Volume 146, Issue 726 p. 483-504
RESEARCH ARTICLE

Droplet size distributions in turbulent clouds: experimental evaluation of theoretical distributions

Kamal Kant Chandrakar

Kamal Kant Chandrakar

Department of Physics, Michigan Technological University, Houghton, Michigan, USA

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Izumi Saito

Izumi Saito

Department of Physical Science and Engineering, Nagoya Institute of Technology, Nagoya, Japan

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Fan Yang

Fan Yang

Brookhaven National Laboratory, Upton, New York, USA

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Will Cantrell

Will Cantrell

Department of Physics, Michigan Technological University, Houghton, Michigan, USA

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Toshiyuki Gotoh

Toshiyuki Gotoh

Department of Physical Science and Engineering, Nagoya Institute of Technology, Nagoya, Japan

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Raymond A. Shaw

Corresponding Author

Raymond A. Shaw

Department of Physics, Michigan Technological University, Houghton, Michigan, USA

Correspondence

R. A. Shaw, Department of Physics, Michigan Technological University, Houghton, MI 49931, USA.

Email: [email protected]

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First published: 30 October 2019
Citations: 15
Funding information JSPS KAKENHI, 18K13611; MEXT KAKENHI, 15H02218; National Aeronautics and Space Administration, 80NSSC17K0449; National Science Foundation, AGS-1754244; US Department of Energy, DE-SC0012704

Abstract

Precipitation efficiency and optical properties of clouds, both central to determining Earth's weather and climate, depend on the size distribution of cloud particles. In this work theoretical expressions for cloud droplet size distribution shape are evaluated using measurements from controlled experiments in a convective-cloud chamber. The experiments are a unique opportunity to constrain theory because they are in steady-state and because the initial and boundary conditions are well characterized compared to typical atmospheric measurements. Three theoretical distributions obtained from a Langevin drift-diffusion approach to cloud formation via stochastic condensation are tested: (a) stochastic condensation with a constant removal time-scale; (b) stochastic condensation with a size-dependent removal time-scale; (c) droplet growth in a fixed supersaturation condition and with size-dependent removal. In addition, a similar Weibull distribution that can be obtained from the drift-diffusion approach, as well as from mechanism-independent probabilistic arguments (e.g., maximum entropy), is tested as a fourth hypothesis. Statistical techniques such as the χ2 test, sum of squared errors of prediction, and residual analysis are employed to judge relative success or failure of the theoretical distributions to describe the experimental data. An extensive set of cloud droplet size distributions are measured under different aerosol injection rates. Five different aerosol injection rates are run both for size-selected aerosol particles, and six aerosol injection rates are run for broad-distribution, polydisperse aerosol particles. In relative comparison, the most favourable comparison to the measurements is the expression for stochastic condensation with size-dependent droplet removal rate. However, even this optimal distribution breaks down for broad aerosol size distributions, primarily due to deviations from the measured large-droplet tail. A possible explanation for the deviation is the Ostwald ripening effect coupled with deactivation/activation in polluted cloud conditions.

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