Microphysical Scaling Relations in a Kinematic Model of Isolated Shallow Cumulus Clouds

Abstract

The rain formation in shallow cumulus clouds by condensational growth and collision?coalescence of liquid drops is revisited with the aim of understanding the controls on precipitation efficiency for idealized cloud drafts. For the purposes of this analysis, a one-dimensional kinematic cloud model is introduced, which permits the efficient exploration of many microphysical aspects of liquid shallow clouds with both spectral and two-moment bulk microphysical formulations. Based on the one-dimensional model and the insights gained from both microphysical approaches, scaling relations are derived that provide a link between microphysical and macroscopic cloud properties. By introducing the concept of a macroscopic autoconversion time scale, the rain formation can be traced back to quantities such as cloud depth, average vertical velocity, lapse rate, and cloud lifetime. The one-dimensional model also suggests that the precipitation efficiency can be expressed as a function of the ratio of the macroscopic autoconversion time scale and cloud lifetime and that it exhibits threshold-like behavior.