The evolution of the structure of the atmospheric boundary layer during the cooling phase of the diurnal cycle is studied with the help of a one-dimensional numerical model. The model uses a turbulent energy equation for the determination of the eddy exchange coefficients, which also involve the local value of the Monin-Obukhov length. The surface temperature is prescribed as a function of time and the geostrophic wind is held constant. Results are presented in nondimensional form and cover a wide range of possible values for the external parameters. After several hours of cooling the inversion layer is found to reach a maximum depth, which depends strongly upon the magnitude of the geostrophic wind and, to a lesser extent, on the cooling rate of the ground surface.