Southern Ocean Surface Buoyancy Balance

Computation of the Southern Ocean overturning transport requires knowledges of the surface buoyancy structure in the Southern Ocean. This surface buoyancy can either be prescribed or computed via a horizontal residual advection diffusion equation for the surface layer of the Southern Ocean:

\[\partial_t b_{SO} = -v^\dagger_{SO}\partial_y b_{SO} + \partial_y\left(K_s\partial_y b_{SO}\right) + \mathcal{B}_{SO}\]

Here \(\mathcal{B}_{SO}\) is the surface forcing, which can be prescribed either via a buoyancy restoring to a specified profile or via a fixed flux condition, or via a combination of the two (as in Jansen & Nadeau (2019)). \(K_s\) is a horizontal eddy diffusivity in the mixed layer, and \(v^\dagger_{SO}\) is the residual meridional advection defined as

\[v^\dagger_{SO} = \frac{\Psi_{SO}}{L_x h}\]

where \(h\) is the Southern Ocean mixed layer depth.