Dynamics and microphysics in small developing cumulus clouds

This study summarizes and generalizes findings from recent studies, focusing on the connection between Cu dynamic properties, such as velocity field, entrainment/detrainment, and cloud microphysical properties, such as cloud dilution rate and droplet size distribution parameters. Special attention is paid to the mechanisms of cloud-surrounding interactions. In particular, we focus on numerical and analytical derivations from the results of 10-m-resolution Large Eddy Simulations (LES) with spectral bin microphysics and statistical analysis of the motion of passive tracers. We used wavelet filtration to separate the cloud's dynamic and microphysical fields into turbulent and convective ones. The main parameters of cloud turbulence and convective motions were evaluated. Turbulence was shown to form an interface zone of a few tens of meters between the cloud and the surrounding air. Convection-scale motions are responsible for dynamic and microphysical properties' formation in the cloud interior. The special role of the vortex ring (toroidal vortex, TV) arising in the upper part of developing clouds is stressed. This TV is responsible for dynamic and microphysical cloud structure formation. It determines the cloud's size, internal dynamics, and ascent velocity of the cloud top. It is demonstrated numerically and analytically that the TV-related cloud circulation leads to a mean adiabatic fraction of 0.4-0.5. The close relationship between this value and the shapes of the size distribution functions is demonstrated. The TV determines the width of the cloud core and disappears as soon as the core becomes diluted. Knowledge of the effects TV has on cloud microphysics and dynamics allows us to propose parameterization of the main dynamic and microphysical properties of small Cu using sounding data and aerosol concentrations. Significance statement: a) Turbulence forms a narrow interface zone along the cloud's edges and is not responsible for the dilution of the cloud body. b) The entrainment and detrainment in growing Cu are closely related to a convective-scale ring vortex (toroidal vortex, TV). The air circulation related to the TV is the main reason of cloud body dilution leading to the decrease in the adiabatic fraction. c) The mechanisms of entrainment related to the TV resolve "cloud top-liquid water paradox" and explain formation of relatively high cloud top under strong average cloud dilution. d) One of the main deficiencies of most convective parameterizations is the assumptions of cloud horizontal homogeneity and the coincidence of the altitudes of maximum entrainment and maximum vertical velocity. Due to existence of the TV, the entrainment level is located below the level of maximum velocity. The altitude of the maximum entrainment ascends together with the ascent of TV. e) The TV controls microphysical properties like adiabatic fraction (AF). There is a high correlation of properties of droplet size distributions and the value of AF.