“…As one moves toward models with smaller domains, e.g., numerical weather prediction models or cloud resolving models (CRM), relevant dynamical processes are better resolved and this requires more precise numerical cloud models. Frequently, single-moment or two-moment bulk microphysics schemes are employed in these models (e.g., Lin et al, 1983;Hobbs, 1983, 1984;Ferrier, 1994;Walko et al, 1995;Feingold et al, 1998;Rasch and Kristjansson, 1998;Simpson et al, 2003;Hong et al, 2004;Thompson et al, 2004;Morrison and Pinto, 2005;Hong and Lim, 2006;Li et al, 2008;Thompson et al, 2008;Wang and Feingold, 2009a,b;Lim and Hong, 2010). These models predict either the first moment of a cloud particle size distribution (i.e., number concentration) or both the first and third moments (i.e., number concentration and mass mixing ratio), respectively.…”