This is the second in a series of posts on the effects of cloud droplet spectral dispersion. Today we’ll look at a 2000 paper by Liu and Daum in Geophysical Research Letters, Spectral dispersion of cloud droplet size distributions and the parameterization of cloud droplet effective radius.

Parameterization of effective radius (rAbstract:_{e}) as proportional to the cube root of the ratio of cloud liquid water content (L) to droplet concentration (N), i.e., r_{e}=Î±(L/N)1/3, is becoming widely accepted. The principal distinction between different parameterization schemes lies in the specification of the prefactor Î±. This work focuses on the dependence of Î± 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 Î± 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 Î± (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 Î± as a function of spectral dispersion alone can result in substantial differences in r_{e}estimated from different parameterization schemes, suggesting that accurately representing re in climate models requires predicting Î± in addition to L and N.

The relative dispersion of the cloud is the ratio of the standard deviation of the distribution to the mean radius. A low dispersion means that the particles are all around the same size; a high dispersion means the sizes are more spread out. As mentioned in the last article, spectral dispersion is thought to play an important role in the anthropogenic modification of clouds.

Cloud droplet effective radius, r_{e}, is a key variable that is used in the radiative transfer calculations of liquid water clouds. In some global climate models, r_{e} is parameterized as a function of liquid water content and cloud droplet number concentration, such that r_{e} is directly proportional to L^{1/3} and inversely proportional to N^{1/3}. r_{e} is also directly proportional to Î±, the prefactor. If all the cloud droplets are of the same size, monodisperse, then the prefactor is about 62. This is obviously non-physical because no cloud can have a monodisperse size distribution. For polydisperse size distributions, the prefactor is increased; the broader the size distribution, the larger the prefactor.

This paper talks about several of the parameterizations of the prefactor, and how the effective radii derived from using it compares with field data. The best model is that developed by Liu et.al. (1995). The cynic in me notes that it was written by the same author as this paper. At large spectral dispersions (greater then 1.0), all but the Liu parameterization underestimate the effective radius of the distribution. The Liu parameterization actually overestimates the effective radius at high spectral dispersions. The parameterizations all did fairly equal at very low spectral dispersions (less than 0.4). The paper notes that the bias introduced by the other parameterizations is enough to cause problems in climate models.

The main conclusion of this paper is that it demonstrates that it is necessary in global climate models to include the spectral dispersion in the calculation of effective radius. Just a short summary of this paper because I’m not a modeler. But it does show that including the effects of spectral dispersion are important to be included in any climate change model.

References:

Liu, Y., L. You, W. Yang, and F. Liu, On the size distribution of cloud droplets, *Atmos. Res.*, **35**, 201-216, 1995.