Abstract

It is now widely accepted that cumulus cloud size distributions follow power-laws, at least over part of the cloud size spectrum. Providing reliable fits to empirical size distributions is however not a simple task, and this is reflected by the large spread in power-law exponents reported in the literature. Two well-documented idealized high-resolution numerical simulations of convective situations are here performed and analyzed in order to gain a clearer understanding of cumulus size distributions. Advanced statistical methods, including maximum likelihood estimators and goodness-of-fit tests, are employed to produce the most accurate fits possible. Various candidate distributions are tested including exponentials, power-laws and other heavy-tail functions. Size distributions estimated from clouds identified just above cloud base are found to be best modeled by exponential distributions. If one considers instead clouds identified from an integrated condensed water path, robust power-law behaviors start to emerge, in particular when deep convection is involved. In general however, these empirical distributions are best represented by alternative heavy-tail distributions such as the Weibull or cutoff power-law distributions. In an attempt to explain these results, it is suggested that exponential size distributions characterize a population where clouds interact only weakly, whereas heavy-tail distributions are the manifestation of a cloud population that self-organizes towards a critical state.