Skewness of cloud droplet spectrum and an improved estimation for its relative dispersion

The relative dispersion of the cloud droplet spectrum is a very important parameter in describing and modeling cloud microphysical processes. Based on the definition of skewness as well as theoretical and data analyses, a linear fitting relationship (α = 2.91ε−0.59) between skewness (α) and relative dispersion (ε) is established and a new method is developed to estimate the relative dispersion of the cloud droplet spectrum. The new method does not depend on any assumption of a particular distribution for the cloud droplet spectrum and has broader applicability than the previous methods. Comparisons of the three methods for the relative dispersion with the observed data supported the following conclusions. (1) The skewness of the cloud droplet spectrum is asymmetrically distributed. An assumption of zero skewness in quantifying the relative dispersion inevitably results in relatively large deviations from the observations. Errors of the estimated relative dispersion due to the omission of the skewness term are not solely related to the skewness, but rather to the product of the skewness and relative dispersion. (2) The use of the assumption that the cloud droplet spectrum takes a gamma distribution is similar to the assumption that the skewness is twice the relative dispersion. This leads to a better accuracy in estimating the relative dispersion than that with zero skewness assumption. (3) Comparisons with observations show that the new method is more accurate than the one under gamma distribution assumption and is the best among all the three methods. (4) It is believed that finding a better correlation between the skewness and the relative dispersion would further reduce the deviations for the estimated relative dispersion.