Cloud entrainment, the mixing between cloudy and clear air at the boundary of clouds, constitutes one paradigm for the relevance of small scales in the Earth system: By regulating cloud lifetimes, meter- and submeter-scale processes at cloud boundaries can influence planetary-scale properties. Understanding cloud entrainment is difficult given the complexity and diversity of the associated phenomena, which include turbulence entrainment within a stratified medium, convective instabilities driven by radiative and evaporative cooling, shear instabilities, and cloud microphysics. Obtaining accurate data at the required small scales is also challenging, for both simulations and measurements. During the past few decades, however, high-resolution simulations and measurements have greatly advanced our understanding of the main mechanisms controlling cloud entrainment. This article reviews some of these advances, focusing on stratocumulus clouds, and indicates remaining challenges.

Cloud-Top Entrainment in Stratocumulus Clouds

[1] An aircraft field study (POST; Physics of Stratocumulus Top) was conducted off the central California coast in July and August 2008 to deal with the known difficulty of measuring entrainment rates in the radiatively important stratocumulus (Sc) prevalent in that area. The Center for Interdisciplinary Remotely-Piloted Aircraft Studies Twin Otter research aircraft flew 15 quasi-Lagrangian flights in unbroken Sc and carried a full complement of probes including three high-data-rate probes: ultrafast temperature probe, particulate volume monitor probe, and gust probe. The probes' colocation near the nose of the Twin Otter permitted estimation of entrainment fluxes and rates with an in-cloud resolution of 1 m. Results include the following: Application of the conditional sampling variation of classical mixed layer theory for calculating the entrainment rate into cloud top for POST flights is shown to be inadequate for most of the Sc. Estimated rates resemble previous results after theory is modified to take into account both entrainment and evaporation at cloud top given the strong wind shear and mixing at cloud top. Entrainment rates show a tendency to decrease for large shear values, and the largest rates are for the smallest temperature jumps across the inversion. Measurements indirectly suggest that entrained parcels are primarily cooled by infrared flux divergence rather than cooling from droplet evaporation, while detrainment at cloud top causes droplet evaporation and cooling in the entrainment interface layer above cloud top.

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Entrainment rates and microphysics in POST stratocumulus

. Stochasticity of the collisional growth of cloud droplets is studied using the super-droplet method (SDM) of Shima et al.(2009). Statistics are calculated from ensembles of simulations of collision–coalescence in a single well-mixed cell. The SDM is compared with direct numerical simulations and the master equation. It is argued that SDM simulations in which one computational droplet represents one real droplet are at the same level of precision as the master equation. Such simulations are used to study fluctuations in the autoconversion time, the sol–gel transition and the growth rate of lucky droplets, which is compared with a theoretical prediction. The size of the coalescence cell is found to strongly affect system behavior. In small cells, correlations in droplet sizes and droplet depletion slow down rain formation. In large cells, collisions between raindrops are more frequent and this can also slow down rain formation. The increase in the rate of collision between raindrops may be an artifact caused by assuming an overly large well-mixed volume. The highest ratio of rain water to cloud water is found in cells of intermediate sizes. Next, we use these precise simulations to determine the validity of more approximate methods: the Smoluchowski equation and the SDM with multiplicities greater than 1. In the latter, we determine how many computational droplets are necessary to correctly model the expected number and the standard deviation of the autoconversion time. The maximal size of a volume that is turbulently well mixed with respect to coalescence is estimated at Vmix  =  1.5  ×  10−2 cm3. The Smoluchowski equation is not valid in such small volumes. It is argued that larger volumes can be considered approximately well mixed, but such approximation needs to be supported by a comparison with fine-grid simulations that resolve droplet motion.

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Stochastic coalescence in Lagrangian cloud microphysics

. Turbulence observed during the Physics of Stratocumulus Top (POST) research campaign is analyzed. Using in-flight measurements of dynamic and thermodynamic variables at the interface between the stratocumulus cloud top and free troposphere, the cloud top region is classified into sublayers, and the thicknesses of these sublayers are estimated. The data are used to calculate turbulence characteristics, including the bulk Richardson number, mean-square velocity fluctuations, turbulence kinetic energy (TKE), TKE dissipation rate, and Corrsin, Ozmidov and Kolmogorov scales. A comparison of these properties among different sublayers indicates that the entrainment interfacial layer consists of two significantly different sublayers: the turbulent inversion sublayer (TISL) and the moist, yet hydrostatically stable, cloud top mixing sublayer (CTMSL). Both sublayers are marginally turbulent, i.e., the bulk Richardson number across the layers is critical. This means that turbulence is produced by shear and damped by buoyancy such that the sublayer thicknesses adapt to temperature and wind variations across them. Turbulence in both sublayers is anisotropic, with Corrsin and Ozmidov scales as small as  ∼  0.3 and  ∼  3 m in the TISL and CTMSL, respectively. These values are  ∼  60 and  ∼  15 times smaller than typical layer depths, indicating flattened large eddies and suggesting no direct mixing of cloud top and free-tropospheric air. Also, small scales of turbulence are different in sublayers as indicated by the corresponding values of Kolmogorov scales and buoyant and shear Reynolds numbers.

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Physics of Stratocumulus Top (POST): turbulence characteristics

A numerical experiment is designed to study the interaction at the stratocumulus top between a mean vertical shear and the buoyancy reversal due to evaporative cooling, without radiative cooling. Direct numerical simulation is used to eliminate the uncertainty introduced by turbulence models. It is found that the enhancement by shear-induced mixing of the turbulence caused by buoyancy reversal can render buoyancy reversal comparable to other forcing mechanisms. However, it is also found that (i) the velocity jump across the capping inversion Δu needs to be relatively large and values of about 1 m s−1 that are typically associated with the convective motions inside the boundary layer are generally too small and (ii) there is no indication of cloud-top entrainment instability. To obtain these results, parameterizations of the mean entrainment velocity and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background sh...

Wind Shear and Buoyancy Reversal at the Top of Stratocumulus

. High spatial resolution measurements of temperature and liquid water content, accompanied by moderate-resolution measurements of humidity and turbulence, collected during the Physics of Stratocumulus Top experiment are analyzed. Two thermodynamically, meteorologically and even optically different cases are investigated. An algorithmic division of the cloud-top region into layers is proposed. Analysis of dynamic stability across these layers leads to the conclusion that the inversion capping the cloud and the cloud-top region is turbulent due to the wind shear, which is strong enough to overcome the high static stability of the inversion. The thickness of this mixing layer adapts to wind and temperature jumps such that the gradient Richardson number stays close to its critical value. Turbulent mixing governs transport across the inversion, but the consequences of this mixing depend on the thermodynamic properties of cloud top and free troposphere. The effects of buoyancy sorting of the mixed parcels in the cloud-top region are different in conditions that permit or prevent cloud-top entrainment instability. Removal of negatively buoyant air from the cloud top is observed in the first case, while buildup of the diluted cloud-top layer is observed in the second one.

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I. Jen-La Plante

Papers

Physics of Stratocumulus Top (POST): turbulent mixing across capping inversion