Towards quantifying droplet clustering in clouds

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 128; no. 582; pp. 1043 - 1057
• Main Authors: Shaw, R. A., Kostinski, A. B., Larsen, M. L.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01-04-2002; Wiley
• Subjects: Cloud physics; Earth, ocean, space; Exact sciences and technology; External geophysics; Meteorology; Pair‐correlation function; Poisson process; Pair correlation function; Statistical test; Fluctuations; Fractal; Spatial distribution; Cloud physics; Correlation analysis; Concentration; Droplet; Poisson process; Power spectrum
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1256/003590002320373193

Droplet positions in atmospheric clouds are random but possibly correlated on some scales. This ‘clustering’ must be quantified in order to account for it in theories of cloud evolution and radiative transfer. Tools as varied as droplet concentration power spectrum, Fishing test, and fractal correlation analysis have been used to describe the small‐scale nature of clouds, and it has been difficult to compare conclusions systematically. Here we show, by using the correlation‐fluctuation theorem and the Wiener–Khinchin theorem, that all of these measures can be related to the pair‐correlation function. It is argued that the pair‐correlation function is ideal for quantifying droplet clustering because it contains no scale memory and because of its quantitative link to the Poisson process. Copyright © 2002 Royal Meteorological Society