The quantity is the horizontal diffusivity, while denotes vertical diffusivity. Both are quantities determined by turbulent mixing in the fluid column. Also is the fluid density, the reference density, g the gravitational acceleration, p the pressure and f the Coriolis parameter. Note that , where is the angular rotation of the Earth in radians/sec and is the latitude. Only the vertical component of Coriolis force has been retained in the momentum equations.
Note that equation (34) incorporates hydrostatic approximation, and can be readily integrated in the vertical to provide the pressure p at any depth z:
where is the atmospheric pressure and is the free surface height. Although is usually neglected, it is essential for simulation of the atmospheric loading effects on the ocean, which are important for example in hurricane-induced storm surge processes.
Note also that the form of the Coriolis terms is general in the sense that no approximations such as the f-plane or -plane have been invoked. The former approximation ignores the latitudinal variations of f, while the latter makes a linear approximation , where is and y is the coordinate in the latitudinal direction equal to , where R is the radius of the Earth.