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 roo t of the ratio of cloud liquid water content (L) to droplet concentration ( N), i.e., r(e) = alpha(L/N)(1/3), is becoming widely accepted. The principa l distinction between different parameterization schemes lies in the specif ication of the prefactor alpha. This work focuses on the dependence of alph a on the spectral dispersion of the cloud droplet size distribution. Relati onships by Pontikis and Hicks [1992] and by Liu and Hallet [1997] that acco unt for the dependence of a on the spectral dispersion are compared to each other and to cloud microphysical data collected during two recent field st udies. The expression of Liu and Wallet describes the spectral dependence o f alpha (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 alpha as a function of spectral dispersion alone ca n result in substantial differences in r(e) estimated from different parame terization schemes, suggesting that accurately representing r(e) in climate models requires predicting alpha in addition to L and N.