A STATISTICAL-MODEL OF DROP-SIZE SPECTRA FOR STRATOCUMULUS CLOUDS

The purpose of this work is to present a simplified model of cloud-dro plet spectra that can be used as a tool for interpreting cloud microph ysical observations in boundary-layer clouds, and as a way to begin qu antifying the couplings between cloud microphysics, dynamics and radia tive properties for eventual use in cloud parametrizations. The model is steady-state, ignores nucleation effects, and is formulated to prod uce horizontally averaged statistics. The major difference between thi s model and previous work lies in the model assumption that droplet sp ectra at a given level within a cloud are horizontal averages over a l arge number of air parcels, each of which can have a different lifting condensation level (LCL). Vertical motions are driven by buoyancy, so that liquid water and vertical velocity are simple functions of heigh t above the LCL. This relationship, treated statistically over a large number of parcels, relates turbulent kinetic energy to horizontally a veraged statistics of the droplet spectra. The broadening of droplet s pectra is thus directly related to the turbulent kinetic energy within a cloud. In validating the model, results are compared with observati ons. It is shown that the basic droplet spectra predicted by the model are quite realistic for stratus and stratocumulus. The modelled dropl et spectra broaden from cloud base to cloud top as is frequently obser ved, and the relationship between drop spectrum width and mean radius agrees quite well with observations.