An equilibrium statistical model for the spreading phase of open-ocean convection

A "most probable state" equilibrium statistical theory for random distribut ions of hetons in a closed basin is developed here in the context of two-la yer quasigeostrophic models for the spreading phase of open-ocean convectio n. The theory depends only on bulk conserved quantities such as energy, cir culation, and the range of values of potential vorticity in each layer The simplest theory is formulated for a uniform cooling event over the entire b asin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sit es, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection,,vith a stabilizing barotropic rim current and localized temperature anomaly.