Droplet Stochastic Activation and Spectrum Broadening in the Presence of Turbulence- and Entrainment-Induced Supersaturation Fluctuations

We use parcel stochastic simulations to study the effect of cloud turbulence, entrainment, and entrained cloud condensation nuclei (CCN) activation on the evolution of the cloud droplet-size distribution. Entrainment events, turbulent mixing inside the parcel, and the resulting stochastic droplet activation and growth by condensation are simulated using a Monte Carlo scheme. The model accounts for the addition of environmental CCN into the cloud parcel by entraining eddies. This approach is made possible by describing the cloud microphysics using Lagrangian particles, the so-called super-droplets. These are either deliquesced CCN or activated cloud droplets. In consistency with previous large-eddy simulations (LES), our idealized parcel model reproduces broadening of the droplet size distribution towards smaller sizes due to permanent insertion of environmental CCN. Turbulence plays a key role in stochastically activating the entrained CCN and broadening the spectrum also towards larger sizes.

Köhler theory for droplet growth is presented in a form suitable to describe stochastic activation/deactivation in turbulent environments. The supersaturation experienced by individual cloud particles is separated into mean (resolved) and fluctuating (unresolved) parts. The mean part dictates the shape of the so-called mean-field Köhler potential (that describes droplet curvature and dissolved substances effects). The fluctuating part of the supersaturation drives the “random walk” of droplets radii along the mean-field Köhler potential landscape. In parcels that are unsaturated on average, the Köhler potential exhibits a characteristic potential well. Under these conditions, supersaturation fluctuations may aid a haze droplet to climb the potential barrier and grow beyond its activation radius (i.e., to stochastically activate). In this framework, we explore the interplay between fluctuating and mean-field thermodynamics during the supersaturation build-up in a rising parcel. It is shown that the feedback on vapor of stochastically activated droplets (under unsaturated conditions) buffers the increase of the mean supersaturation driven by cloud updraft. This significantly extends the distance over which droplets are activated inside the rising parcel. Importantly, the scheme developed in this work is ready to be used as a stochastic subgrid-scale model of the microphysics in realistic LES of natural clouds.