Parameterization of Cloud Droplet Effective Radius: Effects of Spectral Dispersion and Skewness of Cloud Droplet Size Distributions

Effective radius re (defined as the ratio of the third to the second moment of a droplet size distribution) is one of the crucial variables that determine the radiative properties of liquid water clouds (Hansen and Travis 1974). The inclusion and parameterization of re in climate models has proven to be critical for assessing global climate change (Slingo 1990; Dandin et al. 1997). There has been increasing evidence for parameterizing re as a 1/3 power law of the ratio of the cloud liquid water content (L) to the droplet concentration (N) (Pontikis and Hicks 1992; Bower and Choularton 1992; Bower et al. 1994; Martin et al. 1994; Liu and Hallett 1997; Reid et al. 1999). The “1/3” power-law takes the form