ALBERT

Description: 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.

Description: 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.

Description: We report the development of a novel Lagrangian microphysics methodology for improved simulations of warm ice-free clouds. The approach applies the traditional Eulerian method for the momentum and continuous thermodynamic fields, the temperature and water vapor mixing ratio, and uses Lagrangian super-droplets to represent condensed phase such as cloud droplets and drizzle/rain drops. In all other applications of the Lagrangian warm-rain microphysics, the super-droplets outside clouds represent un-activated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows studying in detail not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in Eulerian bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology focusing on the activation and diffusional growth. Details of the activation implementation, transport of SDs in the physical space, and the coupling between super-droplets and the Eulerian temperature and water vapor field are discussed in detail. Some of these are relevant to the original super-droplet methodology as well and to the ice phase modeling using the Lagrangian approach. As a computational example, the scheme is applied to an idealized moist thermal rising in a stratified environment, with the original super-droplet methodology providing benchmark to which the new scheme is compared.

Description: Stochasticity in collisional growth of cloud droplets is studied in a box model using the super-droplet method (SDM). The SDM is compared with direct numerical simulations and the master equation. We use the SDM to study fluctuations in autoconversion time and the sol-gel transition. We determine how many computational droplets are necessary to correctly model expected number and standard deviation of autoconversion time. Also, growth rate of lucky droplets is determined and compared with a theoretical prediction. Size of the coalescence cell is found to strongly affect system behavior. In small cells, correlations in droplet sizes and droplet depletion affect evolution of the system. In large cells, unrealistic collisions between rain drops, caused by the assumption that the cell is well-mixed, become important. Maximal size of a volume that is turbulently well-mixed with respect to coalescence is estimated at Vmix = 1.05 · 10−2 cm3. It is argued that larger cells can be considered approximately well-mixed, but only through comparison with fine-grid simulations. In addition, validity of the Smoluchowski equation is tested. Discrepancy between the SDM and the Smoluchowski equation is observed if droplets are initially relatively small. This implies that cloud models that use the Smoluchowski equation might produce rain too soon.

Description: A new anelastic large-eddy simulation model with an Eulerian dynamical core and a Lagrangian particle-based microphysics is presented. The dynamical core uses the MPDATA advection scheme and the generalized conjugate residual pressure solver, while the microphysics scheme is based on the Super-Droplet Method. Algorithms for coupling of the Lagrangian microphysics with the Eulerian dynamics are presented, including spatial and temporal discretizations and a condensation sub-stepping algorithm. The model is free of numerical diffusion in the droplet size spectrum. Activation of droplets is modeled explicitly, making the model less sensitive to local supersaturation maxima than models in which activation is parametrised. Simulations of a drizzling marine stratocumulus give results in agreement with other LES models. Relatively low number of computational particles is sufficient to obtain the correct averaged properties of a cloud. High computational performance is achieved thanks to the use of GPU accelerators.

Description: We report the development of a novel Lagrangian microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional Eulerian method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses Lagrangian super-droplets to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the Lagrangian warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in Eulerian bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the activation implementation, transport of super-droplets in the physical space, and the coupling between super-droplets and the Eulerian temperature and water vapor field are discussed in detail. Some of these are relevant to the original super-droplet methodology as well and to the ice phase modeling using the Lagrangian approach. As a computational example, the scheme is applied to an idealized moist thermal rising in a stratified environment, with the original super-droplet methodology providing a benchmark to which the new scheme is compared.

Description: A new anelastic large-eddy simulation (LES) model with an Eulerian dynamical core and Lagrangian particle-based microphysics is presented. The dynamical core uses the multidimensional positive-definite advection transport algorithm (MPDATA) advection scheme and the generalized conjugate residual pressure solver, whereas the microphysics scheme is based on the super-droplet method. Algorithms for coupling of Lagrangian microphysics with Eulerian dynamics are presented, including spatial and temporal discretizations and a condensation substepping algorithm. The model is free of numerical diffusion in the droplet size spectrum. Activation of droplets is modeled explicitly, making the model less sensitive to local supersaturation maxima than models in which activation is parameterized. Simulations of a drizzling marine stratocumulus give results in agreement with other LES models. It is shown that in the super-droplet method a relatively low number of computational particles is sufficient to obtain correct averaged properties of a cloud, but condensation and collision–coalescence have to be modeled with a time step of the order of 0.1 s. Such short time steps are achieved by substepping, as the model time step is typically around 1 s. Simulations with and without an explicit subgrid-scale turbulence model are compared. Effects of modeling subgrid-scale motion of super-droplets are investigated. The model achieves high computational performance by using graphics processing unit (GPU) accelerators.

Description: The impact of giant sea salt aerosols released from breaking waves on rain formation in marine boundary layer clouds is studied using large eddy simulations (LES). We perform simulations of marine cumuli and stratocumuli for various concentrations of cloud condensation nuclei (CCN) and giant CCN (GCCN). Cloud microphysics are modeled with a Lagrangian method that provides key improvements in comparison to previous LES of GCCN that used Eulerian bin microphysics. We find that GCCN significantly increase precipitation in stratocumuli. This effect is strongest for low and moderate CCN concentrations. GCCN are found to have a smaller impact on precipitation formation in cumuli. These conclusions are in agreement with field measurements. We develop a simple parameterization of the effect of GCCN on precipitation, accretion, and autoconversion rates in marine stratocumuli.