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Statistical Physics, Information Theory and Cloud Droplet Size Distributions

Specification of cloud droplet size distributions is essential for the calculation of radiation transfer in clouds and cloud-climate interactions, and for remote sensing of cloud properties. Despite the effort and progress made over the last few decades, a number of vital issues remain unsolved. For example, 1) It is well known that observed droplet size distributions are generally much broader than those predicted by the classical uniform model (Howell 1949). This so-called spectral broadening issue has puzzled many generations of cloud physicists. 2) An increasing amount of observational evidence has shown that the Weibull distribution best describes observed droplet size distributions (Liu et al. 1995; Costa et al. 2000; Liu and Daum 2000; Daum and Liu 2001). The physical reason for this is not clear. 3) It has been found that droplet size distributions depend on the scale over which they are sampled or simulated (Liu and Hallett 1998; Miles et al. 2000). To answer these issues and develop ways to deal with cloud-related problems, a new formalism has been developed by integrating cloud physics with the ideas that have flourished in statistical physics and information theory (Liu et al. 1995, Liu 1995; Liu and Hallett 1997, 1998). This theory takes an approach different from traditional theories, and produces promising results. Here we review the theory, discuss major results derived from it, and explore its implications for treating clouds in climate models and addressing indirect aerosol effects.