Approximate Equations for Large Scale Atmospheric Motions
  A systematic derivation of a set of equations governing large scale atmospheric motions is presented. They are derived by introducing new variables scaled in terms of a small parameter.The solution is expanded in powers of this parameter.This leads to the hydrostatic pressure and geostrophic wind equations.The resulting set of equations is similar to that proposed by J. Charney. 
Joseph B. Keller and Lu Ting