Formulation of Autoconversion and Drop Spectra Shape in Shallow Cumulus Clouds

Two-moment autoconversion parameterizations as compared to accretion parameterizations exhibit significant errors suggesting that additional moments are needed to increase their accuracy. We develop a three-moment autoconversion parameterization using output from an LES model with size-resolved microphysics. Adding the third moment decreases the errors of parameterization and improves precipitation prediction. However, the errors are still significantly larger than errors of accretion rate. An analysis of the cloud drop size distributions (DSDs) in the simulated tropical convective cloud system reveals that most DSDs have a significant fraction of cloud liquid water content q(c) in the midsize droplet range (radii from 20 to 40 mu m). Our data indicate that more than 30% of DSDs have over half of q(c) contained in the midsize range and about 60% of spectra have, at least, one-third of q(c) in this range. Even when the rain/drizzle mode is small (radar reflectivity Z < -10 dBZ), there is a significant number of spectra in which fraction of q(c) in the midsize range is as large as 60%. These DSDs are more complex than the frequently used gamma or lognormal distributions, which exhibit a single mode and can be defined by three microphysical moments. The need to define DSDs by more than three moments explains the large errors in the three-moment autoconversion parameterization. The limitation of three-parameter gamma or lognormal distributions should be kept in mind when applying them in precipitating shallow cumulus clouds.