Abstract: In this paper, based on the system of equations quantitatively describing the equilibyium model, with consideration of latent heat and frictional stress, and assuming rmonics, for the horizontal distribution of the field take the form of the approximate analytical solutions of vertical velocity and vorticity tendency on the standard level were obtained.The solutions were a set of linear polynomial in which all the term of thermal advection and vorticity advection were included, the values of these coefficients in the polynomial demonstrated the effect of these advection term on the vertcal velocity or vortcity tendency respectively. The coefficient were calculated for several standard cases. These might be help to explore qualitatively the main physical process of the development of synoptical and subsynoptical scale systems. It seems available in subtropical situation.