The development of convection in the lower atmosphere created by diurnal heating of the earth's surface is investigated by the use of a nonlinear numerical model. It is found that under the influence of the stable stratification normally present at upper levels and with relatively strong convection, three distinctly different layers are always established, namely, a thin superadiabatic surface layer, a mixed layer, and a thin inversion layer which forms the base of a slightly modified upper stable layer. The temperature fluctuation has two maxima, one located just above the surface layer and the second in the inversion layer, while within the main body of the mixed layer the temperature fluctuation is minimal. On the other hand, the mean vertical velocity has its maximum in the middle of the mixed layer. Convection also penetrates far into the stable layer, but the horizontal cell size is much larger in the stable layer than in the mixed layer. Internal gravity waves are also set up by convection, with their maximum amplitude concentrated in the inversion layer just above the top of the mixed layer. Comparison with observations shows that the results obtained from our numerical model are in good agreement with observations, including the change of the depth of the mixed layer with time. A simple formula for the forecasting of the mixed layer depth has also been developed.