Dynamics of the planetary boundary layer with fine structure in the large scale background field

On the basis of Wu and Blumen's work (1982) on the geostrophic momentum approximation (GMA) in the planetary boundary layer (PBL) and Tan and Wu (1992, 1994) on the Ekman momentum approximation (EMA) in the PBL, some improvements about the eddy exchange coefficient K, the advective inertial force and the lower boundary condition of the PBL are developed in this paper: (1) apply the K which is a gradually varying function of height instead of a constant value in the Ekamn layer, and introduce a surface layer; (2) take the effect of the vertical advective inertial force into account; (3) the solution technique is extended from level terrain to orographically formed terrain. Under the condition of the equilibrium among four forces (the pressure-gradient force, Coriolis force, eddy viscous force and inertial force including horizontal and vertical advective inertial forces), we have obtained the analytical solutions of the distributions of the wind and the vertical velocity. The computation of an individual example shows that: (1) both the wind velocity near surface and the angle between which and the non-viscous wind are more consistent with usual observations than that of Wu and Blumen (1982); (2) comparing with the horizontal advective inertial force, the vertical advective inertial force can not be neglected, when the orography is considered, the effect of the latter is even more important than the former.