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Abstract:
Condensation is the dominating growth mechanism of small droplets in developing clouds. In this regard, the standard theory of Köhler for droplet formation gives the saturation conditions by which an aerosol particle is in equilibrium with its surrounding environment or, contrarily, grows unboundedly due to condensation. While this theory provides clear-cut threshold supersaturation values for droplet activation, clouds are eminently turbulent, subject to environmental constraints and are composed of large families of droplets competing for water vapor. This work proposes a nonlinear stochastic framework to extend this standard theory in order to account for (i) turbulent effects on droplet de/activation, and (ii) stagnating environmental conditions in the condensational growth equation. The latter effects are modelled by a nonlinear sink term modifying Köhler’s equation and the former by stochastic perturbations driven by white noise.The resulting Brownian models allow for dynamic transitions between haze and cloud droplets under fluctuations of supersaturation, yielding a hysteresis phenomenon when the latter is varying slowly and monotonically like an ascending air parcel. In our Brownian models, particle's size distributions are described by Gibbs states. Comparisons with experimental data obtained from closed chamber clouds are conducted. The results show that predictions made by Gibbs states match to a high-degree of accuracy the experimentally obtained distributions. Concretely, our Brownian models can predict bimodal distributions in which haze and activated droplets coexist, when the standard theory cannot. With such attributes, we believe that our Brownian modelling framework might provide a basis for future developments of cloud droplet activation parameterizations.
