On Idealized Models of Turbulent Condensation in Clouds

Abstract Various microphysical models attempt to explain the occurrence of broad droplet size distributions (DSDs) in clouds through approximate representations of the stochastic droplet growth by condensation in a turbulent environment. This work analyzes specific idealized models, where the variability of droplet growth conditions arises primarily from variability in the turbulent vertical velocity of the air carrying these droplets. Examples are the stochastic eddy-hopping model operating in adiabatic parcels and certain types of direct numerical simulation (DNS)-like models. We show that such models produce droplet size statistics that are spatially inhomogeneous along the vertical direction, causing the predicted DSD to depend on the DSD spatial sampling scale Δ. In these models, Δ is implicitly related to the spatial extent of the droplet turbulent diffusion (approximated by Brownian-like excursions) and thus grows like t 1/2 . This leads to spurious continuous DSD broadening, as the growth in time (also like t 1/2 ) of the standard deviation of droplet squared radius arises essentially from the growth of the sampling scale Δ. Also, the DSDs predicted by the models discussed here are nonlocally broad (in the sense that large and small droplets are not well mixed in sufficiently small volumes) and thus do not necessarily indicate enhanced probabilities of gravity-induced droplet coagulation. In the effort to build a firm physical basis for subgrid parameterizations, this study presents a framework to explain the merits and limitations of idealized models, indicating how to assess and use them wisely as a subgrid representation of turbulent condensation in large-eddy simulations of clouds. Significance Statement The droplet size distribution is a prime characteristic of a cloud, controlling the initiation of precipitation and how the cloud modulates solar radiation. Microphysical processes shaping the droplet size distribution, such as droplet growth by condensation in the turbulent cloud flow, occur on scales that are small compared with the resolution of the numerical models used to simulate the entire cloud. Such subgrid-scale aspects are incorporated in these models by parameterizations relating microphysical processes to the model variables. In the effort to build a firm physical basis for such parameterizations, this study analyzes idealized representations of turbulent condensation at subgrid-scales and presents a framework to explain the merits and limitations of these representations, indicating how to overcome their deficiencies.