Statistical Parameterization of Heterogeneous Oceanic Convection

A statistical convective adjustment scheme is proposed that attempts to account for the effects of mesoscale and submesoscale variability of temperature and salinity typically observed in the oceanic convective regions. Temperature and salinity in each model grid box are defined in terms of their mean, variance, and mutual correlations. Subgrid-scale instabilities lead to partial mixing between different layers in the water column. This allows for a smooth transition between the only two states (convection on and convection off) allowed in standard convective adjustment schemes. The advantage of the statistical parameterization is that possible instabilities associated with the sharp transition between the two states, which are known to occasionally affect the large-scale model solution, are eliminated. The procedure also predicts the generation of correlations between temperature and salinity and the presence of convectively induced upgradient fluxes that have been obtained in numerical simulations of heterogeneous convection and that cannot be represented by standard convective adjustment schemes.