An explicit study of aerosol mass conversion and its parameterization in warm rain formation of cumulus clouds

Abstract. The life time of atmospheric aerosols is highly affected by in-cloud scavenging processes. Aerosol mass conversion from aerosols embedded in cloud droplets into aerosols embedded in raindrops is a pivotal pathway for wet removal of aerosols in clouds. The aerosol mass conversion rate in the bulk microphysics parameterizations is always assumed to be linearly related to the precipitation production rate, which includes the cloud water autoconversion rate and the cloud water accretion rate. The ratio of the aerosol mass concentration conversion rate to the cloud aerosol mass concentration has typically been considered to be the same as the ratio of the precipitation production rate to the cloud droplet mass concentration. However, the mass of an aerosol embedded in a cloud droplet is not linearly proportional to the mass of the cloud droplet. A simple linear relationship cannot be drawn between the precipitation production rate and the aerosol mass concentration conversion rate. In this paper, we studied the evolution of aerosol mass concentration conversion rates in a warm rain formation process with a 1.5-dimensional non-hydrostatic convective cloud and aerosol interaction model in the bin microphysics. We found that the ratio of the aerosol mass conversion rate to the cloud aerosol mass concentration can be statistically expressed by the ratio of the precipitation production rate to the cloud droplet mass concentration with an exponential function. We further gave some regression equations to determine aerosol conversions in the warm rain formation under different threshold radii of raindrops and different aerosol size distributions.