Comparison of Dynamical Simulations and Statistical Predictions for Models of Open-Ocean Deep Convection

Open-ocean deep convection plays an important role in maintaining the thermohaline circulation, which governs the poleward transport of heat in the ocean. It is mainly observed in the Labrador Sea, the Greenland Sea, and the Weddell Sea in the Atlantic Ocean, as well as in the Gulf of Lyons in the Mediterranean Sea. In these weakly stratified ocean basins, large scale vigorous cooling at the surface produces a density inversion and the possibility of overturning. Because of constraints due to the Earth's rotation and the finite ocean depth, the fluid cannot overturn on the scale of cooling, but rather responds through the development of many small-scale convection cells. Such small-scale dynamic processes cannot be resolved in global climate models, and must therefore be parametrized adequately. Recently, DiBattista and Majda (JPO 1999) derived an equilibrium statistical theory for a simplified quasi-geostrophic two-layer model by Legg and Marshall(JPO 1993), where each convective tower is idealized as a heton, that is a purely baroclinic alignment of two point vortices of identical strength but opposite sign. This theory predicts the spread of heat and potential vorticity following cold-air outbreaks based just on a few large-scale parameters. DiBattista, Majda, and Marshall (JPO 2000) extended this theory to include the effect of preexisting wind-driven gyres or sea-bottom topography. Consistent with observation, their statistical theory predicts the concentration of cold temperature anomalies about peaks of upwelling isopycnals.

Here we quantitatively evaluate the success of the statistical theory in predicting the congregation of heat and potential vorticity. To do so, we add well-resolved finite-area hetons to ambient flow preconditioned by wind-driven gyres or bottom topography, and observe the temporally evolving regions of strain and coalescence of the convectively forced potential vorticity. Our numerical simulations of two-layer geostrophic dynamics demonstrate again the remarkable predictive capabilities of equilibrium statistical theories, which was shown previously by Grote and Majda in the simpler context of purely barotropic flow (Phys. Fluids 1997 and Nonlinearity 2000). This approach may open up the possibilities for parametrization of open-ocean convection events via large-scale statistical theories, without resolving the highly complex detailed dynamics involved.