A Generalized Systems Theory for the Effect of Varying Fluctuations on Cloud Droplet Size Distributions

Abstract

A systems theory has previously been developed by Liu and Hallett to interpret droplet size distributions in turbulent clouds by utilizing ideas from statistical physics and information theory. The present paper generalizes that systems theory to allow for varying fluctuations. The generalized theory provides a self-consistent theoretical framework for a wide range of fluctuations. It reduces to that presented previously when liquid water content is conserved, and becomes consistent with the uniform growth models for nonturbulent, adiabatic clouds. The theory indicates that there exists an important characteristic scale, defined as the saturation scale, beyond which droplet size distributions do not change with further increases in averaging scale, but below which droplet size distributions strongly depend on the scale over which they are sampled and are therefore ill-defined without an adequate specification of scale. It is further demonstrated that the saturation scale and the details of scale dependence depend on the level of fluctuations; stronger fluctuations lead to larger saturation scales and stronger scale dependency of droplet size distributions. The potential scale mismatch leads to issues regarding the comparability between models and observations, and the direct coupling of numerical models of different scales, which in turn underscores the significance of understanding and quantifying the scale dependence of droplet size distributions. The importance of fluctuations suggests the need to measure and analyze turbulence simultaneously and at the same scales with measurements of droplet size distributions in order to provide a practical limit to the sample size required to reach the saturation scale, and to specify the effect of turbulence. The ideas presented in this paper have general applications to fields where fluctuations exist.