The Shape and Density Evolution of Snow Aggregates

Abstract

Abstract Snow aggregates evolve into a variety of observed shapes and densities. Despite this diversity, models and observational studies employ fractal or Euclidean geometric measures that are assumed universal for all aggregates. This work therefore seeks to improve understanding and representation of snow aggregate geometry and its evolution by characterizing distributions of both observed and Monte Carlo–generated aggregates. Two separate datasets of best-fit ellipsoid estimates derived from Multi-Angle Snowflake Camera (MASC) observations suggest the use of a bivariate beta distribution model for capturing aggregate shapes. Product moments of this model capture shape effects to within 4% of observations. This mathematical model is used along with Monte Carlo simulated aggregates to study how combinations of monomer properties affect aggregate shape evolution. Plate aggregates of any aspect ratio produce a consistent ellipsoid shape evolution whereas thin column aggregates evolve to become more spherical. Thin column aggregates yield fractal dimensions much less than the often-assumed value of 2.0. Ellipsoid densities and fractal analogs of density (lacunarity) are much more variable depending on combinations of monomer size and shape. Simple mathematical scaling relationships can explain the persistent triaxial ellipsoid shapes that appear in both observed and modeled aggregates. Overall, both simulations and observations prove aggregates are rarely oblate. Therefore, the use of the proposed bivariate ellipsoid distribution in models will allow for similar-sized aggregates to exhibit a realistic dispersion of masses and fall speeds.