This study attempts to formulate an improved model for the turbulent atmospheric boundary layer (ABL). The present model employs three new ingredients: 1) an updated expression for the pressure-velocity correlation, 2) an updated expression for the pressure-temperature/concentration correlation, and 3) deduced fully explicit anisotropic expressions for the turbulent fluxes of momentum, heat/concentration. A parameterization scheme is used to represent the impact of urban buildings on the airflow in mesoscale atmospheric models. The buildings are not explicitly resolved in this model, but their effect on the grid-averaged variables is parameterized as extra terms in the transport equations of momentum, heat, turbulent kinetic energy and its dissipation rate. This improved model gives a more realistic picture of the impact of the urban surfaces on the airflow as compared to the one-parametric turbulence models.