E. Linacre and B. Geerts
In Note 1.G we discussed that the atmosphere is almost always in hydrostatic balance, and we said that hydrostatic balance means that the surface pressure can be explained entirely (100%) by the weight of the air above. There is a very slight error (i.e. of about 0.25%) in this (1). The error is NOT the result of the centrifugal force due to the spinning of the Earth. This effect is included in g, the gravitational acceleration, which is smaller at the equator than at the poles.
The error arises because the Earth is spherical, so the air above unit area is slightly wedge-shaped, and therefore the sideways force of the adjacent air tends to squeeze upwards the air in the wedge.
(1) Bannon, P.R., C.H. Bishop and J.B. Kerr 1997. Does the surface pressure equal the weight per unit area of a hydrostatic atmosphere? Bull. Amer. Meteor. Soc., 78, 2637-42.