Ocean kinetic energy backscatter parametrizations on unstructured grids: Impact on mesoscale turbulence in a channel

We present a new energy backscatter parametrization for primitive equation ocean models at eddy-permitting resolution, specifically for unstructured grids. Traditional eddy parametrizations in terms of viscosity closures lead to excessive dissipation of kinetic energy when used with eddy-permitting meshes. Implemented into the FESOM2 ocean model, the backscatter parametrization leads to a more realistic total dissipation of kinetic energy. It maintains a reservoir of dissipated energy and reinjects this subgrid energy at larger scales at a controlled rate. The separation between dissipation and backscatter scales is achieved by using different-order differential operators and/or spatial smoothing. This ensures numerical model stability. We perform sensitivity studies with different choices of parameter settings and viscosity schemes in a configuration with a baroclinically unstable flow in a zonally reentrant channel with a horizontally uniform mesh. The best backscatter setup substantially improves eddy-permitting simulations at 1/4 degrees and 1/6 degrees resolution, bringing them close to a 1/12 degrees eddy-resolving reference. Improvements are largest for levels of kinetic energy and variability in temperature and vertical velocity. A selected optimal default scheme is then tested in a mixed resolution setup -a channel with narrow transitions between an eddy-permitting and an eddy-resolving subdomain. The backscatter scheme is able to adapt dynamically to the different resolutions and moves the diagnostics closer to the high resolution reference throughout the domain. Our study is a first step toward using backscatter in global variable-mesh ocean models and suggests potential for substantial improvements of ocean mean state and variability at reduced computational cost.