Spectral dispersion of cloud droplet size distributions and the parameterization of cloud droplet effective radius

Parameterization of effective radius (re) as proportional to the cube root of the ratio of cloud liquid water content (L) to droplet concentration (N), i.e., re = α(L/N)⅓, is becoming widely accepted. The principal distinction between different parameterization schemes lies in the specification of the prefactor α. This work focuses on the dependence of α on the spectral dispersion of the cloud droplet size distribution. Relationships by Pontikis and Hicks [1992] and by Liu and Hallet [1997] that account for the dependence of α on the spectral dispersion are compared to each other and to cloud microphysical data collected during two recent field studies. The expression of Liu and Hallet describes the spectral dependence of α (or re) more accurately than the Pontikis and Hicks relation over the observed range of spectral dispersions. The comparison shows that the different treatments of α as a function of spectral dispersion alone can result in substantial differences in re estimated from different parameterization schemes, suggesting that accurately representing re in climate models requires predicting α in addition to L and N.