Linear relation between convective cloud drop number concentration and depth for rain initiation

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Mixed-Phase Clouds: Progress and Challenges (2017, background): “Both the high cloud base (Freud and Rosenfeld 2012) and abundant aerosols can lead to smaller cloud droplet sizes.”
Review of Aerosol–Cloud Interactions: Mechanisms, Significance, and Challenges (2016, methodology): “8 (Freud and Rosenfeld 2012), the collision and coalescence does not lead to much rain formation when re is smaller than ;14mm, while above this value the coalescence rate increases very fast (Freud and Rosenfeld 2012; Gerber 1996).”
Global observations of aerosol‐cloud‐precipitation‐climate interactions (2014, background): “This has been documented extensively for a wide range of conditions around the world [Freud and Rosenfeld, 2012].”
Representation of microphysical processes in cloud‐resolving models: Spectral (bin) microphysics versus bulk parameterization (2015, background): “In real clouds, the effective radius typically increases with height, which allows one to link raindrop formation to the critical value of the effective radius [Freud et al., 2008; Freud and Rosenfeld, 2012].”