During cold air outbreaks, cold and stably stratified air masses are advected from land or ice surfaces over a warmer sea surface. Due to the heating from below, a convective boundary layer develops. For small fetches, convection is organized in the form of horizontal roll vortices, which at greater distances join in a zone with open or closed cells. The formation of the convective boundary layer, and the associated roll vortices, is simulated with a numerical model and results are compared with observations obtained during the MASEX experiment off the east coast of the United States. To validate the model, a comparison with a one-dimensional mixed-layer model is also made. with special attention given to the exact representation of the observed initial and boundary conditions. Comparisons between model results and observations show good qualitative and quantitative correspondence in mean temperature and heat flux profiles respectively at different distances from the coast. Maximum values of vertical velocity are well reproduced. Turbulent kinetic energy is found to be concentrated in the small updraft regions of the rolls, which is in accordance with observations from the MASEX-experiment.