Ocean eddy parameterizations: Stochastic and deterministic approaches for kinetic energy injection

In this study, we introduce a variety of ocean eddy parameterizations and discuss how they affect the representation of mesoscale turbulence in ocean models. They ultimately all aim at reducing overdissipation at eddy-permitting resolutions by utilizing the inverse energy cascade and energy conversions between potential and kinetic energy. Mesoscale eddies play a crucial role in the global oceans. They transport tracers and heat, cascade energy across scales and interact with the mean currents and the atmosphere. However, their representation at resolutions close to the Rossby radius of deformation is insufficient. Such eddy-permitting, i.e. barely eddy resolving grids are still commonly applied for decadal climate simulations and will remain state-of-the-art at high latitudes for years to come. These simulations generally suffer from an excessive dissipation of kinetic energy, leading to reduced eddy variability, eddy formation and eddy-mean flow interactions. Reducing overdissipation via optimized viscous closures is one way forward. Another option is to reinject some of the overdissipated energy back into the resolved flow via so called kinetic energy backscatter parameterizations. We will investigate different methods how to complement our own viscous and backscatter schemes with stochastic components, to account for unresolved chaotic variations of dissipative processes and for scale interactions across the resolution limit. For this purpose, we use data informed approaches such as linear inverse models to generate stochastic patterns based on high resolution reference simulations of idealized channel and double gyre configurations. Our results show that incorporation of such schemes can help to substantially improve the kinetic energy and mean flow characteristics. Furthermore, the varied application of the noise can reveal pathways of energy conversion between potential and kinetic energy, shedding light on the simulated energy cascades at such model resolutions. Aside from the learned construction of the stochastic patterns based on high resolution data, these new schemes come at a small additional computational cost, especially compared to higher resolution simulations. When tuned with caution, they provide a means to incorporate model uncertainty and to reduce systematic biases in ocean models.