A third-order turbulence model of the marine stratocumulus layer, including cloud ensemble relations and detailed radiative computation, is used to study a case observed over the North Sea during the JASIN experiment. It is shown that the model is able to reconstruct the observed structure of the boundary layer, starting from only the large-scale information. A strong diurnal cycle, induced by the absorption of solar radiation of the cloud layer, is studied in some detail. The role of intermittent cumuli observed below the stratocumulus, and the significance of the cloud-top instability criterion are also investigated.