Introduction

The characteristics and evolution of the cloud droplet and crystal size spectra determines cloud radiative properties and the formation of precipitation. Accounting for these processes in cloud-resolving models and climate models requires correct understanding and then parameterization of cloud microstructure and its dependence on predicted atmospheric parameters. During the past five decades, cloud physics and cloud optics have widely used empirical parameterizations of cloud particle size spectra such as the gamma distributions or exponential spectra described in Chapter 2.

These empirical spectra were used in the remote sensing of clouds and also in the modeling and parameterization of cloud properties and processes, both in the cloud-resolving models (CRM) and in some advanced general circulation models (GCMs). A new impetus for bulk microphysical models was given during the past two decades by development of the double-moment bulk schemes that include prognostic equations for the number concentrations of hydrometeors in addition to the mixing ratio, which allows a higher accuracy in predicting the cloud microphysical properties. The double moment schemes are used in cloud models (e.g., Ferrier, 1994; Harrington et al., 1995; Meyers et al., 1997; Cohard and Pinty, 2000; Girard and Curry, 2001; Seifert and Beheng, 2001, 2006; Morrison et al. 2005a,b; Milbrandt and Yau, 2005a,b). These schemes are also incorporated into advanced mesoscale weather prediction models such as the Weather Research and Forecast (WRF) model (e.g., Morrison et al. 2005a,b) and the weather prediction Consortium for Small-Scale Modeling (COSMO) model (e.g., Zubler et al., 2011). The most advanced general circulation models (GCMs) also began using such double-moment microphysics parameterizations that were included earlier only in cloud-resolving models (e.g., Sud and Lee, 2007; Morrison and Gettelman, 2008; Sud et al, 2009). These parameterizations are also based on using gamma distributions or exponential spectra with prescribed parameters.