Coupling of Wind and Potential Temperature in an Ekman Model in the Stratified Atmospheric Boundary Layer

A linear Ekman model in the stratified atmospheric boundary layer (ABL) is proposed based on the steady-state version of the linearized three-dimensional primitive equations with the inclusion of the vertical diffusivity. Due to the inclusion of the potential temperature equation and hydrostatic equation, pressure and potential temperature couple with wind in the proposed model, and thus are not arbitrarily specified variables as in previous studies on the baroclinicity in the Ekman model. The extended thermal wind balance equation and the Ekman potential vorticity equation are derived to describe the coupling. The two equations, along with the equation describing the constraint on potential temperature, are employed to derive the analytical solutions of the proposed Ekman model. Because potential temperature is not a specified variable but part of the solution, the derived analytical solutions have very different forms from those derived in previous studies. The differences illustrate the impact of the inclusion of the potential temperature equation and hydrostatic equation on wind, pressure, and potential temperature in the proposed Ekman model. It is found that the computed wind profiles based on the proposed model can capture some important features of the observed wind profiles.