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

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.

Consideration of Initial Cloud Droplet Size Distribution Shapes in Quantifying Different Entrainment‐Mixing Mechanisms

“…(1995), Chandrakar et al. (2020), and Wu and McFarquhar (2018), the shape of CDSD is critical for understanding cloud processes. In fact, the CDSDs in adiabatic clouds are not necessarily narrow as they can be broadened due to processes such as turbulent fluctuation and/or giant cloud condensation nuclei (Chandrakar et al., 2016; Desai et al., 2018; Feingold et al., 1999; Johnson, 1982; Lu, Liu, Niu, & Xue, 2018; McGraw & Liu, 2006; Prabhakaran et al., 2020; Yin et al., 2000).…”

Scaling of Turbulence and Microphysics in a Convection–Cloud Chamber of Varying Height

“…The rate of aerosol injection strongly influences the shape of the droplet size distribution, as well as the liquid water content, for the stationary state within a convection–cloud chamber (Chandrakar et al., 2016; Chandrakar, Saito, et al 2020; Krueger, 2020). We consider the question, how well can the microphysical properties be matched as the scale of a convection–cloud chamber is increased?…”

Detection of small drizzle droplets in a large cloud chamber using ultrahigh-resolution radar

“…In a realistic cloud chamber environment, we expect a population of cloud droplets with various sizes that can be repre- sented by a DSD. Particularly, when condensation and fallout are the main sources and sinks for the evolution equation for the DSD, the DSD in the cloud chamber can be approximately described by theoretically derived distributions (Saito et al, 2019;Chandrakar et al, 2020;Krueger, 2020). Here we adapt the theoretical DSD formula derived by Krueger (2020) to investigate the ability of a radar to detect a drizzle embryo present in a small sample volume under different chamber environment conditions.…”