The geostrophic wind is defined as the wind resulting from the balance between the Coriolis force and the pressure gradient force. Frictional effects are neglected, which is usually a very good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere. However, although ageostrophic terms are relatively small, they are important for the time evolution of the flow.
The geostrophic wind (ug,vg) can be derived from the primitive equations, using the geostrophic approximation:
where g is the force of gravity (9.81 m/s^2), f is the Coriolis parameter (approximately 1e-4; varies with latitude) and Z is the geopotential height field. The validity of this approximation is dependent on the local Rossby number: It is invalid at the equator because f is zero there, and therefore generally not used in the tropics.
Other variants of the equation are possible, e.g. using the pressure field instead of Z, but are slightly more complex.