Marine Stratocumulus Convection. Part I: Governing Equations and Horizontally Homogeneous Solutions

Abstract

A coupled, convective-radiative, boundary-layer model of marine stratocumulus clouds is presented. The model, which is a slight generalization of the cloud-topped, mixed-layer model of Lilly (1968), has as dependent variables the cloud-top height, cloud-base height, mixed-layer moist static energy and total water content, the turbulent fluxes of moist static energy and total water, the cloud-top jumps of moist static energy and total water, the cloud-top temperature, and the net radiative flux divergence at cloud top and in the mixed layer. Under horizontally homogeneous steady-state conditions the governing equations reduce to a system of algebraic equations which is easily solved. This system has been solved for sea surface temperatures between 13 and 18°C and large-scale divergences between 1?10?6 and 6?10?6 s?1. These calculations have been performed for the case when all the radiative cooling is confined to the cloud-top jump condition and for the case when some of the cooling is allowed to extend into the mixed layer. The results show that the general pattern of mixed-layer response to sea surface temperature and large-scale divergence is not highly sensitive to the radiation partition. The results also show that the thermodynamic properties of the mixed layer and the surface fluxes of moist static energy and water vapor are sensitive to sea surface temperature but not to large-scale divergence. However, the mixed-layer depth is sensitive to large-scale divergence. Roughly speaking, the depth is inversely proportional to divergence so that halving the divergence approximately doubles the depth of the layer, which means that the cloud top seeks a certain subsidence (entrainment) rate. The turbulent fluxes of heat, water vapor and liquid water are discontinuous at cloud base. These discontinuities are interpreted in terms of convective parcel paths.