A scale-dependent vertical structure for energy backscatter parameterizations

Ocean mesoscale eddies constitute a crucial component of ocean energy cascade, engaging in energy exchange with large-scale circulations, submesoscale eddies, and internal waves. State-of-the-art ocean climate models, which partially resolve mesoscale eddies (i.e., eddy-permitting), often exhibit weaker and more surface-intensified eddy kinetic energy (EKE) than in higher-resolution simulations and observations. The energy backscatter scheme has been employed in eddy-permitting simulations to enhance the energy of mesoscale eddies by compensating for the excessive dissipation caused by the viscosity closure. In this scheme, a proper vertical structure for the backscatter coefficient is necessary to simulate a more realistic vertical distribution of kinetic energy. 

Here we propose a parameterization for the vertical structure of subgrid EKE and implement it within the backscatter scheme in idealized eddy-permitting simulations of MOM6. The parameterization is grounded in the observation that the EKE is surface-intensified and decays faster with depth at smaller horizontal scales. The diagnosed vertical structure of EKE from eddy-resolving simulations is well-captured by surface quasi-geostrophic (SQG) modes, whose vertical structure depends on the eddy horizontal scale, Coriolis parameter, and stratification profile. Based on the SQG mode, we formulate a scale-aware parameterization of the vertical structure, accounting for the variation of subgrid eddy scale with the model horizontal grid spacing. This vertical structure is then applied to the energy backscatter coefficient used in 1/2° and 1/4° idealized simulations of basin-scale ocean circulations. The diagnostics of these eddy-permitting simulations are compared to those of a 1/32° reference simulation. The inclusion of the vertical structure in the backscatter improves the simulation of global kinetic energy distributions, large-scale circulation pathways, and isopycnal structures, compared with the eddy-permitting simulations without backscatter or with a depth-independent backscatter. Sensitivity tests show that a more surface-intensified backscatter tends to result in weaker total kinetic energy and more tilted isopycnals. This work provides insights into the parameterization of mesoscale energetics and its vertical variation in eddy-permitting simulations.