Towards quantifying droplet clustering in clouds

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.