Fractal Analyses of High-Resolution Cloud Droplet Measurements

Abstract

Fractal analyses of individual cloud droplet distributions using aircraft measurements along one-dimensional horizontal cross sections through clouds are performed. Box counting and cluster analyses are used to determine spatial scales of inhomogeneity of cloud droplet spacing. These analyses reveal that droplet spatial distributions do not exhibit a fractal behavior. A high variability in local droplet concentration in cloud volumes undergoing mixing was found. In these regions, thin filaments of cloudy air with droplet concentration close to those observed in cloud cores were found. Results suggest that these filaments may be anisotropic. Additional box counting analyses performed for various classes of cloud droplet diameters indicate that large and small droplets are similarly distributed, except for the larger characteristic spacing of large droplets. A cloud-clear air interface defined by a certain threshold of total droplet count (TDC) was investigated. There are indications that this interface is a convoluted surface of a fractal nature, at least in actively developing cumuliform clouds. In contrast, TDC in the cloud interior does not have fractal or multifractal properties. Finally a random Cantor set (RCS) was introduced as a model of a fractal process with an ill-defined internal scale. A uniform measure associated with the RCS after several generations was introduced to simulate the TDC records. Comparison of the model with real TDC records indicates similar properties of both types of data series.