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.