Two energetically-motivated backscatter schemes in the ocean component of CESM3

Abstract: Global ocean models at resolutions that do not resolve mesoscale eddies lack variability, not just on scales that they cannot represent because they are below the grid scale, but also on resolvable scales. This talk presents two backscatter parameterizations that increase variability on the resolved scales. Both parameterizations appear in the momentum equations, and both schemes set the rate of backscatter, viz. the rate at which energy is injected to the resolved scales, proportional to the rate at which other parameterizations remove energy from the resolved scales. One scheme, stochastic GM+E, sets the amplitude of a stochastic backscatter proportional to the rate at which the GM parameterization removes potential energy from resolved scales; this models the physical process whereby mesoscales transfer energy towards larger scales. The other scheme, Leith+E, sets the coefficient of a negative Laplacian viscosity in such a way that the backscatter rate is proportional to the rate at which a biharmonic hyperviscosity removes kinetic energy from the resolved scales. On its own, this does not model a physical process per se, but rather corrects the error associated with excess kinetic energy dissipation by the biharmonic term. The Leith+E parameterization however also adjusts the biharmonic coefficient so that the Laplacian/biharmonic combination still truncates the enstrophy cascade at the grid scale, following the original Leith scheme, which is itself motivated by the original Smagorinsky scheme.

Both of these parameterizations are implemented in the MOM6 ocean model, which forms (inter alia) the ocean component of the forthcoming third version of the Community Earth System Model. Results are presented on the impact of these parameterizations at nominal 2/3-degree resolution. Stochastic GM+E acts primarily outside the tropics, where it impacts SST variability and southern-hemisphere sea ice extent. Leith+E primarily acts in the tropics, where it impacts SST variability and the representation of the sub-thermocline zonal jet structure in the equatorial Pacific.