Alternative Formulations
A number of alternative formulations leading to Stommel model $$ r \nabla^2 \psi + \beta \frac{\partial \psi}{\partial x} = F_\tau(x, y) $$ are possible. These alternatives are less well justified than the derivation from the planetary-geostrophic equations, but their different assumptions show the model is robust and indicate how it can be extended to include topographic or nonlinear effects, and show how the model might be extended to include topographic or nonlinear effects

In what follows, we will introduce two such alternative formulations