A Golden Spiral of Thermodynamic Histories: Characterizing Trajectories of Ice Crystals in Cirrus Clouds as Modeled by Particle-based Microphysics in CM1

Cloud particles follow diverse paths as they travel and evolve through the atmosphere. Particle-based Lagrangian cloud models, where a population of cloud particles is represented by a smaller, number-weighted set of superparticles, are able to account for the diverse meteorological conditions that cloud particles travel through. Recent work has combined this Lagrangian approach with a large eddy simulation (LES) in CM1 to model a cirrus cloud case from the Ice Cryo-Encapsulation Balloon (ICEBall) field campaign. In comparing various mechanisms for ice crystal depositional growth along many diverse trajectories, the results from this study indicate that individual thermodynamic histories play the dominant role in microphysical variability of ice crystals, rather than the crystals’ instantaneous microphysical properties or current environmental conditions. We leverage the ability of this particle-based modeling approach to track the diverse supersaturation histories of the crystals, which influence their microphysical evolution. We categorize the diverse trajectories of ice crystals into a smaller set of representative thermodynamic histories by applying an unsupervised clustering technique to the supersaturation trajectories. The centroids of the four identified clusters correspond to representative thermodynamic histories. We find that these four clusters lie along distinct sections of a 1-dimensional, smoothly varying spiral manifold. The equation of best fit regression in this space converges to a squared golden spiral, allowing us to describe the range of supersaturation histories with a single scalar parameter theta. Lower values of this spiral theta parameter correspond to slow to moderate depositional growth of the ice crystals, and higher values correspond to trajectories of fast-growing then precipitating particles. The spiral theta value characterizes the lifetime of the ice crystals in the cloud.