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A single nonprecipitating cumulus congestus setup is applied to compare droplet spectra grown by the diffusion of water vapor in Eulerian bin and particle-based Lagrangian microphysics schemes. Bin microphysics represent droplet spectral evolution applying the spectral density function. In the Lagrangian microphysics, computational particles referred to as superdroplets are followed in time and space with each superdroplet representing a multiplicity of natural cloud droplets. The same cloud condensation nuclei (CCN) activation and identical representation of the droplet diffusional growth allow the comparison. The piggybacking method is used with the two schemes operating in a single simulation, one scheme driving the dynamics and the other one piggybacking the simulated flow. Piggybacking allows point-by-point comparison of droplet spectra predicted by the two schemes. The results show the impact of inherent limitations of the two microphysics simulation methods, numerical diffusion in the Eulerian scheme and a limited number of superdroplets in the Lagrangian scheme. Numerical diffusion in the Eulerian scheme results in a more dilution of the cloud upper half and thus smaller cloud droplet mean radius. The Lagrangian scheme typically has larger spatial fluctuations of droplet spectral properties. A significantly larger mean spectral width in the bin microphysics across the entire cloud depth is the largest difference between the two schemes. A fourfold increase of the number of superdroplets per grid volume and a twofold increase of the spectral resolution and thus the number of bins have small impact on the results and provide only minor changes to the comparison between simulated cloud properties.

This paper presents a comparison of simulations applying either a traditional Eulerian bin microphysics or a novel particle-based Lagrangian approach to represent CCN activation and cloud droplet growth. The Eulerian microphysics solve the evolution equation for the spectral density function, whereas the Lagrangian approach follows computational particles referred to as superdroplets. Each superdroplet represents a multiplicity of natural droplets that makes the Lagrangian approach computationally feasible. The two schemes apply identical representation of CCN activation and use the same droplet growth equation; these make direct comparison between the two schemes practical. The comparison, the first of its kind, applies an idealized simulation setup motivated by laboratory experiments with the Pi Chamber and previous model simulations of the Pi Chamber dynamics and microphysics. The Pi Chamber laboratory apparatus considers interactions between turbulence, CCN activation, and cloud droplet growth in moist Rayleigh–Bénard convection. Simulated steady-state droplet spectra averaged over the entire chamber are similar, with the mean droplet concentration, mean radius, and spectral width close in Eulerian and Lagrangian simulations. Small differences that do exist are explained by the inherent differences between the two schemes and their numerical implementation. The local droplet spectra differ substantially, again in agreement with the inherent limitations of the theoretical foundation behind each approach. There is a general agreement between simulations and Pi Chamber observations, with simplifications of the CCN activation and droplet growth equation used in the simulations likely explaining specific differences.

Numerical simulations of the impact of ultrafine cloud condensation nuclei (CCN) on deep convection are analyzed to investigate the idea proposed by Fan et al. that addition of ultrafine CCN to an otherwise pristine environment leads to convective invigoration. The piggybacking methodology is applied, allowing rigorous separation of the impact of aerosols from different flow realizations that typically occur when even a small element of the model physics or modeling setup is changed. The setup follows the case of daytime convective development over land based on observations during the Large-Scale Biosphere–Atmosphere (LBA) experiment in Amazonia. Overall, the simulated impacts of ultrafine CCN are similar to the previous study by the authors on the impact of pollution on deep convection. There is no convective invigoration above the freezing level, but there is a small invigoration (increase in vertical velocities) below due to the supersaturation and buoyancy differences in conditions with additional ultrafine CCN compared to unperturbed pristine conditions. As in the previous study, the most significant impact is on the upper-tropospheric convective anvils that feature higher cloud fractions in conditions with ultrafine CCN. The increase comes from purely microphysical considerations as the increased cloud droplet concentrations from ultrafine CCN lead to increased ice crystal concentrations and, consequently, smaller sizes and fall velocities, and longer residence times. Mesoscale organization due to low-level shear has a small effect on the simulated ultrafine CCN impacts. Finally, an alternative explanation of increased lightning above oceanic shipping lines seen in satellite observations and argued to result from convective invigoration is provided.

