Scaling laws for shallow moist convection

Large-Eddy Simulation is used to investigate the similarity structure of shear free non-precipitating moist convection. The experimental framework is that of a uniformly stratified atmosphere with an exponentially decaying moisture profile. The layer is forced by a constantly evolving sea-surface temperature chosen to maintain a constant surface buoyancy flux. Large-scale advective and radiative tendencies are set to zero. Thus the nominal parameters in the problem are the external stratification, moisture scale height, and surface buoyancy flux. Numerical experiments which survey the parameter space are conducted. In any particular experiment initially the boundary layer is everywhere unsaturated and grows following the convective boundary layer scaling for a constant buoyancy flux, in that the boundary layer depth grows as the square root of time. With the appearance of clouds the boundary layer grows linearly in time. Physically this scaling can be explained by noting that the cloud layer grows by detraining and evaporating water mass in the inversion layer, because the evaporation rate scales with the cloud layer depth this yields an equivalent forcing which scales with time and a boundary layer growth which also is linear in time. Other aspects of the scaling, such as a Bowen ratio dependence of the cloud fraction, and the cloud base mass flux, will be presented and justified, as will the basic structure of the simulated cloud fields.