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. We 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.
Advantages of the Lagrangian particle-based approach when compared
to the Eulerian bin methodology will be explained and illustrated
with computational examples. Prospects of applying the method to
more comprehensive simulations involving clouds, for instance
targeting deep convection or frontal cloud systems, will be discussed.