Spectral width of the cloud droplet spectrum is important for radiative properties and drizzle/rain development in warm ice‐free clouds. We use an adiabatic rising parcel model to study activation and diffusional growth of cloud droplets, focusing on the spectral width evolution, and contrasting clean and polluted environments. A comprehensive droplet growth equation is used that includes kinetic, solute, and surface tension effects. We show that those effects have an appreciable impact on the spectral width evolution above the cloud base. Without those effects, the droplet area standard deviation should not change once activation is completed. In contrast, simulation results show that the area standard deviation does increase with height, especially for weak updrafts and polluted environments. Implications of those results for cloud modeling, especially applying conventional bin microphysics, are discussed. Plain Language Summary Shape of the droplet spectrum is an important parameter affecting cloud radiative properties as well as drizzle and rain development in warm ice‐free clouds. We consider formation and growth of cloud droplets in an air parcel rising across the subcloud layer, reaching the cloud base, and continuing its rise carrying cloud droplets growing by condensation of water vapor. We focus on the evolution of the spectrum shape. We show that the simplified droplet growth equation often applied in cloud simulations is not accurate enough to faithfully predict shape of the droplet spectrum aloft, especially in polluted weak‐updraft shallow clouds such as a continental stratocumulus. Key Points Evolutions of cloud droplet spectral width in an adiabatic parcel rising through cloud base differ between clean and polluted environments Smaller droplet sizes make the solute and surface tension effects more influential for spectral width evolutions in polluted clouds Conventional bin microphysics are not suitable for studying weak‐updraft shallow polluted clouds such as continental stratocumulus

Representation of cloud microphysics is a key aspect of simulating clouds. From the early days of cloud modeling, numerical models have relied on an Eulerian approach for all cloud and thermodynamic and microphysics variables. Over time the sophistication of microphysics schemes has steadily increased, from simple representations of bulk masses of cloud and rain in each grid cell, to including different ice particle types and bulk hydrometeor concentrations, to complex schemes referred to as bin or spectral schemes that explicitly evolve the hydrometeor size distributions within each model grid cell. As computational resources grow, there is a clear trend toward wider use of bin schemes, including their use as benchmarks to develop and test simplified bulk schemes. We argue that continuing on this path brings fundamental challenges difficult to overcome. The Lagrangian particle-based probabilistic approach is a practical alternative in which the myriad of cloud and precipitation particles present in a natural cloud is represented by a judiciously selected ensemble of point particles called superdroplets or superparticles. The advantages of the Lagrangian particle-based approach when compared to the Eulerian bin methodology are explained, and the prospects of applying the method to more comprehensive cloud simulations—for instance, targeting deep convection or frontal cloud systems—are discussed.

This paper presents a novel methodology to use direct numerical simulation (DNS) to study the impact of isotropic homogeneous turbulence on the condensational growth of cloud droplets. As shown by previous DNS studies, the impact of turbulence increases with the computational domain size, that is, with the Reynolds number, because larger eddies generate higher and longer-lasting supersaturation fluctuations that affect growth of individual cloud droplets. The traditional DNS can only simulate a limited range of scales because of the excessive computational cost that comes from resolving all scales involved, that is, from large scales at which the turbulent kinetic energy (TKE) is introduced down to the Kolmogorov microscale, and from following every single droplet. The novel approach is referred to as the “scaled-up DNS”. The scaling up is done in two parts, first by increasing both the computational domain and the Kolmogorov microscale and second by using super-droplets instead of real droplets. To ensure proper dissipation of TKE and scalar variance at small scales, molecular transport coefficients are appropriately scaled up with the grid length. For the scaled-up domains, say, meters and tens of meters, one needs to follow billions of real droplets. This is not computationally feasible, and so-called super-droplets are applied in scaled-up DNS simulations. Each super-droplet represents an ensemble of identical real droplets, and the number of real droplets represented by a super-droplet is referred to as the multiplicity attribute. After simple tests showing the validity of the methodology, scaled-up DNS simulations are conducted for five domains, the largest of 643 m3 volume using a DNS of 2563 grid points and various multiplicities. All simulations are carried out with vanishing mean vertical velocity and with no mean supersaturation, similarly to past DNS studies. As expected, the supersaturation fluctuations as well as the spread in droplet size distribution increase with the domain size, with the droplet radius variance increasing in time t as t1∕2 as identified in previous DNS studies. Scaled-up simulations with different multiplicities document numerical convergence of the scaled-up solutions. Finally, we compare the scaled-up DNS results with a simple stochastic model that calculates supersaturation fluctuations based on the vertical velocity fluctuations updated using the Langevin equation. Overall, the results document similar scaling to previous small-domain DNS simulations and support the notion that the stochastic subgrid-scale model is a valuable tool for the multi-scale simulation of droplet spectral evolution applying a large-eddy simulation model.

