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

Parameterization of effective radius ( r e ) as proportional to the cube root of the ratio of cloud liquid water content (L) to droplet concentration (N), i.e., r e = 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 r e ) 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 r e estimated from different parameterization schemes, suggesting that accurately representing r e in climate models requires predicting α in addition to L and N.