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.