Following our previous investigation of the turbulence impact on cloud-base single-size CCN activation, this study considers a similar problem assuming CCN size distribution obtained from field measurements. The total CNN concentration is taken as either 200 cm −3 to represent clean conditions, or as 2000 cm −3 to represent polluted conditions. CCN is assumed to be sodium chloride. The CCN activation in the rising nonturbulent adiabatic parcel is contrasted with the activation within a rising adiabatic parcel filled with inertial-range homogeneous isotropic turbulence. The turbulent parcel of 64 3 m 3 and the turbulent kinetic energy dissipation rate of 10 −3 m −2 s −3 are used in most of the simulations. Results for a range of mean parcel ascent rates, between 0.125 and 8 m s −1 , are discussed. Overall, the adiabatic turbulent parcel simulations show results consistent with the adiabatic nonturbulent parcel, with higher activated CCN concentrations for stronger parcel ascent rates. The key difference is a blurriness of the separation between dry CCN size bins featuring activated and nonactivated (haze) CCN, especially for weak mean ascent rates. The blurriness comes from CCN getting activated and subsequently deactivated in the fluctuating supersaturation field, instead of all becoming cloud droplets above the cloud base. This leads to significantly larger spectral widths in turbulent parcel simulations compared to the nonturbulent parcel when activation is completed. Modeling results are discussed in the context of the impact of turbulent fluctuations on CCN activation documented in laboratory experiments using the Pi chamber.

Motivated by recent discussions concerning differences of convective dynamics in polluted and pristine environments, the so-called convective invigoration in particular, this paper provides an analysis of factors affecting convective updraft buoyancy, such as the in-cloud supersaturation, condensate and precipitation loading, and entrainment. We use the deep convective period from simulations of daytime convection development over land discussed in our previous publications. An entraining parcel framework is used in the theoretical analysis. We show that for the specific case considered here, finite (positive) supersaturation noticeably reduces pseudo-adiabatic parcel buoyancy and cumulative convective available potential energy (cCAPE) in the lower troposphere. This comes from keeping a small fraction of the water vapor in a supersaturated state and thus reducing the latent heating. Such a lower-tropospheric impact is comparable to the effects of condensate loading and entrainment in the idealized parcel framework. For the entire tropospheric depth, loading and entrainment have a much more significant impact on the total CAPE. For the cloud model results, we compare ensemble simulations applying either a bulk microphysics scheme with saturation adjustment or a more comprehensive double-moment scheme with supersaturation prediction. We compare deep convective updraft velocities, buoyancies, and supersaturations from all ensembles. In agreement with the parcel analysis, the saturation-adjustment scheme provides noticeably stronger updrafts in the lower troposphere. For the simulations predicting supersaturation, there are small differences between pristine and polluted conditions below the freezing level that are difficult to explain by standard analysis of the in-cloud buoyancy components. By applying the piggybacking technique, we show that the lower-tropospheric buoyancy differences between pristine and polluted simulations come from a combination of temperature (i.e., latent heating) and condensate loading differences that work together to make polluted buoyancies and updraft velocities slightly larger when compared to their pristine analogues. Overall, the effects are rather small and contradict previous claims of a significant invigoration of deep convection in polluted environments.

This paper investigates spectral broadening of droplet size distributions through a mechanism referred to as the eddy hopping. The key idea, suggested a quarter century ago, is that droplets arriving at a given location within a turbulent cloud follow different trajectories and thus experience different growth histories and that this leads to a significant spectral broadening. In this study, the adiabatic parcel model with superdroplets is used to contrast droplet growth with and without turbulence. Turbulence inside the parcel is described by two parameters: (i) the dissipation rate of the turbulent kinetic energy ε and (ii) the linear extent of the parcel L. As expected, an adiabatic parcel without turbulence produces extremely narrow droplet spectra. In the turbulent parcel, a stochastic scheme is used to account for vertical velocity fluctuations that lead to local supersaturation fluctuations for each superdroplet. These fluctuations mimic the impact of droplets hopping turbulent eddies in a natural cloud. For L smaller than a few meters, noticeable spectral broadening is possible only for strong turbulence—say, ε > 100 cm2 s−3. For L typical for grid lengths of large-eddy simulation (LES) models (say, L between 10 and 100 m), the impact is significant even with relatively modest turbulence intensities. The impact increases with both L and ε. The representation of eddy hopping developed in this paper can be included in a straightforward way in the subgrid-scale scheme of a Lagrangian LES cloud model and may lead to a significant acceleration of simulated rain development through collision–coalescence.

A simple methodology is proposed to extract impacts of cloud microphysics on macrophysical cloud-field properties in large-eddy simulations of shallow convection. These impacts are typically difficult to assess because of natural variability of the simulated cloud field. The idea is to use two sets of thermodynamic variables driven by different microphysical schemes or by a single scheme with different parameters as applied here. The first set is coupled to the dynamics as in the standard model, and the second set is applied diagnostically—that is, driven by the flow but without the feedback on the flow dynamics. Having the two schemes operating in the same flow pattern allows for extracting the impact with high confidence. For illustration, the method is applied to simulations of precipitating shallow convection applying a simple bulk representation of warm-rain processes. Because of natural variability, the traditional approach provides an uncertain estimate of the impact of cloud droplet concentration on the mean cloud-field rainfall even with an ensemble of simulations. In contrast, the impact is well constrained while applying the new methodology. The method can even detect minuscule changes of the mean cloud cover and liquid water path despite their large temporal fluctuations and different evolutions within the ensemble.