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A Simple Model for Droplet Size Distribution in Atmospheric Clouds

Richard WilliamsRCA Laboratories, Princeton, NJ 08540

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Peter J. WojtowiczRCA Laboratories, Princeton, NJ 08540

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Abstract

We have used the basic probability methods of statistical mechanics to derive a droplet-size distribution function for atmospheric clouds. These methods apply to systems that have well-defined constraints, but for which microscopic processes cannot easily be followed in detail. Clouds, in their early stages of evolution, appear to be such a system. The derived expression gives the distribution as a function of the droplet volume, rather than its diameter. This agrees with a wide variety of observations on clouds for which the distribution is not bimodal, and is a convenient way to analyze data. In addition, the theory uniquely relates the width of the droplet-size distribution to the moisture content of the cloud and the concentration of condensation nuclei.

Abstract

We have used the basic probability methods of statistical mechanics to derive a droplet-size distribution function for atmospheric clouds. These methods apply to systems that have well-defined constraints, but for which microscopic processes cannot easily be followed in detail. Clouds, in their early stages of evolution, appear to be such a system. The derived expression gives the distribution as a function of the droplet volume, rather than its diameter. This agrees with a wide variety of observations on clouds for which the distribution is not bimodal, and is a convenient way to analyze data. In addition, the theory uniquely relates the width of the droplet-size distribution to the moisture content of the cloud and the concentration of condensation nuclei.

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