A Toy Model for the Response of the Residual Overturning Circulation to Surface Warming

A simple model for the deep-ocean overturning circulation is presented and applied to study the ocean's response to a sudden surface warming. The model combines one-dimensional predictive residual advection-diffusion equations for the buoyancy in the basin and Southern Ocean surface mixed layer with diagnostic relationships for the residual overturning circulation between these regions. Despite its simplicity, the model reproduces the results from idealized general circulation model simulations and provides theoretical insights into the mechanisms that govern the response of the overturning circulation to an abrupt surface warming. Specifically, the model reproduces a rapid shoaling and weakening of the Atlantic meridional overturning circulation (AMOC) in response to surface warming, followed by a partial recovery over the following decades to centuries, and a full recovery after multiple millennia. The rapid partial recovery is associated with adjustment of the lower thermocline, which itself is shown to be accelerated by the weakened AMOC. Full equilibration instead requires adjustment of the abyssal buoyancy, which is shown to be governed by diapycnal diffusion and surface fluxes around Antarctica.