Collection/Aggregation in a Lagrangian cloud microphysical model: Insights from column model applications

Lagrangian cloud models (LCMs) are considered the future of cloud microphysical modeling. However, LCMs are computationally expensive due to the typically high number of simulation particles (SIPs) necessary to represent microphysical processes such as collection/aggregation successfully. In this study, the representation of collection/aggregation is explored in one-dimensional column simulations, allowing for the explicit consideration of sedimentation, complementing the authors' previous study on zero-dimensional collection in a single grid box. Two variants of the Lagrangian probabilistic all-or-nothing (AON) collection algorithm are tested that mainly differ in the assumed spatial distribution of the droplet ensemble: The first variant assumes the droplet ensemble to be well-mixed in a predefined three-dimensional grid box (WM3D), while the second variant considers explicitly the vertical coordinate of the SIPs, reducing the well-mixed assumption to a two-dimensional, horizontal plane (WM2D). Both variants are compared to established Eulerian bin model solutions. Generally, all methods approach the same solutions, and agree well if the methods are applied with sufficiently high accuracy (foremost the number of SIPs, timestep, vertical grid spacing). However, it is found that the rate of convergence depends on the applied model variant.  Most importantly, the study highlights that results generally require a smaller number of SIPs per grid box for convergence than previous box simulations indicated. The reason is the ability of sedimenting SIPs to interact with an effectively larger ensemble of particles when they are not restricted to a single grid box. Since sedimentation is considered in most commonly applied three-dimensional models, the results indicate smaller computational requirements for successful simulations than previously assumed, encouraging a wider use of LCMs in the future.