Air parcel's                     Upward Directed Vertical               Downwards                                 Upwards Directed

Vertical              due to    Pressure Gradient             and        Directed             and                    Buoyancy

Accelaration                    Acceleration                                Gravity Accel                              Acceleration

 

At synoptic scale, buoyancy acceleration is one order of magnitude smaller than the vertical pressure gradient acceleration, which is about the same magnitude as the acceleration of gravity.  Thus, at the synoptic scale, buoyancy acceleration can be dropped on an order of magnitude basis.  Since the upward directed pressure gradient is then balanced by the downward acceleration of gravity, the equation above becomes the hydrostatic equation.