Modeling of cloud microphysics. Can we do better?

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 single-moment bulk warm-rain schemes, through double- and triple-moment bulk warm-rain and ice schemes, to complex bin (spectral) schemes that predict the evolution of cloud and precipitation particle size distributions. 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. Scientists argue that continuing on this path brings fundamental challenges due to the complexity of processes involved (especially for ice), the multiscale nature of atmospheric flows that Eulerian approaches are not able to cope with, conceptual issues with the Smoluchowski equation that is solved by bin schemes to predict evolution of the particle size distributions, and numerical problems when applying bin schemes in multidimensional cloud simulations. 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 super-droplets or super-particles. There are advantages of the Lagrangian particle-based approach when compared to the Eulerian bin methodology. Applying the method to more comprehensive simulations involving clouds, for instance targeting deep convection or frontal cloud systems, are prospects of the future.

Left 4 panels (from Grabowski et al. Bull. Amer. Meteor. Soc. 2019): Schematic of real droplets, super-droplets, and bin microphysics. (a) Cloud droplets with different sizes (horizontal axis) each containing a different cloud condensation nuclei (CCN) size (vertical axis). (b) The droplet ensemble can be represented by a two-dimensional number density function. (c) If CCN is of no interest, the ensemble can be represented by a one-dimensional number density function. If used in a cloud model, each bin in (b) and (c) needs to be advected in physical space and all bin combinations have to be considered in collision–coalescence calculations. (d) A super-droplet representation of the ensemble. Each symbol shows a single super-droplet on the same plane as in (a), with colors depicting an increasing multiplicity parameter from very low multiplicity (dark blue), through low to moderate multiplicity (green and yellow), to high multiplicity (red). Transport and growth of the real droplet ensemble in (a) is represented in a computationally tractable way by the orders-of-magnitude-smaller su- perdroplet ensemble in (d).

Right 4 panels (from Grabowski, J. Atmos. Sci., in review): Droplet spectral density functions from cloud chamber simulations averaged over the chamber volume away from boundaries and presented applying the linear (left panels) and log (right panels) scales for bin microphysics (marked as BIN; upper panels) and super-droplets (SDs, lower panel) simulations for three CCN concentrations: 20, 100 and 500 cm-3 (marked by color). Thin dashed lines in right panels are included to better expose similarity between the spectra. The key point of the figure is that bin and super-droplet spectra look very similar between the two simulation approaches.