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.