Analysis of Tools Used to Quantify Droplet Clustering in Clouds

The spacing of cloud droplets observed along an approximately horizontal line through a cloud may be analyzed using a variety of techniques to reveal structure on small scales, sometimes called clustering, if such structure exists. A number of techniques have been applied and others have been suggested but not yet rigorously defined and applied. In this paper techniques are studied and evaluated using synthetic droplet spacing data. For the type of small-scale structure (clustering) modeled in this study, the most promising analysis approach is to use a combination of the power spectrum and the fishing statistic. Standard deviations and confidence intervals are determined for the power spectrum, the pair correlation function, and a modified fishing statistic. The clustering index and the volume-averaged pair correlation are shown to be less usefully normalized forms of the fishing statistic.