In (hydrostatic) atmospheric general circulation models, for example the so-calle Primitive Equations, consisting of the horizontal momentum equation, the hydrostatic balance, the continuity equation, and the energy balance
$$ \begin{eqnarray} \nonumber \frac{\partial}{\partial t}\vec{v} & = & \vec{v}\times(f+\xi)\vec{e}_z - \omega\frac{\partial}{\partial p}\vec{v} -\nabla \left(\Phi+\frac{\vec{v}^2}{2}\right) + \vec{R} \\ \frac{\partial }{\partial p}\Phi & = & -\frac{1}{\rho} = -\frac{RT}{p}\\ \nonumber 0 & = & \nabla\cdot\vec{v} + \frac{\partial}{\partial p} \omega \\ \nonumber c_p\frac{d}{d t} T & = & \frac{\omega}{\rho} + Q_{rad} + Q_{lat} + \eta + \epsilon . \end{eqnarray} $$
are solved numerically. How are these equations modified and complemented, when the atmospheric model is to be coupled to a full ocean general circulation model, what additional effects and equations have to be included?
As the salinity plays an important role in driving the oceanic circulations among other things, for example a balance equation for the salinity, appropriately coupled to the other governing equations will certainly be needed.
