A numerical model of a non-stationary atmospheric planetary boundary layer (PBL) over a horizontally homogeneous flat surface is derived on the basis of similarity theory. The two most typical turbulence regimes are reproduced: one corresponding to a convectively growing PBL and another corresponding to a stably stratified quasi-equilibrium PBL. The PBL is treated as a unit. Hence. its evolution is characterized by temporal changes of intrinsic parameters, such as the PBL depth, the vertically averaged values of potential temperature. specific humidity and components of wind velocity, the near-surface values of heat, water vapor and momentum fluxes. The internal structure of the PBL is considered self-similar. This allows one to represent the interaction between the air flow and the underlying surface by means of universal heat/mass transfer and resistance laws. Numerical experiments on the diurnal variations of meteorological fields in the lower 2 km layer confirm the ability of the model to reproduce the main features of the phenomena, known from observations.