On the size distribution of cloud droplets

The cloud droplet size distribution pattern of statistical significance is addressed after discussing the four uncertainties (subjective, measurement, mathematical and instinctive) about the classical “one-to-one” descriptions. The case study shows that the Weibull distribution n(D) = N0Dq−1exp( −λDq) could be the distribution pattern. A system theory on atmospheric particle systems is developed by introducing Shannonʹs entropy, extending the classical statistical mechanics into atmospheric particle systems, and connecting the size distributions with the physical and/or chemical laws which control the systems. With this new theory the maximum likelihood distribution of atmospheric particles is derived to be a form of the Weibull distribution; the maximum likelihood distribution of cloud droplets is of the form n(D) = N0D2exp(−λD3), a special case of the Weibull distribution, under the assumptions of dynamically conservative total cloud droplet number and mass. The theory is in good agreement with the observations.