Sensitivity of the kinetic energy backscatter parameterization to its vertical structure in eddy-permitting ocean simulations

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 kinetic energy backscatter scheme has been employed in eddy-permitting simulations to enhance the energy of mesoscale eddies. 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 and realistic 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. Based on theoretical understanding, we formulate a scale-aware parameterization of the vertical structure, accounting for variations of the vertical structure of subgrid EKE with model resolution. This vertical structure is then applied to the energy backscatter coefficient used in 1/2, 1/4, and 1/8 degree idealized simulations of basin-scale ocean circulations. 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 simulations using 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. Examination of this parameterization scheme in realistic 1/4 degree simulations of GFDL OM4.0 is ongoing.