A framework for parameterization of heterogeneous ocean convection

We propose a new framework for parameterization of ocean convection processes. The new framework is termed "patchy convection" since our aim is to represent the heterogeneity of mixing processes that take place within the horizontal scope of a grid cell. We focus on applying this new scheme to represent the effect of pre-conditioning for deep convection by subgrid scale eddy variability. The new parameterization separates the grid-cell into two regions of different stratification, applies convective mixing separately to each region, and then recombines the density profile to produce the grid-cell mean density profile. The scheme depends on two parameters: the areal fraction of the vertically-mixed region within the horizontal grid cell, and the density difference between the mean and the unstratified profiles at the surface. We parameterize this density difference in terms of an unresolved eddy kinetic energy. We illustrate the patchy parameterization using a 1D idealized convection case before evaluating the scheme in two different global ocean-ice simulations with prescribed atmospheric forcing; (i) diagnosed eddy velocity field applied only in the Labrador Sea (ii) diagnosed global eddy velocity field. The global simulation results indicate that the patchy convection scheme improves the warm biases in the deep Atlantic Ocean and Southern Ocean. This proof-of-concept study is a first step in developing the patchy parameterization scheme, which will be extended in future to use a prognostic eddy field as well as to parameterize convection due to under-ice brine rejection.