A Gaussian product stochastic Gent McWilliams parameterization
Abstract The locally averaged horizontal buoyancy flux by mesoscale eddies is computed from eddy resolving quasigeostrophic simulations of ocean mesoscale eddy dynamics. This flux has a very non Gaussian distribution peaked at zero, not at the mean value. This non Gaussian flux distribution arises because the flux is a product of zero mean random variables: the eddy velocity and buoyancy. A framework for stochastic Gent McWilliams (GM) parameterization is presented. Gaussian random field models for subgrid scale velocity and buoyancy are developed. The product of these Gaussian random fields is used to construct a non Gaussian stochastic parameterization of the horizontal subgrid scale density flux, which leads to a non Gaussian stochastic GM parameterization. This new non Gaussian stochastic GM parameterization is tested in an idealized box ocean model, and compared to a Gaussian approach that simply multiplies the deterministic GM parameterization by a Gaussian random field. The non Gaussian approach has a significant impact on both the mean and variability of the simulations, more so than the Gaussian approach; for example, the non Gaussian simulation has a much larger net kinetic energy and a stronger overturning circulation than a comparable Gaussian simulation. Future directions for development of the stochastic GM parameterization and extensions of the Gaussian product approach are discussed.