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.