasi-geostrophic (QG) double-gyre ensemble, and a realistic 24-member eddying (1/12 degrees) ensemble of the North Atlantic. We assert that the Reynolds decomposition along the ensemble dimension, rather than the spatial or temporal dimension, allows us to capture the intrinsic spatiotemporal variability of the mean flow and eddies. The tensor exhibits good performance in reconstructing the eddy fluxes of passive tracers, here defined as fluctuations about the ensemble thickness-weighted averaged (TWA) mean. However, the inability of the tensor to reconstruct eddy fluxes of QG potential vorticity, which encapsulates the eddy-mean flow interaction, and other active tracers raises the question: To what extent can the diagnosed tensor be applied to inform the parametrization of mesoscale dynamics?