Towards a stochastic Gent-McWilliams parameterization

The Gent-McWilliams (GM) parameterization mimics the effects of mesoscale turbulent eddies on the mean flow in terms of adiabatic diffusion that reduces available potential energy. This representation of baroclinic instability significantly improves the mean state of non-eddy-resolving ocean model solutions. Hence, it is standard procedure to employ the GM parameterization in the ocean components of state-of-the-art climate models. However, due to its diffusive nature and the corresponding lack of backscatter, the GM parameterization tends to damp intrinsic ocean variability. For the detection and projection of climate change it is crucial that climate models adequately simulate the intrinsic low-frequency ocean variability. Here we demonstrate how the GM parameterization can be extended such that eddy-driven low-frequency ocean variability is excited. First, we diagnose the instantaneous eddy forcing related to the baroclinic energy pathway via spatial filtering that adequately accounts for the representation error of the equations of motion on the non-eddy-resolving model grid. Second, we parameterize the resulting large-scale eddy forcing by complementing the GM term with a dynamical field expansion. For that, the spatial fields are obtained from the large-scale available potential energy budget. The expansion coefficients are ultimately modelled stochastically, and convergence is accomplished via delay embedding. The resulting stochastic GM parameterization induces the eddy-driven large-scale low-frequency variability. It is efficiently computed from the equations of motion, and provides a clear physical interpretation related to the reservoir and conversion of available potential energy.