A novel layered QG model

The quasigeostrophic equations model the dynamics of a rapidly rotating stratified fluid on horizontal scales that are large compared to the depth of the fluid layer.  The full 3D equations are often simplified by assuming something about the vertical composition of the fluid.  The simplest assumption is that there is one homogeneous layer.  Unfortunately this simple model does not capture important features of the earth's oceans (everyone's favorite rotating stratified fluid).  A more complicated model assumes that there are two homogeneous layers, but that the bottom layer is infinitely thick. This model captures some interesting features of the ocean but not all.  We derive a correction to the infinite-depth two layer model that still preserves the simplicity of the equations but hopefully can describe more features of the ocean.