A numerical model which predicts the time variation of the thermodynamic structure of the trade-wind boundary layer is developed. Horizontally homogeneous conditions are assumed and the large-scale divergence, sea surface temperature and surface wind speed are specified externally. The model predicts the average value of mixing ratio and moist static energy in the subcloud and cloud layer and the slopes of these quantities in the cloud layer; the model also predicts the height of the transition layer (the layer which defines the boundary between the cloud and subcloud layer) and the height of the trade inversion. Subcloud layer convective fluxes are specified by using the bulk aerodynamic method for specifying the surface fluxes and a mixed-layer parameterization of the fluxes at the top of the subcloud layer. The moist convective processes are parameterized in terms of a mass flux which varies linearly with height and a cloud-environment difference in thermodynamic quantities which also varies l... Abstract A numerical model which predicts the time variation of the thermodynamic structure of the trade-wind boundary layer is developed. Horizontally homogeneous conditions are assumed and the large-scale divergence, sea surface temperature and surface wind speed are specified externally. The model predicts the average value of mixing ratio and moist static energy in the subcloud and cloud layer and the slopes of these quantities in the cloud layer; the model also predicts the height of the transition layer (the layer which defines the boundary between the cloud and subcloud layer) and the height of the trade inversion. Subcloud layer convective fluxes are specified by using the bulk aerodynamic method for specifying the surface fluxes and a mixed-layer parameterization of the fluxes at the top of the subcloud layer. The moist convective processes are parameterized in terms of a mass flux which varies linearly with height and a cloud-environment difference in thermodynamic quantities which also varies l...